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The researcher's complete guide to water potential

Everything you need to know about measuring water potential— what it is, why you need it, how to measure it, method comparisons. Plus see it in action using soil moisture release curves.

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WHY MEASURE WATER POTENTIAL?

An ecologist installed an extensive soil moisture sensor network to study the effect of slope orientation on plant available water . He collected reams of soil moisture data, but ultimately he was frustrated because he couldn’t tell how much of the water was available to plants .

He’s not alone in his frustration. Accurate, inexpensive soil moisture sensors have made soil moisture a justifiably popular measurement, but as many people have discovered, a good hammer doesn’t make every soil water problem a nail. Water content can only show how much water there is. Hydraulic conductivity shows how fast water can move. But water potential shows if water is available to plants, whether it will move, and where it’s going to go.

Intensive variables don’t change with size or situation

To understand water potential and why you need it, it’s necessary to explain extensive vs. intensive properties. Most people look at soil moisture only in terms of one variable: soil water content. But two types of variables are necessary to describe the state of matter or energy in the environment. An extensive variable describes the extent (or amount) of matter or energy. And the intensive variable describes the intensity (or quality) of matter or energy.

Table 1. Examples of extensive and intensive variables

Soil water content is an extensive variable. It describes how much water is in the environment. Soil water potential is an intensive variable. It describes the intensity or quality (and in most cases the availability) of water in the environment. To understand how this works, think of extensive vs. intensive variables in terms of heat. Heat content (an extensive variable) describes how much heat is stored in a room. Temperature (an intensive variable) describes the quality (comfort level) or how your body will perceive the heat in that room.

Figure 1 shows a large ship in the arctic vs. a hot rod that’s just been heated in a fire. Which of these two items has a higher heat content? Interestingly, the ship in the arctic has a higher heat content than the hot rod, but it’s the rod that has a higher temperature. If we put the hot rod in contact with the ship, which variable governs how the energy will flow? The intensive variable, temperature, governs how energy will move. Heat always moves from a high temperature to a low temperature.

Learn more about intensive vs. extensive variables .

Water content doesn’t predict how water moves

Similar to heat content, water content is an amount. It’s an extensive variable. It changes with size and situation. Consider the following paradoxes:

• A soil with fairly low volumetric water content can have plenty of plant-available water, and a soil with high water content can have almost none
• Gravity pulls water down through the profile, but water moves up into the soil from a water table
• Two adjacent patches of soil at equilibrium can have significantly different water content

In these and many other cases, water content data are confusing because they don’t predict how water moves. Water potential measures the energy state of water and thus explains realities of water movement that otherwise defy intuition. Just as temperature defines the comfort level of a human, water potential defines the comfort level of a plant. If the water potential is known, it’s possible to predict whether plants will grow well or be stressed in any environment.

How water potential defines the comfort level of a plant

Water content is not an indicator of plant “comfort” because soil, clay, sand, potting soil, and other media, all hold water differently. Imagine a sand with 30% water content. Due to its low surface area, the sand will be too wet for optimal plant growth, threatening a lack of aeration to the roots, and flirting with saturation. Now consider a fine-textured clay at that same 30% water content. The clay may appear only moist and be well below optimum “comfort” for a plant due to the surface of the clay binding the water and making it less available to the plant.

Water potential measurements clearly indicate plant available water, and unlike water content, there is an easy reference scale —plant optimal runs from about -2 to 5 kPa which is on the very wet side, to approximately -100 kPa, at the drier end of optimal. Below that, plants will be in deficit, and past -1000 kPa they start to suffer. Depending on the plant, water potentials below -1000 to -2000 kPa cause permanent wilting. Table 1 illustrates the easy reference scale for some types of crops. Plants will stay out of stress and yield more when kept within this water potential comfort range.

Most applications require both water potential and water content

Though water potential is a better indicator of plant available water than water content, in most situations, it’s useful to use both water potential sensors and soil moisture sensors .

The intensity measurement of water potential doesn’t translate directly into the quantity of water stored or needed. Water content information is also required in applications such as irrigation management and water balance studies. For more information, read: “ When to water–Dual measurements solve the mystery ”.

Watch Water Potential 101

In this webinar, Dr. Doug Cobos differentiates water potential from water content , discusses the theory, application, and key components of water potential, as well as the implications water potential has for researchers and irrigation management.

A WATER POTENTIAL DEFINITION

Water potential is the energy required, per quantity of water, to transport an infinitesimal quantity of water from the sample to a reference pool of pure free water. To understand what that means, compare the water in a soil sample to water in a drinking glass. The water in the glass is relatively free and available; the water in the soil is bound to surfaces diluted by solutes and under pressure or tension. In fact, the soil water has a different energy state from “free” water. The free water can be accessed without exerting any energy. The soil water can only be extracted by expending energy. Soil water potential expresses how much energy you would need to expend to pull that water out of the soil sample.

Soil water potential  is a differential property. For the measurement to have meaning, a reference must be specified. The reference typically specified is pure, free water at the soil surface. The water potential of this reference is zero. Water potential in the environment is almost always less than zero, because you have to add energy to get the water out.

Water potential answers two key questions

1. Water movement

Water will always flow from high potential to low potential. This is the second law of thermodynamics—energy flows along the gradient of the intensive variable. Water will move from a higher energy location to a lower energy location until the locations reach equilibrium, as illustrated in Figure 3. For example, if a soil’s water potential were -50 kPa, water would move toward the more negative -100 kPa to become more stable.

2. Plant water availability

Liquid water moves from soil to and through roots, through the xylem of plants, to the leaves, and eventually evaporates in the substomatal cavities of the leaf. The driving force for this flow is a water potential gradient. Thus, in order for water to flow, the leaf water potential must be lower than the soil water potential. In Figure 4, the soil is at -0.3 MPa and the roots are slightly more negative at -0.5 MPa. This means the roots will pull water up from the soil. Then the water will move up through the xylem and out through the leaves. And the atmosphere, at -100 MPa, is what drives this gradient.

Irrigators and scientists use  water potential sensors  in conjunction with  water content sensors  to understand  plant water availability . In Figure 5, you can observe where the water content declines and at what percentage the plants begin to stress.  It’s also possible to recognize when the soil has too much water: the water content is above where water potential sensors start to sense plant stress.  Using this information, researchers can identify the plant optimal range at 12% to 17% volumetric water content.  Anything below or above that range will be too little or too much water.

To learn more about how soil water potential indicates plant water availability, read “ When to water: Dual measurements solve the mystery “.

Water potential names, ranges, and units

Figure 6 illustrates that there are different water potential instruments that measure different ranges. Watch the video to see how you can combine METER LABROS instruments to measure the full range of soil water potential. Learn more about how to measure water potential and which instruments are used for what purpose  here .

Water potential is frequently called water tension, soil suction, and soil pore water pressure. We typically use units of pressure to describe soil water potential, including megapascals (MPa), kilopascals (kPa), bars, and meters (mH 2 O), centimeters (cmH 2 O), or millimeters of water (mmH 2 O).

Water potential is actually  measured  in energy per unit of mass, so the official units should be joules per kilogram, but if you take into account the density of water, the units become kilopascals, therefore we typically describe it using units of pressure.

Water potential components

The total water potential is the sum of four different components.

• Matric potential: The binding of water to surfaces
• Osmotic potential: Binding to solutes in the water
• Gravitational potential: The position of water in a gravitational field
• Pressure potential: Hydrostatic or pneumatic pressure on the water

How to calculate water potential

Soil water potential is the sum of four different components: gravitational potential + the matric potential + the pressure potential + the osmotic potential (Equation 1).

Matric potential is the most significant component as far as soil is concerned because it relates to the water that is adhering to soil surfaces. In Figure 7, the matric potential is what created the water film clinging to the soil particles. As water drains out of the soil, the air-filled pore spaces get bigger, and the water gets more tightly bound to the soil particles as the matric potential decreases.

Matric potential

Matric potential arises because water is attracted to most surfaces through hydrogen bonding and van der Waals forces. Soil is made up of small particles , providing lots of surfaces that will bind water. This binding is highly dependent on soil type. For example, sandy soil has large particles which provide less surface-binding sites, while a silt loam has smaller particles and more surface-binding sites.

Watch the video below to visualize matric potential in action.

The following figure, showing  moisture release curves  for three different types of soil, demonstrates the effect of surface area. Sand, containing 10% water, has a high matric potential, and the water is readily available to organisms and plants. Silt loam, containing 10% water, will have a much lower matric potential, and the water will be significantly less available.

Matric potential is always negative or zero and is the most significant component of soil water potential in unsaturated conditions.

Learn more about moisture release curves and the relationship between soil water potential and soil water content  here .

Tensiometers  and the  TEROS 21  are both soil water potential sensors that measure matric potential in the field. To find out which  field water potential sensor is right for your application, read “ Which soil sensor is perfect for you? ”

Osmotic potential

Osmotic potential describes the dilution and binding of water by solutes that are dissolved in the water. This potential is also always negative.

Osmotic potential only affects the system if there is a semi-permeable barrier that blocks the passage of solutes. This is actually quite common in nature. For example, plant roots allow water to pass but block most solutes. Cell membranes also form a semi-permeable barrier. A less-obvious example is the air-water interface, where water can pass into air in the vapor phase but salts are left behind.

Where  C  is the concentration of solute (mol/kg),  ɸ  is the osmotic coefficient (-0.9 to 1 for most solutes),  v  is the number of ions per mol (NaCl= 2, CaCl 2  = 3, sucrose = 1),  R  is the gas constant, and  T  is the Kelvin temperature.

Osmotic potential is always negative or zero and is significant in plants and some salt-affected soils.

Gravitational potential

Gravitational potential arises because of water’s location in a gravitational field. It can be positive or negative, depending on where you are in relation to the specified reference of pure, free water at the soil surface. Gravitational potential is then

Where  G  is the gravitational constant (9.8 m s -2 ) and  H  is the vertical distance from the reference height to the soil surface (the specified height).

Pressure potential

Pressure potential is a hydrostatic or pneumatic pressure being applied to or pulled on the water. It is a more macroscopic effect acting throughout a larger region of the system.

There are several examples of positive pressure potential in the natural environment. For example, there is a positive pressure present below the surface of any groundwater. You can feel this pressure yourself as you swim down into a lake or pool. Similarly, a pressure head or positive pressure potential develops as you move below the water table. Turgor pressure in plants and blood pressure in animals are two more examples of positive pressure potential.

Pressure potential can be calculated from

Where P is the pressure (P a ) and P W  is the density of water.

Though pressure potential is usually positive, there are important cases where it is not. One is found in plants, where a negative pressure potential in the xylem draws water from the soil up through the roots and into the leaves.

Water potential and relative humidity

Water potential and relative humidity are related by the Kelvin equation. If you know temperature and humidity, you can calculate the water potential using this equation

Where  Ψ  is water potential (MPa),  H R  is the relative humidity (unitless),  R  is the universal gas constant (8.3143 J mol -1  K  -1 ),  M W   is the mass of water (18.02 g/mol), and  T  is Kelvin temperature.

What is water potential? Points to remember

Water potential:

• Describes the energy state of water in the environment
• Defines the availability of water for organisms

Key points:

• Water will always flow from high potential to low potential
• This is the second law of thermodynamics–energy flows along the gradient of the intensive variable

Find more answers to the question ‘what is water potential’ here:  Return to main water potential page  or  Talk to an expert  about using water potential in your application.

Soil water potential references for further study

Kirkham, Mary Beth.  Principles of soil and plant water relations . Academic Press, 2014. Book link

Taylor, Sterling A., and Gaylen L. Ashcroft.  Physical edaphology. The physics of irrigated and nonirrigated soils . 1972. Book link

Hillel, Daniel.  Fundamentals of soil physics . Academic press, 2013. Book link

Dane, Jacob H., G. C. Topp, and Gaylon S. Campbell.  Methods of soil analysis physical methods . No. 631.41 S63/4. 2002.

Watch Water Potential 201

Dr. Colin Campbell’s webinar “Water Potential 201: Choosing the Right Instrument” covers  water potential instrument  theory, including the challenges of measuring  water potential  and how to choose and use various water potential instruments.

WHICH WATER POTENTIAL METHOD IS RIGHT FOR YOU?

Essentially, there are only two primary measurement methods for  water potential — tensiometers  and  vapor pressure methods . Tensiometers work in the wet range— special tensiometers  that retard the boiling point of water have a range from 0 to about -0.2 MPa. Vapor pressure methods work in the dry range—from about -0.1 MPa to -300 MPa (0.1 MPa is 99.93% RH; -300 MPa is 11%).

Historically, these ranges did not overlap, but recent advances in tensiometer and temperature-sensing technology have changed that. Now, a skilled user with  excellent methods  and  the best equipment  can measure the  full water potential range  in the lab.

There are reasons to look at secondary measurement methods, though. Vapor pressure methods are not useful in situ, and the accuracy of the tensiometer must be paid for with constant, careful maintenance (although a  self-filling version  of the tensiometer is available).

Additionally, there are traditional methods like gypsum blocks, pressure plates, and filter paper that should be understood. This section briefly covers the strengths and limitations of each method.

Pressure plates

The pressure plate was introduced in the 1930s by L.A. Richards. It doesn’t actually measure the  water potential  of a sample. Instead, it brings the sample to a specific water potential by applying pressure to the sample and allowing the excess water to flow out through a porous ceramic plate. When the sample comes to equilibrium, its water potential will be equivalent to the pressure applied.

Pressure plates are typically used to make  soil moisture characteristic curves . Once the soil samples reach a specific water potential under pressure, the researcher can remove the sample from the plate and dry it to measure its water content. A soil moisture characteristic can be produced by making these measurements at different pressures in the pressure plate apparatus.

The accuracy of pressure plates is important, because they are often used to calibrate other secondary measurement methods.

Pressure plates have equilibrium issues

In order to make an accurate moisture release curve with a pressure plate, you have to ensure that the sample has fully come to equilibrium at the designated pressure. Several reviewers, including Gee et. al (2002), Cresswell et. al (2008), and Bittelli and Flury (2009) have noted problems with this assumption.

Errors, particularly at low water potentials, may be caused by clogged pores in the ceramic of the pressure plate, flow restriction within the sample, loss of hydraulic contact between the plate and the soil due to soil shrinkage, and re-uptake of water when the pressure on the plate is released. At low water potentials, low hydraulic conductivities can cause equilibrium to take weeks or even months. Gee et. al (2002) measured the water potentials of samples equilibrated for 9 days on 15 bar pressure plates and found them to be at -0.5 MPa instead of the expected -1.5 MPa. Especially when constructing a moisture release curve to estimate hydraulic conductivity and determine  plant available water , pressure plate measurements at potentials less than -0.1 MPa (-1 bar) can cause significant error (Bittelli and Flury, 2009).

Additionally, Baker and Frydman (2009) establish theoretically that the soil matrix would drain differently under a positive pressure than it does under suction. They postulate that equilibrium water contents achieved using suction will be significantly different than those that occur under natural conditions. Anecdotal evidence seems to support this idea, though further testing is needed. Ultimately, pressure plates may have enough accuracy in the wet range (0 to -0.5 MPa) for some applications, but other methods can provide better accuracy, which may be especially important when using the data for  modeling  or calibration.

Vapor pressure methods

The  WP4C Dew Point Hygrometer  is one of the few commercially available instruments that currently uses this technique. Like traditional  thermocouple psychrometers , the dew point hygrometer equilibrates a sample in a sealed chamber.

A small mirror in the chamber is chilled until dew just starts to form on it. At the dew point, the WP4C measures both mirror and sample temperatures with 0.001◦C accuracy to determine the relative humidity of the vapor above the sample.

The most current version of this dew point hygrometer has an accuracy of ±1% from -5 to -300 MPa and is also relatively easy to use. Many sample types can be analyzed in five to ten minutes, although wet samples take longer.

Limitations

At high water potentials, the temperature differences between saturated vapor pressure and the vapor pressure inside the sample chamber become vanishingly small.

Limitations to the resolution of the temperature measurement mean that vapor pressure methods will probably never supplant tensiometers.

The dew point hygrometer has a range of -0.1 to -300 MPa, though readings can be made beyond -0.1 MPa using special techniques. Tensiometers remain the best option for readings in the 0 to -0.1 MPa range.

Tensiometers and the Wind/Schindler technique

The  HYPROP  is a unique lab instrument that uses the Wind/Schindler evaporation method to make moisture release curves on soils with  water potentials  in the tensiometer range.

Hyprop uses two precision mini-tensiometers to measure water potential at different levels within a saturated 250 cm 3  soil sample while the sample rests on a laboratory balance. Over time, the sample dries, and the instrument measures the changing water potential and the changing sample weight simultaneously. It calculates the moisture content from the weight measurements and plots changes in water potential correlated to changes in moisture content.

Results are verified, and values for dry range and saturation are calculated according to a selected model (i.e., van Genuchten/Mualem, bimodal van Genuchten/Mualem, or Brooks and Corey).

Hyprop has high accuracy and produces a complete moisture release curve in the wet range. The curve takes three to five days to complete, but the instrument operates unattended.

Hyprop’s range is limited by the range of tensiometers, although the mini-tensiometers have been used to measure beyond -250 kPa (-0.25 MPa) because of their boiling retardation feature.

Below -250 kPa the tensiometers cavitate. Power users have the option of adding a final point to the curve at the air-entry point for the ceramic tensiometer cup (-880 kPa; -0.88 MPa).

Tensiometers

Water potential,  by definition , is a measure of the difference in potential energy between the water in a sample and the water in a reference pool of pure, free water. The  tensiometer  is an actualization of this definition.

The tensiometer tube contains a pool of (theoretically) pure, free water. This reservoir is connected (through a permeable membrane) to a soil sample. Thanks to the second law of thermodynamics, water moves from the reservoir to the soil until its energy is equal on both sides of the membrane. That creates a vacuum in the tube. The tensiometer uses a negative pressure gauge (a vacuometer) to measures the strength of that vacuum and describes water potential in terms of pressure.

Tensiometers are probably the oldest type of water potential instrument (the initial concept dates at least to Livingston in 1908), but they can still be quite useful. In fact, in the wet range, a high-quality tensiometer, used skillfully, can have excellent accuracy.

The tensiometer’s range is limited by the ability of water inside the tube to withstand a vacuum. Although water is essentially incompressible, discontinuities in the water surface such as edges or grit provide nucleation points where water’s strong bonds are disrupted and cavitation (low-pressure boiling) occurs. Most tensiometers cavitate around -80 kPa, right in the middle of the plant-available range.

However, METER Group Ag, in Germany, builds  tensiometers  that are modern classics thanks to precision German engineering, meticulous construction, and fanatical attention to detail.  These tensiometers have terrific accuracy and a range that (with a careful operator) can extend to -250 kPa.

Secondary methods: capitalizing on the moisture characteristic

Water content tends to be easier to measure than water potential, and since the two values are related, it’s possible to use a water content measurement to find water potential.

A graph showing how water potential changes as water is adsorbed into and desorbed from a specific soil matrix is called a moisture characteristic or a moisture release curve.

Every matrix that can hold water has a unique moisture characteristic, as unique and distinctive as a fingerprint. In soils, even small differences in composition and texture have a significant effect on the moisture characteristic.

Some researchers develop a moisture characteristic for a specific soil type and use that characteristic to determine water potential from water content readings. Matric potential sensors take a simpler approach by taking advantage of the second law of thermodynamics.

Matric potential sensors

Matric potential sensors  use a porous material with known moisture characteristic. Because all energy systems tend toward equilibrium, the porous material will come to water potential equilibrium with the soil around it.

Using the moisture characteristic for the porous material, you can then measure the water content of the porous material and determine the water potential of both the porous material and the surrounding soil. Matric potential sensors use a variety of porous materials and several different methods for determining water content.

Accuracy depends on custom calibration

At its best, matric potential sensors have good, but not excellent, accuracy. At its worst, the method can only tell you whether the soil is getting wetter or drier. A sensor’s accuracy depends on the quality of the moisture characteristic developed for the porous material and the uniformity of the material used. For good accuracy, the specific material used should be calibrated using a primary measurement method. The sensitivity of this method depends on how fast water content changes as water potential changes. Precision is determined by the quality of the moisture content measurement.

Accuracy can also be affected by temperature sensitivity. This method relies on isothermal conditions, which can be difficult to achieve. Differences in temperature between the sensor and the soil can cause significant errors.

Limited range

All matric potential sensors are limited by hydraulic conductivity: as the soil gets drier, the porous material takes longer to equilibrate. The change in water content also becomes small and difficult to measure. On the wet end, the sensor’s range is limited by the air-entry potential of the porous material being used.

Filter paper

The filter paper method was developed in the 1930s by soil scientists as an alternative to the methods then available. A specific type of filter paper (Whitman No. 42 Ashless) is used as the porous medium. Samples are equilibrated with the filter paper medium. Samples are equilibrated with the filter paper in a sealed chamber at constant temperature. Gravimetric water content of the filter paper is determined using a drying oven, and the water potential is inferred from the predetermined moisture characteristic curve of the filter paper. Deka et al. (1995) found that at least 6 days were required for full equilibration.

The range of filter paper is commonly accepted to be down to -100 MPa if allowed to equilibrate fully. However, as illustrated, errors from temperature gradients become exceptionally large at water potentials near zero.

This method is inexpensive and simple, but it is not accurate. It requires isothermal conditions, which can be difficult to achieve. Small temperature variations can cause significant errors.

Commercially available matric potential sensors

Gypsum blocks: cheap and simple.

Gypsum blocks are often used as simple indicators of irrigation events. Gypsum blocks measure the electrical resistance of a block of gypsum as it responds to changes in the surrounding soil. The electrical resistance is proportional to water potential.

Gypsum blocks are incredibly cheap and fairly easy to use.

Disadvantages

The readings are temperature-dependent and have very low accuracy. Also, gypsum dissolves over time, especially in saline soils, and loses its calibration properties. Gypsum blocks tell you wet or dry but not much more.

Granular matric sensors: easy and cheap, but limited accuracy

Like gypsum blocks, granular matric sensors measure electrical resistance in a porous medium. Instead of gypsum, they use granular quartz surrounded by a synthetic membrane and a protective stainless steel mesh.

Compared with gypsum blocks, granular matric sensors last longer and work in wetter soil conditions. Performance can be improved by measuring and compensating for temperature variations.

Measurements are temperature-dependent and have low accuracy. Also, even with good soil-to-sensor contact, granular matric sensors have rewetting problems after they have been equilibrated to very dry conditions because water has a reduced ability to enter the coarse medium of the granular matrix from a fine soil. Range is limited on the wet end by the air entry potential of the matrix. Granular matric sensors can only start measuring water content/potential when the largest pores in the matrix start to drain.  Additionally, these sensors use a gypsum pellet, which dissolves over time, giving poor long-term stability.

Ceramic-based sensors

Ceramic-based sensors use a ceramic disc as the porous medium. The quality of the sensor depends on the specific qualities of the ceramic.

Accuracy is limited by the fact that each disc has a somewhat unique moisture characteristic. Uniformity in the ceramic material yields greater accuracy but significantly limits the range. Custom calibration of each individual sensor improves accuracy dramatically but is time consuming. Recent innovations in calibration technique may offer better commercial calibration options.

Range is limited on the wet end by the air entry potential of the ceramic. Ceramic-based sensors can only start measuring water content/potential when the largest pores in the ceramic start to drain.  On the dry end, range is limited by the total porosity contained in small pores that drain at low water potentials.

Heat dissipation sensor

The heat dissipation sensor measures moisture content of the ceramic by measuring its thermal conductivity. Using a ceramic cylinder containing a heater and a thermocouple, it measures baseline temperature, heats for a few seconds, and then measures temperature change. By plotting the change in temperature vs. log time, it determines the moisture content of the ceramic. Moisture content is translated into water potential using the moisture characteristic of the ceramic disc. Note that because the sensor is heated, it must be powered by a system with large power reserves (e.g., Campbell Scientific data logger or equivalent).

Unless it is individually custom-calibrated, the heat dissipation sensor has only moderate accuracy.

On the very dry end, there is a lot of sensitivity in the thermal conductivity curve, which gives heat dissipation sensors extended usefulness in the dry range (-1 to -50 mPa).  On the wet end, the heat dissipation sensor is limited by the air entry potential of the ceramic.

Dielectric matric potential sensor

Dielectric matric potential sensors  measure the charge-storing capacity of a ceramic disc to determine its water content. They then use the moisture characteristic of the disc to convert water content to water potential.

Because they use a dielectric technique, the sensors are highly sensitive to small changes in water. Like all ceramic-based sensors, matric potential sensors require custom calibration for good accuracy.

Dielectric matric potential sensors are low power and maintenance-free.

Without calibration, the sensors have an accuracy of just ±40% of the reading. However, a recent,  custom-calibrated version  of the sensor promises an accuracy of ±10% of the reading.

More resources for how to measure water potential

• Gee, Glendon W., Anderson L. Ward, Z. F. Zhang, Gaylon S. Campbell, and J. Mathison. “The influence of hydraulic nonequilibrium on pressure plate data.”  Vadose Zone Journal  1, no. 1 (2002): 172-178.
• Cresswell, H. P., T. W. Green, and N. J. McKenzie. “The adequacy of pressure plate apparatus for determining soil water retention.”  Soil Science Society of America Journal  72, no. 1 (2008): 41-49.
• Bittelli, Marco, and Markus Flury. “Errors in water retention curves determined with pressure plates.”  Soil Science Society of America Journal  73, no. 5 (2009): 1453-1460.
• Baker, Rafael, and Sam Frydman. “Unsaturated soil mechanics: Critical review of physical foundations.”  Engineering Geology  106, no. 1 (2009): 26-39.  Article link .
• Deka, R. N., M. Wairiu, P. W. Mtakwa, C. E. Mullins, E. M. Veenendaal, and J. Townend. “Use and accuracy of the filter‐paper technique for measurement of soil matric potential.”  European Journal of Soil Science  46, no. 2 (1995): 233-238.  Article link .

Watch water potential 301

Leo Rivera teaches the skills needed to create a soil-water characteristic curve with wet end tensiometer data ( HYPROP ) and dry end dew point data ( WP4C ) that actually match up in the middle.

These techniques potentially make it possible for researchers to push their instruments past their specifications. Learn about issues surrounding these measurements, including the effects of hysteresis and changes in sample preparation methods required when you move into the wet range.

WATER POTENTIAL IN ACTION

Soil moisture release curves

Soil moisture release curves (also called soil-water characteristic curves or soil water retention curves) are like physical fingerprints, unique to each soil type. Researchers use them to understand and predict the fate of water in a particular soil at a specific moisture condition. Moisture release curves answer critical questions such as: at what moisture content will the soil experience permanent wilt? How long should I irrigate? Or will water drain through the soil quickly or be held in the root zone? They are powerful tools used to predict plant water uptake, deep drainage, runoff, and more.

What is a soil moisture release curve?

There is a relationship between water potential and volumetric water content which can be illustrated using a graph. Together, these data create a curve shape called a  soil moisture release curve . The shape of a soil moisture release curve is unique to each soil. It is affected by many variables such as soil texture, bulk density, the amount of organic matter, and the actual makeup of the  pore structure , and these variables will differ from site to site and from soil to soil.

Figure 9 shows example curves for three different soils. On the X-axis is water potential on a logarithmic scale, and on the Y-axis is volumetric water content. This relationship between soil water content and water potential (or soil suction) enables researchers to understand and predict water availability and water movement in a particular soil type. For example, in Figure 1, you can see that the permanent wilting point (right vertical line) will be at different water contents for each soil type. The fine sandy loam will experience permanent wilt at 5% VWC, while the silt loam will experience permanent wilt at almost 15% VWC.

Where do moisture release curve data come from?

Soil moisture release curves can be made in situ or in the lab. In the field, soil water content and soil water potential are monitored using  soil sensors .

METER’s easy, reliable dielectric sensors report near-real-time soil moisture data directly through the  ZL6 data logger  to the cloud ( ZENTRA Cloud ). This saves an enormous amount of work and expense. The  TEROS 12  measures water content and is simple to install with the  TEROS borehole installation tool . The  TEROS 21  is an easy-to-install field water potential sensor.

In the lab, you can combine METER’s  HYPROP  and  WP4C  to automatically generate complete soil moisture release curves over the entire range of soil moisture.

See how lab and in situ moisture release curves compare

How to use a soil moisture release curve

Figure 11 shows typical moisture release curves for a loamy sand, a silt loam, and a clay soil. At -100 kPa, the sandy soil water content is below 10%. But in the silt loam, it’s approximately 25%, and in the clay soil, it’s close to 40%. Field capacity is typically between -10 and -30 kPa. And the permanent wilting point is around -1500 kPa. Soil that is drier than this permanent wilting point wouldn’t supply water to a plant. And water in a soil wetter than field capacity would drain out of the soil. A researcher/irrigator can look at these curves and see where the optimal water content level would be for each type of soil.

Figure 12 is the same moisture release curve showing the field capacity range (green vertical lines), the lower limit normally set for an irrigated crop (yellow), and the permanent wilting point (red). Using these curves, a researcher/irrigator can see the silt loam water potential should be kept between -10 and -50 kPa. And the water content that corresponds to those water potentials tells the irrigator that the silt loam water content levels must be kept at approximately 32% (0.32 m3/m3). Soil moisture sensors can alert him when he gets above or below this optimal limit.

ZENTRA simplifies everything

Once information is gleaned from a release curve, METER’s  ZL6  data logger and  ZENTRA Cloud  simplify the process of maintaining an optimal moisture level. Upper and lower limits can be set in ZENTRA cloud ( Get a live demo ), and they show up as a shaded band superimposed over near-real-time soil moisture data (blue shading), making it easy to know when to turn the water on and off. Warnings are even automatically sent out when those limits are approached or exceeded.

Learn more about improving irrigation with soil moisture

Lab curves—now easier than ever

15-20 years ago, it took months to get a full, detailed soil moisture release curve in the lab, but we’ve come a long way since then. Why?

Moisture release curves have always had two weak areas: a span of limited data between 0 and -100 kPa and a gap from -100 kPa to -1000 kPa where no instrument could make accurate measurements. Between 0 and -100 kPa, soil loses half or more of its water content. Using pressure plates to create data points for this section of a moisture release curve meant the curve was based on only five data points.

And then there’s the gap. The lowest tensiometer readings cut out at -0.085 MPa, while historically the highest WP4 water potential meter range barely reached -1 MPa. That left a hole in the curve right in the middle of the plant-available range.

In 2008, METER Group AG in Germany released the HYPROP, an instrument capable of producing over 100 data points in the 0 to -0.1 MPa range. This solved the resolution issue with more than 20 times the data behind that section of the curve.

In 2010, METER Group released the redesigned WP4C water potential meter. Significant accuracy and range gains now allow the WP4C to make good readings all the way up to the tensiometer range. Using  HYPROP  with the redesigned  WP4C , a skilled experimenter can now make complete, high-resolution moisture release curves. For in-depth information about how to make full soil moisture release curves in the lab, see our  Moisture Release Curve App Guide .

Wait, there’s more

Soil moisture release curves can provide even more insight and information beyond the scope of this article. Researchers use them to understand many issues like soil shrink-swell capacity, cation exchange capacity, or soil-specific surface area.

Want to learn how soil moisture release curves can be used in your application? Contact us—Our soil scientists have decades of experience helping researchers measure the soil-plant-atmosphere continuum. Or watch our soil moisture release curve webinar:  Soil Moisture 201: Moisture Release Curves—Revealed .

WATER POTENTIAL: A LITTLE HISTORY

Understanding unsaturated water flow in soils

At the turn of the last century, the USDA Bureau of Soils (BOS) recruited several pure physicists to tackle perplexing problems in agriculture. One of these was Edgar Buckingham. When Buckingham came to the Bureau of Soils in 1902, he had already authored a text on thermodynamics. His first experiments at the BOS involved gas transport in soils, but ultimately he came to consider the problem of unsaturated water flow in soil, and this is where he made his greatest contribution to soil physics.

As a classical physicist, Buckingham used mathematics to examine the mysteries and confusion surrounding how water flows in soil. Realizing that water content  did not drive flow  in unsaturated soil, Buckingham’s challenge was to describe the forces that did. He was naturally familiar with electrical and thermal force fields and the flux they created. These concepts were comfortable analogs for the driving force created in soil by gradients in what he called “capillary conductivity.” Buckingham used Ohm’s and Fourier’s laws to describe this flux.

1902 : Edgar Buckingham comes to work for the Bureau of Soils. His experience in thermodynamics helped form the beginning of our understanding of unsaturated water flow in soils.

1930s : L.A. Richards develops the pressure plate, one of the first instruments capable of effectively measuring “capillary conductivity”.

1940s : L.A. Richards and John Monteith publish papers describing how thermocouple psychrometers could be used to measure the water potential of soil samples.

1951 : D.C. Spanner is the first to successfully demonstrate the use of a thermocouple psychrometer to measure water potential in soil.

1983 : METER introduces the first commercially available thermocouple psychrometer (the SC-10 later known as the TruPsi).

Measuring water potential in the lab

Although Edgar Buckingham described and demonstrated “capillary conductivity” in 1907, he was a long way from being able to measure it effectively. The first instrument to do that was the  pressure plate  created by L.A. Richards in the 1930s. A pressure plate doesn’t measure the  water potential  of a sample. Instead, it brings a sample to a specific water potential. The instrument applies pressure to force water out of the sample and into a porous ceramic plate. When the sample comes to equilibrium, its  water potential  will theoretically be equivalent to the pressure applied.

Once the soil samples reach a specific  water potential  under pressure, the researcher can measure the correlated water content. A soil moisture characteristic can be made by making these measurements at different pressures.

Vapor methods

Over a decade after the introduction of the pressure plate, L. A. Richards in the U.S. and John Monteith in Britain published papers describing how a thermocouple psychrometer could be used to measure the water potential of soil samples by equilibrating the sample with vapor in a closed chamber and measuring the relative humidity of the vapor. At equilibrium, the relative humidity of the vapor is directly related to the water potential of the sample.

The term psychrometer, coined in 1818 by the German inventor Ernst Ferdinand August (1795-1870), means “cold measurer” in Greek. A psychrometer is made of two identical thermometers. One (the dry bulb) is kept dry while the other (the wet bulb) is kept saturated. The difference in temperature between the wet and the dry bulb temperatures can be used to calculate the relative humidity of the air.

Thermocouple psychrometers

The first psychrometers used to measure relative humidity above a soil sample were of necessity quite small. The two thermometers were made of tiny, fragile thermocouples. A thermocouple is a temperature sensor made from two dissimilar conductors joined at one spot. The thermocouple converts a temperature gradient into electricity, which can be measured to determine temperature changes.

Thermocouple psychrometers were first successfully used to measure water potential by D.C. Spanner before 1951, but it was a difficult measurement to make. To get the results he wanted, Spanner had to make his own wire out of bismuth antimony—according to John Monteith, a fume hood at Rothamsted bore the marks of these experiments for many years.

Others struggled to repeat his measurements. Samples took up to a week to equilibrate, and then the fragile thermocouples would often read just one sample before they were broken. Still, by 1961 Richards clearly saw vapor methods as the future of water potential measurements (Richards and Ogata, 1961).

Decagon (now METER) introduced its first commercial thermocouple psychrometer (the SC-10 Thermocouple Psychrometer Sample Changer, later TruPsi) in 1983. This instrument used a delicate thermocouple but protected it inside a sealed enclosure. Nine samples were equilibrated simultaneously and rotated under the thermocouple to be measured.

Prior to each measurement, the wet bulb thermocouple was dipped in a tiny reservoir of water. The electrical output of the thermocouple was sent to a nanovoltmeter, which had to be monitored to determine when the temperatures stopped changing.

Dew point water potential meters

In the late 1990s, Decagon (now METER) started producing the  WP4C Dew Point Potentiameter , an improved method for measuring water potential using vapor pressure. Like the psychrometer, it measures the vapor pressure above a sample sealed inside a chamber. Both instruments are primary methods based on thermodynamic principles.

Unlike the psychrometer, the dew point potentiameter uses a chilled-mirror dew point sensor. A small mirror in the chamber is chilled until dew just starts to form on it. At the dew point, the WP4C measures both mirror and sample temperatures with 0.001 °C accuracy to determine the relative humidity of the vapor above the sample. The water potential of the sample is linearly related to the difference between the sample temperature and the dew point temperature.

The dew point sensor has several advantages. It is faster and gives accurate measurements even when the operator is relatively unskilled. Also, the chilled mirror sensor doesn’t require added water and therefore doesn’t increase the water content of the vapor above the sample.

This measurement has the advantage of being a primary method for determining water potential based solidly on thermodynamic principles rather than on calibration.

The most recent version of this instrument can resolve temperatures to a thousandth of a degree, making it possible to measure samples as wet as -0.5 MPa with excellent accuracy.

Our scientists have decades of experience helping researchers and growers measure the soil-plant-atmosphere continuum.

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Webinar: The fight against runoff – a study of hydrology applications

Hydraulic conductivity used to be a measurement reserved for those with ample technical expertise, time, and resources for the arduous measurement process.

The accurate, automated measurements of the SATURO and KSAT make it easier than ever for non-specialists to understand the infiltration properties of the soil impacting their project. In this 30-minute webinar, research scientist Leo Rivera explores applications where the measurement of hydraulic conductivity is making a huge impact, including:

• Studying the risk of landslides, mudslides, and flash floods that frequently occur after wildfires
• Engineering designs for low impact development
• Designing systems for better infiltration, minimizing runoff into urban drainage systems
• Studying the impacts of land management on soil hydraulic properties and soil health

October 29th, 2024 9am PDT

Investigating osmosis: measuring the water potential of a potato cell

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Understanding the osmotic potential of plant cells is a key part of understanding cellular processes. Here we present two methods of determining osmotic potential of plant tissues using potatoes.

Method one, the standard protocol for measuring weight change of tissues in varying osmotic solutions, is reliable but does not demonstrate the changing solute potentials.

The second method, the Chardakov method, is slightly more challenging, but far more visual. Here students can observer changing solute potentials, by observing the resulting density change in sugar solutions in which potato tissue has been immersed. A coloured extract of the bathing solution can be seen to fall, rise or disperse when added to a known molar sugar solution.

This could be attempted as an individual investigation, or could be presented to the class as a demonstration with flex/webcams on the whiteboard.

What's included?

• SAPS Water Potential of a Potato Cell - Technical and Teaching Notes
• SAPS Water Potential of a Potato Cell - Student Sheet
• Cells and tissues

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Teaching resources.

• A-Level Set Practicals - Osmosis in bell pepper pericarp tissue
• Using Potatoes in the Lab

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Article Contents

Introduction, ψ w and water movement through the spac: a brief primer on plant water relations, advantages of monitoring ψ w in plant biology research, plants respond to restricted water supply by avoiding water loss and tolerating reduced ψ w, knowledge of plant water status can add a new level of insight to many types of physiological and molecular data, genetic and genomic analyses are crucial to answer long-standing questions in plant water relations, measurement of plant water status and new methods used to scale up analysis of water status and physiological responses to drought, conclusions, acknowledgments.

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Time for a drought experiment: Do you know your plants’ water status?

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Thomas E Juenger, Paul E Verslues, Time for a drought experiment: Do you know your plants’ water status?, The Plant Cell , Volume 35, Issue 1, January 2023, Pages 10–23, https://doi.org/10.1093/plcell/koac324

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Drought stress is an increasing concern because of climate change and increasing demands on water for agriculture. There are still many unknowns about how plants sense and respond to water limitation, including which genes and cellular mechanisms are impactful for ecology and crop improvement in drought-prone environments. A better understanding of plant drought resistance will require integration of several research disciplines. A common set of parameters to describe plant water status and quantify drought severity can enhance data interpretation and research integration across the research disciplines involved in understanding drought resistance and would be especially useful in integrating the flood of genomic data being generated in drought studies. Water potential (ψ w ) is a physical measure of the free energy status of water that, along with related physiological measurements, allows unambiguous description of plant water status that can apply across various soil types and environmental conditions. ψ w and related physiological parameters can be measured with relatively modest investment in equipment and effort. Thus, we propose that increased use of ψ w as a fundamental descriptor of plant water status can enhance the insight gained from many drought-related experiments and facilitate data integration and sharing across laboratories and research disciplines.

Drought is a topic of strong interest across plant biology from agronomy to ecology and to molecular and cell biology. The prospect that climate change will cause more frequent drought episodes will only add to this interest in the coming years. From an agronomic perspective, the goal of many studies is to identify and study factors that influence crop yield and how these factors are modified by drought. From the ecological perspective, there are strong interests to understand how plants adapt to water-limited environments and how that adaptation scales to community and ecosystem function. Molecular genetics research aims to find the genes and cellular mechanisms plants use to detect and respond to drought stress and thereby develop fundamental knowledge of plant function. A common thread of these types of plant drought research is that they seek to understand the genotype by environment interactions that determine the distribution and productivity of different plant species. All these research fields also have a strong interest in being able to make predictions and interventions: predictions of how climate change will alter ecosystems or crop productivity; and, interventions, such as genetic modification of crop plants or ecosystem management strategies, that can mitigate the effects of drought.

These objectives require scaling across different disciplines and types of experiments. Multiple types of scientists need to be able to compare their studies of drought stress and learn from each other’s results. This in turn requires a common terminology and core methods to quantitate the severity of drought stress and report the most relevant plant responses. Then researchers can get the most insights from their data and have confidence in comparing the results of different studies. But, what are the best methods to quantify drought stress severity? Salt stress can be reported as salt concentration or changes in the conductivity of soil water. Temperature stresses (freezing, chilling, and heat stress) can be standardized based on the timing and extent of the temperature change (and whether ice nucleation is provided in the case of freezing) ( Verslues et al., 2006 ). In this article, we describe equivalent measures for “drought” stress and show how incorporating such measurements can increase the insight gained from many types of experiments, including ‘omics approaches, and also allow us to avoid common pitfalls in data interpretation.

The above sentence refers to “drought” in quotations because some readers may point out, correctly, that the core definition of drought is meteorological (a period of below-average precipitation). However, for much of plant biology, and the majority of papers in this journal, the term drought is instead used to refer to the plant’s relationship with water (i.e. plant water status). Thus, “drought” responses as commonly discussed in most molecular and cellular studies are really responses to an altered water status where water has become less available to the plant because it is at a lower free energy state compared with unstressed conditions. For plant biology, the energy state of water can be quantified and reported in terms of the water potential (ψ w ).

Land plants move copious quantities of water through the soil–plant–atmosphere continuum (SPAC) whereby water taken up from the soil moves upward through the plant vascular system ( Figure 1A ). Most of this water is lost from the plant by transpiration through stomata. The movement of water through the SPAC is driven by differences in ψ w . The ψ w is defined as the amount by which the chemical potential of water is reduced below that of pure water (pure water being zero, thus ψ w is always negative) and is expressed in units of pressure ( Kramer and Boyer, 1995 ). A higher concentration of dissolved solutes will decrease osmotic potential (ψ s ) to lower (more negative) values. Adhesion of water molecules to surfaces also decreases their free energy; this is referred to as the matric potential (ψ m ) and is an important determinant of soil ψ w . However, as most techniques for measuring ψ w cannot separate the effects of solutes versus adherence of water molecules along surfaces (e.g. the surface of soil particles), ψ m is often considered to be part of ψ s for practical purposes. A positive pressure (ψ p ), in turgid cells, for example, will increase ψ w (make it less negative) while a negative pressure (e.g. in xylem as water is pulled up by transpiration) will reduce ψ w . A higher position in gravity (ψ g ) will also make ψ w more negative; but, the effect of gravity is negligible for those not studying large trees and is also typically omitted for practical purposes. Thus, for purposes of most plant biology research, ψ w is essentially determined by two major components, osmotic potential ψ s (which is denoted as π in some cases, also referred to as “solute potential”) and ψ p . Thus, the full set of ψ w components (ψ w = ψ s + ψ m + ψ p + ψ g ) can be reduced to the basic ψ w equation of ψ w = ψ s + ψ p ( Kramer and Boyer, 1995 ).

Water movement through the SPAC and water status of soils, solutions and plant tissue can be described in a unified manner by ψ w . A, Diagram of water movement through the SPAC. A continuous column of water exists from the soil, through the root tissue and into the xylem, and into capillary spaces around leaf cells. Evaporation of water from leaf tissue and adhesion of water molecules pulls water up through the SPAC. The rate of water evaporation from leaf tissue is controlled primarily by the opening and closing of stomata. The boxes give typical values of ψ w and its components inside plant cells (symplast) or just outside these cells (apoplast/xylem) for well-watered conditions or drought conditions. The low ψ w conditions shown would be within the range experienced by crop plants (or other mesophytic plants) and would be at or just above the permanent wilting point (i.e. the ψ w below which the plant cannot regain turgor even overnight when stomata close and transpiration is minimal) for most such species (depending on light, temperature and air humidity conditions). B, Example soil moisture retention curves for five different soils highlighting the potential variability in soil ψ w ( x -axis; Ψ W ) at various soil–water contents ( y -axis; expressed as a percentage of field capacity). The banded area (10–20% of field capacity) highlights the range of soil–water content typically utilized in studies imposing drought stress on plants. Data were collected using the Decagon WP4 Dewpoint Potentiometer. Curves are presented for two common horticultural mixes (Promix BX, Turface) along with several field soils spanning a gradient of texture and composition (sandy loam, clay loam, and silt loam). For plotting purposes, the best fitting model (second-order polynomial of the reciprocal term and soil interaction) was selected by Akaike Information Criterion and showed an adjusted R 2 of 0.9893 ( P  <1 e −10) and significant differences among soils. All statistical analyses were performed with the stats package in the R software environment (R Development Core Team). C, Relationship between PEG-8000 concentration and ψ w . Note that the values are for a given amount of PEG-8000 added to 1 L of water without adjustment of the final volume (a significant increase in volume will occur for higher PEG concentrations). The ψ w of PEG solutions was measured using a Wescor Psypro system with C52 sample chambers following the manufacturer’s instructions and using ψ w standards provided by the manufacturer ( Verslues, 2010 ) or by using a Wescor vapor pressure osmometer. For the osmometer, osmolality readings in mmol kg −1 were converted to ψ w using the van’t Hoff calculation ( Verslues, 2010 ; Banks and Hirons, 2019 ). Both instruments gave essentially identical results. Note that because PEG-8000 is a large hygroscopic molecule, which affects ψ w primarily by adherence to water molecules, there is a nonlinear relationship between PEG content and ψ w , similar to the nonlinear relationship between soil ψ w and water content. Data are replotted from Verslues et al. (2006) and from previously unpublished data of the Verslues laboratory.

At different points in the SPAC, the components of ψ w differ. In the soil, matric forces of water adhering to soil particles are the dominant component of ψ w (except in highly saline soils where dissolved salts also decrease ψ s ). Inside the plasma membrane of plant cells, the active accumulation of solutes decreases ψ s to drive water uptake. This osmotically driven uptake of water produces a positive turgor pressure inside plant cells because they have rigid cell walls which restrict cellular volume. As solutes accumulate, turgor pressure will increase until the cell reaches ψ w equilibrium with its immediate surroundings ( Figure 1A ). In wall-less cells, the accumulation of solutes determines the cell volume. Thus, all cells must osmoregulate (regulate their solute content) at all times, to maintain cell volume or regulate turgor. In the apoplast and xylem, tension (negative pressure) generated by adhesion of water molecules moving up through the plant (and some matric and solute effects) is the major component of ψ w . This upward movement of water is driven by water evaporation from capillary surfaces in the inner air spaces of the leaf. As water vapor, even at near saturation humidities, has a much lower ψ w than liquid water, evaporation can always occur at appreciable rates. Thus, the rate of water loss from the leaf is controlled primarily by stomata. The regulation of stomatal opening and closing, as well as control of stomatal size and density, is key to balancing the competing priorities of controlling water loss while allowing CO 2 uptake.

For readers from a plant physiology background, the above information is well known. For those approaching plant stress biology from other backgrounds who are interested in a more thorough introduction to plant water relations, we recommend the Taiz and Zeiger Plant Physiology textbook (renamed as Plant Physiology and Development for later editions) ( Taiz and Zeiger, 2006 ) as well as the comprehensive book of Kramer and Boyer (1995) or its methods focused companion ( Boyer, 1995 ) or, the following web pages provided by makers of instruments for ψ w measurement (Ψ w versus water content).

A key advantage of ψ w for plant research, compared with other metrics such as soil water content, is that it allows laboratory or field-based stress treatments to be described in a manner that is unambiguous and thus able to be replicated across experimental systems while also giving a clearer picture of the stress severity experienced by the plant. The different distribution of particle sizes among soil types means that the relationship between soil water content versus ψ w varies greatly among soil types ( Figure 1B ). Clay soils (smaller average particle size) have much higher water content at even very low ψ w than sandy soils which have larger average particle size and thus less surface area for water adhesion ( Kramer and Boyer, 1995 ); see also Soil water content versus ψ w ). Thus, a drought stress severity reported in terms of soil water content could not be reproduced in another laboratory by subjecting plants to the same soil water content unless both laboratories used exactly the same soil. Many soils, including the peat-based horticultural soil mixes often used in plant research, exhibit a dramatic decline in soil ψ w once soil water content passes a threshold level ( Figure 1B ; Walczak et al., 2002 ; Fields et al., 2014 ; Dowd et al., 2019 ). Thus, a seemingly small difference in soil water content between different replicates or different genotypes can actually indicate a substantial difference in stress severity. This is most acute for sandy soils (soils comprised mostly of large particles with lower portion of smaller silt and clay-type particles), as these soils have low water-holding capacity.

In some studies, calculation of the fraction of transpirable soil water (FTSW) has been used to estimate the degree of water limitation experienced by plants. FTSW utilizes soil moisture data along with the threshold soil water content (or threshold ψ w ) below which the plant under study can no longer extract water (i.e. transpiration decreases to near zero) to calculate the relative amount of plant available water that remains at various bulk soil water contents ( Serraj and Sinclair, 1997 ). Since the threshold for water extraction is determined largely by ψ w (along with soil hydraulic conductivity), FTSW is strongly correlated with soil ψ w or leaf ψ w (see e.g. Lacape et al., 1998 ; Yan et al., 2017 ; Devi and Reddy, 2020 ). FTSW can be useful for field studies and irrigation scheduling; however, for laboratory or greenhouse studies, measurement of ψ w still offers a more straightforward measure of stress severity that is physically grounded and not dependent upon the properties of the growth media or properties of the plants under study. Use of ψ w also facilitates comparison of results between soil experiments and experiments conducted in other types of media where FTSW is not applicable, such as agar plates or liquid culture. It should also be noted that in studies of plant stress acclimation, it has been observed that many important physiological parameters, such as abscisic acid (ABA) accumulation, proline accumulation, and growth show a linear or near-linear relationship with ψ w (see e.g. van der Weele et al., 2000 ; Verslues and Bray, 2004 ; Liu et al., 2005 ) . Use of ψ w to scale data is further discussed later in this article. Thus, for genetic studies of drought response, FTSW may be a supplement to, but not a replacement for, measurement of ψ w .

For such laboratory- or greenhouse-based studies of controlled soil drying, where the type of growth media used can be deliberately selected, the approach described by Dowd et al. (2019) may be applicable. They analyzed several types of growth media and found dramatic differences in water-holding capacity. They then selected the type of growth media that had a high water-holding capacity over the range of low-to-moderate ψ w treatments they wished to impose (−0.25 to −0.4 MPa; the unstressed control was −0.1 MPa). By using this selection of appropriate growth media, along with monitoring of soil weight and maintaining a high humidity around the soil surface, they were able to expose maize seedlings to stable ψ w treatments over 9 days to quantify the effects of ψ w on maize lateral root development ( Dowd et al., 2019 ). Thus, they could assay effects of reduced ψ w on root development that would not be apparent if they used a media with low water holding capacity over the target range of ψ w and not apparent if they had simply allowed the soil to dry rapidly over the experimental period.

It is also important to note that declines in soil ψ w lead to a dramatic decline in soil hydraulic conductivity (i.e. the water that remains in the soil is more tightly bound to soil particles). This decline in hydraulic conductivity varies greatly among soils and determines how much water the soil can supply to the plant at a given ψ w . Soil hydraulic conductivity can be a key factor in determining stomatal opening (and perhaps other drought-responsive traits) as the plant seeks to match the water supply available from the soil with transpirational demand ( Carminati and Javaux, 2020 ).

For other types of experiments, high molecular weight polyethylene glycol (PEG; such as PEG-8000) is a useful agent to impose low ψ w upon plants, especially when the PEG is incorporated into a solid matrix such as agar plates ( van der Weele et al., 2000 ; Verslues et al., 2006 ). High molecular weight PEG is useful because large PEG molecules reduce ψ w primarily by matric forces rather than osmotic forces and because large PEG molecules are not able to penetrate the pores of plant cell walls and thus cause cytorrhysis (withdrawal of water from and shrinkage of both cell wall and protoplast) rather than plasmolysis where only the protoplast loses water and may separate from the cell wall ( Oertli, 1985 ). For these reasons, treatment with high molecular weight PEG is more similar to soil drying than osmotic stress imposed with low molecular weight solutes. However, high molecular weight PEG does not behave as an ideal solute and there is a nonlinear relationship between PEG concentration and ψ w ( Figure 1C ) which needs to be accounted for when determining the amount of PEG needed to impose a moderate versus more severe low ψ w treatment ( van der Weele et al., 2000 ; Verslues et al., 2006 ). When using PEG for liquid cultures, it should also be kept in mind that solutions of high molecular weight PEG are viscous and can cause root hypoxia unless the solutions are well aerated ( Verslues et al., 1998 ). At the same time, root damage should be avoided as this may allow PEG molecules to enter the plant tissue. Use of PEG-infused agar plates avoids these problems and is a good experimental system for subjecting small plants/seedlings to a constant and defined severity of low ψ w stress ( Van der Weele et al., 2000 ; Verslues et al., 2006 ) while avoiding complications that may arise from using low molecular weight solutes such as mannitol which, in addition to causing plasmolysis, may elicit specific responses unrelated to changes in ψ w ( Trontin et al., 2014 ).

The key factor in our plant physiological definition of drought is the decline in external ψ w . This is primarily caused by reduced soil water content such that the remaining soil water is held by stronger matric forces. Increased solute content of soil water can also be a factor, as well as a high vapor pressure deficit resulting from drying atmospheric conditions (low humidity and high temperature, perhaps accompanied by rapid air movement) which may cause drying of the plant tissue even when soil moisture is still available. The most basic effect of decreased external ψ w is to collapse, or reverse, the ψ w gradient that had allowed the plant tissue to take up water. Thus, when the external ψ w decreases, ψ w of the plant tissue will also decline. If the plant does nothing, this will occur passively by water efflux from cells leading to loss of turgor and decrease in cell volume until equilibrium with external ψ w is reached. Because water flux through the SPAC is rapid, the most immediate need of the plant is to stop the bleeding (of water) by closing stomata. Stomatal closure, along with other drought responses that aim to reduce water loss (e.g. rolling or shedding of leaves, thicker cuticle, increased trichome density, or reduced stomatal density on newly formed leaves) are classically referred to as avoidance responses because they aim to avoid depletion of the available water. For mesophytic plants which genetically prioritize high photosynthesis rates and rapid growth (such as most crop plants), or in cases where soil drying is rapid, avoidance is a key component of the drought response. It is also the dominating factor in many laboratory experiments where plants are grown in a small volume of soil such that terminal drying rapidly occurs once water is withheld from the plant. For these reasons, avoidance responses are the aspects of drought response that we are most familiar with at the molecular genetic level. The stomatal closure responses described above are regulated through relatively well-characterized signaling pathways involving ABA and other plant hormones (see e.g. Vaidya et al., 2019 ; Yang et al., 2019 ; Berrio et al., 2022 ).

While avoidance responses are essential to conserve water and may help slow the rate of soil ψ w decline, this avoidance of water loss cannot itself restore water uptake and turgor. To do this, the plant must decrease its internal ψ w to a value below the external soil ψ w by osmotic adjustment, the active accumulation of additional solutes inside cells ( Figure 1A ). Osmotic adjustment to maintain turgor is a prerequisite for longer term developmental responses such as increasing the root-to-shoot ratio and changing root growth patterns through maintenance of root elongation to reach deeper in the soil profile, hydrotrophic responses, or altered lateral root initiation. Active osmotic adjustment, as opposed to passive increase in solute content by tissue dehydration, is an adaptive tolerance response as it allows the plant to maintain function at reduced ψ w . A simple example of osmotic adjustment in Arabidopsis thaliana is shown in Figure 2A where seedlings were transferred to agar plates which had varying amounts of PEG added to generate a range of ψ w from mild stress (small decrease of ψ w ) that had no apparent detrimental effect to severe stress levels. Seedling ψ s and relative water content (RWC; water content of the tissue relative to its water content when fully hydrated) were measured three days after transfer ( Verslues, 2010 ). The plants were able to fully osmotically adjust and maintain high RWC after transfer to ψ w as low as −1.0 MPa (and because ψ s of the plant tissue is less than ψ w of the agar media, it can be inferred that turgor was also maintained over this range). The extent of osmotic adjustment, and its role in maintaining high RWC even at substantially reduced ψ w , can be easily observed in this experimental system because transpiration is minimal and thus avoidance responses do not dominate the phenotype observations in the way that often occurs in pot-based soil drying experiments.

Quantifying solute content, turgor, and plant tissue water content. A, Seedling osmotic potential (ψ s ) and RWC of A. thaliana (Col-0 accession) seedlings provide a simple illustration of osmotic adjustment and the TLP concept (replotted from Verslues, 2010 ). Seven-day-old seedlings (ecotype Col-0) were transferred to PEG-agar plates of the indicated ψ w and whole seedlings (10–30 per sample, depending on treatment) collected 3 days after transfer. As transpiration is minimal in this system, one can assume that the ψ w of the plant tissue is in near equilibrium with the agar ψ w . Thus, a seedling ψ s below the dashed line indicates a positive turgor pressure. When osmotic adjustment can no longer maintain turgor (at ∼−1.2 MPa), further declines in seedling ψ w occur via water loss (indicated by reduced RWC) and passive concentration of solutes. B, A theoretical PV curve representing the expected relationship between −1/ψ w and RWC for a drying leaf. At high RWC, ψ w-leaf is a function of both turgor pressure ψ p and osmotic potential ψ s and exhibits an exponential decline with drying. The TLP (the red dot) occurs when dehydration proceeds until ψ p  = 0. The linear decline in −1/ψ w past TLP is driven by the passive concentration of solutes with water loss. The linear extension of the relationship to the y -axis reveals the osmotic potential at full hydration (a: −1/ψ s100 ). The osmotic potential at zero turgor (b: −1/ψ sTLP ) can be determined by extending a horizontal line from TLP to the y -axis while the RWC at TLP (c: RWC TLP ) can be determined by a perpendicular line from TLP to the x -axis. Symplastic and apoplastic (AWF) fractions can be inferred from the linear intersection of the fit line with the x -axis. The modulus of elasticity ( ε ) can be inferred from the slope of the ψ p from full hydration to the TLP. C, Example PV curves derived from well-water and drought-stressed plants depicting osmotic adjustment and a shift in TLP. The osmotic potential at full turgor for the drought-stressed plant material (e: −1/ψ s100ds ) can be subtracted from the osmotic potential at full turgor for the well-water watered plant material (d: −1/ψ s100ww ) to obtain an estimate of osmotic adjustment. C, Redrawn from Sanders and Arndt (2012) , adapted by permission from Springer Nature.

While osmotic adjustment is a fundamental aspect of plant responses to low ψ w , whether or not increased osmotic adjustment is of value for improving crop productivity during drought has been controversial. It has been argued that at relatively low ψ w near the permanent wilting point (around −1.5 MPa for most crop plants), the amount of water that could be extracted by osmotic adjustment is likely too small to affect productivity ( Morgan, 1995 , 2000 ; Serraj and Sinclair, 2002 ). At higher soil ψ w , increased osmotic adjustment may lead to more rapid water depletion and thus may not be beneficial under prolonged drought where water conservation and increased water use efficiency (WUE) would be more valuable. However, others have strongly disagreed with this assessment, and have argued that the capacity for osmotic adjustment is associated with crop productivity during drought and that root osmotic adjustment in particular can facilitate further growth to reach water in deeper soil layers ( Blum, 2017 ). It seems likely that whether or not increased osmotic adjustment will allow improved plant productivity depends on the timing and duration of water limitation during the plant life cycle as well as the distribution of water among deep versus shallow soil layers. As we discuss below, a better understanding of how osmotic adjustment is regulated would help both to answer these agronomic questions and to answer fundamental biological questions of how plants detect and respond to changes in water availability.

It must also be kept in mind that plant growth is not determined solely by physical limitations on turgor and water uptake. For example, when Arabidopsis seedlings are exposed to a moderately reduced ψ w (−0.7 MPa) on PEG-agar plates we routinely observe that growth (quantified by fresh and dry weight or root elongation) is reduced by two-thirds compared with the unstressed high ψ w control ( Bhaskara et al., 2017 ; Longkumer et al., 2022 ). The data in Figure 2A make it clear that there is no sustained loss of turgor or tissue dehydration at −0.7 MPa that could explain such reduced growth. Rather the growth reduction observed is the result of active growth restriction in response to low ψ w ( Verslues and Longkumer, 2022 ). We can also hypothesize from these observations that a moderate low ψ w treatment (such as −0.7 MPa, Figure 2A ) would be ideal for identifying genotypes that either fail to restrict growth at low ψ w , and thus have increased growth maintenance compared with the wild-type, or genotypes that are more sensitive, perhaps because of a failure to osmotically adjust, and thus exhibit more severe dehydration and growth restriction compared with the wild-type. Indeed, our research has identified both negative and positive effectors of growth and osmotic adjustment ( Verslues and Bray, 2004 ; Bhaskara et al., 2012 ; Longkumer et al., 2022 ).

A related, but more extensive, method of examining plant water relations often used by ecophysiologists is the generation of pressure–volume (PV) curves ( Figure 2B; Koide et al., 1989 ). In this approach, a sample (typically a leaf, but could be a branch for larger plants or the entire shoot for smaller plants) is detached from the rest of the plant and is subjected to repeated bulk ψ w and fresh weight measurements while being allowed to dehydrate. Fully hydrated weight is also measured to allow the RWC of the sample to be calculated at each of the ψ w measurement points. This is referred to as a PV curve because traditionally the ψ w was measured using a pressure chamber. However, recent refinements have shown that more rapid methods using a vapor pressure osmometer can also be effective ( Bartlett et al., 2012a , 2012b ;  Banks and Hirons, 2019 ). After performing a series of such measurements, a plot of −1/ψ w versus RWC is constructed ( Figure 2B ). PV curves generally exhibit a steep initial nonlinear decline driven by a rapid drop in turgor (ψ p ) until at a certain RWC the turgor pressure is lost (turgor loss point [TLP]). The linear decline in ψ w past TLP is subsequently driven by the passive concentration of solutes with water loss. During the linear phase of the PV curve, the ψ w will equal the osmotic potential (ψ w  = ψ s ). Linear extension of this portion of the function can be used to estimate several parameters including the ψ s at full hydration (−1/ψ s100 ), ψ s at the point of turgor loss (−1/ψ sTLP ) and RWC at the TLP (RWC TLP ) ( Figure 2B ). Information about cell wall elasticity (ε, modulus of elasticity) can be derived from the slope of ψ p between full hydration to the TLP: a steep slope (high ε) results from rigid cell walls while a shallow slope indicates elastic walls (low ε). Finally, estimates of the apoplastic water fraction (AWF) can be derived from the RWC at which ψ w approaches infinity. The PV curve highlights how RWC can be difficult to interpret in the absence of other water relations data, especially whether ψ w has decreased past the TLP. Without such data, it can be ambiguous whether a decreased RWC is associated with a reduction in turgor; or, whether turgor has already been lost and decreased RWC indicates dehydration of the tissue that is likely to damage cellular structure.

It has been proposed that ψ s at the point of turgor loss (ψ sTLP ) is a key determinant of plant adaptation to water-limited environments, as more negative values of ψ sTLP extend the range of ψ w over which the leaf can remain turgid and functional ( Bartlett et al., 2012a , 2012b ). Theoretically, plants may improve their drought tolerance by accumulating intracellular solutes (decrease ψ s ) to decrease their TLP, decreasing intracellular volume while maintaining a relatively high amount of apoplastic water (increasing AWF), and increasing cell wall flexibility (decreasing ε) so that cell volume can decrease without a loss of turgor. Bartlett et al. (2012a , 2012b ) provide a detailed discussion and examples of how various PV parameters may impact TLP. Also, the physiological literature contains reports of the water relations characteristics of most model or crop species. For example, a number of papers have reported water relations parameters for A. thaliana ( Des Marais et al., 2012 ; Scoffoni et al., 2018 ), information that may be valuable for designing and interpreting Arabidopsis drought stress experiments.

Similar to the ψ s and RWC data in Figure 2A , PV curve analysis ( Figure 2B ) can provide valuable baseline information for experimental design. For example, what is the range of ψ w over which a plant is likely to retain the capacity to generate turgor and preserve cellular function? Studies employing ‘omics analyses, or other techniques, to understand how the plant acclimates and continues to function at low ψ w would need to collect samples from tissue at ψ w above the TLP. Conversely, we may expect that at ψ w below the TLP where extensive cell shrinkage and cytorrhysis occur, many changes in gene expression or protein accumulation are likely to be involved in cellular damage control and can be interpreted in that light ( Lang et al., 2014 ). A limitation of PV curve analysis has been that it is laborious and requires specialized pressure chamber equipment, although, as mentioned above, this limitation may no longer apply. Also, because a detached sample is used, PV curve analysis may not capture plastic responses of osmotic adjustment or cell wall properties as the plant acclimates to different moisture conditions over time. In this case, a series of samples would need to be analyzed from plants exposed to different moisture conditions to see if ψ s100 or ψ sTLP are shifted as the plant acclimates to different environmental conditions ( Bartlett et al., 2012a , 2012b ). For instance, osmotic adjustment can be calculated with PV curves by subtracting the ψ s100 of drought-stressed plants from ψ s100 of well-watered plants ( Figure 2C ).

Interpretation of experimental data, including ‘omics data and various genetic analyses, can be greatly enhanced by knowledge of plant water status and ψ w of the soil or growth media. Perhaps the most fundamental use of ψ w and plant water relations data is to allow the experimenter to unambiguously tell the difference between low ψ w avoidance versus tolerance. Many molecular genetic studies involve comparison of genetically modified plants (e.g. a mutant or transgenic line) to a wild-type control. A common experimental design is to grow the different genotypes in separate pots and subject them to a fixed duration of water withholding before phenotypic assay (often plant survival after re-watering; Figure 3 ). In this case, the severity of stress experienced by the plant is not controlled by the experimenter. Rather it is determined by the plant itself through the amount of water removed from the soil by transpiration. Plants that have less water loss through transpiration will deplete the soil water more slowly and thus be exposed to a less severe stress (higher ψ w ) at the end of the water withholding period than plants with more rapid transpiration. Not surprisingly, the plants that were exposed to a less severe stress (higher ψ w ) will typically have a higher survival rate at the end of the experiment. In the absence of measurements of soil ψ w or water content, it is difficult, or impossible, to conclusively determine whether differences in survival are the result of differences in avoidance of water loss or differences in tolerance-related parameters. While both can be important, the underlying mechanisms are different.

Potential pitfalls in uncontrolled soil drying experiments. The diagram depicts a scenario in which a reference genotype (wild-type) is compared with another genotype that is similar but has a slower growth rate resulting in a smaller plant size (less leaf area) at the start of the soil drying period (e.g. a mutant or transgenic line that has reduced growth compared with its wild-type background). If each genotype is grown in separate pots and subjected to a set period of soil drying, the smaller genotype will deplete the soil water more slowly by virtue of having less transpiring leaf area. In this case, the smaller genotype will likely have better recovery and less tissue damage after this set period of soil drying; however, this may not indicate a difference in drought resistance as the two genotypes were never exposed to the same severity of stress (the smaller genotype remained at higher ψ w ). A more robust comparison of drought resistance between these two genotypes could be achieved by modifying the experiment design such that the soil water content (pot weight) is monitored and adjusted through the experiment to ensure that both genotypes experience the same ψ w . Alternatively (or in addition), both genotypes can be grown close together in the same symmetrical container such that they fully inter-root and thus experience the same soil ψ w regardless of which genotype transpires more rapidly.

A further complication is that mutants or transgenic lines that constitutively grow more slowly, often for reasons unrelated to stress response, can better survive the water withholding period solely by virtue of their relatively small transpiring leaf area. Such a difference is of uncertain value in terms of increasing plant productivity during drought. Similarly, unequal rates of soil water depletion can also complicate phenotypic analysis of genotypes that have altered ABA levels or altered sensitivity to ABA in stomatal closure. In uncontrolled soil drying experiments, these stomatal-dependent differences in soil water depletion will dominate the experimental results. If one wants to examine other, nonstomatal-related effects, steps need to be taken to ensure that all genotypes are exposed to the same soil ψ w . Similar concerns exist for comparisons among genotypes with altered stomal size or stomatal density. From a practical point of view for plant improvement, both avoidance of water depletion to conserve soil water and improve WUE (without sacrificing productivity in biomass gain or seed yield) as well as improved response to reduced ψ w can all be of value. Which type of response may be most useful for plant improvement is a matter of debate and depends upon the timing, duration, and severity of drought in different environments. If genetic and molecular studies can do a better job of disentangling these two types of drought responses, we can provide more relevant information to develop new germplasm for use by agronomists who study crop productivity in the field.

The limitations of uncontrolled soil drying experiments and endpoint survival measurements have been highlighted in several studies. Skirycz et al. (2011) found that mutants reported to have increased survival after water withholding did not differ from the wild-type in growth responses to water limitation when they were exposed to an equal and moderate severity of soil drying using an automated pot weighing and watering system. Similarly, the dwarf mutant chiquita1-1 ( chiq1-1 ), also referred to as constitutively stressed 1 , was originally described as drought “tolerant” based on uncontrolled soil drying survival assays ( Bao et al., 2020 ). Later experiments where soil water content was monitored and controlled found that chiq1-1 had reduced water usage because of its small size but did not differ in tolerance compared with the wild-type when both were exposed to the same severity of soil drying ( Ginzburg et al., 2022 ). Another example of the avoidance of water loss phenomenon is provided in this issue by Wang et al. (2023) , who describe a component in ABA signaling, SPIRAL1 (SPR1), that mediates microtubule disassembly during ABA-induced stomatal closure in Arabidopsis. When subjected to water withholding experiments, spr1 mutant plants failed to close their stomata and therefore exhibited significantly greater water loss and lower survivability than the wild-type after a fixed time of water withholding. This indicates that SPR1 primarily affects drought avoidance. Such experiments do not themselves completely rule out additional effects of SPR1 on drought tolerance. However, determining whether or not SPR1 also affects microtubules in other cell types leading to differences in low ψ w tolerance would require further experiments where spr1 is exposed to the same external ψ w and parameters, such as osmotic adjustment and RWC, and growth maintenance quantified.

Similarly, in cases where transcriptome or proteome data are collected at the end of uncontrolled soil drying experiments, it is difficult (or impossible) to deconvolute the effect of unequal soil drying from true genotype-dependent differences. This pitfall can be avoided by weighing pots and doing a partial re-watering to adjust all genotypes to the same soil water content or by growing the different genotypes together in a container that is sufficiently small and symmetrical to allow the plants to fully inter-root throughout the soil volume and thus be exposed to the same degree of drying even if different plants have differing rates of water usage ( Verslues et al., 2006 ). At the same time, plants must be grown in a sufficient volume of soil to allow adequate root growth and prevent rapid drying that can obscure drought acclimation responses that occur over longer time scales as several days or longer are often needed for differences in growth, metabolism, or proteome remodeling to become apparent. As discussed above, consideration of the water holding capacity of the growth media can help in designing experimental conditions that allow the rate of soil drying and stability of the desired ψ w treatment to be optimized ( Dowd et al., 2019 ).

Many molecular stress studies focus on comparing the responses of well-watered control plants with plants that experience a single severity of drought stress. Unfortunately, stress treatments are often poorly controlled and therefore measurements collected from the stressed plants usually exhibit increased variability relative to measurements from control plants. It is simply easier to target a homogenous and benign soil ψ w in a control treatment compared with consistently maintaining a specific soil ψ w in treatment pots experiencing dynamic drying. This complicates the statistical analyses of stress experiments, often violating assumptions of homoscedasticity, and can reduce the power to observe real treatment impacts when they occur. Moreover, a single stress level may not capture the important range of response to the stress gradient plants would experience in nature. Many eco-physiological studies focus on exploring stress responses across a more dynamic and natural gradient of stress frequency and amplitude ( Beier et al., 2012 ). These types of experiments are important as we anticipate that many stress responses result in nonlinear physiological or performance impacts. Measures of plant water status can also be used to evaluate relationships between physiological responses and the severity of water stress. For example, ψ w measurements from leaves during the day can be a strong indicator of plant water stress as a function of soil water availability and atmospheric demand. This is because midday ψ w reflects the balance of the amount of water supplied by the root system and transported through the xylem, and the strong demand caused by transpiration. Measures of plant ψ w -predawn are also valuable as a picture of water status in the absence of transpiration as stomates are generally closed at night. Predawn leaf ψ w is expected to be in equilibrium with the “wettest” soil ψ w accessed by roots ( Richter, 1997 ) and should generally reflect the ψ w of the soil prospected by the root system, although a number of factors can complicate this relationship ( Donovan et al., 2001 ). Predawn ψ w measures can therefore provide a whole-plant metric of the stress severity imposed by declining soil ψ w . Moreover, the difference in predawn ψ w and ψ w measured midday can give insight into the degree of maximum stress that plants experience due to the entire SPAC continuum, including transpiration loss from leaves ( Martínez-Vilalta et al., 2014 ). Thus, measurements of plant ψ w can be used to scale data to facilitate comparisons across different types of experiments and experimental conditions including plants grown in growth chambers versus greenhouse or field; or experiments using different types of growing media with differing soil water holding capacity; or comparisons among different species, cultivars, and genotypes.

From a biological perspective, using ψ w measurements to identify genes that are differentially expressed can be more powerful and may give greater insight than only considering a contrast of a single stress treatment with a control. On a practical level, using actual ψ w measurements to scale data can obviate the need to always “hit” a certain target level of stress when imposing the water limitation treatment. For example, Meyer et al. (2014) studied stress responses of switchgrass using a progressive dry-down experiment. The experiment generated predawn ψ w measurements ranging from −4.8 to −0.6 MPa in the drought treatment and from −1.5 to −0.2 MPa in the controls. Analyses of covariation revealed nonlinear relationships between gene expression, predawn ψ w , and paired physiological traits ( Figure 4 ) suggesting critical thresholds in drought stress responses that are likely associated with turgor loss. Similarly, Lovell et al. (2016) used ψ w -predawn and ψ w -midday to compare gene expression responses of switchgrass to soil drying in pots, field cylinders, and field rainout shelters to identify a core set of drought-responsive genes. Measuring ψ w -predawn not only allowed the three distinct experimental designs to be incorporated into a single analysis framework, it also allowed variability in stress generated from dry down rates (leading to differences in ψ w -predawn) to be incorporated in the analysis, thus increasing statistical power. This type of meta-analysis may allow more general discoveries of key biological processes involved in adaptive stress responses and recovery from water deficit.

Nonlinear relationship between gene expression and predawn leaf ψ w in a switchgrass drought experiment. Each line represents paired gene expression and physiological data from a progressive dry-down experiment with switchgrass. The sets of genes correspond to transcripts with significant nonlinear relationships with leaf ψ w . The fit lines for two clusters of stress-responsive genes indicate critical thresholds in expression that are likely related to turgor loss. Reprinted from Meyer et al. (2014) .

We note that in this case, the use of ψ w to scale the data is more robust than using RWC. This is because RWC does not directly measure the severity of the stress but rather represents a composite of the stress severity along with the plant response to stress in avoiding water loss and osmotic adjustment to retain water and turgor. Defining stress severity in terms of ψ w allows the severity measurement to be independent of the plant’s stress response so that convolution of severity and response does not hamper data interpretation. That said, RWC measurements can be valuable in experiments conducted below the ψ w-TLP as they give an indication of the extent of dehydration and the extent of cellular damage the plant has experienced.

Despite the well-developed methodology of plant water relations measurements illustrated above, and in contrast to drought avoidance responses, little is known about the genetic and cellular mechanisms that determine the capacity for osmotic adjustment or that determine cell wall properties that influence PV relationships in vegetative tissues (as opposed to guard cells which are distinct and not symplastically connected to other cells). Such mechanisms are not only important for drought research but also are a critical part of cell biology. For example, when external ψ w does not change, cellular ψ s remains constant even as cells transition from expansion (where rapid solute deposition is needed to drive water uptake) to cell maturation where cell expansion has ceased, and thus intracellular solute and water amounts are constant. The constancy of ψ s and turgor during cell expansion and transition to elongation was demonstrated by Sharp et al. (1990) and Spollen and Sharp (1991) who found that even though low ψ w increased solute content and decreased turgor overall, there was no change in these parameters as root cells exited the root elongation zone and ceased to expand.

In response to reduced external ψ w , the mechanisms that control cellular solute content must be altered to allow more solutes to accumulate. A decrease of cellular ψ s by −0.5 MPa, which is within the capability of most plants, requires a 200 mM increase in solute content (assuming they act as ideal solutes). There is information about the regulation of individual proteins potentially related to water status, for example, aquaporins that control membrane water permeability ( Ehlert et al., 2009 ; Sutka et al., 2011 ; Chaumont and Tyerman, 2014 ). However, the integrative mechanisms by which these molecular responses are coordinated to couple solute deposition with external ψ w and solute dilution by cell expansion to maintain an appropriate ψ s and turgor remain unknown. Interpretation of mutant or overexpression phenotypes is sometimes limited because effects on osmotic adjustment and plant water status were inferred rather than directly measured and avoidance versus tolerance effects may be convoluted ( Osakabe et al., 2013 ; Um et al., 2018 ; Ren et al., 2021 ). Also, the solutes that accumulate differ between different compartments and these processes must somehow be coordinated ( Wilson et al., 2014 ). This also illustrates how it is perhaps unlikely (although sometimes assumed) that changing the production or transport of a single solute is sufficient to change overall osmotic adjustment and water relations. For example, the stress signaling protein phosphatase highly ABA-induced1 (HAI1) has a greater effect on ψ s than the closely related phosphatases HAI2 (also known as AIP1), ABA-insenstive1 (ABI1), or ABI2, even though mutants of all four phosphatases have increased proline accumulation compared with wild-type ( Bhaskara et al., 2012 ). Similarly, cell wall responses to drought that can influence growth and PV relationships are varied and incompletely understood. There has been recent interest in how cell wall integrity affects cellular drought responses (see e.g. Bacete et al., 2022 ). Despite some recent progress, investigation of the genetic and cellular underpinnings of true tolerance of low ψ w remains an underexplored area of drought research.

At least part of the reason for our limited understanding of the cellular basis of water relations and true drought tolerance mechanisms such as osmotic adjustment is that these phenotypes have seldom been the focus of molecular genetic studies. The studies mentioned above all started from the study of specific genes or metabolic pathways which may, or may not, affect core water relations parameters such as osmotic adjustment. Forward genetic or reverse genetic screening for drought tolerance traits has been surprisingly limited. In part, this is due to the difficulty in measuring such traits rapidly enough and in a nondestructive manner as well as by lack of reporters that directly respond to differences in solute content or ψ w . New types of sensors and techniques may help alleviate this bottleneck (see below). We anticipate that joining new high-throughput tools for measuring water status and ‘omics responses to stress will drive many new discoveries. For example, Condorelli et al. (2022) recently used genome wide association (GWA) studies of a Durum wheat diversity panel to identify candidate genes underlying osmotic adjustment.

Plant water relations measurements are sometimes seen as laborious and require specialized equipment only available in a few laboratories. However, basic measurements of soil ψ w or plant tissue ψ w can be performed using readily available instruments (e.g. the WP4C) or several types of soil probes) for costs that are reasonable compared with the level of investment that is often required for ‘omic analyses whose interpretation would be enhanced by use of soil or plant ψ w data. We think that the above examples convincingly show how much additional insight can be gained when water relations measurements are incorporated into the experimental design. Recent advances in techniques and instrumentation have made water relations measurements easier and more accessible. In one example, Sack and co-workers have described how ψ sTLP can be determined more rapidly by using a vapor pressure osmometer (such as the widely available Wescor Vapro model) for direct estimation of ψ s at full hydration (also referred to as π 0 ; Bartlett et al., 2012a , 2012b;   Banks and Hirons, 2019 ).

Perhaps the biggest single change in instrumentation for drought research is the availability of automated weighing and watering systems. These systems allow individual pots to be weighed and rewatered up to predetermined soil water content to maintain plants under well-watered conditions or under a set severity of soil drying from mild stress to more severe stress. This can allow many plants to be exposed to the same severity of stress. Controlled soil drying can also be scaled to field studies using large soil monoliths and weighing lysimeters that allow gravimetric measures of evapotranspiration of plants from field soil ( Schmidt et al., 2013 ). However, as described above, soil water content is not a parameter that can be used to report and reproduce the level of stress across laboratories because of different soil water holding capacities. Thus, the automated weighing and water approach can be coupled with the generation of soil moisture curves to relate soil water content to ψ w for the soil type used ( Figure 1B ) and also potentially to PV curve analysis ( Figure 2, B and C ) to determine whether the stress imposed would be expected to push plants past the ψ w-TLP . As long as the same soil is consistently used, the soil moisture curves would only need to be generated once and could then be used to calibrate soil water content versus ψ w for many subsequent experiments. A similar approach can be taken to incorporate the information in PV curves into the design of high-throughput experiments. This would allow the severity of stress imposed to be selected more precisely and reported in a manner that could be repeated in other laboratories, even if they are using a different type of soil. Thus, measurements of ψ w are helpful at the experimental design stage both for reporting stress severity and for choosing the soil water content that imposes the desired severity of stress and also at later stages to improve interpretation of the resulting data.

Typically, automated weighing and watering combined with automated imaging to track plant growth parameters and hyperspectral cameras are increasingly being used to extract more data from such imaging analysis. Interestingly, data from hyperspectral imaging have been used to predict plant water relations parameters once proper calibration models were developed ( Cotrozzi et al., 2020 ). Weighing and watering systems which track the amount of water added to each pot may also be used in calculations of gravimetric WUE, provided that nontranspirational soil drying is minimized. For those researchers without access to automated phenotyping systems, relatively simple procedures such as growing several genotypes together in one pot combined with manual pot weighing and watering along with checks of soil ψ w can still allow robust measurements of growth responses to low ψ w (see e.g. Bhaskara et al., 2017 ) and relatively simple procedures are available for medium throughput gravimetric WUE assays ( Bhaskara et al., 2022 ). Agar plates incorporating high molecular weight PEG, when prepared properly, also allow medium throughput analysis of seedling low ψ w responses while better mimicking the cytorrhytic type of water loss that plants experience during soil drying ( Verslues et al., 2006 ).

Even more rapid detection of plant ψ w , perhaps even rapid enough for evaluations of large plant populations or to enable forward genetic screening for altered water relations, may become possible using new sensing technology. Jain et al. (2021) have described a hydrogel (which they named “AquaDust”) that reports leaf ψ w based on changes in Förster Resonance Energy Transfer (FRET) between two fluorophores as the gel expands or contracts due to changes in hydration state. After infiltration into maize leaves, AquaDust FRET emission could be calibrated by using a pressure chamber to impose defined ψ w onto the leaf. Postcalibration, AquaDust had sufficient resolution to detect ψ w gradients along maize leaves. Cuevas-Velazquez et al. (2021) developed a genetically encoded FRET sensor which may detect osmotic changes inside living cells. They hypothesized that intrinsically disordered proteins, in their case an Arabidopsis late embryogenesis abundant (LEA) protein, may change conformation in response to changes in cellular osmolarity and this conformation change could be reported by the FRET signal between fluorophores attached to each of the protein. Changes in FRET were observed in response to large osmotic shifts in yeast, plant, or mammalian cells, but interestingly not in Arabidopsis which was the source of the LEA protein used to construct the sensor. Further testing and development of this technology will be of interest. In addition, several studies have reported the use of terahertz radiation to analyze tissue water content and construct PV curves ( Baldacci et al., 2017 ; Browne et al., 2020 ; Li et al., 2020 ). Further development of all these tools is promising both to enable more extensive field measurements of plant water status and also to facilitate higher throughput laboratory screening.

Plant biology is fundamentally intertwined with the study of plant–water relations, and yet the various fields of plant biology have historically taken disparate approaches to the analysis and reporting of plant water relations. Plant physiologists have traditionally studied parameters defining the relationship between the environment and plant–water status in exhaustive detail, but have yet to uncover many of the molecular or genetic processes that explain the diversity of traits and responses to water-deficit we see in nature. Ecologists often focus on larger temporal and spatial scales, evaluating how precipitation and water availability impact plant population or community dynamics, but these studies are often divorced from the physiological functions driving outcomes. Molecular and cell biologists usually simplify their experimental systems to afford greater control and precision, but in doing so handicap their ability to interpret or understand nature as it actually exists ( Bergelson et al., 2021 ). Each of these perspectives has made valuable contributions to our understanding of plant function. Nevertheless, we argue that an integration of water relations data into cell and molecular studies is needed to truly gain an understanding of plant function and ultimately, to address the many impacts of climate change and ongoing threats to food security.

In this article, we have tried to show that converging on common and fundamentally sound ways of defining and reporting the severity of water limitation is not only advantageous for all types of drought researchers, it is also increasingly possible as water relations measurements continue to be refined and streamlined by new technologies and techniques, while genomic technologies also become ever more widely used. As a baseline for designing drought experiments, we would recommend that experiments seeking to compare the responses of multiple genotypes include sufficient data of plant or soil ψ w to determine whether all the genotypes experienced the same decline in ψ w during the stress period. This will allow a clear distinction of whether any differences in phenotype can be attributed to altered response to low ψ w or altered water use such that some genotypes avoided water depletion and thus were not exposed to the same ψ w as other genotypes. Also, as discussed above, using ψ w to directly scale data can also enhance data interpretation, especially when combined with knowledge of related parameters such as the TLP. In this case, one can unambiguously determine if a loss of turgor, cellular dehydration, and damage have occurred versus moderate stresses where the plants can successfully acclimate to the reduced ψ w and maintain cellular turgor and, at least partially, maintain growth. Applying these distinctions to large transcriptome or proteome data sets will help clarify damage responses versus acclimation responses to reduced ψ w . For higher throughput laboratory experiments with model plants such as Arabidopsis, there are well-established protocols for making plates of defined ψ w severities that cover the range from mild stress to more severe low ψ w ( van der Weele et al., 2000 ; Verslues et al., 2006 ). As long as the protocols are followed (e.g. do not autoclave high molecular weight PEG), these experimental systems can apply stable ψ w treatments (such that repeated checking of media ψ w can be minimized) that mimic many of the key aspects of soil drying.

We also recommend a certain degree of circumspection in interpreting laboratory results. Drought is a complex phenomenon and the record of basic research in model organisms having an impact on improving drought resistance of crop plants or understanding the cellular basis for differences in the ecophysiology of drought-prone environments is not especially good. This is not because model organisms commonly studied are somehow flawed or lack drought resistance mechanisms. Rather, a key limitation is how we design experiments using these model organisms and how we interpret the data. There is much to learn as we still do not know either the genes and molecular mechanisms of how plants detect changes in water status, osmoregulate, and control turgor pressure, nor do we know what genetic factors will be most important to improve crop productivity ( Nuccio et al., 2018 ) or understand ecosystem transformations as climate changes ( Novick et al., 2022 ). Knowing your plants’ water status is fundamental to all these efforts.

We apologize to the authors of many relevant studies that were not mentioned. Mention of specific instruments or instrument manufacturers does not constitute endorsement over other manufacturers or products. We thank Patrice Salomé (ASPB) for assistance with the artwork in Figure 1A , Ashutosh Tiwari (Academia Sinica) for assistance with the artwork in Figure 3 , and Caio G. Pereira (UT Austin) for help with artwork in Figure 2, B and C . We also thank Jason Bonnette for help collecting soil moisture release curve data. Finally, we thank Robert Heckman and Bhaskara Badiger (University of Texas-Austin) and two anonymous reviewers for their useful comments on the manuscript.

This research was supported by the Office of Science (BER), U.S. Department of Energy, Grant No DE-SC0021126, and by a research grant from the Human Frontier Science Program RGP0011/2019 to T.E.J. and by an Academia Sinica Investigator Award (AS-IA-108-L04) to P.E.V.

Conflict of interest statement . The authors declare no conflicts of interest.

T.E.J and P.E.V designed the research, analyzed data, and both wrote the manuscript.

The authors responsible for distribution of materials integral to the findings presented in this article in accordance with the policy described in the Instructions for Authors ( https://academic.oup.com/plcell ) are: Thomas E. Juenger ( [email protected] ) and Paul E. Verslues ( [email protected] ).

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Biology practicals

Investigating osmosis in potatoes, select lesson.

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Ecosystems and material cycles

Exchange and transport in animals, animal coordination, control and homeostasis, plant structures and their functions, health, disease and the development of medicines, natural selection and genetic modification, cells and control, key concepts, practical skills, working scientifically, explainer video, ​​in a nutshell.

By putting potato cylinders into different concentrations of sucrose solution, you will be able to investigate osmosis in a real-life example. Depending  on the water concentrations in the solutions , the potato cylinders will gain or lose mass, due to osmosis.

Equipment list

The following equipment list can be used to conduct an experiment to investigate osmosis in potato cylinders.

Experiment 1: Investigating osmosis in potatoes

​​experimental variables.

All experiments have three different variables: the independent, dependent and control variables. The independent variable is the one you change. The dependent variable is the one which depends on what has been changed, therefore it is the one that is measured. The control variable is one which has been kept the same.

Safety precautions

When carrying out experiments, it is very important to consider safety precautions. This is so you and others do not get hurt.

This is your instructions on how to complete the experiment.

This is how you can use your data to be able to form conclusions.

Your graph should show a negative correlation between sucrose solution concentration and percentage change in mass. As the sucrose concentration increases, the percentage change in mass increases. In the strongest sucrose concentration, the potato cylinder will have decreased its mass the most. This is because there is a greater concentration gradient between the potato cells which have a higher water potential, and the sucrose solution which has a lower water potential. As a result, a greater number of water molecules will move out of the potato cells by osmosis. This makes the potato cells flaccid and they will decrease their overall mass.

Once you have completed your experiment, it will be important to consider the quality of your data and how accurate your results are. Identify potential sources of random or systematic error and suggest possible improvements and further investigations. 

A limitation of this experiment could be that there are slight differences in the size of the potato cylinders. Therefore, for each sucrose concentration, the experiment should be repeated with several cylinders. By doing this, any anomalies can be identified and a mean value can be calculated. This will make the percentage change in mass more accurate.

6 Exercises

4 Exercises

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Learning Goals

Faqs - frequently asked questions, what are the control variables for the osmosis required practical for gcse biology.

The control variables for the osmosis required practical for GCSE biology include the volume of sucrose solution used and the dimensions of the potato cylinders.

What is the independent variable for the osmosis required practical for GCSE biology?

The independent variable for the osmosis required practical for GCSE biology is the concentration of sucrose solution.

What is an example of a hazard in the osmosis required practical for GCSE biology?

One of the hazards in the osmosis required practical is the scalpel. The scalpel may cut your skin. Be careful when picking up the scalpel and make sure to put it somewhere safe once you have finished using it.

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Water Potential: Measurements, Methods and Components

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In this article we will discuss about:- 1. Subject-Matter of Water Potential 2. Measurement of Water Potential 3. Methods 4. Components 5. Water Potential in Cells 6. Movement of Water from Cell to Cell.

Subject-Matter of Water Potential:

In recent years the term chemical potential of water is replaced by water potential. This is designated by the Greek letter psi (Ψ). Water potential is measured in bars. The latter is a pressure unit. When the water potential in a plant cell or tissue is low the latter is capable of absorbing water.

On the other hand, if the water potential of the cell tissue is high it indicates their ability to make available water to the desiccating surrounding cells. Clearly water potential is used as a measure to determine whether the tissue is under water stress or water deficit.

It needs mentioning that it is the difference between the water potential in a system under study and that in a reference state which is taken as the water potential value.

The reference state is pure water at the temperature and atmospheric pressure comparable to that of the system being investigated. As will be clear from Fig. 6-2, the water potential in the reference state is arbitrarily taken a value of 0 bar. The same figure also shows range of Ψ in the different tissues. As will be observed herbaceous leaves of mesophytes have water potentials ranging from —2 to —8 bars.

When the water decreases in the soil the water potential tends to become more negative than —8 bars. It may be added that if the water potential falls beyond —15 bars, most plant tissues stop growing.

The response of herbaceous and desert-growing plant leaves vary when the water potential falls below —20 to —30 bars. Similarly seeds and pollen or spores are having very low water potentials and the values may be as low as —60 to —100 bars.

Measurement of Water Potential:

In studies concerning plant water relations, information on water potential in plant cells and tissues is very vital. Several methods are used to measure water potential but none of them is infallible.

Methods of Water Potential:

Some of the methods are given below:

i. Vapour Equilibrium Method:

Here the pressure of water vapour in equilibrium with the water in a tissue sample enclosed in a small chamber is measured.

The water vapour pressure is measured with the help of thermocouple psychrometer. This is an accurate method to measure tissue water potential.

Some of these psychrometers can measure the water potential of attached leaves up to ± 1 bar.

ii. Vapour Immersion M ethod:

This method is based on the fact that when a plant tissue is placed in an atmosphere in which water vapour is maintained at constant vapour pressure, there will be a net transfer of water between the tissues and the surrounding atmosphere till an equilibrium is reached.

The difference in the water potentials of the tissue and the environment will determine the quantity of water transferred.

iii. Liquid Immersion M ethod:

Usually two methods are employed and these are the liquid immersion and dye methods. The former is similar to the vapour immersion method. In general, dye method has several advantages.

iv. Pressure Chamber Method:

Using pressure chamber water potential can be measured within minutes. Further compared to other methods, no precise temperature controls are needed.

The apparatus is also relatively less expensive. This method is especially suited for field studies.

Components of Water Potential:

Keeping in view that a typical plant cell is made up of a vacuole, a cell wall and the cytoplasm between the two, usually three major sets of internal factors are visualized which contribute towards water potential (Fig. 6-3).

These are shown below:

Ψ or Ψ w = Ψ M + Ψ s + Ψ p ; Ψ s = Ψ π

From the given equation it may be inferred that water potential in a plant cell is equal to the sum of the matric potential (Ψ M ) which is due to the binding of water molecules to protoplasmic and cell wall contents, the solute potential (Ψ s ; Ψ π ) due to the dissolved solutes in the vacuoles and lastly the pressure potential (Ψ p ) which is due to the pressure developed within cells and tissues. These potentials like the water potential are expressed in terms of bars.

In the followings brief accounts of the three components of water potential are given:

i. Matric Potential:

Matric refers to the matrix. It is the force of adsorption with which some water is held over the surface of collodial particles in the cell wall and cytoplasm.

It is also written in negative values. In the young cells, seeds and cells of xerophytes its value is appreciable. In the cells of mesophytic plants this is nearly —0.1 atm.

In such instances matric potential is often ignored since it does not contribute significantly to the total water potential.

Accordingly sometimes the equation is modified as below:

Ψ or Ψ w = Ψ s + Ψ p

ii. Solute Potential:

This refers to the potential developed by the solute particles in a solution. It is equal to the osmotic potential. Solute potential depends upon the number of particles. In fact, solute potential has replaced the old term osmotic pressure.

The difference is that while the former is expressed in bars with a negative, the latter is written as positive bars. Accordingly when the solute potential decreases it attains more negative value. Several methods are used to measure solute potential in an extracted cell sap. One of these is through the usage of thermocouple psychrometer. Solute potential values vary in plant cells from different species.

iii. Pressure P otential:

This is the hydrostatic pressure which develops in a plant cell due to the inward flow of water: (Ψ p ). It is also referred to the turgor pressure. Environmental conditions greatly influence the volume, water content, water potential and pressure potential of a cell. In a plasmolysed plant cell, the turgor pressure is zero.

Thus water potential equals the solute pressure or negative osmotic pressure. Or the other hand, in the fully turgid state, the water potential of the cell is zero. At this moment, pressure potential or turgor pressure is equal to solute pressure. Currently very few methods are available to measure pressure potential.

Figure 6-3. A summary diagram showing relationship of different potentials in a cell having elastic walls.

Water Potential in Cells:

The concepts developed on the basis of artificial systems using sugar solution can be successfully transferred to a cell (Fig. 6-4).

Cell is enclosed by a semipermeable membrane and osmosis takes place across this membrane. If a cell is immersed in a solution having high Ψ π (e.g. pure water or a dilute solution), water will diffuse in the cell and the latter will become turgid.

The external solution is referred to as hypotonic solution. In a situation where cell is immersed in a solution having Ψ π equal to its cell sap, no net water diffusion would occur and the cell will remain flaccid or lacks turgor. This solution is called isotonic solution. If the concentration of external solution is more than the cell sap, its Ψ π will be lower than that of the cell sap. If a cell is immersed in such a solution (hypertonic), water will diffuse out and the protoplast will pull inside and become plasmolyzed [Fig. 6-4 (C)].

If such a plasmolyzed cell is placed again in a hypotonic solution, it will again become turgid.

Water potential of a cell has two components (e.g., osmotic and pressure potentials) as follows:

Ψ = Ψ π + Ψ p

When a cell is immersed in water or a solution and comes in equilibrium the water poential of cell (Ψinside) is equal to the water potential outside (Ψ outside):

Ψ π (inside) + Ψ p (inside) = Ψ (inside) = Ψ (outside)

Ψ (outside) is also the total of Ψ π (outside) and Ψ p (outside). At atmospheric pressure Ψ p = 0, therefore Ψ (outside) = Ψ π (outside).

Thus at equilibrium

Ψ π (inside) + Ψ p (inside) =Ψ π (outside)

This may also be mentioned as Ψ π (inside) = Ψ π (outside) -Ψ p (inside) and this osmotic potential of the cell sap can thus be measured.

Movement of Water from Cell to Cell:

Differences in water potential (∆Ψ) are important for the water movement in and out of the cell. These differences are relevant as compared with the environments. Likewise water moves from cell to cell by diffusing down the water potential gradient between the two cells.

The direction of water movement and the force of movement are linked with water potential in each cell and also on the difference between the water potential of the two cells (Fig. 6-5).

In the instance mentioned below we observe that:

V = volume of the solution containing a given amount of the solutes

T = temperature as expressed in degree absolute

R = gas constant (solute molecules freely diffuse as if they were a gas, the constants K 1 and K 2 can be replaced by it).

Water movement as explained on the basis of old approach to osmosis:

For a long time osmosis was explained on the basis of water diffusion from a zone of high concentration to the lower concentration (diffusion pressure deficit: DPD).

However, this is not correct since some of the solutions occupy a volume smaller than the same weight of pure water.

It was also believed that a solution in a cell was as if sucking water into the cell by a force regarded as a negative pressure.

Several terms w ere used to explain these concepts. In recent years several of these terms have been discarded and more acceptable explanations based on thermodynamic concepts have been advanced. Terms used currently and their old equivalent corresponding terms are given in Table 6-1.

Related Articles:

• Experiment to Demonstrate Osmotic Pressure in Plant Tissues
• Mechanism of Absorption of Water | Plant Physiology

Biology , Plant Physiology , Movement of Substances , Water Potential

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Investigating Transport Across Membranes (A-level Biology)

Investigating transport across membranes, investigating diffusion.

We can investigate how diffusion occurs in biological cells by using cubes of agar jelly. The basic concept of this experiment is outlined below:

Table of Contents

• The agar jelly contains a pH indicator. We can make up agar jelly with an alkaline solution (e.g. sodium hydroxide) and add a few drops of phenolphthalein to it before the jelly sets. Phenolphthalein is a pH indicator which turns pink in the presence of alkaline solutions, thus, the jelly will have a bright pink colour.
• The agar jelly is placed in an acidic solution. Once the jelly has set, we can cut it up into cubes and place it in an acidic solution, such as dilute hydrochloric acid.
• The agar jelly is neutralised by the diffusion of the acid. The acidic solution will slowly diffuse into the agar jelly and neutralise the alkaline solution. As it does, the jelly will lose its pink colour and become colourless, as phenolphthalein turns colourless in non-alkaline environments.

We can alter different parts of this experiment to model how different factors affect the rate of diffusion.

Investigating the effects of surface area on diffusion

• Cut the agar jelly into different sized cubes to investigate the effects of surface area . Cut the jelly into cubes of different sizes and work out each cube’s surface area to volume ratio . For example, a cube with 2cm edges will have a surface area to volume ratio of 3:1.
• Place the cubes in the same volume and concentration of acid. Put the cubes into containers which hold the same volume and concentration of hydrochloric acid. Then measure the time it takes for the different cubes to go colourless.
• The cube with the largest surface area: volume ratio will go colourless the quickest. The cube with the largest surface area: volume ratio has the greatest amount of space available for the hydrochloric acid to diffuse into the jelly so it will be neutralised the fastest.

Investigating the effects of concentration on diffusion

• Place the agar jelly cubes in different concentrations of acid. Cut the agar jelly into equal sized cubes and put them in different containers, each with a different concentration of hydrochloric acid. Measure the time it takes for the different cubes to go colourless.
• The cube placed in the highest concentration of acid will go colourless the quickest. The cube placed in the container with the highest concentration will have the greatest concentration of acid being diffused into the jelly per minute. As such, it will go colourless the quickest.

Investigating the effects of temperature on diffusion

• Place the agar jelly cubes in different temperatures. Cut the agar jelly into equal sized cubes and put them in different containers, each with the same concentration of hydrochloric acid. Put the containers in water baths heated to different temperatures. Be careful not to heat the water baths over 65° as the agar jelly will melt.
• The cube placed in the highest temperature of acid will go colourless the quickest. As high temperatures speed up the rate of diffusion, the cube in the hottest container will be neutralised the quickest.

Investigating Osmosis

Osmosis is the movement of water molecules from an area of high water potential to an of low water potential by osmosis. Water potential is determined by the concentration of solutes in the solutions on either side of the cell membrane.

Investigations using plant tissue

This experiment involves placing plant tissue, e.g. potato cylinders, in varying concentrations of sucrose solutions to determine the water potential of the plant tissues.

• Prepare the different concentrations of sucrose solutions . Using distilled water and 1M sucrose solution, prepare a series of dilutions such that you now have 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0M sucrose. Place 5cm 3 of each dilution into separate beakers.
• Prepare equal sized pieces of potato chips. Using a cork borer, cut out 18 pieces of potato chips, all of equal sizes.
• Weigh the mass of the potato chips. Dry the potato chips gently with a paper towel. Divide them into groups of three and weigh each group.
• Place each group of potato chips in each solution . The potato chips should be left in the solutions for a minimum of 20 minutes.   All groups should be left in the solution for the same amount of time.

• Weigh the mass of the potato chips again. Once your desired amount of time has passed, remove the chips from the solutions, and dry them gently using a paper towel. Reweigh each group again.
• Calculate % change in mass. Using the mass of the potato chips before and after being placed in the solution, calculate the % change in its mass.
• Plot the % change in mass on a calibration curve. The calibration curve helps us determine the water potential in the potato sample. Plot the % change in mass against concentration of sucrose solution.   The point at which the curve crosses the x axis is when the sucrose solution is isotonic with the potato samples i.e. the water potential of the sucrose solution is the same as the water potential of the potatoes. At this point, there is no movement of water in or out of the potato. Overall:
• The potato samples in the dilute solutions will have a net increase in mass – the water potential is greater in the potato than in the sucrose solution, so water moves into the potato samples via osmosis.
• The potato samples in the concentrated solutions will have a net decrease in mass – the water potential is lower in the potato than in the sucrose solution, so water moves out of the potato samples via osmosis.

Investigations using Visking tubing

Visking tubing is an artificial membrane that is selectively permeable as it has many microscopic pores. This allows smaller molecules such as water and glucose to pass through it, while larger molecules such as starch and sucrose are unable to cross the membrane.

• Prepare three equal-sized pieces of Visking tubings. Run the tubing under tap water to soften it and knot each tubing on one end to create a bag.
• Place a rubber bung at the open end of the Visking tubing. Find rubber bungs with an opening in the centre that will fit the open end of the Visking tubing. Then seal the tubing using the bung and fix it in place using a rubber band.
• Prepare sucrose solutions with concentrations of 0.5M and 1.0M. You may wish to add a food dye to the 0.5M solution so that it is easier to see later on.
• Pipette in the 0.5M sucrose solution. Using a pipette or a syringe, fill each tubing through the opening of the rubber bung with the 0.5M sucrose solution. Make sure it is filled completely to the brim with no air bubbles.
• Insert capillary tubes into each of the tubings . Insert a capillary tube through the rubber bung’s opening. Mark the level at which the sucrose solution has risen to in the capillary tube.
• Place each Visking tubing into containers of different solutions. Prepare three beakers, each containing distilled water, 0.5M sucrose, and 1.0M sucrose. Place each Visking tubing into each of the beakers and leave them in for the same amount of time.
• Measure the change in liquid level. Mark the new liquid level on the capillary tube before removing the Visking tubing from its beaker. Measure the change in the liquid level. Overall:
• The liquid level of the Visking tubing placed in distilled water will have risen as the sucrose solution in the tubing is hypertonic to the water i.e. the sucrose is more concentrated. Thus, there is net movement of water into the Visking tubing via osmosis.
• The liquid level of the Visking tubing placed in 0.5M sucrose will remain the same as the solution inside the tubing and outside the tubing are isotonic i.e. the solutions are the same concentration.
• The liquid level of the Visking tubing placed in 1.0M sucrose will have decreased as the solution inside the tubing is hypotonic to the solution outside the tubing i.e. the solution inside the tubing is less concentrated.

Transport across membranes is the movement of substances such as ions, molecules, and fluids from one side of a biological membrane to the other. This process is crucial for maintaining cellular homeostasis and allowing cells to exchange materials with their environment.

Investigating transport across membranes is important because it helps us understand the mechanisms by which cells regulate the flow of substances in and out of the cell. This is essential for understanding cellular processes such as metabolic reactions, waste removal, and communication between cells.

There are several methods used to investigate transport across membranes, including: Diffusion experiments to study the movement of substances through the lipid bilayer Osmosis experiments to study the movement of water across a semi-permeable membrane Active transport experiments to study the movement of substances against a concentration gradient with the use of energy Electrochemical experiments to study the movement of ions across the membrane

Factors that can affect transport across membranes include the size of the substance being transported, the charge of the substance, the concentration gradient, and the presence of specific transport proteins.

Transport across membranes can be measured in a variety of ways, including measuring changes in substance concentration, changes in electrical potential, and changes in fluid movement.

The limitations of investigating transport across membranes include the difficulty of obtaining pure and intact biological membranes, the potential for damage to the membrane during experimentation, and the limitations of experimental techniques.

In A-Level Biology, knowledge of transport across membranes can be applied to understand cellular processes such as the movement of nutrients and waste, the regulation of cell volume, and the communication between cells. This knowledge is also important for understanding diseases and disorders related to the malfunction of transport processes, such as cystic fibrosis and diabetes.

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CIE 1 Cell structure

Roles of atp (a-level biology), atp as an energy source (a-level biology), the synthesis and hydrolysis of atp (a-level biology), the structure of atp (a-level biology), magnification and resolution (a-level biology), calculating cell size (a-level biology), studying cells: confocal microscopes (a-level biology), studying cells: electron microscopes (a-level biology), studying cells: light microscopes (a-level biology), life cycle and replication of viruses (a-level biology), cie 10 infectious disease, bacteria, antibiotics, and other medicines (a-level biology), pathogens and infectious diseases (a-level biology), cie 11 immunity, types of immunity and vaccinations (a-level biology), structure and function of antibodies (a-level biology), the adaptive immune response (a-level biology), introduction to the immune system (a-level biology), primary defences against pathogens (a-level biology), cie 12 energy and respiration, anaerobic respiration in mammals, plants and fungi (a-level biology), anaerobic respiration (a-level biology), oxidative phosphorylation and chemiosmosis (a-level biology), oxidative phosphorylation and the electron transport chain (a-level biology), the krebs cycle (a-level biology), the link reaction (a-level biology), the stages and products of glycolysis (a-level biology), glycolysis (a-level biology), the structure of mitochondria (a-level biology), the need for cellular respiration (a-level biology), cie 13 photosynthesis, limiting factors of photosynthesis (a-level biology), cyclic and non-cyclic phosphorylation (a-level biology), the 2 stages of photosynthesis (a-level biology), photosystems and photosynthetic pigments (a-level biology), site of photosynthesis, overview of photosynthesis (a-level biology), cie 14 homeostasis, ectotherms and endotherms (a-level biology), thermoregulation (a-level biology), plant responses to changes in the environment (a-level biology), cie 15 control and co-ordination, the nervous system (a-level biology), sources of atp during contraction (a-level biology), the ultrastructure of the sarcomere during contraction (a-level biology), the role of troponin and tropomyosin (a-level biology), the structure of myofibrils (a-level biology), slow and fast twitch muscles (a-level biology), the structure of mammalian muscles (a-level biology), how muscles allow movement (a-level biology), the neuromuscular junction (a-level biology), features of synapses (a-level biology), cie 16 inherited change, calculating genetic diversity (a-level biology), how meiosis produces variation (a-level biology), cell division by meiosis (a-level biology), importance of meiosis (a-level biology), cie 17 selection and evolution, types of selection (a-level biology), mechanism of natural selection (a-level biology), types of variation (a-level biology), cie 18 biodiversity, classification and conservation, biodiversity and gene technology (a-level biology), factors affecting biodiversity (a-level biology), biodiversity calculations (a-level biology), introducing biodiversity (a-level biology), the three domain system (a-level biology), phylogeny and classification (a-level biology), classifying organisms (a-level biology), cie 19 genetic technology, cie 2 biological molecules, properties of water (a-level biology), structure of water (a-level biology), test for lipids and proteins (a-level biology), tests for carbohydrates (a-level biology), protein structures: globular and fibrous proteins (a-level biology), protein structures: tertiary and quaternary structures (a-level biology), protein structures: primary and secondary structures (a-level biology), protein formation (a-level biology), proteins and amino acids: an introduction (a-level biology), phospholipid bilayer (a-level biology), cie 3 enzymes, enzymes: inhibitors (a-level biology), enzymes: rates of reaction (a-level biology), enzymes: intracellular and extracellular forms (a-level biology), enzymes: mechanism of action (a-level biology), enzymes: key concepts (a-level biology), enzymes: introduction (a-level biology), cie 4 cell membranes and transport, transport across membranes: active transport (a-level biology), transport across membranes: osmosis (a-level biology), transport across membranes: diffusion (a-level biology), signalling across cell membranes (a-level biology), function of cell membrane (a-level biology), factors affecting cell membrane structure (a-level biology), structure of cell membranes (a-level biology), cie 5 the mitotic cell cycle, chromosome mutations (a-level biology), cell division: checkpoints and mutations (a-level biology), cell division: phases of mitosis (a-level biology), cell division: the cell cycle (a-level biology), cell division: chromosomes (a-level biology), cie 6 nucleic acids and protein synthesis, transfer rna (a-level biology), transcription (a-level biology), messenger rna (a-level biology), introducing the genetic code (a-level biology), genes and protein synthesis (a-level biology), synthesising proteins from dna (a-level biology), structure of rna (a-level biology), dna replication (a-level biology), dna structure and the double helix (a-level biology), polynucleotides (a-level biology), cie 7 transport in plants, translocation and evidence of the mass flow hypothesis (a-level biology), the phloem (a-level biology), importance of and evidence for transpiration (a-level biology), introduction to transpiration (a-level biology), the pathway and movement of water into the roots and xylem (a-level biology), the xylem (a-level biology), cie 8 transport in mammals, controlling heart rate (a-level biology), structure of the heart (a-level biology), transport of carbon dioxide (a-level biology), transport of oxygen (a-level biology), exchange in capillaries (a-level biology), structure and function of blood vessels (a-level biology), cie 9 gas exchange and smoking, lung disease (a-level biology), pulmonary ventilation rate (a-level biology), ventilation (a-level biology), structure of the lungs (a-level biology), general features of exchange surfaces (a-level biology), understanding surface area to volume ratio (a-level biology), the need for exchange surfaces (a-level biology), edexcel a 1: lifestyle, health and risk, phospholipids – introduction (a-level biology), edexcel a 2: genes and health, features of the genetic code (a-level biology), gas exchange in plants (a-level biology), gas exchange in insects (a-level biology), edexcel a 3: voice of the genome, edexcel a 4: biodiversity and natural resources, edexcel a 5: on the wild side, reducing biomass loss (a-level biology), sources of biomass loss (a-level biology), transfer of biomass (a-level biology), measuring biomass (a-level biology), net primary production (a-level biology), gross primary production (a-level biology), trophic levels (a-level biology), edexcel a 6: immunity, infection & forensics, microbial techniques (a-level biology), the innate immune response (a-level biology), edexcel a 7: run for your life, edexcel a 8: grey matter, inhibitory synapses (a-level biology), synaptic transmission (a-level biology), the structure of the synapse (a-level biology), factors affecting the speed of transmission (a-level biology), myelination (a-level biology), the refractory period (a-level biology), all or nothing principle (a-level biology), edexcel b 1: biological molecules, inorganic ions (a-level biology), edexcel b 10: ecosystems, nitrogen cycle: nitrification and denitrification (a-level biology), the phosphorus cycle (a-level biology), nitrogen cycle: fixation and ammonification (a-level biology), introduction to nutrient cycles (a-level biology), edexcel b 2: cells, viruses, reproduction, edexcel b 3: classification & biodiversity, edexcel b 4: exchange and transport, edexcel b 5: energy for biological processes, edexcel b 6: microbiology and pathogens, edexcel b 7: modern genetics, edexcel b 8: origins of genetic variation, edexcel b 9: control systems, ocr 2.1.1 cell structure, structure of prokaryotic cells (a-level biology), eukaryotic cells: comparing plant and animal cells (a-level biology), eukaryotic cells: plant cell organelles (a-level biology), eukaryotic cells: the endoplasmic reticulum (a-level biology), eukaryotic cells: the golgi apparatus and lysosomes (a-level biology), ocr 2.1.2 biological molecules, introduction to eukaryotic cells and organelles (a-level biology), ocr 2.1.3 nucleotides and nucleic acids, ocr 2.1.4 enzymes, ocr 2.1.5 biological membranes, ocr 2.1.6 cell division, diversity & organisation, ocr 3.1.1 exchange surfaces, ocr 3.1.2 transport in animals, ocr 3.1.3 transport in plants, examples of xerophytes (a-level biology), introduction to xerophytes (a-level biology), ocr 4.1.1 communicable diseases, structure of viruses (a-level biology), ocr 4.2.1 biodiversity, ocr 4.2.2 classification and evolution, ocr 5.1.1 communication and homeostasis, the resting potential (a-level 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Water transport, perception, and response in plants

• JPR Symposium
• Toward unveiling plant adaptation mechanisms to environmental stresses
• Published: 11 February 2019
• Volume 132 , pages 311–324, ( 2019 )

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• Johannes Daniel Scharwies 1 , 2 &
• José R. Dinneny 1 , 2  

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Sufficient water availability in the environment is critical for plant survival. Perception of water by plants is necessary to balance water uptake and water loss and to control plant growth. Plant physiology and soil science research have contributed greatly to our understanding of how water moves through soil, is taken up by roots, and moves to leaves where it is lost to the atmosphere by transpiration. Water uptake from the soil is affected by soil texture itself and soil water content. Hydraulic resistances for water flow through soil can be a major limitation for plant water uptake. Changes in water supply and water loss affect water potential gradients inside plants. Likewise, growth creates water potential gradients. It is known that plants respond to changes in these gradients. Water flow and loss are controlled through stomata and regulation of hydraulic conductance via aquaporins. When water availability declines, water loss is limited through stomatal closure and by adjusting hydraulic conductance to maintain cell turgor. Plants also adapt to changes in water supply by growing their roots towards water and through refinements to their root system architecture. Mechanosensitive ion channels, aquaporins, proteins that sense the cell wall and cell membrane environment, and proteins that change conformation in response to osmotic or turgor changes could serve as putative sensors. Future research is required to better understand processes in the rhizosphere during soil drying and how plants respond to spatial differences in water availability. It remains to be investigated how changes in water availability and water loss affect different tissues and cells in plants and how these biophysical signals are translated into chemical signals that feed into signaling pathways like abscisic acid response or organ development.

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Acknowledgements

The information, data, or work presented herein was funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR 1565-1555 and in part by a Faculty Scholar grant from the Howard Hughes Medical Institute and the Simons Foundation, both awarded to JRD.

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Scharwies, J.D., Dinneny, J.R. Water transport, perception, and response in plants. J Plant Res 132 , 311–324 (2019). https://doi.org/10.1007/s10265-019-01089-8

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Confronting the water potential information gap

Kimberly a. novick.

1 O’Neill School of Public and Environmental Affairs, Indiana University – Bloomington. Bloomington, IN USA.

Darren L. Ficklin

2 Department of Geography, Indiana University – Bloomington. Bloomington, IN USA.

Dennis Baldocchi

3 Department of Environmental Science, Policy, and Management. University of California, Berkeley. Berkeley, CA, USA

Kenneth J. Davis

4 Department of Meteorology and Atmospheric Science and Earth and Environmental Systems Institute, The Pennsylvania State University, University Park, PA, USA.

Teamrat A. Ghezzehei

5 Life and Environmental Sciences Department, University of California – Merced. Merced, CA, USA.

Alexandra G. Konings

6 Department of Earth System Science, Stanford University. Stanford, CA, USA.

Natasha MacBean

Nina raoult.

7 Laboratoire des Sciences du Climat et de l’Environnement. Paris, France.

Russell L. Scott

8 Southwest Watershed Research Center, USDA – Agricultural Research Service. Tucson, AZ, USA.

9 Department of Plant Science. The Pennsylvania State University, University Park, PA, USA.

Benjamin N. Sulman

10 Environmental Sciences Division, Oak Ridge National Laboratory. Oak Ridge, TN, USA.

Jeffrey D. Wood

11 School of Natural Resources, University of Missouri, Columbia, MO, USA

Author Contributions : K.A.N. conceived of the study, with substantial input from D.L.F, A.G.K., K.J.D., T.G., R.S.L, B.N.S., Y.S., and N.M. Data analyses were performed by K.A.N, T.G., D.L.F. and N.R., who also created the resulting figures. D.B., R.L.S., K.A.N. and J.D.W contributed AmeriFlux data used in Figure 4 . All authors wrote the text and provided substantial conceptual input to the manuscript.

Associated Data

The FLUXNET tower data appearing in Fig. 3 are from the FLUXNET 2015 dataset (DOIs 10.18140/FLX/1440186 for SD-Dem, 10.18140/FLX/1440071 for US-HA1, and 10.18140/FLX/1440160 FI-SOD. The AmeriFlux tower data appearing in Fig. 4 are available from the AmeriFlux network with the following DOIs: 10.17190/AMF/1246080 for US-MMS, 10.17190/AMF/1246081 for US-MOz, 10.17190/AMF/1246104 for US-SRM, and DOI: 10.17190/AMF/1245971 for US-TON.

Water potential directly controls the function of leaves, roots, and microbes, and gradients in water potential drive water flows throughout the soil-plant-atmosphere continuum. Notwithstanding its clear relevance for many ecosystem processes, soil water potential is rarely measured in-situ, and plant water potential observations are generally discrete, sparse, and not yet aggregated into accessible databases. These gaps limit our conceptual understanding of biophysical responses to moisture stress and inject large uncertainty into hydrologic and land surface models. Here, we outline the conceptual and predictive gains that could be made with more continuous and discoverable observations of water potential in soils and plants. We discuss improvements to sensor technologies that facilitate in situ characterization of water potential, as well as strategies for building new networks that aggregate water potential data across sites. We end by highlighting novel opportunities for linking more representative site-level observations of water potential to remotely-sensed proxies. Together, these considerations offer a roadmap for clearer links between ecohydrological processes and the water potential gradients that have the ‘potential’ to substantially reduce conceptual and modeling uncertainties.

Gradients in the water potential (Ψ) of soils and plants form the energetic basis for the transport of water, and elements contained therein, through a connected continuum linking the deepest soil layers to the top of plant canopies ( Figure 1 ). Ψ can be a positive or negative pressure, though it is typically negative -- a tension force -- in unsaturated soils and within plant hydraulic systems. Ψ gradients have been recognized as the fundamental driver of water fluxes between soils, streams, and groundwater for more than a century, and they appear in some of the most foundational equations in hydrology 1 (e.g. Darcy’s Law, Richard’s Equation). Likewise, the critical role of Ψ gradients in driving water flows through the soil-plant-atmosphere continuum has been known for decades 2 .

Water flows “downhill” along gradients of water potential in the soils (Ψ S , where water potential is relatively high, often >-1 MPa) through the stems (Ψ x ) to the leaves ( Ψ L , where potential is relatively low) and eventually to the air ( Ψ air , where it can be as low as −100 MPa). Water potential also directly controls key biological processes, including microbial function, mortality risk arising from damaged plant xylem, and plant-atmosphere gas exchange. While observations of environmental drivers, soil moisture content ( θ ) and carbon and water fluxes are broadly accessible from environmental networks and remote sensing, Ψ timeseries are more discrete, sparse, and generally not coordinated or discoverable.

Beyond redistributing water through ecosystems, Ψ is also a direct control of many biophysical processes. Soil water potential (Ψ S ) regulates flow of water into and out of soil microbe cells and determines their metabolism 3 . In plants, leaf water potential (Ψ L ) is a key driver of stomatal conductance and photosynthetic carbon uptake 4 , 5 , and its close connection to branch and stem water potential (Ψ X ) controls the risk of drought-driven xylem embolism and mortality 6 , 7 . Consequently, most ecosystem services, including water storage, food and fiber supply, and water and climate regulation, are fundamentally linked to Ψ.

While undeniably important for soil and plant function, for reasons discussed in more detail below, Ψ S is rarely measured in-situ 8 , 9 , and observations of plant Ψ have historically been limited to destructive and disjunct manual measurements. The objective of this paper is to demonstrate key uncertainties linked to the dearth of soil and plant Ψ data, and to discuss the theoretical and modeling progress that could be enabled with richer and more discoverable information about Ψ. We begin by discussing issues surrounding the measurement, modeling, and synthesis of soil water potential, and then address additional considerations linked to the measurement and prediction of water potential in plants. We then present a road map for creating accessible and open Ψ databases and discuss promising new approaches for detecting Ψ using remote sensing.

Water flows “downhill” energetically, moving from areas of higher-to-lower potential, such that Ψ S gradients are the driving force of subsurface water flows 1 . In most unsaturated soils, Ψ S is dominated by the matric potential, which becomes more negative when soils dry, and the effective radii of water-filled pore spaces in the soil become smaller. This process produces the general shape of the water retention curve (also known as the ‘moisture characteristic’ or ‘water release’ curve), which relates Ψ S to volumetric soil moisture content ( θ ). Critically, variation in soil physical properties can cause Ψ S to differ by an order of magnitude across soil types, even if soil moisture content is the same 10 , 11 ( Figure 2a ).

Across soil types, Ψ S can differ by an order of magnitude for a given soil moisture content (panel a, with curves generated from the van Genutchen model 11 ,, see methods ). Panels b-d illustrate the uncertainty in the water retention curve attributable to PTF parameter uncertainty. The shaded area shows the 90% confidence interval due solely to variation in a single parameter of the van Genuchten model (the ‘n’ shape parameter, which is linked to pore size) within just one standard deviation of its reported distribution for each soil class from a popular PTF 18 . Thick lines in panels b-d are the same as in panel a. The PTF-driven uncertainty in the water retention curve propagates into large uncertainty for modeled fluxes and pools. Specifically, variation in the van Genuchten ‘n’ parameter within again just one standard deviation of its reported range 18 causes the 90% confidence intervals on modeled evapotranspiration (ET), soil moisture content ( θ , and Ψ S (shaded gray areas, panels e-f) to vary by a magnitude comparable to the mean value of each parameter (thick black line). Simulations were run using the HYDRUS 1-D 79 model for a forest site in Indiana, US 80 during a drought event (see methods for details).

Field observations of θ are common 12 , but with a few exceptions 9 , 13 , Ψ S is rarely measured systematically in field research settings 8 , 9 . The reasons why θ became the predominant metric for describing soil water status are not entirely clear 8 , but may reflect the fact that no single instrument captures the entire range of Ψ S (from saturation to the very dry end), and sensors for measuring Ψ S in the field have historically been associated with unique limitations and uncertainty 8 , 14 .

Even if Ψ S data were plentiful, strategies for relating θ to Ψ S would still be necessary in models to connect water balance equations with potential-driven flows. Most hydrologic and land surface models thus rely on water retention curve models 15 , with those proposed by Campbell (1974) 10 or van Genuchten (1980) 11 ranking high in popularity. Pedotransfer functions (PTFs) predict the parameters of water retention curve models using empirical equations driven by a limited set of soil characteristics (typically %sand, %clay, and bulk density 16 – 18 ).

While developing PTFs is an active field 15 , PTF parameter distributions are poorly constrained and prevent confident transformation of θ to Ψ S . For example, even relatively small variations in a single parameter of the van Genuchten model cause Ψ S to vary by an order of magnitude over a wide range of θ ( Figure 2b – 2d ). Soil structure, which differs from soil texture and is governed by biophysical properties, may be a key omission in PTFs 19 explaining some of this uncertainty. For example, growth of roots and mycorrhizae into soil pores, and deposition of root exudates, increase overall water retention 20 , 21 , and macropores can create preferred flow pathways that are challenging to incorporate into PTFs. Moreover, depth into the soil may also affect hydraulic properties by controlling connectivity with root systems and through slowly-evolving changes in soil morphology. Finally, most PTFs assume that the water retention curve is static; but many relevant processes occurring in natural landscapes (including drying-rewetting cycles, fire, and management shifts) may cause time-dependent hysteresis of the water retention curve 22 – 24 .

This uncertainly linked to PTFs propagates through water cycle models in highly consequential ways. 25 – 26 Prior work performed in the Shale Hills Critical Zone Observatory confirms that van Genuchten model parameters are the dominant source of model uncertainty in a coupled 3-D land-surface and hydrological model 27 , and that water retention curve parameters must be measured locally and optimized through data assimilation 28 for watershed hydrologic variables to be predicted with any degree of certainty 29 . Here, using a popular 1-D water balance model, we further demonstrate that uncertainty in a single PTF parameter drives large uncertainty in modeled predictions of evapotranspiration, soil moisture, and Ψ S ( Figure 2e ).

The parameters of the water retention curve are also key sources of uncertainty explaining variability in carbon cycle fluxes from global-scale land surface models. Here, we used a global sensitivity experiment 30 to explore the variability of these parameters along with other key parameters of the ORCHIDEE land surface model 31 , 32 (see methods for details). The parameters of the water retention curve explained between 10–32% of the modelled GPP variance across three diverse sites ( Figure 3 ). Moreover, when considering the wider set of soil hydrology parameters (including the hydraulic conductivity, field capacity, and permanent wilting point of the soil), the percentage of explained GPP variance increased to 22–53% across sites.

A sensitivity analysis of key model parameters of the ORCHIDEE land surface model 31 , 32 was performed to demonstrate the relative importance of each parameter in simulating daily GPP at three contrasting FLUXNET sites: a) a temperate broadleaf forest (Harvard Forest, FLUXNET code US-Ha1 82 ); b) a boreal needleleaf forest (Sodankyla, FI-Sod, 83 ); and c) a semi-arid savanna (Demokeya, SD-Dem 84 ). The Sobol method 30 was used to perform the sensitivity analysis; this method is based on variance decomposition and is able to capture interactions between parameters. More details can be found in the methods .

The dearth of information about Ψ S is not only a problem for models, but also confounds observation-driven work. Because θ is widely measured, and Ψ S is not, it is extremely common to see key response variables like carbon and water fluxes explained as a function of measured θ 33 – 35 . These relationships are usually non-linear and threshold driven 36 – 37 . This is not surprising, as these responses embed site-to-site variability in the water retention curve, which itself is nonlinear and threshold-driven ( Fig. 2a – d ). The shape of these response functions thus depends very much on whether Ψ S or θ is chosen as the driving variable 38 . Indeed, the relationship between gross primary productivity (GPP) and soil water status is more linear and less spatially heterogeneous when Ψ S , as opposed to θ , appears on the x-axis ( Figure 4 ). Likewise, substantial skill in predicting soil respiration can be gained when model functions are driven explicitly by Ψ S 3 . Thus, more abundant and aggregated site-level Ψ S information could reduce conceptual uncertainty about how ecosystem fluxes respond to soil water deficits, and permit other sources of spatio-temporal variability to be more discernable.

Across four AmeriFlux sites for which site-specific water retention curves were measured 38 , 85 – 87 , the relationship between GPP (normalized by its well-watered rate) and Ψ S (bottom row) is more linear than the relationship between GPP and θ (top row). Moreover, cross-site heterogeneity in the response functions is reduced when it is Ψ S , as opposed to θ , on the x-axis (compare panel e to panel j). GPP estimates were obtained from AmeriFlux, with site codes given in parentheses. Error bars indicate one standard error of the mean, which is quite small for some of the binned averages. See methods for more details.

Plant water potential: Key concepts and controversies

The effective radii of evaporating water surfaces within plant cell walls are extremely small, resulting in tension forces strong enough to pull water upwards from soils, where it is already tightly bound, to the leaves. Thus, the difference between Ψ L and Ψ S is the driving force for transpiration, which is closely coupled with photosynthetic carbon uptake. Moreover, branch and stem water potential (Ψ X ), which are coupled with Ψ L , interact with anatomical features of the plant’s water transport system to determine the risk of xylem embolism that can lead to mortality 6 , 7 , 39 – 41 . Stomatal regulation of gas exchange is also critical for buffering plants from the very low water potential of the atmosphere (see Figure 1 ), which is extremely sensitive to relative humidity.

Historically, observations of plant Ψ have been limited to manually collected “snapshots” (e.g. with a pressure chamber 43 ). These data have proven indispensable for shaping our theoretical understanding of how plants respond to soil water stress 6 , 7 , 40 , 44 . However, because pressure chamber measurements are destructive and labor intensive, they are typically limited to weekly or seasonal temporal resolutions. While the weekly timescale is well matched to soil drying, it is too coarse to capture faster-acting hydrodynamic processes, including stomatal response to vapor pressure deficit (VPD 45 ) and the depletion and refilling of plant water pools over the course of a day 46 . Moreover, with some exceptions 47 , Ψ L and Ψ X are not often monitored over long time periods (e.g. years to decades), and centralized databases and networks for time series of Ψ do not yet exist.

The discrete and undiscoverable nature of plant Ψ observations limit our ability to characterize the distributions of the minimum plant water potentials that are so critical for determining plant mortality risk 41 . The gap also limits understanding of how plant and soil water potential are coordinated and coupled. For example, a fundamental assumption in plant eco-physiology is that Ψ L and Ψ X are equilibrated with Ψ S across the root zone in pre-dawn hours 48 . This assumption has allowed eco-physiologists to circumvent the Ψ S data scarcity problem by relying on pre-dawn Ψ L observations as a proxy for root-zone Ψ S – an approach that treats the plants as an instrument for recording the soil water environment. Yet experiments have shown that nighttime transpiration – while small – can still occur 49 , 50 , lowering pre-dawn Ψ L and decoupling it from Ψ S 51 . Synthetic assessments of pre-dawn equilibrium are hindered by the absence of nocturnal Ψ L observations collected together with data on Ψ S and/or stem water flows (e.g. from sap flux), or at least often enough to determine if stationarity in pre-dawn Ψ L , which should be a hallmark of equilibrium, has been achieved.

Likewise, the water potential information gap limits understanding of how soil and plant water potential are coupled at mid-day. The relationship between mid-day Ψ L and the root-zone Ψ S is frequently used to classify plant water use strategies 44 , 52 , 53 . For example, plants with conservative water use strategies (“isohydric” species) close stomata quickly as Ψ S declines, whereas “anisohydric” plants keep stomata open longer, sustaining gas exchange but with more rapid declines in Ψ L that may increase the risk of xylem embolism. The (an)isohydry framework is popular but controversial, with several studies highlighting critical interactions with other environmental drivers beyond Ψ S 54 – 56 , including VPD 57 . Moreover, coordinated observations of sapflow, enhanced with data on soil and stem water potentials, hold great promise for understanding how the dynamics of hydraulic conductance of different plant organs influence whole-plant hydraulic physiology 58 . Plant hydraulics schemes relying on concepts like isohydry are rapidly being incorporated in hydrologic and Earth system models 59 – 61 . Benchmarking and testing these schemes would benefit from open and spatially representative databases of plant and soil Ψ timeseries, measured together at a temporal frequency (e.g. hourly) over which key drivers like VPD vary.

Coordinated observation of plant and soil Ψ could also offer new perspectives on the critical role of root hydraulic function. Pre-dawn observations of Ψ L and Ψ S from multiple depths could reveal interspecific patterns in functional rooting depth – a trait that is difficult to measure by other means and partially responsible for model difficulty in capturing plant drought responses 62 . When complemented with data on Ψ x and/or root sap flow, profile observations of Ψ S would also illuminate the important but poorly understood consequences of hydraulic redistribution of water from wetter to drier soil layers through plant roots 63 – 64 . While root Ψ x is difficult to measure with pressure chambers, it could be monitored more easily with psychrometers or other techniques for continuous observation of plant Ψ x . Data on root Ψ x , especially when paired with laboratory-derived root xylem vulnerability curves, would also be useful for understanding the dynamics of root hydraulic conductance, noting that roots may be among the most vulnerable components of the plant hydraulic system 65 – 66 . Finally, differences in Ψ S and root Ψ x could also improve our understanding of gradients in Ψ occurring at the root-soil interface 67 .

Recent advances in measurement technology have substantially improved the ease and reliability of Ψ S observations. In the lab, sensor improvement has reduced the time necessary to generate the “wet end” of the water retention curve 68 . A second instrument, typically a dew-point potentiometer, is required to capture the dry end of the curve, but this step proceeds relatively quickly. While the instrumentation and expertise necessary to characterize water retention curves may be siloed within soil science disciplines, this barrier could be easily overcome through cooperative arrangements and/or knowledge transfer. At the same time, technology is improving for more confident observation of Ψ S in-situ 8 . Tensiometers, which are accurate when soil is relatively wet (e.g. Ψ S > −0.1 MPa), are widely used in agricultural settings for the purposes of irrigation scheduling. In the drier range, soil matric potential can be measured using psychrometry or from dielectric measurements, with several commercial sensors available at a relatively low cost (e.g. the Teros 21 product, Meter Group). While the accuracy of sensors like these is greatest when Ψ S is above −2 MPa, this is still lower than the wilting point of many plant species 8 .

With respect to plants, psychrometers permitting continuous and long-term observation of both Ψ L and Ψ X are becoming more widely and commercially available (e.g. the PSY1 products, ICT International), drawing from a long history of psychrometric approaches for measuring plant water potential 69 . Stem psychrometers can now be deployed on branches and boles of some species for weeks to months at a time 55 , and evidence is mounting that high-frequency Ψ L and Ψ x data can indeed improve our understanding of plant water use strategies and dynamics 55 , 70 . Psychrometers are still relatively expensive, best suited for broadleaf and non-resinous species, and sensitive to biases linked to temperature fluctuations and wounding effects. Thus, for now, psychrometer data is best viewed as complimentary to pressure chamber measurements. Nonetheless, for many plants, these instruments allow for the collection of Ψ L and/or Ψ x data at the hourly timescales necessary to be harmonized with observed carbon and water fluxes (e.g. from sap flux and flux towers) and to more rigorously test model frameworks.

Ultimately, addressing environmental questions at policy- and management-relevant scales requires the collection and standardization of observations across many sites. This need has motivated the recent development of many environmental observation networks, including highly-centralized initiatives like NSF’s National Ecological Observatory Network (NEON 71 ), as well as more bottom-up networks like AmeriFlux 72 and FLUXNET 73 and the new international SAPFLUXNET network 74 . Other approaches include “network-of-networks” cyberinfrastructure like the International Soil Moisture Network, 13 which aggregates soil moisture observations from dozens of individual networks.

Both bottom-up and top-down approaches could be useful for building new Ψ networks. On the one hand, centralized and standardized deployment of new Ψ sensors, ideally in locations that are already nodes of other networks, would have the advantage of uniformity in instrumentation and data quality control that facilitates cross-site synthesis. On the other, a community-driven effort to aggregate and redistribute both existing and new Ψ data could follow the highly successful ‘coalition’ model employed by networks like AmeriFlux 72 , increasing the discoverability of data while allowing room for innovation at the site level. Even a concerted effort to generate and/or collect laboratory-based water retention curves from existing network sites could substantially constrain how much of the non-linearity in the response of fluxes to observed soil water content can be explained by soil physics (e.g. see Fig. 4 ). The success of a water potential network would be maximized with: a) a focus on collecting data from sites that also support continuous plant- and/or stand-scale carbon and water fluxes, b) cyberinfrastructure to support the discoverability and distribution of these databases; c) a focus in at least some locations on within-site spatial heterogeneity in Ψ dynamics, to better understand of how many observation points (and at what depths) are necessary to substantially improve model skill; and d) training programs, such as summer short-courses or distributed graduate seminars, to transfer knowledge about how to interpret network observations and to share best practices for sensor deployment.

Even with well-developed observation networks, it is not possible to measure key physiological variables like Ψ everywhere and all the time. Thus, strategies for linking these variables to proxies observable from space are required for regional- and continental-scale work, with microwave remote sensing representing a particularly promising approach. Microwave observations can be used to determine vegetation optical depth (VOD), which is sensitive to plant water content 75 and should be monotonically related to Ψ L 76 , 77 . Comparison of observed Ψ L with either spaceborne 78 or tower-based 70 radiometry confirms that VOD and Ψ L follow similar dynamics, especially after accounting for the effect of changing biomass and leaf area. However, the exact relationship between VOD and Ψ L is influenced by vegetation type 76 , and further study of this relationship is currently hindered by the sparsity of Ψ L data.

Importantly, microwave remote sensing observations can be made at night, which raises the question: can nocturnal microwave remote sensing of Ψ L be used to infer dynamics of root-zone Ψ S ? Answering this question requires a critical understanding of when and where pre-dawn Ψ L is equilibrated with root-zone Ψ S . This knowledge gap can be addressed with network observations of Ψ L from psychrometry, or observations of plant and soil water potential collected in the same site, which could then guide the design and interpretation of both tower- and satellite-mounted microwave remote sensing systems. The approach will also require further refinement of retrieval algorithms for separating the contribution of plant and soil water content, for example by leveraging emerging approaches for the remote sensing of vegetation structure 77 .

In conclusion, we have highlighted how more numerous, discoverable, and continuous observations of soil and plant Ψ can improve not only our conceptual understanding of biophysical processes throughout the soil-plant-atmosphere continuum, but also serve as a much-needed new tool for benchmarking and calibrating hydrologic and land-surface models and remote sensing products. While in-situ and site-specific observations of Ψ S , Ψ L , and Ψ x may not yet be “easy,” recent advancements in sensor technology have certainly made them easier than in decades past. The time is right for a new focus on the collection of these data in the field, and the development of new networks to aggregate observations across sites complemented by new approaches for integrating these observations into Earth system models.

Water retention curve uncertainty:

The water retention curves in Figure 2 were created using the van Genuchten water retention curve model 11 relating Ψ S to θ . As described in more detail in the Supplementary Information , most parameters of the model were held constant within each soil type, specified as the mean values reported in the updated ROSETTA pedotransfer function 18 (see Supplementary Table S1 ). The ‘ n ’ parameter was allowed to vary by randomly selecting a value from a uniform distribution bounded by ±1 standard deviation as reported for the ROSETTA PTF 18 . Overall, this was a conservative approach; drawing the values of n from the full distribution reported for each soil type expands the range of predicted Ψ S by orders of magnitude.

The HYDRUS 1-D simulations:

Uncertainty in the water retention curve linked to pedo-transfer uncertainty (e.g. as Figure 2a – d ) was propagated through predictions of Ψ S and θ (at depths of 15 cm) and surface evapotranspiration (ET, cm day) using the HYDRUS 1D soil water dynamics model 79 . Fifty simulations were performed for the Bradford Woods deciduous forest site in south-central Indiana, where the HYDRUS 1D model had been previously calibrated 80 . In general, model settings were left unchanged, with a few exceptions as discussed in more detail in the Supplementary Information . The soil at Bradford Woods is characterized by a 40 cm depth AP horizon dominated by sandy loam, and a BW Horizon dominated by silt loam from a depth of 40 cm to 208 cm. The very bottom of the soil layer (depths 208 – 230 cm) was prescribed to be clay loam. The parameters of the van Genuchten model used in the HYDRUS simulations are shown in Supplementary Table S2 , where again most were held constant, but n varied for the sandy and silt loam layers by drawing it from within one standard deviation of its distribution reported in the updated ROSETTA PTF 18 . The shaded areas in Figure 2e – f thus illustrate the resulting variation in ET, Ψ S , and θ due solely to variability in n .

The ORCHIDEE GPP sensitivity analysis:

The ORCHIDEE land surface model (CMIP6 version) 31 , 32 , which is the terrestrial part of the IPSL (Institute Pierre-Simon Laplace) Earth system model, was used to explore the sensitivity of modeled GPP to uncertainty in a wide range of parameters. ORCHIDEE relies on the van Genuchten model to calculate Ψ S , as well as the hydraulic conductivity and diffusivity required to solve the Richard’s diffusion equation. ORCHIDEE discretizes the first 2 m of the soil column over 11 layers. For this experiment, we ran ORCHIDEE over three single mesh locations using local half-hourly forcing data to drive the model at each site (see Table Supplementary Table S3 ), and considered modelled GPP at a daily time-step. The sensitivity analysis results shown in Figure 3 were generated using Sobol’s method 30 , using the SALib python package 81 to sample the parameter space and execute the SA algorithms. Briefly, the model was run using different parameter ensembles, with parameters varied within their reported ranges of uncertainty. Then, each modeled GPP timeseries was compared to GPP derived from flux tower observations. The variance of simulated GPP was then decomposed into fractions which can be attributed to each parameter tested. These results shown in Figure 3 capture both independent and interactive contributions of each parameter to the total variance. When interactions are removed, the independent contribution of water retention curve parameters is still significant, and actually increases for the semi-arid site (see details in Supplementary Section 3 ).

The AmeriFlux GPP analysis:

Half-hourly or hourly data from the four flux towers referenced in Figure 4 were acquired from the AmeriFlux network ( ameriflux.lbl.gov ) and subjected to a standardized quality control, gapfilling, and partitioning approaches. The sites and quality control procedures are described in more detail in Supplementary Table S5 . The methods used to determine the relationship between GPP and soil moisture are similar to those previously used to explore the relationship between surface conductance and soil moisture 35 . Briefly, analysis was constrained to the peak of the growing season to limit bias linked to phenological variation in LAI. Estimates of Ψ S for each site were determined from site-specific water retention curves 38 , 82 – 84 . The data were then sorted into nine bins representing the 15 th , 30 th , 45 th , 60 th , 70 th , 80 th , 90 th , and 100 th quantiles of the observed values of soil moisture content in each site. Within each bin, data were constrained to relatively high light (net radiation > 300 W/m 2 ) conditions with VPD limited to 1 ≤ VPD ≤ 1.5 Pa in US-MMS, US-TON, and US-MOz, and 1.5 ≤ VPD ≤ 2 kPa in the more arid US-SRM site. The mean GPP, Ψ S , and θ were then calculated for each bin using the filtered data, and normalized by the maximum bin-averaged value observed at each site.

Supplementary Material

Supplementary information, acknowledgments.

KAN acknowledges support from NSF (DEB, Grant 1552747) and the AmeriFlux Management Project via the US Department of Energy, Office of Science Lawrence Berkeley National Laboratory. AGK was supported by NASA Terrestrial Ecology (award 80NSSC18K0715). JDW acknowledges support from the U.S. Department of Energy, Office of Science, through Oak Ridge National Laboratory’s Terrestrial Ecosystem Science Focus Area. KJD and YS were supported by National Science Foundation Grant EAR - 1331726 (S. Brantley) for the Susquehanna Shale Hills Critical Zone Observatory.

Competing interests : The authors declare no competing interests.

Code availability Statement : The HYDRUS-1D program used to create the results of Figure 2e – g is available for public download from https://www.pc-progress.com/en/Default.aspx?hydrus-1d . A reference version of the ORCHIDEE land-surface model, used for Figure 3 , is available at https://orchidee.ipsl.fr/ . Details on the parameterizations of these models are presented in the Supplementary Information .

Data availability statement:

• Secondary School

What are limitations to an osmosis lab

Limitations of conducting osmosis in a lab include different sizes or parts of the substance used (such as potato), external factors such as temperature and evaporation rate, and improper handling.

Explanation:

Osmosis is a process involving the movement of solvent particles from an area where they are highly populated to an area where they are less populated. The movement or translocation makes sure that the solute and solvent concentrations are equal on both sides.

Osmosis can be easily performed. This is the reason it is usually included in high school laboratories experiments. But while performing this process in the lab, some obstacles are faced . These are :

• The piece of the substance used may be distinct in size every time. For example, when strips of potatoes are kept in sucrose solution the size may vary distinctly.
• Different parts of the substance may have different water-carrying potentials. Thus, similar parts must always be used.
• Some characteristics of water may get disturbed due to changing external environments such as temperature. This may become a hindrance during the experiment. The experiment must be properly controlled.
• The experiment must be properly handled. Without proper precautions, the results may vary.

There were several limitations to this experiment, which may have hindered or altered its accuracy and end results: We did not measure the exact amount of liquid put into each test tube: we did not exclude the factor of liquid amount having an effect over the potato strip.

New questions in Biology

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• Published: 17 September 2024

Assimilation of ground-based GNSS data using a local ensemble Kalman filter

• Changliang Shao 1 &
• Lars Nerger 2  

Scientific Reports volume  14 , Article number:  21682 ( 2024 ) Cite this article

Metrics details

• Atmospheric dynamics

Tropical cyclones become increasingly nonlinear and dynamically unstable in high-resolution models. The initial conditions are typically sub-optimal, leaving scope to improve the accuracy of forecasts with improved data assimilation. Simultaneously, the lack of real ground-based GNSS observations over the ocean poses significant challenges when evaluating the assimilation results in oceanic regions. In this study, an Observation System Simulation Experiment is carried out based on a tropical cyclone case. Assimilation experiments using the WRF-PDAF framework are conducted. Conventional and GNSS observation operators are implemented. A diverse array of synthetic observations, encompassing temperature (T), wind components (U and V), precipitable water (PW), and zenith total delay (ZTD), are assimilated utilizing the Local Error-Subspace Transform Kalman filter (LESTKF). The findings highlight the improvement in forecast accuracy achieved through the assimilation process over the ocean. Multiple observation types further improve the forecast accuracy. The study underscores the crucial role of GNSS data assimilation techniques. The assimilation of GNSS data presents potential for advancing weather forecasting capabilities. Thus, the construction of ground-based GNSS observation stations over the ocean is promising.

Introduction

Data assimilation (DA) plays a crucial role in improving the accuracy and reliability of numerical weather prediction (NWP) models. DA helps to bridge the gap between model simulations and real-world observations. It enhances the accuracy, skill, and reliability of the atmosphere simulations, providing valuable information for a range of applications, including weather forecasting, climate studies, and environmental assessments 1 , 2 . Global Navigation Satellite System (GNSS) data, such as those provided by the Global Positioning System (GPS), Galileo navigation satellite system (Galileo), global navigation satellite system (GLONASS), and BeiDou navigation satellite system (BDS), have gained significant attention in recent years due to their potential for improving atmospheric models and weather forecasting. Assimilating GNSS data into atmospheric models using techniques like Ensemble Kalman Filtering (EnKF) has shown significant impact on improving the accuracy and performance of the models 3 in different applications as outlined below.

Improved Initial Conditions: Assimilating GNSS data helps in refining the initial conditions of atmospheric models by incorporating real-time and high-resolution (e.g., 5-min series in the Nevada Geodetic Laboratory (NGL) 4 product ( http://geodesy.unr.edu , last accessed: 27 July 2024) information about atmospheric parameters such as water vapor content. This leads to a better representation of the current state of the atmosphere and reduces the uncertainties associated with the initial conditions 5 . Positive impacts on weather forecasting, particularly for short-term (up to 6 h) 6 and short-range (48 h) 7 forecasts have been shown. The assimilation helps in capturing mesoscale weather phenomena such as convective systems, thunderstorms, and localized rainfall patterns 8 . It contributes to the better representation of atmospheric processes and improves the skill of weather forecasts, especially in regions where traditional observations are sparse or limited.

Enhanced Moisture Analysis: GNSS data assimilation plays a crucial role in improving moisture analysis in atmospheric models. It provides high-temporal and spatial resolution observations of precipitable water vapor and zenith total delay, which are vital for understanding the moisture distribution in the atmosphere. Assimilating GNSS data leads to a more accurate representation of moisture fields, enabling improved forecasts of precipitation and humidity patterns 9 .

Vertical Profiling: GNSS data assimilation enables improved vertical profiling of atmospheric parameters, which is crucial for understanding the vertical structure of the atmosphere. By assimilating GNSS data, the vertical distribution of water vapor and other variables can be accurately estimated, aiding in the analysis of atmospheric stability, moisture transport, and cloud formation processes 10 .

Real-time Assimilation: One of the key advantages of GNSS data is its availability in real-time. Assimilating GNSS data in real-time allows for timely updates of atmospheric models, leading to improved nowcasting and short-term/range forecasts. Data of zenith total delay (ZTD) and precipitable water (PW) are available within 1 h from the moment the original satellite signal is received by the ground-based station. This latency period encompasses both data processing and transmission times. Real-time assimilation enables the models to capture rapidly changing atmospheric conditions, providing valuable information for severe weather events and rapid weather developments 11 .

Some of the most important challenges for the assimilation of GNSS data include the required greater sophistication of forward models to allow using the indirect observations PW and ZTD, the need to analyze a range of hydrometeors, the need to account for the flow-dependent multivariate “balance” between atmospheric water and both dynamical and mass fields, and the inherent non-Gaussian nature of atmospheric water variables 12 , 13 , 14 . Furthermore, GNSS observations over the ocean have gained significant attention in recent years, as reported by Ji et al. 15 and He et al. 16 . Nevertheless, establishing real ground-based GNSS stations on the sea remains challenging, leading to insufficient GNSS data availability. Consequently, the employment of idealized cases serves as an alternative approach to assess the influence of this observation type.

The objective of this study is to assess the impact of assimilating ground-based GNSS data within an idealized tropical cyclone scenario using an ensemble-based Kalman filter. This is achieved by integrating the Weather Research and Forecasting Model (WRF) 17 with the Parallel Data Assimilation Framework (PDAF; http://pdaf.awi.de , last access: August 1, 2024) 18 and performing and analyzing idealized assimilation experiments. Our goal is to gain insights into the potential benefits of utilizing ground-based GNSS data over the sea to enhance the accuracy and reliability of tropical cyclone predictions. For GNSS observations we focus on the online assimilation of PW and ZTD data, which are critical for improving tropical cyclone predictions. Compared to previous studies, we assimilate multiple observations, including temperature (T), horizontal wind components (U and V), and the additional variables PW and ZTD, using the localized error subspace transform ensemble Kalman filter (LESTKF) 19 . To implement this approach, we develop ground-based GNSS observation operators within the WRF-PDAF framework. These operators enable the seamless integration of GNSS data into the assimilation process. We then conduct a twin experiment over the ocean, based on a mesoscale idealized case of a tropical cyclone. By analyzing the assimilation results, we expect to gain valuable insights into the impact of ground-based GNSS data on tropical cyclone predictions. This study contributes to the ongoing efforts to improve the accuracy and reliability of tropical cyclone forecasting systems, ultimately leading to better decision-making and mitigation strategies for communities at risk.

The remainder of the study is structured as follows. “Methodology” introduces ensemble filters and the observation operators for the DA. The setup and configuration of the DA system are outlined in “Setup of data assimilation program”. “Experimental design” discusses details of the experimental design for the idealized case studies. “Results and analysis” examines the parallel performance of the DA system build by coupling WRF and PDAF, the assimilation behavior of an example application with WRF. Finally, conclusions are drawn in “Discussion and conclusions”.

Methodology

Ensemble Kalman filters (EnKFs, see e.g., Vetra-Carvalho et al. 20 ) are data assimilation methods that combine the information from an ensemble of model states with observations to update the model state variables. In EnKFs, ensemble members are generated by perturbing the model initial conditions, and the assimilation is performed by computing analysis increments based on the ensemble spread and the observation-model misfit. Here, ensemble spread is the ensemble standard deviation (STD), which provides a measure of the distribution of the ensemble members around the ensemble mean. The analysis increments are subsequently added to the ensemble members to obtain the updated state variables. EnKF variants are particularly suitable for assimilating GNSS data due to their ability to handle non-linear dynamics of atmospheric models, like the LETKF 21 and the LESTKF [28, and also non-Gaussian distributions, like the NETF 22 and the LKNETF 23 .

In this section, we introduce the WRF-PDAF model, the GNSS data for DA, the LESTKF assimilation scheme, and the observation operators.

The WRF model is a widely used numerical weather prediction system, providing a versatile platform for simulating a broad spectrum of atmospheric processes suitable for both regional and global weather simulations. Developed by Shao and Nerger 24 , WRF-PDAF integrates WRF-ARW version 4.4.1 with PDAF version 2.0 to facilitate robust data assimilation. This integration enables the incorporation of profile data into WRF, enhancing its initial conditions and contributing to improved forecast accuracy. The online coupling strategy of WRF-PDAF, in which PDAF is directly coupled to WRF, utilizes a fully parallel structure for data assimilation. Here, the data assimilation program integrates all model states concurrently utilizing a sufficient number of processes and the data assimilation is performed without the need of restarting the model. This approach guarantees the model’s consistent temporal advancement, resulting in highly efficient data assimilation.

In this study, the model setup is the three-dimensional equivalent of case considered by Rotunno and Emanuel 25 . The domain size is 3000 km × 3000 km × 25 km, containing 200 × 200 × 20 grid points with a horizontal grid spacing of 15 km and a vertical grid spacing of 1.25 km. The Kessler microphysics scheme and the YSU boundary-layer physics are employed, while radiation schemes are not utilized. A capped Newtonian relaxation scheme is used on potential temperature 25 which is a crude approximation for longwave radiation. This scheme is useful for idealized studies of maximum tropical cyclone intensity. The simulation spans a period of six days, starting from September 1, at 00:00 UTC (010000) and ending on September 7, at 00:00 UTC (070,000). The model time step is set to 60 s.

To initialize the simulation, both initial and boundary conditions are required. For our idealized tropical cyclone case the initial horizontally homogeneous environment is specified via a sounding data. The initial state is motionless ( \(u=v=0\) ) and horizontally homogeneous, except an analytic axisymmetric vortex in hydrostatic and gradient-wind balance is added. The lateral boundary conditions are periodic to facilitate the simulation process. The default setup may not be optimal for complicated diagnosis of precipitation. These parameters of the default setup are adjustable to accommodate various requirements and preferences. Shao and Nerger 26 applied WRF-PDAF to conduct assimilation experiments of temperature profiles at different densities. The main difference in this study is the additional assimilation of PW and ZTD data. Additionally, we have supplemented the experiments with single-point experiments.

GNSS Data for DA

GNSS data, such as PW and ZTD observations, provide information about atmospheric moisture and can be assimilated using EnKFs to improve the representation of moisture fields in the model 27 , 28 . GNSS signals are bent, attenuated and delayed both by the ionosphere and troposphere. The ionospheric delay can be mostly reduced by linear combination of double-frequency observations. The water vapor content is responsible for the “wet” delay in the troposphere. A prevalent approach involves mapping the GNSS signal in the zenith direction and integrating it over a specified time period to derive a vertical column of tropospheric delay above each station, commonly referred to as the ZTD 29 . GNSS signals transmit through the troposphere and the signal delays are caused. The observed ZTD can be split into two parts: Zenith Hydrostatic Delay (ZHD) and Zenith Wet Delay (ZWD). The ZHD is estimated with the Saastamoinen 30 formula. In real cases, Precipitable Water vapor (PW) is retrieved from the ZWD as follows:

Here Q is the proportionality factor. \({T}_{m}\) denotes the vertical weighted mean temperature (in K) of the atmosphere. \({e}_{l}\) , \({T}_{l}\) and \(\Delta {h}_{l}\) denote the average vapor pressure (in hPa), average temperature (in K) and the thickness of the atmosphere at the \(l-\) th layer, respectively. \(l\) is the layer index, ranging from the bottom layer \(lts\) to the top layer \(lte\) , specifically depending on the datasets used, such as ERA5 29 , 31 . \(P\) , \(\varphi\) and \(h\) are pressure, latitude and height of the station, respectively.

The GNSS data originates from ground-based stations, with real-time ZTD and PW data available on an hourly basis from these stations. Both the station’s geographical location and the temporal resolution of the ZTD and PW data have to taking into account. For the data assimilation, the synthetic PW and ZTD observations are calculated hourly by the observation operators for PW and ZTD, respectively, acting on different model fields, as described in " PW and ZTD Observation operators ". The two-dimensional ZTD/PW observations are positioned on all of the horizontal grid points. Synthetic U, V, and T observations represent sounding profile observations. In terms of profile data, the operators for T, U, and V directly operator on the model grid locations without any interpolations. Each profile consists of a vertical column of observations of T, U, and V located on grid points. It is usually impossible in the real scenario, even on land. However, this is precisely the purpose of our implementation of OSSE. We want to understand how data assimilation performs under this assumption.

The LESTKF has been applied in different studies to assimilate satellite data into atmosphere models 32 , ocean models 33 , atmosphere–ocean coupled models 34 , 35 and hydrological models 36 . The LESTKF is an efficient formulation of the EnKF, reviewed here to be able to discuss the particularities of the DA with respect to the ensemble filter. The analysis Eqs. ( 6 )–( 13 ) transform the forecast ensemble \({X}^{f}\) of \({N}_{e}\) model states into the analysis ensemble \({X}^{a}\) :

Here, \({\widetilde{x}}^{f}\) is the forecast ensemble mean state and \({1}_{{N}_{e}}^{T}\) is the transpose of a vector of size \({N}_{e}\) holding the value one in all elements. \(w\) is a vector of size \({N}_{e}\) , which transforms the ensemble mean and \(\widetilde{W}\) is a matrix of size \({N}_{e}\times {N}_{e}\) , which transforms the ensemble perturbations. \(T\) is a projection matrix into the error subspace with \(j={N}_{e}\) rows and \(i={N}_{e}-1\) columns. \(H\) is the observation operator. \(R\) is the observation error covariance matrix. \(A\) is a transform matrix in the error subspace. \(\alpha\) with \(0<\alpha \le 1\) is the forgetting factor 37 . \(U\) and \(S\) are the matrices of eigenvectors and eigenvalues, computed from the eigenvalue decomposition of \({A}^{-1}\) .

A local analysis is performed by updating the model fields at each grid point of the model independently. Only observations within horizontal and vertical localization radii are considered when updating a grid point. Consequently, the observation operator is local and computes an observation vector within the influence radius based on the global model state. Additionally, each observation is weighted according to its distance from the grid point 21 . The localization weight for the observations is computed using a fifth-order polynomial with a shape resembling a Gaussian function 38 . The weighting is applied to the matrix \({R}^{-1}\) in Eqs. ( 7 ) and ( 9 ). So, the localization process results in individual transformation weights \(w\) and \(\widetilde{W}\) for each local analysis domain.

PW and ZTD Observation operators

Observation operators are used to transform model variables into observation space, thus computing the model equivalent to the actual observation. Specifically related to GNSS data the operator for PW is

where \(i,j\) are horizontal model node indices. \(k\) is the index of the model layer, and \(kts\) =1 and \(kte\) =20 are the bottom layer and the top layer index as defined in " WRF-PDAF ", respectively. \(\rho\) is air density (kg/m3), \(q\) is specific humidity (1), and \(\Delta h\) is the height difference between two consecutive model layers (m).

The observation operator for ZTD is

Here, \({h}_{sfc}\) is the height of the model surface (m), \(p\) is pressure (Pa) and \(t\) is temperature (K). \(q\) , \(t\) and \(\Delta h\) are calculated from the model fields of WRF as follows:

The model fields used in these functions are the perturbation geopotential ( \(ph\) , m2/s), perturbation potential temperature ( \(th\) , K), water vapor mixing ratio ( \(qv\) , kg/kg), perturbation pressure ( \(p\) , Pa), and base-state geopotential ( \(phb\) , m2/s).

The observation operators of PW and ZTD are constructed based on the traditional approach. Our contribution lies in more explicitly formulating the equations within the WRF-PDAF system, thereby enabling accurate implementation. In one hand, since the operators of ZTD and PW are different, the results of the data assimilation should not be the same. Comparing the two different results is meaningful. In another hand, assimilating PW and ZTD should yield similar performance, which can be used to demonstrate the correctness of the construction of the observation operator and the assimilation process, making the results convincing.

Setup of data assimilation program

To enable the data assimilation, PDAF is coupled into the existing WRF framework. This coupling allows for the assimilation of GNSS data into WRF to improve its initial conditions and subsequently enhance its forecasts.

PDAF is a freely available open-source software developed to facilitate the implementation and application of ensemble and variational DA methods. It offers a generic framework that includes fully implemented and parallelized ensemble filter algorithms such as the LETKF, LESTKF, NETF, and LKNETF, along with related smoothers. PDAF provides functionality for adapting the model parallelization for parallel ensemble forecasts and includes routines for parallel communication between the model and filters. Like many large-scale geoscientific simulation models, PDAF is implemented in Fortran and parallelized using the Message Passing Interface (MPI) standard 39 and OpenMP 40 , ensuring optimal compatibility with such models. It can also be used with models implemented in other programming languages such as C and Python.

The online coupling strategy for DA is selected here utilizing the fully parallel structure. For this implementation, the time stepping for all ensemble states are is computed concurrently utilizing a sufficient number of processes on a compute cluster. With this, each model task integrates only one model state and the model is always going forward in time.

In this study, all of the variables needed by PDAF are inserted from WRF into the state vector. There are the x-wind component ( \(u\) , m/s), y-wind component ( \(v\) , m/s), z-wind component ( \(w\) , m/s), perturbation geopotential ( \(ph\) , m2/s), perturbation potential temperature ( \(th\) , K), Water vapor mixing ratio ( \(qv\) , kg/kg), Cloud water mixing ratio ( \(qc\) , kg/kg), Rain water mixing ratio ( \(qr\) , kg/kg), Ice mixing ratio ( \(qi\) , kg/kg), Snow mixing ratio ( \(qs\) , kg/kg), Graupel mixing ratio ( \(qg\) , kg/kg), perturbation pressure ( \(p\) , Pa), density ( \(\rho\) , kg/m3) and base-state geopotential ( \(phb\) , m2/s). Note that the variables \(p\) , \(\rho\) and \(phb\) are only used by the observation operators, but will not be updated by PDAF. So, only the rest of the variables will be updated and returned to WRF.

Experimental design

In the ideal cases, synthetic observations are used and generated from the model variables via observation operators. In this study, all synthetic observations were generated by adding Gaussian errors directly at the grid points without any interpolations. The standard deviations of the Gaussian errors were set to 1.2 K, 1.4 m/s, 1.4 m/s, 1 cm, and 4 cm for T, U, V, PW, and ZTD, respectively, following Bao and Zhang 41 , 32.Pawel et al. 42 and Li et al. 43 . Therefore, the conventional observation operators, including U, V, and T, are just acting on the location of the model grid. For PW and ZTD, the model state variables are transformed into the observation space using the appropriate GNSS observation operators introduced in " PW and ZTD Observation operators ". The PW and ZTD observations are then assimilated into the WRF model using the LESTKF.

In this section, the details of the ideal tropical cyclone case, the design of a single point experiment, and the experimental design of GNSS DA are described.

The tropical cyclone case

Tropical cyclones, also known as hurricanes or typhoons depending on the region, are powerful and destructive weather phenomena that form over warm ocean waters near the equator. These intense storms derive their energy from the latent heat released when moist air rises and condenses into clouds and precipitation. The Coriolis effect causes the storm to spin, with the direction of rotation determined by the hemisphere in which the cyclone forms. Tropical cyclones can have devastating impacts on coastal communities and infrastructure. Forecasting and monitoring tropical cyclones are essential for mitigating their impacts.

The test case used here is the idealized tropical cyclone case provided by WRF, which serves as a simplified representation of real-world atmospheric conditions. It provides a controlled environment for evaluating the performance of data assimilation methods utilizing identical twin experiments. This test case here we use is the same with Shao and Nerger 24 , where one can find more details about the idealized tropical cyclone.

The atmospheric state variables, such as temperature, humidity, and wind fields from a forward run of the model create the known true state for comparison with assimilation results. This truth is used to generate synthetic observations. A control state is generated separately for the period September 3, at 12:00 UTC (031,200) to September 7, at 00:00 UTC (070,000) using the same initial fields as the truth. Therefore, the control state and true state are identical in all aspects except for their respective start times. The control simulation provides initial state estimate for the data assimilation. The flowchart of the cases is shown as Fig.  1 .

The flowchart of the twin experiments. The black line represents the true state, and the blue line represents the control state.

Synthetic observations were generated hourly from the true state starting from 040,800 and ending at 051,400. The observations were generated for both single-point experiments and cycled DA experiments assimilating multiple variables. For the single-point experiments, only one set of observations of U, V, and T was generated at 040,800. These observations were located at the horizontal center of the model domain and vertical level 5, corresponding to a height of 10 km. In the cycled DA experiments assimilating multiple variables, a total of 30 hourly observations of U, V, T, PW, and ZTD were generated. The U, V, and T observations were generated at all grid points in the model domain. On the other hand, PW and ZTD observations were generated from each vertical column of the model using the observation operators. In addition, Gaussian noise with standard deviation as described on " Experimental design ". The generated observations are free of bias.

For the twin experiments, an initial perturbation is added to the control state at 031,200 to generate 40 ensemble members. The ensemble is spun up for 20 h. Subsequently, in the cycled DA, the observations are assimilated hourly into the ensemble during the analysis period from 040,800 to 051,400. Finally, an ensemble forecast is run without further assimilation from 051,400 until 070,000.

Single-point experiments

The single point experiments focus on assimilating observations at a specific location within the model domain. The design involves selecting a grid point of interest and assimilating observations at that point. These experiments allow for a detailed assessment of the assimilation impact on the model state variables at a specific location. Here, T is used to denote potential temperature th. As depicted in Table 1 , the assimilation of a single observation of T, U and V located at the specific location was carried out in three separate experiments, namely exp.1, exp.2 and exp.3. The observations T, U, and V have offsets of 1 k, 1 m/s, and 1 m/s, respectively, relative to the control fields. These observations were assimilated to compute a multivariate update of U, V and T. To determine the optimal localization distance, the different horizontal distances 800 km, 150 km, and 50 km are tested in each experiment. Localization distances of 200 km and 100 km were also tested for tuning, but not shown here. The vertical localization radius is identical in all cases matching the height of the model top. The purpose of these tests was to select the localization distance that yielded the best results. To facilitate analysis and verification, there is no radius for PW or ZTD.

In this study, a forgetting factor of α = 0.97 was used in Eq. ( 9 ). The forgetting factor is a scaling parameter applied to the ensemble spread in order to avoid underestimation of the forecast uncertainty. The ensemble variance is inflated by \(1/\alpha\) . The forgetting factor was determined based on the ensemble spread, which reflects the variability or uncertainty within the ensemble members. By appropriately adjusting the forgetting factor and setting observation errors, the assimilation process can effectively incorporate the available information from observations and ensemble members, resulting in improved forecast accuracy and reliability.

Experimental design for cycled DA

The experimental design for DA with multiple observations involves assimilating synthetic conventional and GNSS observations into the WRF model. The GNSS DA experiment aims to enhance the representation of moisture fields through the integration of GNSS observations. This assimilation process aims to utilize the precision PW and ZTD data to refine and correct the model predictions of humidity and other related atmospheric variables. The ultimate objective is to achieve a more accurate representation of moisture fields, thereby enhancing the overall accuracy and reliability of weather predictions. The impact of assimilating these observations on the model representation of atmospheric moisture is evaluated through a comparison between the assimilated and true states. By conducting these experiments on an idealized case, the performance and effectiveness of WRF-PDAF in assimilating observations and improving the model representation of atmospheric variables can be evaluated.

Table 2 provides an overview of the experiments performed here. Two single runs were used to generate the true state (Exp. 4, ‘True’) and control state (Exp. 5, ‘CTRL’), as described in " The tropical cyclone case ". These distinct states served as the basis for further analysis and experimentation in the study. To generate the initial ensemble, perturbations were generated using second-order exact sampling 37 from the model variability of hourly snapshots from 010000 to 031,200. These perturbations were added to the control state at 031,200 to generate an ensemble of 40 states. Subsequently, a free ensemble run of the 40 members (Exp. 6, ‘ENS’) was conducted. The purpose of this ensemble run was to generate a collection of model states that encompassed a range of possible variations and uncertainties. The same initial ensemble members were utilized in the assimilation experiments. Starting from the initial ensemble, assimilation experiments were conducted over 30 analysis cycles. Different experiments assimilating the conventional observations U, V, T, or separately the GNSS observations PW or ZTD, as listed in Table 2 , were performed. In addition, the experiments 10 and 11 assimilated a combination of direct observations alongside with GNSS observations. PW and ZTD are assimilated separately to assess how far these observations have different effects. This integration leverages the complementary nature of the two datasets. These different assimilation experiments were carried out to evaluate the impact of assimilating specific types of observations on the model state.

Results and analysis

Figure  2 shows the increments resulting from the single-point assimilation experiments detailed in Table 1 . Note that each assimilation of T, U, and V observations can affect all of the U, V, and T model fields through the multivariate DA update. In contrast to the isotropic increments of 3DVAR and 4DVAR, the increments used in LESTKF are anisotropic due to the flow-dependent features of the background error covariance.

The spatial distribution of the T, U and V increments of the single-point experiments at 031,200 with different localization distances 800 km, 150 km, and 50 km (( a – c : results of exp. 1 assimilating T; ( d – f ): results of exp. 2 assimilating U; ( g – i )): results of exp. 3 assimilating V). The shade represents the T increments (K), while the arrows represent the wind velocity (combined U and V) increments (m/s).

If there is no localization, the increments will be distributed throughout the entire simulation region. However, increments far from the observation are generally unreliable, and the correlations between the observation point and distant grid points were considered spurious. To address this concern, selecting an appropriate localization distance becomes crucial. Past research often made such choices or even developed adaptive schemes based on the root mean square error (RMSE). However, in our study, since the dynamics are known in the ideal case, we aim to determine the localization distance from the dynamic perspective. A well-suited localization distance should accurately reflect the relationships between temperature and wind while also avoiding spurious correlations. When the localization distance was set to 800 km, the region with spurious correlations reduced compared to using no localization, but some areas with spurious increments remained (Fig.  2 , column (1). When the localization distance was further reduced to 150 km, the increments were only distributed closely around the single observation point (Fig.  2 , column (2). The fifth-order polynomial mentioned in " LESTK F" resulted in decreasing increments as the distance from the observation point increases. Moreover, positive T increments caused cyclonic-type wind increments, while negative T increments caused anticyclonic-type wind increments, consistent with the gradient-wind balance. The localization distance of 50 km led to even smaller areas of increments around the single observation point (Fig.  2 , column (3). However, the area of increments was too limited to clearly observe the relationship of the gradient-wind balance, especially in Fig.  2 f,i. Despite the reduced spurious correlations, the extremely localized increments hindered the ability to capture the meso-scale flow patterns and relationships. Based on the results and observations provided, a localization distance of 150 km was chosen as the most suitable for the assimilation experiments in this study.

Cycled GNSS DA

In Fig.  3 a, the RMSE of specific humidity (Qv) from the different experiments listed in Table 2 is displayed. The RMSE of the ensemble forecast (ENS) is lower than that of the control run from the true state (True). This means that the ensemble members generated using second-order exact sampling represent the range of possible atmospheric states and the ensemble mean properly represents the most likely forecast. The RMSE when assimilating U, V, T data (UVT) is lower than that of ENS, indicating that the assimilation process improves the accuracy of the model prediction. The RMSEs from the experiments daPW and daZTD appear to be similar, with the RMSE of daZTD is slightly lower than daPW. The RMSEs from the experiments daUVT, daUVTPW, and daUVTZTD are similar. However, the RMSEs from daUVTPW and daUVTZTD are lower than that of daUVT. Among all the experiments, the lowest RMSE is observed in daUVTZTD.

Upper row: Time series of RMSE ( a ) and STD ( b ) of Qv from 031,200 to 070,000. Lower row: Vertical profile of time-average of Qv RMSE ( c ) and STD ( d ). The blue dotted lines in ( a ) and ( b ) show the start time of the DA process, while the red dotted lines represent the its endpoint).

In Fig.  3 b, the STD of the ensemble of Qv is shown for the different experiments. The STD provides an estimate of the uncertainty in the state estimate. The STD of the experiment daPW is slightly lower than that of ENS. The STD of experiment daZTD is lower than that of daPW. This suggests that the assimilation of either PW or ZTD data has helped to reduce the uncertainty among the ensemble members, leading to a more consistent forecast. The experiments daUVT, daUVTPW and daUVTZTD have almost the same STD, which is lower than the others. This suggests that the assimilation of conventional data and of multiple observations (U, V, T, PW/ZTD) in these experiments have led to a similar reduction in the spread of specific humidity among the ensemble members, contributing to a more constrained forecast. The pattern of the STDs is similar to the RMSEs during the analysis period, indicating, as expected, that the ensemble STD is influenced by the assimilation process. Lower RMSEs correspond to lower STDs. An approach to evaluate the capability of an ensemble system in quantifying prediction uncertainty is by examining the relationship between the spread among the forecasts of individual ensemble members and the skill of their mean forecast, known as the spread-skill relationship 44 . Several methods exist to quantify this relationship. Talagrand 45 argued that a statistically consistent ensemble should have an average STD matching the RMSE of its mean forecast. We observe that, indeed, the STD and RMSE generally correspond quite well. However, all of the STDs become closer during forecast period, especially at the later time of the experiment. In Fig.  3 c,d, it can be observed that the decreases in RMSEs and STDs of Qv are primarily seen at the middle and low levels (below level 12). This suggests that the assimilation process has a more significant impact on improving the accuracy and reducing the variability of Qv at these levels. However, the results of T, U, and V show the decreases in RMSEs and STDs of these variables at all levels (figures omitted). Figure  3 provides insights into the performance of different data assimilation experiments in improving the accuracy and reducing the STD of Qv, T, U, and V variables during the specified time period (from 031,200 to 070,000).

With the aid of flow-dependent cross-variable background error covariances, the assimilation of U, V, and T yields Qv corrections, resulting in an improved state compared to assimilating PW or ZTD alone. This could be attributed to the nature of the observations themselves. The U, V, and T observations are direct measurements and represent three-dimensional variables, providing a comprehensive and detailed information about the atmospheric conditions. On the other hand, the PW and ZTD observations are indirect two-dimensional data, which may have some limitations in capturing the complete atmospheric state. The direct and three-dimensional nature of U, V, and T observations likely contributes to their larger impact on the assimilation process and the resulting improvements in the state. Furthermore, the assimilation of GNSS data generates slight wind and temperature corrections through the same flow-dependent mechanism (figures omitted). Additionally, the assimilation of multiple data types (U, V, T, PW/ZTD) contributes to an enhanced initial cyclone circulation. This improvement can be credited to the assimilation of diverse data types, which effectively corrects the temperature, wind, and Qv fields. This indicates that despite the significant improvements achieved through conventional observations, the inclusion of GNSS observations can offer additional valuable information, leading to further enhancements in cyclone simulation.

In the idealized case, the primary distinction between PW and ZTD stems from the different observation operators outlined in Eqs. ( 14 – 15 ). Simultaneously, due to varying observational errors, the RMSE exhibits different performances. This discrepancy is also reflected in the lower RMSEs and STDs of U, V, and T from daUVTZTD compared to daUVTPW. In previous real case studies 14 , 46 , opinions vary on whether assimilating PW or ZTD yields better results. From our perspective, the superiority of either depends on the quality of the data itself. In real cases, ZTD is derived first, followed by the derivation of PW from ZTD. It is crucial to note that the value of PW does not solely depend on the ZTD but is also influenced by the additional variables (p, t) in Eqs. ( 1 – 5 ). If the quality of ZTD surpasses that of p and t, the quality of PW may be inferior to that of ZTD, and vice versa.

To assess the estimate model fields, we show the ensemble means for the ensemble experiments as it is common practice in ensemble DA. The spatial distribution of T, U, and V at the 850mb level at the initial time (031,200) are shown in Fig.  4 . Figure  4 a represents the true state, showing the actual distribution of T, U, and V. Figure  4 b represents the control run, which is similar to the ensemble run (Fig.  4 c), but both differ significantly from the true state. Figure  4 d displays the difference obtained by subtracting the true state from the ensemble mean. The differences of T are positive in the outer areas but negative in the central region, while most wind velocities exhibit an anticyclonic pattern. As a result of the distinct start times, the cyclone in the true state has progressed for 60 h, whereas the control state’s cyclone remains at its earlier stage. During the development of the cyclone, the temperature in the central region increases, while it decreases in the outer areas. Concurrently, the wind field intensifies over time. This phenomenon can be attributed to the interplay between thermodynamics and dynamics within the cyclonic system.

Spatial distribution of T, U, and V at the 850 mb level at initial time 031,200 of the control run (single state for True and Ctr; ensemble mean for the ensemble experiment). The shade represents the temperature (K) distribution, while the arrows represent the wind velocity (m/s). 4 ( a ): True; 4 ( b ): CTRL; 4 ( c ): ENS; 4 ( d ): difference between ENS and True.

Given its lowest RMSE, the daUVTZTD experiment is selected for further comparative analysis in this study. At this first analysis step of the DA process the analysis state gets closer to the true state compared to CTRL and ENS. The misfit between daUVTZTD and True is smaller than that between ENS and True at the initial time (figures omitted). However, the difference is larger compared to the final assimilation time. The larger error after the first analysis is mainly due to the substantial magnitude of the prescribed observation errors. Thus, the impact of the observations may not be immediately evident or prominent. However, by incorporating model observational information over time, the state estimate is gradually improved.

Figure  5 represents the 30th DA cycle and final assimilation time, which is 50 h after the start time of control run. In the control run (Fig.  5 b), T is lower, and the cyclone is weaker than in the true state (Fig.  5 a). In ENS (Fig.  5 c), T is higher than in the true state, whereas the cyclonic circulation remains weaker. An evident underestimation of temperature is observed at the cyclone center, whereas the temperature is overestimated in the areas outside the cyclone edge. The analysis state (Fig.  5 d) is closest to the true state. The overall DA-induced change in the model state, depicted in Fig.  5 e, demonstrate the impact of DA. The improvements of T are predominantly concentrated at the center of the cyclone and the surrounding area outside the edge of the cyclone. The differences between the analysis and the true state (Fig.  5 f) are very small across the model domain.

T, U and V at level 850mb at 30th DA time 051,400. The shade represents the temperature (K) distribution, while the arrows represent the wind velocity (m/s). 5 ( a ): True state; 5 ( b ): CTRL; 5 ( c ): ENS; 5 ( d ): daUVTZTD; 5 ( e ): difference between daUVTZTD and ENS; 5 ( f ): difference between daUVTZTD and True.

Next to the effect on the temperature and velocity fields, we assess the effect of the DA on Qv in Fig.  6 . At 051,400, Qv in the control run (Fig.  6 b) appears to be higher than that in the true state (Fig.  6 a) across the entire region. In contrast, the ensemble run (Fig.  6 c) shows a lower Qv compared to the control run, yet it lacks accuracy in simulating the cyclone pattern around its center. Similar to the temperature, the Qv distribution of the analysis state (Fig.  6 d) is the closest to the true state. The DA-induced change, depicted in Fig.  6 e, illustrates the impact of the DA on the Qv field, with adjustments evident throughout the domain but predominantly concentrated at the cyclone’s center. The resulting misfits between the analysis state and the true state (Fig.  6 f) are generally very small across the entire simulation region.

The spatial distribution of Qv at level 850mb at 30th analysis time 051,400. The shade represents the distribution of Qv (g/kg), while the contours delineate the differences in Qv with an interval of 1 g/kg. Specifically, Fig. 6 ( a ) depicts the true state, 6 ( b ) shows CTRL, 6 ( c ) represents ENS, 6 ( d ) displays the results of daUVTZTD, 6 ( e ) illustrates the increments between the daUVTZTD and the ENS simulations, and 6 (f). depicts the misfits between the daUVTZTD and the true state.

As the assimilation cycles progress, an increasing amount of information is assimilated into the background field. With more observations being incorporated, the analysis field progressively approaches the true field. At the 30 th assimilation cycle, all available observations have been assimilated, resulting in the analysis field being the closest approximation to the true field (see Fig.  5 ). After a subsequent 20 h forecast without DA, the T and Qv patterns of the control run are significantly different from the true state, and the cyclone is still weaker than in the true state. T of the ensemble run near the center is lower than the true state, and the cyclone remains weaker than that in the true state. The analysis state is still closer to the true state than CTRL and ENS, but the misfits between daUVTZTD and the true state are larger than those at the time of final assimilation (figures omitted). In the absence of observation constraints, the simulated values in the assimilation experiments gradually deviate from the real values. However, despite this deviation, the assimilation experiments consistently outperformed the control state over time. For the limited spread of analysis ensemble, the 40 ensemble realizations for the daUVTZTD show similar behavior. It is worth noting that at 051,400, several isolated points emerge in both the T (Fig.  5 f) and the Qv (Fig.  6 f) fields, particularly in the surrounding area outside the cyclone edge.

In addition, we assess the impact of the DA on rainfall, focusing on the 24-h accumulated precipitation. At 051,400, the maximum precipitation in the control run (Fig.  7 b) is less than that of the true state (Fig.  7 a). The patterns of their distribution are notably distinct. The ensemble run (Fig.  7 c) exhibits an even lower rainfall level than the control run, and it continues to miss the cyclonic pattern centered around its core. In line with the findings for other variables, the distribution of rainfall in the analysis state (Fig.  7 d), aligns most closely with the true state.

The spatial distribution of 24h cumulative precipitation (in mm) at the 30th analysis time 051,400. Shown are the ( a ) true state, ( b ) CTRL, (c) ENS, ( d ) daUVTZTD.

Table 3 shows that the mean RMSEs of Qv, T, U, and V in all vertical levels, as well as 24 h rainfall for the ensemble forecast (ENS) are similar to those of the single control run (CTRL) at the initial time. At the 1st DA cycle, RMSEs for the ensemble forecast are smaller than those of the control run, and the RMSEs for the analysis are smaller than those for the ensemble run. At the 30st DA cycle—the final assimilation time—the RMSEs for daUVTZTD are the smallest among all experiments and assimilation times. After 20-h free forecast, the RMSEs for the ensemble forecast are still smaller than those for the control run. The RMSEs for assimilation run daUVTZTD are smaller than those for ENS, but larger than those for the analysis at the 30st DA cycle. In contrast to the results from previous studies 47 , 48 , the RMSEs in our study show significant reductions by the DA, primarily attributed to the inclusion of additional conventional data and a higher assimilation rate of GNSS data. These enhancements have collectively contributed to reducing the forecast errors and increasing the accuracy of our simulations.

Discussion and conclusions

In this study, a tropical cyclone twin experiment was conducted to evaluate the effect of assimilating conventional and GNSS data in different configurations. The assimilation results provide valuable insights into the performance of the ensemble Kalman filter LESTKF applied in WRF-PDAF, the developed GNSS operator, the impact of GNSS DA on the model forecast accuracy, and the behavior of the analyzed fields. A suitable localization distance needs to be selected to balance the assimilation impact with the preservation of meso-scale flow patterns. Specifically, the localization distance chosen for this study was determined based on the model dynamics, rather than solely relying on numerical values of the RMSE. This decision was made due to the evident correlation between temperature and wind in the idealized scenario, which provides a more physically meaningful basis for selecting the localization distance. However, the localization distance is case-dependent and not a general value. In practical applications, a typical localization radius of 1000 km is commonly used for global modeling and data assimilation systems 49 . However, for convective weather systems utilizing high-resolution models and observations, a much shorter radius of 10 km has been found to be more appropriate 50 . Nonetheless, experiments with real data conducted by Dong et al. (2011) suggest that a smaller localization radius is necessary to achieve better analysis accuracy with denser observing networks. Periáñez et al. 51 determined an optimal localization radius through heuristic arguments, assuming a uniform observing network, and also recommend using a smaller localization radius for denser observations. Kirchgessner et al. 52 proposed a scheme for adaptive localization without tuning. These studies indicate a potentially complex relationship between observing networks and localization radii. However, in real-world applications, the localization radius may be influenced by other factors. For instance, it is known that localization affects the balance in the model state, and a longer localization radius will have a smaller impact on the balance. Consequently, one might prefer a longer localization radius in multivariate assimilation applications. Additionally, when assimilating real observations, biases can occur, and the observation error covariance matrix might be inaccurately estimated. It remains unclear to what extent these factors necessitate adapting the localization radius to achieve overall optimal assimilation results. Therefore, tuning is still necessary. Perhaps, the effective spatial resolution 53 of the model 54 could be applied to determine the localization. Corresponding to " PW and ZTD Observation operators ", assimilating PW and ZTD yields similar results. This proves that the construction of the assimilation operator and the implementation of the assimilation process are reliable. From another perspective, different operators of PW and ZTD caused differences in the DA performance. The DA results are influenced by the magnitude of the observation errors. In real cases, the superiority of either also depends on the data quality as described in " Cycled GNSS DA ".

This study outperforms previous research 55 , 56 , 57 , 58 , 59 , 60 by achieving the most accurate assimilation results, evidenced by the lowest RMSEs and the most similar distributions with the true state. This superior performance can be attributed to the utilization of high-fidelity synthetic observations, which are not only precise but also have a high spatial resolution, characterized by a full 100% density on model grids. However, assimilating observations at lower density can still have a significant effect, at least for conventional observations as was shown by Shao and Nerger 26 . The analysis step significantly improves the accuracy of the model forecast compared to the control run or ensemble forecast. Assimilating the conventional observations U, V, and T, leads to increments that align with expected atmospheric features, such as cyclone patterns in this ideal case. Compared with previous studies, multiple observations, such as T, U, V, as well as PW and ZTD, which are derived from GNSS data, were assimilated using the LESTKF. This generally improved the forecast accuracy, compared to assimilating either conventional or GNSS data. The lower RMSEs compared to previous studies show the effectiveness of the applied assimilation method and the selected observed variables.

The key findings are significant as they contribute to the understanding of the impact of assimilating ground-based GNSS data on the forecast accuracy of tropical cyclone. They highlight the effectiveness of the assimilation process in improving the accuracy of the forecast and provide insights into the behavior of analyzed fields in a tropical cyclone. Additionally, the study identifies the benefits of assimilating multiple observation types. Assimilating ground-based GNSS data, such as PW and ZTD, offers several benefits in the tropical cyclone simulation. Ground-based GNSS data provide valuable information about atmospheric water vapor and can improve the representation of moisture fields in numerical weather prediction models. Assimilating ground-based GNSS data can hence improve the initialization of water vapor fields, and help capture mesoscale features related to atmospheric moisture. The findings of this study highlight the potential applications of assimilating ground-based GNSS data in improving weather forecasts in marine areas and demonstrate that it is essential to establish real ground-based GNSS observation stations over the ocean. By understanding the behavior of analyzed fields and the impact of assimilation, researchers and meteorologists can enhance forecast accuracy.

In conclusion, this research demonstrates the effectiveness of ground-based GNSS data assimilation using the ensemble Kalman filter LESTKF in improving tropical cyclone simulation accuracy. The findings emphasize the benefits of assimilating multiple observation types, and the potential applications of assimilating ground-based GNSS data. The construction of ground-based GNSS observation stations over the ocean is highly promising and essential. The utilization of the flow-dependent, cross-variable background error covariances in the LESTKF enables us to fully leverage the advantages of this data. By further advancing the LESTKF and incorporating GNSS operators in the data assimilation process, we can enhance simulation capabilities for tropical cyclones and have the opportunity to provide more accurate and reliable predictions for various applications, including network design, weather monitoring, disaster management, and climate studies. However, the study should acknowledge potential limitations, such as the use of an idealized twin experiment with synthetic observations. Representation and model errors are not present here. The inherent non-Gaussian nature of atmospheric water variables are also not considered. Future research directions may involve investigating alternative data assimilation methods, in particular nonlinear methods, to address the limitations and challenges encountered. Investigating advanced techniques, such as adaptive localization or ensemble-based adaptive observation strategies, can potentially enhance the assimilation process.

Data availability

Dataset can be download at https://doi.org/ https://doi.org/10.5281/zenodo.10335684 .

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Acknowledgements

The calculations for this research were conducted on the high-performance computer of the Alfred Wagner Institute.

Changliang Shao (No. 202105330044) is supported by the China Scholarship Council for one-year research at AWI, the Joint Open Project of KLME & CIC-FEMD, NUIST (KLME202407) and Key Laboratory of Space Ocean Remote Sensing and Application, Ministry of Natural Resources (202402001).

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Changliang Shao

Alfred-Wegener-Institut, Helmholtz-Zentrum Für Polar- Und Meeresforschung (AWI), Bremerhaven, Germany

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Changliang Shao and Lars Nerger planned the campaign; Changliang Shao performed the experiments, analysed the data and wrote the manuscript draft; Lars Nerger reviewed and edited the manuscript.

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Shao, C., Nerger, L. Assimilation of ground-based GNSS data using a local ensemble Kalman filter. Sci Rep 14 , 21682 (2024). https://doi.org/10.1038/s41598-024-72915-w

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Winter season outdoor cultivation of an autochthonous chlorella -strain in a pilot-scale prototype for urban wastewater treatment.

1. Introduction

2. materials and methods, 2.1. microalgae, 2.2. wastewater, 2.3. experimental design, 2.4. environmental parameters, 2.5. growth rate of algae and ph of culture substrates, 2.6. psii maximum quantum yield of algae, 2.7. photosynthetic pigments of algae, 2.8. characteristics of the cultivation substrate, 2.9. light microscopy of algae samples for exopolysaccharides detection (eps), 2.10. data analysis, 3.1. environmental parameters, 3.2. algal growth aspects, 3.3. psii maximum quantum yield and photosynthetic pigments content of algae, 3.4. nutrients removal from the cultivation substrate and e. coli load, 3.5. morphological aspects of algae, 4. discussion, 5. conclusions, supplementary materials, author contributions, data availability statement, acknowledgments, conflicts of interest.

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Benà, E.; Giacò, P.; Demaria, S.; Marchesini, R.; Melis, M.; Zanotti, G.; Baldisserotto, C.; Pancaldi, S. Winter Season Outdoor Cultivation of an Autochthonous Chlorella -Strain in a Pilot-Scale Prototype for Urban Wastewater Treatment. Water 2024 , 16 , 2635. https://doi.org/10.3390/w16182635

Benà E, Giacò P, Demaria S, Marchesini R, Melis M, Zanotti G, Baldisserotto C, Pancaldi S. Winter Season Outdoor Cultivation of an Autochthonous Chlorella -Strain in a Pilot-Scale Prototype for Urban Wastewater Treatment. Water . 2024; 16(18):2635. https://doi.org/10.3390/w16182635

Benà, Elisa, Pierluigi Giacò, Sara Demaria, Roberta Marchesini, Michele Melis, Giulia Zanotti, Costanza Baldisserotto, and Simonetta Pancaldi. 2024. "Winter Season Outdoor Cultivation of an Autochthonous Chlorella -Strain in a Pilot-Scale Prototype for Urban Wastewater Treatment" Water 16, no. 18: 2635. https://doi.org/10.3390/w16182635

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