Researchers sometimes shy away from evapotranspiration (ET) measurements because calculating ET involves several parameters that can be difficult to measure or estimate.
Systems that make these measurements can be expensive, difficult to install, and finicky to maintain. However, knowing ET is key to understanding what’s happening to the water in your system. In this article, we’ll cover the different methods of measuring ET—including the level of effort and error inherent in each—and how to avoid costly pitfalls.
Consider this: on a clear sunny day, a well-watered crop such as rice can lose between 7 and 10 millimeters of water. For a single day growing period, that’s a lot of lost water.
Calculating evapotranspiration can tell you how much water these rice plants lose in a day
When you know how much water is being lost, you can:
Replenish water with irrigation
Explore phenotype water use
See indications of drought
Extrapolate biomass production
Use the data for growth models
Method 1: Measuring Evapotranspiration Directly
To measure evapotranspiration directly, you need to know the ability of water vapor to move from inside the leaves of the canopy (the starting point) to the atmosphere (the ending point).
Equation 1: Equations for and related to calculating evapotranspiration using direct measurements
Equation 1 seems simple, but the conductance to vapor depends both on the conductance of vapor in the air (which we can calculate with a turbulent transport equation) and the conductance to vapor of the surface or canopy.
Canopy conductance changes over time, depending on several factors that cause stomata to open and close. Additionally, we need to know the leaf temperature—a measurement that is possible, but difficult. Even the “simple” approach is not so simple to execute. We need a better solution.
Is there a way to measure evapotranspiration directly? The answer is yes: using an Eddy Covariance System. The Campbell Scientific Eddy Covariance System measures the up and down eddies moving above a given system.
Eddy Covariance System from Campbell Scientific
With these data we can find out how much water vapor, CO2, or trace gases are moving into and out of that ecosystem. Eddy Covariance Systems such as these are accurate, but they have some key drawbacks:
Cost. The increased features of an eddy covariance system push it beyond the budget of many researchers. Time. Getting quality data requires time-intensive installation, maintenance, and effort.
Method 2: Measuring Evapotranspiration Indirectly
Evapotranspiration can be measured indirectly using the residual of an energy balance or energy budget analysis. Indirect measurement comes with lower cost, but it has associated assumptions that limit its accuracy without the proper sensors and analysis.
Equations for calculating evapotranspiration indirectly
The continuity equation (or an energy balance) says that the net radiation coming into a system (Rn) minus all the sources or sinks of radiation in that system—sensible heat flux (H), latent heat flux (λE), and soil heat flux (G)—should sum to zero.
Figure 5: The energy balance of evapotranspiration.
Evaporation is part of that equation, so rearranging it provides a simple equation that says that the evaporation should be related to the net radiation, sensible heat flux, and soil heat flux divided by the latent heat of vaporization (λ).
However, the radiation term (Rn) includes properties that are difficult to calculate. We have to know something of the radiation coming into our system, but also, importantly, we have to know the radiation that’s emitted by that system (a canopy, for instance). The basic assumption in evapotranspiration is that energy and mass flow are connected. If we know all other forms of energy movement, latent heat flux is the residual; therefore, we can solve for evaporation.
Howard Penman simplifies the equation
Solving for evaporation is more complex than our summary suggests, which Howard Penman of the Rothamsted Research Station in the United Kingdom knew many years ago. His understanding of the link between energy balance and evaporation led him to write a famous paper in 1948 on natural evaporation from open water, bare soil, and grass.
Penman produced an equation based on this energy balance (or energy budget) that could analyze evaporation based on the other parts of the energy balance. But one of the problems with this paper was that it included an “<span style=”color: #099531; font-weight: bold;”>f</span>” value, an empiricism that tried to account for the things that he couldn’t solve for in the equation. As a result, Penman’s equation worked quite well for Rothamsted and a few other areas, but it wasn’t universally applicable.
Several years after Penman’s paper, a scientist named John Monteith made a critical step forward in our understanding of evapotranspiration. Dr. Monteith recognized the importance of adding heat and vapor conductance to Dr. Penman’s equation. Before John Monteith, no one recognized the importance of understanding how water vapor moves from inside the leaf to the outside of the leaf and into the atmosphere, or understanding how sensible heat moves from the canopy to the air.
The first page of Howard Penman’s landmark paper, “Natural evaporation from open water, bare soil, and grass“, Proceedings of the Royal Society of London (1948) A193:120–146. Dr. Penman spent nights in the shed at the research station with an alarm clock to wake him every hour so that he could take different measurements. This story is a reminder to today’s researchers to be grateful for their data loggers.
Dr. Monteith combined these ideas of vapor conductance into a few terms inside this equation. The equation for (gv) relates the canopy and boundary layer (the air), as well as the conductance of heat to the boundary layer. Figure 6 not only recognizes the original heat capacity over the latent heat of vaporization, but it also multiplies that by a ratio of the conductance to heat to the conductance of vapor, which gives us our psychrometer constant (λ*). This equation recognizes the adjustments we have to make when things are out of a unity proportion.
Figure 6: The Penman-Monteith Equation.
This new equation was exciting. John Monteith understood the importance of heat and vapor conductance in evapotranspiration. Removing the empiricism of Penman’s original equation made it a practical solution for a broad set of locations.
Applying the Penman-Monteith equation to calculate evapotranspiration
When you look at this equation, two questions come to mind:
Does the Penman-Monteith equation work everywhere?
What happens if you don’t have values for some aspects of the equation?
While the Penman-Monteith equation may require some simplifications to measure evapotranspiration, it is applicable for most locations. And, when some values aren’t available, there are ways to make estimates.
Figure 7: Diagram of energy exchanges in evapotranspiration.
Let’s consider some of these practical aspects of the Penman-Monteith. This energy-balance method of calculating evapotranspiration is the basis for the ATMOS 41 from METER and the ClimaVUE50 from Campbell Scientific. Using one of these Penman-Monteith based systems offers some significant benefits over other methods. First, it’s far more affordable than calculating evapotranspiration directly. Additionally, these systems are easier to maintain and can be set up in just a few minutes.
Of course, these benefits come with challenges:
The ATMOS 41 and ClimaVUE50 rely on some assumptions that have the potential to affect accuracy. Figure 7 shows what these systems measure for incoming solar radiation. But they’re not going to measure the long-wave radiation—both downwelling and upwelling—as represented by the black arrows, so we have to make an assumption about that value.
The ATMOS 41 and ClimaVUE50 also require an ongoing canopy assessment of your particular canopy at daily or hourly intervals. This system will indicate the evapotranspiration from a reference canopy, which must be converted for your canopy using a crop coefficient.
The Penman-Monteith equation also requires measurements that may be beyond what we can measure with a typical weather station.
Net radiation converted from solar radiation
Soil heat flux over a day
Canopy conductance
Using a complete suite of instruments, we can easily estimate evapotranspiration. We may not have a perfect measurement of evapotranspiration, but we would come close.
A four-band net radiometer, like the SN-500 Net Radiation Sensor from Apogee, collects both upwelling and downwelling shortwave radiation and long-wave radiation, which gets us a long way toward an accurate measurement of net radiation, which is a key piece of this analysis.
An all-in-one weather station like the ATMOS 41 or ClimaVUE50 can measure total solar radiation, windspeed, humidity, and air temperature, corrected for solar radiation and windspeed.
A soil heat flux plate allows us to get estimates of soil heat flux across the day.
Simplifying to potential evapotranspiration in FAO 56
Even with all of these instruments, we have to make some assumptions or simplifications. The FAO 56 formulation from the Food and Agriculture Organization of the United Nations is one such simplification.
Figure 8: Simplifying Penman-Monteith to FAO 56.
In this method, you can see how we’ve simplified some of the expressions within the Penman-Monteith equation. Figure XX provides an equation to estimate evapotranspiration of an idealized grass canopy. The idealized grass is 12 centimeters high and well-watered. If we assume our weather station is mounted at two meters, then the boundary layer conductances to heat and to vapor become a constant of 0.2 multiplied by the wind speed. We do not need to use the turbulent transport equation from Figure XYZ.
The conductance to vapor is also simplified here. We assume the canopy conductance is about 0.6 moles per meter squared per second. That’s greater than the 0.2 moles per meter squared per second conductance typical of an individual, well-watered leaf. As a rule of thumb, we can multiply the individual leaf conductance value by 3 to get a canopy conductance to find the conductance to vapor, which includes the canopy conductance and the boundary layer conductance. We combine them together in FIGURE ABOVE to get an overall gv as a function of the wind speed. The same is then done for the psychrometer constant (λ*). The multiplier includes the wind speed.
The other part that is estimated is the net radiation. Looking at the net radiation expression in Figure XYZ, our solar radiation value is multiplied by our constant. Then we subtract things related to the average temperature, the vapor pressure, and a function of cloudiness. This simplification accounts for the long-wave radiation portion and is based on lots of experiments that tie the net radiation to the total incoming solar radiation.
Why does FAO 56 work? Because we multiply the result by our crop coefficient to adjust it to our specific need. Using the coefficient of a specific surface—like the 12-centimeter grass we mentioned above—and other values like the canopy conductance and net radiation, we can make this estimate of evapotranspiration.
FAO 56 Penman-Monteith equation
After following the FAO 56 formulation, we are left with this version of the Penman-Monteith Equation.
Figure 9: Penman-Monteith equation, with parameters defined
Notice this constant of 0.408. That number is one divided by λ, or the latent heat of vaporization. Two other values described in the list of parameters are Cn and Cd, or the numerator constant and the denominator constant. These are related to some of the canopy simplifications mentioned earlier–essentially a &lquot;lookup table&rquot; of the values that would be used in each of the following cases:
a short reference or a tall reference
a daily or hourly calculation
a daytime measurement or night measurement
Different formulations of the Penman-Monteith
There are two common formulations of the Penman-Monteith Equation:
FAO 56, described above, which was designed to create a consistent and transparent basis for a globally valid standard for crop water requirement calculations.
While there is little to no difference between these two formulations, different companies will choose one to suit particular applications. ZENTRA Cloud from METER provides a daily calculation based on FAO 56, while Campbell Scientific products use the ASCE hourly calculation.
Daily and hourly calculations rarely show significant variation, unless there is substantial variation in one or more of the measurements in less than a day.
Measurements and Models
Looking down the list of parameters in the Penman-Monteith equation, it’s notable that only two are measured directly: temperature and wind speed. The rest of the parameters are modeled to one degree or another. Some of them, like saturation vapor pressure and vapor pressure are straightforward relationships based on temperature and relative humidity. Others, especially net radiation, are heavily modeled.
So, which of these measurements are the most important? Where should we be the most concerned about accuracy? Let’s take a look at how overall evapotranspiration numbers respond to various input errors.
Figure 10: Evapotranspiration measurement sensitivity to errors in inputs.
In Figure 10, three measurements are held constant while varying one other. The time (midday in summer) and location (mid-latitude) of the measurement are held constant. In this figure, the steeper the slope, the more sensitive the calculation of evapotranspiration is to that measurement.
Notice that the steepest slope is incoming radiation, as measured by a pyranometer, indicating that incoming radiation is the most important parameter. Because these measurements interact, there are some other generalizations that we can make:
If wind decreases, or relative humidity increases, then the radiation becomes that much more important.
If radiation decreases, then wind speed has larger influence on the calculation of evapotranspiration.
Some commonly asked questions about evapotranspiration
What percent of irrigation water given based on daily evapotranspiration measurements is really used for the plant?
From the natural systems standpoint, the answer to this question varies tremendously based on variables like plant type, environment, surface wetness of the soil, and canopy closure.
Let’s say we have a completely closed potato canopy, watered by a center pivot irrigation. Some water will evaporate off the leaves. But in this scenario, it is possible that around 90% of the water given actually makes it into the soil and is accessed by the roots. In a desert environment with a sparse canopy and different plants, that number would be completely different.
Where do you recommend installing the weather station to use this type of evapotranspiration method in an agricultural crop?
Some general recommendations:
Mount your sensors at two meters or close to the expected maximum height of the canopy.
Be aware of where the prevailing winds are coming from, and choose the downwind side. You want the sensors to be in contact with the wind that is moving the eddies of your canopy of interest.
Note that a local weather station, even if it’s within a few kilometers of your field, can have very different values from your specific site. That’s why site-specific measurement is critical to getting accurate data.
What are some suggestions you might have for those trying to measure evapotranspiration in settings like open water, greenhouses, and vineyards?
Happily, evapotranspiration is one of the most intensely studied topics in environmental biophysics literature. The following journal articles address some evapotranspiration in specific circumstances:
Blonquist Jr, J. M., R. G. Allen, and Bruce Bugbee. “An evaluation of the net radiation sub-model in the ASCE standardized reference evapotranspiration equation: Implications for evapotranspiration prediction.”Agricultural water management 97, no. 7 (2010): 1026-1038. (Article link)
Fuchs, Marcel, Ehud Dayan, David Shmuel, and Isaac Zipori. “Effects of ventilation on the energy balance of a greenhouse with bare soil.” Agricultural and Forest Meteorology 86, no. 3-4 (1997): 273-282. (Article link)
Ham, J. M. “Uncertainty analysis of the water balance technique for measuring seepage from animal waste lagoons.” Journal of environmental quality 31, no. 4 (2002): 1370-1379. (Article link)
Kimball, Bruce A., Kenneth J. Boote, Jerry L. Hatfield, Laj R. Ahuja, Claudio Stockle, Sotirios Archontoulis, Christian Baron et al. “Simulation of maize evapotranspiration: an inter-comparison among 29 maize models.” Agricultural and Forest Meteorology 271 (2019): 264-284. (Article link)
How do you tie evapotranspiration to in-soil measurements?
One of the things that we see as a critical step forward in the future is tying evapotranspiration with soil measurements. When we use water potential, we can see how the plants are doing in the soil. Adding some remote sensing, tied in with satellite data, we can locate where we should put sensors to evaluate stress. Evapotranspiration measurements can work together with in-soil measurements to get the best overall assessment of plant health.
Additional Resources
We also recommend taking a look at our other webinars and articles on weather stations to learn more about sensor options for calculating evapotranspiration.
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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
