Chapter_4 (1)

Introduction I Evapotranspiration (ET) is the processes by which liquid water at the Earth’s surface is transformed into water vapor. Direct transformation from liquid to vapor over a water surface or bare soil is called evaporation , while vaporization of water due to a plant’s metabolism and growth is called transpiration . ET, though a relatively slow flux, is one of the most important elements of the hydrologic water cycle. ET controls water mass and energy transfer within land-vegetation-atmosphere continuum. Additionally, ET contributes significantly to freshwater losses in water resources and agricultural systems. Therefore, effective management of ET can significantly improve water and food security. ET is primarily a water vapor mass flux and thus its measurement is not trivial, especially at the large scale. ET requires the following ingredients to occur: - An energy source (e.g., Sun’s radiative energy, wind kinetic energy) - Liquid/solid water (e.g., lakes, soil moisture, snow-covered surfaces, etc.) - A transport mechanism (e.g., molecular diffusion, convection, conduction) Figure 1: Schematic of ET (left), shade balls dumped into a reservoir to mitigate evaporation (middle) and a dried agricultural field due to excessive evaporation (right). Evapotranspiration Ardeshir Ebtehaj 1

Transport Mechanisms I Diffusion or conduction: Diffusion of water mass or conduction of heat or momentum are due to random molecular motion . The transfer occurs from areas of higher concentration of the variable of interest to areas of lower concentration. Heat, momentum and mass molecular transport mechanisms are typically explained via conduction, viscosity, and diffusion coefficients , respectively. Advection: Transfer of heat, momentum or mass due to the bulk motion of fluid parcels . Turbulent diffusion: Turbulence is irregular swirls of fluid motion. In atmosphere, it is mainly generated by mechanical shear due to wind velocity or thermally driven buoyant forces , leading to heat, mass, and momentum transfer. Turbulent diffusion is similar to molecular diffusion; however, in turbulent diffusion we are dealing with random motion of the fluid parcels beyond the effects of molecular diffusion. Convection: Combination of advection and turbulent diffusion in transfer of heat, mass and momentum. The amount of heat, moisture, and momentum transport in the atmosphere are measured by their fluxes. A flux is the transfer of a quantity per unit area per unit time. Evapotranspiration Ardeshir Ebtehaj 4

Transport Mechanisms IV Heat Flux Fourier’s Law of Conduction: H = - D H dT dz = - ρ a c p α dT dz [W m -2 ] D H : thermal conductivity [W m -1 K -1 ] T : temperature [K] z: distance [m] c p : specific heat [J kg -1 K -1 ] α : thermal diffusivity [m 2 s -1 ] ρ a : air density ≈ 1.3 [kg m -3 ] Turbulent Sensible Heat Flux: H = - ρ a c p K H dT dz [W m -2 ] K H : thermal eddy diffusivity [m 2 s -1 ] Note: K H α Evapotranspiration Ardeshir Ebtehaj 7

ABL Stability II Why is stability of ABL important? When the atmosphere is stable , the turbulent moisture and heat fluxes are suppressed , whereas in unstable atmospheres, they are enhanced . Therefore, ET is a function of atmospheric stability condition. There are two main turbulent transport mechanisms that drive ABL instability: Static instability: Buoyancy driven turbulence (buoyancy wind shear kinetic energy ) Dynamic instability: Wind shear driven turbulence (wind shear buoyancy kinetic energy) How can we characterize stability of ABL? There are several dimensionless parameters that are commonly used to define atmospheric stability from data. The gradient Richardson number is a dimensionless parameter encoding the ratio of the buoyancy versus shear production of energy of tubulence: R i = g Tv . ∂ Tv ∂ z ( ∂ u ∂ z ) 2 = Buoyant turbulence production Shear turbulence production where z denotes vertical direction, T v is the virtual temperature, g is gravitational acceleration, and u is the average wind velocity in the wind direction. The values of R i are interpreted as Statically Unstable: R i < 0 Neutral Condition: R i = 0 Statically Stable: R i > 0 Evapotranspiration Ardeshir Ebtehaj 10

ASL Wind Profile I Log Law in Neutral ABL In order to understand ET fluxes from the Earth’s surface to the ASL, we must have an understanding of the mean wind velocity profile as it is the main driver of the turbulent diffusive fluxes. It has been (theoretically) shown that the average velocity profile in a neutral ASL follows a logarithmic shape as follows: u = u * κ ln z z 0 . where z 0 [m] is the momentum roughness length , u * [m s -1 ] is the friction velocity , and κ 0 . 41 is the Von Karman constant . Additionally, over a canopy, where the roughness elements are densely packed, the wind velocity becomes theoretically zero at height d + z 0 , where d is called the zero-plane displacement height (Figure 4). As a result, we have u = u * κ ln z - d z 0 . Figure 4: Typical logarithmic variation of a vertical wind profile in neutral ASL over an almost flat (left) and densely packed canopy (Credit: Stull, 1988) Evapotranspiration Ardeshir Ebtehaj 13

ASL Wind Profile IV Atmospheric stability also affects the profile of moisture and temperature. There are several parameterizations that correct for the temperature φ H and moisture φ E profiles under non-neutral atmosphere. Here, we focus on the formulation by Dyer and Hicks (1970) as follows: Correction factors for non-neutral atmosphere φ 2 M = φ H = φ E = (1 - 16 R i ) - 0 . 5 = (1 - 16 ζ ) - 0 . 5 R i < 0 or ζ < 0 ( unstable ) φ M = φ H = φ E = 1 1 - 5 R i = 1+5 ζ 0 ≤ R i ≤ 0 . 2 or ζ > 0 ( stable ) Since we have τ = ρ a K M d u / dz , u 2 * = τ/ρ a and d u / dz = u * κ ( z - d ) φ M , we can conclude, K M = κ u * ( z - d ) φ - 1 M . The same derivation holds for the eddy diffusivity of heat and moisture fluxes for non-neutral atmosphere as follows: K H = κ u * ( z - d ) φ - 1 H K E = κ u * ( z - d ) φ - 1 E , which can be used for computation of the turbulent heat and moisture fluxes under stable or unstable atmosphere. Obviously, the correction factors are equal to one for a neutral atmosphere. Evapotranspiration Ardeshir Ebtehaj 16

ASL Evaporation and Heat Fluxes III Similarly, we can also derive an equation for the sensible heat flux near the land surface as follows: Land Surface Heat Flux in Neutral Condition H = ρ a c p T 0 - T ( z ) r ah r ah = ln ( z - d z 0 m ) ln ( z - d z 0 h ) κ 2 u ( z ) where r ah is called aerodynamic heat resistance [s m -1 ] . Estimating the values of z 0 v and z 0 h require profile data for moisture and heat. These roughness parameters tend to be more variable than z 0 m . Reynold’s analogy allows us to assume z 0 v = z 0 h , and if there is no available heat or moisture profile data, then we may assume z 0 v = z 0 h = 0 . 1 z 0 m (Allen et al. 2005). The reason for the difference is that rough surfaces dissipate momentum more efficiently than heat and moisture fluxes. Land Surface Heat/Moisture Flux in Non-neutral Condition (Thom 1975) H = ρ a c p T 0 - T ( z ) r ah E = ρ a q 0 v - q v ( z ) r av Evapotranspiration Ardeshir Ebtehaj 19

ASL Evaporation and Heat Fluxes IV As we explained, the heat and moisture fluxes are increased (decreased) for unstable (stable) atmosphere and the correction factors are obtained through the φ ( · ) functions. Land Surface Heat/Moisture Flux in Non-neutral Condition (Thom 1975) r ah = r ah × ( φ H φ M ) r av = r av × ( φ E φ M ) Land Surface Heat/Moisture Flux in Non-neutral Condition (Businger 1971) r ah = ln ( z - d z 0 m ) - ψ M ( ζ ) ln ( z - d z 0 h ) - ψ H ( ζ ) κ 2 u ( z ) r av = ln ( z - d z 0 m ) - ψ M ( ζ ) ln ( z - d z 0 v ) - ψ E ( ζ ) κ 2 u ( z ) ψ H ( ζ ) = ψ E ( ζ ) = - 5 ζ ζ > 0 (stable) 2 ln ( 1+ x 2 2 ) ζ < 0 (unstable) ψ M ( ζ ) = - 5 ζ ζ > 0 (stable) 2 ln ( 1+ x 2 ) + ln ( 1+ x 2 2 ) - 2 tan - 1 ( x ) + π 2 ζ < 0 (unstable) x = (1 - 16 ζ ) 0 . 25 note: x is in radian. Evapotranspiration Ardeshir Ebtehaj 20

ASL Evaporation and Heat Fluxes V In Summary: We defined moisture and heat fluxes near the soil in terms of more easily obtainable parameters as follows: Aerodynamic Method for Computation of Evaporation Flux: E = ρ a q v 0 - q va r av [ kg m -2 s -1 ] , q v 0 : mean near surface specific humidity [kg-water kg-air -1 ] q va : mean air specific humidity [kg-water kg-air -1 ] r av : aerodynamic vapor resistance [s m -1 ] Note: By definition, the latent heat flux is LE = L v E [W m -2 ]. Sensible Heat Flux: H = ρ a c p T 0 - T a r ah [W m -2 ] , T 0 : mean surface virtual potential temperature [K] T a : mean near surface air temperature [K] r ah : aerodynamic heat resistance [s m -1 ]. To estimate the above fluxes, we need: B Meteorological state variables: u , T a , and q va –from models or observations. B Surface state variables: T 0 and q 0 –from models or observations. B Surface parameters: e.g., z 0 m , z 0 h , z 0 v , the displacement height ( d )–from observations and calibration studies. To reiterate, typically we assume r ah = r av and that z 0 v = z 0 h = 0 . 1 z 0 m , while z 0 m = 0 . 1 h when do not have any other prior data. Evapotranspiration Ardeshir Ebtehaj 21

ASL Evaporation and Heat Fluxes VI Soil Moisture Effects on ET Flux: For a saturated soil surface or open water, the evaporation is at its potential rate ( E p ) and it is reasonable to assume that q v 0 = q vs (saturated specific humidity). However, the soil moisture water deficit and its implications on the rate of evaporation fluxes may be characterized as follows: E = β ( θ ) E p θ : soil moisture content [cm 3 cm -3 ] β ( θ ) : soil moisture correction multiplier, 0 ≤ β ( θ ) ≤ 1 β ( θ ) = 1 θ ≥ θ fc θ - θ wp θ fc - θ wp θ wp ≤ θ ≤ θ fc 0 θ ≤ θ wp θ fc : soil moisture content at field capacity [cm 3 cm -3 ] θ wp : soil moisture content at wilting point [cm 3 cm -3 ] Evapotranspiration Ardeshir Ebtehaj 22

Canopy Effects on Evaporation I Transpiration in ABL and ET fluxes Plant’s synthesize visible solar energy (photosynthesis) for their metabolism. Throughout this process, water is evaporated by areal parts of the plant such as leaves, stems, etc. The process of water vaporization from soil to atmosphere through plant’s metabolism is called transpiration . On plant’s leaves there are pores called stomata that allow plants to uptake CO2 for photosynthesis and release oxygen and water vapor to the atmosphere through the process of transpiration, which reduces the plants temperature. The process and rate of transpiration are controlled by the dynamics of stomata. Figure 7: Pathway for water loss from surface of a leaf (Credit: Jones, 1983) Evapotranspiration Ardeshir Ebtehaj 23

Canopy Effects on Evaporation II Stomata respond to environmental forcings (e.g., air temperature, humidity, wind speed, sunlight intensity, soil water supply, etc.) by changing their opening size . When plants are under stress, typically stomata close their aperture to protect the plants against excessive water loss and wilting. As a general rule, larger leaves have more stomota which increases the ET rate from the leaves. Some plants have a waxy cuticle that reduces ET from the leaf surface (e.g., Xerophyte plants) such as the Cactus family. As noted, environmental stress affects plant’s transpiration rate as follows: - Increase of light (net radiation) increases the transpiration up to an asymptotic limit - Transpiration increases and reaches to a maximum as a function of optimal temperature. - Increase of water vapor pressure deficit often decreases the ET. - Increase of soil moisture increases the rate of transpiration Note that from a mass transport point of view, moisture gradient is the main driver of the plant’s transpiration . Inside of the plant’s leaf, the air is saturated, while it is likely that the outside air is sub-saturated. In general, plants naturally attempt to increase their survivability in response to environmental stresses. The guard cells that control the size of the stomatal openings play a very critical and complex regulatory role. For instance when temperature increases above the tolerance limits of the plant, the stomatal openings start to reduce their sizes to reduce the rate of evaporation and increase the chance of survival. This complex regulatory role is often simplified and parameterized through the canopy resistance factors . Evapotranspiration Ardeshir Ebtehaj 24

Canopy Effects on Evaporation III The canopy resistance can be modeled based on the stomatal resistance as follows: Canopy resistance r c : r c = r s LAI [s -1 m] r s : stomatal resistance at leaf level [s -1 m] r c : canopy resistance [s -1 m] LAI: Leaf Area Index [-] LAI is the one-sided green leaf area per unit ground surface area and ranges from 0 < LAI < 10, where the upper bound refers to dense conifer forests. Figure 8: Schematic showing the concept of the Leaf Area Index (LAI). Evapotranspiration Ardeshir Ebtehaj 25

Canopy Effects on Evaporation IV As mentioned, there are many forcings that impact stomata behavior at leaf level and thus the r s . One can model stomata resistance at a leaf-scale as follows: r s = r min f Rs · f Ta · f δ e · f θ where r min is the minimal stomatal resistance determined from experiments on the plant. The forcing parameters ( f ) may be parameterized as follows: Forcings affecting the stomatal resistance r s Radiation: f Rs = 1 . 105 R is 1 . 007 R is +104 . 4 , where R is is incident shortwave radiation [W m 2 ] Air Water Vapor Deficit: f δ e = 1 - 0 . 00023 δ e , where δ e = e s ( T a ) - e ( T a ) [N m -2 ] Temperature: f Ta = Ta (40 - Ta ) 1 . 18 690 , where 0 ≤ T a ≤ 40 [ ◦ C] Soil Moisture: f θ = 1 θ ≥ θ fc θ - θ wp θ fc - θ wp θ wp ≤ θ ≤ θ fc where θ [cm 3 cm -3 ] 0 θ ≤ θ wp Evapotranspiration Ardeshir Ebtehaj 26

Canopy Effects on Evaporation V Figure 9: Examples of forcing functions based on equations shown above (Margulis, 2016). When f factors increase the resistance decrease and thus the transpiration flux increase and vice versa. Evapotranspiration Ardeshir Ebtehaj 27

Canopy Effects on Evaporation VI With this in mind, we can now consider that the overall resistance to evaporation is a combination of some canopy resistance ( r c ), that accounts for the various vapor transport mechanisms within the canopy and soil surface and the aerodynamic vapor resistance ( r av ) that accounts for the effects of the wind velocity and turbulent transport. Since these resistances are in series, we can sum them into a single term: r ac = r c + r av [s m -1 ] Figure 10: Simplified schematic of resistances to evaporation from a plan canopy and typical values of r c . (Adapted from Allen et al. 1998) Evapotranspiration Ardeshir Ebtehaj 28

Modeling ET I Energy Balance Models of ET So far, we have focused primarily on flux-based or aerodynamic methods for calculating sensible and latent heat fluxes. However, it is also very common to further constraint the calculate ET flux based on the surface energy balance (SEB). R n = LE + H + G By convention, net radiation R n , is positive when toward the surface, whereas H , LE , and G are positive away from the surface. Figure 11 shows the typical diurnal cycle of the energy balance. Figure 11: Schematic of typical diurnal variation of the surface energy balance for a well watered soil surface (Stull, 2015). Evapotranspiration Ardeshir Ebtehaj 29

Modeling ET II However, from SEB, we have one equation and three unknowns , considering we can easily estimate or measure R n . Since the ground heat flux does not vary significantly compared to the sensible and latent heat fluxes, we typically define the available energy that is partitioned to the sensible and latent heat fluxes as follows: Q n = R n - G . Experimental evidence suggests that we can assume G is some fraction of R n . Based on the field data G ≈ 0 . 05 R n over vegetation canopies and G ≈ 0 . 315 R n over the bare soil . This assumption leaves us with one equation and two unknowns. Therefore, to the solve the land surface energy balance equation, we only need an extra equation. Bowen Ratio Method: To add an extra equation that enables us to obtain the sensible and latent heat flux, we can use the Bowen ratio , which is simply the ratio of sensible to latent heat flux: β = H LE = ρ a c p T v 0 - Tva r ah L lv ρ a q v 0 - q va rav = c p ( T v 0 - T va ) L lv ( q v 0 - q va ) = c p P ( T v 0 - T va ) 0 . 622 L lv ( e 0 - e a ) Note that in the above expansion, we used q v = e / P to calculate the Bowen ratio using easily measured water vapor pressure rather tan the specific humidity. In order for us to cancel out terms in the above equation, we had to assume r ah = r av . Some typical values for β are: β 5 semi - arid β 0 . 5 grassland β 0 . 2 irrigated agriculture β 0 . 1 open water It is clear that the Bowen ratio decreases over moist surfaces as most energy is going to evaporation that is larger LE and smaller H . As explained, if the Bowen ratio is given and we have Q n , one can use these two equations to estimate the sensible H and latent LE heat fluxes: Q n = LE + H H = β LE ⇒ LE = Q n 1 + β and H = β Q n 1 + β . Evapotranspiration Ardeshir Ebtehaj 30

Modeling ET III Penman-Monteith Now we have covered both flux-based aerodynamic methods and an energy balance approach for calculating evaporative and sensible heat fluxes. The methods that combine these two, known as combination methods , are the best models of ET that we currently have simply because their solution is constrained to both flux models and land surface energy balance equation. The most popular of which is the Penman-Monteith equation . To derive this equation, we begin with the sensible heat flux as defined previously: H = ρ a c p T 0 - T a r ah T 0 : Air temperature at the surface T a : Air temperature at height of measurement For the latnet heat flux we also have, LE = L lv ρ a q v 0 - q va r av = L lv ρ a ε ( e s 0 - e a ) r av P where e s 0 : Saturation vapor pressure near the surface [Pa] e a : Vapor pressure at height of measurement [Pa] where we used q v = ε e P , e : water vapor pressure [Pa], P: air pressure [Pa], and = 0 . 622. NOTE: One of the key assumptions to the Penman-Monteith approach is that the near surface air is saturated with water vapor and thus we assumed e 0 = e s 0 . At this point, we are going to drop the overbar on all the variables for notational convenience. Just know we are referring to mean values of quantities as Penman-Monteith is typically used for daily and/or hourly mean values. Evapotranspiration Ardeshir Ebtehaj 31

Modeling ET IV T [K] e [pa] T T a 0 e sa e s0 Approximation Actual s = e s0 - e sa T 0 - T sa Figure 12: Linearizion of the Clausius-Clapeyron equation around T a . Meteorological stations typically measure the air temperature and water vapor pressure at 2 meters above the surface and not near the soil surface. This is why Penman sought a way in 1948 to determine ET from air measurements above the surface (e.g., T a at 2 m). Penman decided to use a first-order Taylor approximation (see Figure 12) to linearize the Clausius-Clapeyron equation around T a (e.g., at 2 meter) for relating the unknown e s 0 to the measured e sa as follows: e s 0 e sa + ∂ e s ∂ T T = Ta ( T 0 - T a ) where e sa is the saturation vapor pressure at T a . As previously explained, the Clausius-Clapeyron equation follows an exponential form and thus its derivative can be explained as follows: Evapotranspiration Ardeshir Ebtehaj 32

Modeling ET V Use of the Clausius-Clapeyron in Penman-Monteith Clausius-Clapeyron: e s ( T ) = 6 . 11 exp - L v R v 1 T - 1 273 . 15 [hPa]. L v : latent heat of vaporization = 2 . 5 x 10 6 [J kg -1 ] R v : water vapor gas constant = 461 [J kg -1 K -1 ] Note that in the above equation 6.11 [hPa] and T = 273 . 15 [K] refer to the triple point pressure and temperature, which is used as an arbitrary saturation point. In other words, the CC equation in its original form is e s ( T 0 ) = e s ( T a ) exp - L v Rv ( 1 T 0 - 1 Ta ) , thus Slope of Clausius-Clapeyron: = ∂ e s ∂ T T = Ta = L v R v · e sa T 2 a [Pa K -1 ] A finite difference approximation of the slope: ≈ e s 0 - e sa T 0 - T a From here, let us now substitute for e s 0 = e sa + ( T 0 - T a ) into the equation for LE : LE = L v ρ a ε ( e sa - e a + ( T 0 - T a )) r av P Evapotranspiration Ardeshir Ebtehaj 33

Modeling ET VI and then substitute in for ( T 0 - T a ) using the equation for H , because we don’t know T 0 but measure H : LE = L v ρ a ε ( e sa - e a + H r ah ρ acp ) r av P Now we will clean up the expression by defining the psychrometric constant as γ = P cp ε L v and γ * = γ · rav r ah , which will yield: LE = ρ a c p γ * r ah ( e sa - e a ) + γ * H Thus far, we have only used aerodynamic equation, so let us use the information content of the energy balance equation by substituting H = Q n - LE : LE = ρ a c p γ * r ah ( e sa - e a ) + γ * ( Q n - LE ) From here, we now want to solve for LE as follows: (1 + γ * ) LE = ρ a c p γ * r ah ( e sa - e a ) + γ * Q n Multiply the whole equation by γ * : ( + γ * ) LE = ρ a c p r ah ( e sa - e a ) + Q n Evapotranspiration Ardeshir Ebtehaj 34

Modeling ET VII Use the relation cp r ah = ε L v P γ * rav from the definition of the psychrometric constant, we have ( + γ * ) LE = γ * ρ a L v ε P ( e sa - e a ) r av + Q n and finally using the relation q v = ε e P and solving for LE , we obtain the original Penman equation: Penman Equation (1948) LE = γ * + γ * ρ a L lv ( q sa - q a ) r av + + γ * Q n where γ * = γ r av r ah One can clearly see that in this equation the term on the LHS is the air moisture deficit while the second term is the available energy for evaporation . However, Penman’s original equation could be applied only over water, bare soil, and short vegetation as it assumes that the surface is completely saturated. The equation also does not account for plant transpiration. Therefore, one of Penman’s student’s, John Monteith modified the original equation to account for the effect of the canopy on ET. As mentioned previously, the actual resistance to vapor pressure is: r ac = r c + r av [s m -1 ] Evapotranspiration Ardeshir Ebtehaj 35

Modeling ET VIII as shown in Figure 10. Now if we just update the value of γ * in the original Penman equation as follows: γ * = γ · r av r ah := γ · r av + r c r ah γ 1 + r c r ah with the assumption that r ah = r av , we have the Penman-Monteith equation, which has been the most widely used method for computation of ET fluxes in the past decades. Typically, for brevity, we could assume r ah = r av = r a . Using this, the final form of the Penman-Monteith equation is: Penman-Monteith Equation (1965) LE = γ * + γ * ρ a L lv ( q sa - q a ) r a + + γ * Q n where γ * = γ 1 + r c r a Therefore, ET can be estimated if one has the required measurements, namely net radiation, air temperature, air humidity, wind speed as well as estimates for the roughness lengths and canopy resistance. Evapotranspiration Ardeshir Ebtehaj 36

Modeling ET IX FAO Standardized Penman-Monteith Equation There have also been attempts to further simplify the Penman-Monteith equation for more practical use. In 1998, the Food and Agriculture Organization (FAO) of the UN put out a simplified standardized method of the equation as follows: Figure 13: FAO Standardized Penman-Monteith Equation (Credit: Allen et al. 1998). Evapotranspiration Ardeshir Ebtehaj 37

Modeling ET X This equation is calculating the daily ET of a standardized reference crop which is a well-watered short grass (0.12 m tall). Additionally, the equation assumes measurements are all at 2 m height. Then using the reference ET 0 , one can obtain the daily crop ET c values as follows: ET c = K c ET 0 where K c is a crop coefficient that accounts for the difference from the reference crop http://www.fao.org/docrep/X0490E/x0490e0b.htm . Various values of K c have been recorded for differing crops under various climatic conditions and growth stages (Figure 15). Figure 14: Mean values of K c for fully grown crops (left) and the range of its variability (right) under varying climatic conditions (Credit: Allen et al.1998). The upper bounds represent extremely arid and windy conditions, while the lower bounds are valid under very humid and calm weather conditions. Evapotranspiration Ardeshir Ebtehaj 38

Modeling ET XI Figure 15: Typical changes of the crop coefficient throughout the growth season. There are formulas to construct the evolution of the crop coefficient at this FAO web page [link]. Priestley-Taylor Equation If meteorological data of humidity and wind velocity are not available, an even simpler form of Penman-Monteith is the Priestley Taylor equation: LE = α + γ Q n where field experiments found for well watered fields, on average α ≈ 1 . 2 - 1 . 3. As you can see, this equation essentially states that the aerodynamic component of the Penman-Monteith accounts for 30 percent of the total ET in a well-watered condition. Evapotranspiration Ardeshir Ebtehaj 39