Evaporation From Unsaturated Soils as a Function of the Air and Soil Sides of the Land Surface

A theoretical framework for computing the evaporation from unsaturated soils is presented and validated based on laboratory experiments that were conducted in an uncontrolled environment where forcing variables vary in time according to diurnal meteorological cycles. This theory introduces a dimensionless number that controls the ratio between the actual and potential evaporation from unsaturated soils. The dimensionless number depends on the transfer velocity, which characterizes evaporation into the atmosphere, the diffusion coefficient of water vapor in the soil, and the water table depth. We show that depending on the value of the dimensionless number, evaporation can be limited by either the air‐side or the soil‐side of the land surface. For large transfer velocity values, evaporation is controlled by water vapor diffusion in the soil, while for shallow water tables, evaporation is controlled by water vapor transport from the land surface into the atmosphere. Despite the good agreement between the shape of the observed and predicted evaporation rates, a fitted dimensionless parameter is required to match the predicted evaporation rates. Possible explanations for this disagreement are given in the discussion.


Introduction
Evaporation into the atmosphere is a process that can be understood as part of either the surface energy budget or a water vapor transport toward the atmosphere (Brutsaert, 1982;Stull, 1988). From the water vapor transport point of view, the air humidity is usually less than 100% in the atmosphere, whereas near wet surfaces, the concentration of water vapor is saturated. Consequently, a vertical gradient of water vapor concentration is produced, which drives a diffusive mass flux of water vapor from the surface into the atmosphere (Adams et al., 1990;Brutsaert, 1982). In this way, evaporation can be written as follows: where E denotes evaporation expressed as ( kg H2O /m 2 /s), k t is the transfer velocity (m/s), ρ v∞ is the water vapor concentration ( kg H2O /m 3 ) far away from the surface, and ρ vi is the water vapor concentration (kg H2O /m 3 ) at the surface. Note that kg H2O and kg air are used to differentiate between water vapor mass and air mass, respectively. Both ρ v∞ and ρ vi can be written as follows (Brutsaert, 1982;Stull, 1988): where ρ a denotes the air density (kg air /m 3 ), q (kg H2O /kg air ) is the mixing ratio, e a is the partial pressure of water vapor (Pa), and P is the air pressure (Pa). k t is a flow-dependent parameter (Adams et al., 1990;Garratt, 1992) whose value in field conditions can be obtained by considering the Prandtl mixing length theory that leads to the logarithmic vertical profiles of both the air velocity and water vapor concentration (Adams et al., 1990;Garratt, 1992), which provides the following: where u(z) is the wind speed measured at an elevation z, z o is the hydrodynamic surface roughness, and κ = 0.41 is the von Karmann constant. Corrections to these logarithmic profiles can be considered depending on the atmospheric boundary layer stability (Adams et al., 1990;Garratt, 1992;Mahrt et al., 1984). Finally, it is important to note that if Equation 3 is used, then ρ vi is the water vapor concentration at the hydrodynamic surface roughness z o , which is detailed as follows.
In saturated surfaces such as lakes or the ocean, the water vapor concentration at the surface ρ vi is known and computed to be the saturated water vapor concentration (ρ vsat ) that depends on the surface temperature (Brutsaert, 1982;Garratt, 1992). This evaporation is hereinafter called the potential evaporation, which is defined as In unsaturated soils, the value of ρ vi is smaller than the saturated water vapor concentration, such that the actual evaporation from unsaturated soils is a smaller value than the evaporation from wetted surfaces E max . In particular, it is necessary to account for all the transport mechanisms that mobilize water vapor from the evaporative surface toward the land surface and the surface roughness, from which the water vapor diffuses toward the atmosphere according to Equation 1. In this context, laboratory and field studies have shown that the water table depth below the surface (d) is a key parameter that determines the evaporation from unsaturated soils (Kampf et al., 2005;Or et al., 2013;Shokri & Salvucci, 2011;Wang, 2015), where the actual evaporation decreases with d Or et al., 2013). Lehmann et al. (2008) identified two different stages in evaporation as a function of d (see also Or et al., 2013). In stage 1, the land surface is connected to the water table because capillary forces lift liquid water toward the land surface, where it is evaporated (Shokri & Salvucci, 2011). This occurs if d < δ Sadeghi et al., 2012;Yiotis et al., 2006), where δ denotes the thickness of the capillary region and the land surface presents moist patches surrounded by dry areas. During stage 1, water vapor diffuses across the diffusive sublayer, while the land surface is not entirely covered by liquid water but is rather composed by several water filled pores surrounded by dry areas. Consequently, radial diffusion of water vapor from water filled pores toward dry areas of the land surface can become a limiting factor (E/E max < 1) for water vapor transport across the diffusive sublayer depending on two dimensionless numbers that are formed based on the ratio between the pore size, the spacing between water filled pores, and the thickness of diffusive sublayer length scales (Schlünder, 1988;Shahraeeni et al., 2012).
In contrast, when d > δ, the land surface is dry and the value E/E max decreases with ξ = d − δ.  showed that the vertical diffusion of water vapor across ξ is the transport mechanism that mobilizes water vapor toward the atmosphere. Sophisticated models that consider vertical transport of water (liquid and gas phases) from the water table to the surface can be implemented for computing E (Hernández-López et al., 2014Sakai et al., 2009). However, these models require solving the water transport equations in the soil and coupling them to the atmospheric boundary layer (Davarzani et al., 2014), which makes them difficult to use in hydrological systems where surface water and ground water interact. Examples of these systems include the closed basins that are found in the Altiplano region of the Andes Mountains (Cabrol et al., 2009;de la Fuente & Niño, 2010;Risacher et al., 2003), whose hydrological cycle is also closed such that all the precipitation is completely evaporated within the  Uribe et al., 2015). Attention is placed on wetlands that are found in the central depressions of these basins. These wetlands are formed by groundwater upwelling, whose extension is determined by evaporation from wet and unsaturated soils as well as the terminal saline lakes that are usually found in these systems.
The objective of this article is to present and analyze the results of laboratory-scale experiments that aimed to measure evaporation from unsaturated soils and to relate it to the water table depth and water vapor transport in the atmospheric boundary layer. The novelty of these experiments is that they were conducted in an uncontrolled environment where air and soil temperatures, air humidity, and wind speed vary in time according to diurnal meteorological cycles. These uncontrolled conditions enable to understand the influence of water transport within the soil on evaporation with respect to the water vapor transport in the atmospheric boundary layer and to identify that E/E max is a function of a dimensionless number, Π = k t ξ/D s , where D s is the water vapor diffusion coefficient modified by soil tortuosity (Moldrup et al., 2000).

Conceptual Framework
Here, we understand evaporation as a transport process that mobilizes water vapor from the soil into the atmosphere. This transport occurs across the land surface, which is an interface located at z = 0 (with z positive upwards), with two faces: the air side (z = 0 + ) and the soil side (z = 0 − ) of the land surface. Flux and value continuity are the shared boundary conditions that link both sides of the interface, with ρ vi the unknown water vapor concentration at the land surface and E the vertical flux of water vapor that crosses the land surface. At the air side of the land surface, evaporation is a diffusive flux that is generally written as Equation 1. Below the land surface, the water table is located at a depth d, above which the transport of liquid water through the capillary region of thickness δ also supports evaporation ( Figure 1a). Between the capillary region and the land surface, there is a dry region of thickness ξ, across which the water vapor should pass through to explain the evaporation flux at the surface Shokri et al., 2008). For a constant value of δ, the thickness of the dry region is equal to ξ = max(0, d − δ) such that ξ is equal to 0 if the water table depth is smaller than δ and evaporation occurs at the land surface. Consequently, we assume that E/E max = 1 during stage 1, such that the horizontal diffusion of water vapor at the surface (Schlünder, 1988) and the rate at which capillary effects transport liquid water toward the atmosphere (Shahraeeni et al., 2012) are both large. The validity of this assumption is addressed in section 4. Furthermore, if d > δ, the evaporative plane occurs within the soil, and water vapor crosses the dry region to reach the land surface. Transport processes in this dry region include water vapor diffusion previously identified by Shokri et al. (2008Shokri et al. ( , 2009), so the evaporation can be written as follows:

10.1029/2020WR028643
where D s denotes the molecular diffusion coefficient of water vapor in air corrected by sediment tortuosity (Moldrup et al., 2000). Consequently, assuming that E is uniform, the exact solution of (4) is The diffusion coefficient modified by soil tortuosity, D s , depends on the diffusion coefficient of water vapor in the air (D = 2.12 × 10 −5 (T/(T + 273.15)) 2 m 2 /s, where T is the air temperature, in°C, see Hernández-López et al., 2014), the volumetric air content (θ a ), and the sediment porosity (φ), and several expressions can be used to represent it (Moldrup et al., 2000;Scanlon et al., 2002). In this article, we tested the following expres- Table 8.2 of Scanlon et al., 2002). We also assumed that the volumetric air content is constant within the dry region ( Figure 1) and equals to the sediment porosity. Note that Equations 5 and 6 are valid only if the evaporation plane is placed inside the soil, not when evaporation occurs at the surface of the soil.
Finally, the expression for computing E is written as follows: where E max is defined in Equation 4, and is a dimensionless number that quantifies the influence of water vapor transport in the soil with respect to water vapor transport in the air side of the land surface. Equation 7 is obtained by substituting Equation 6 into Equation 1 to obtain ρ vi , which is later replaced in either Equation 1 or Equation 6. show that for small values of Π the actual evaporation approaches the potential evaporation, which is thus controlled by the air side of the soil surface, such that E/E max = 1 or In contrast, large values of Π are associated with deep water tables or large values of k t , so the actual evaporation is controlled by water vapor transport in the soil as follows: Finally, Equation 7 can be written as Thus, the equivalent transfer velocity Þcan be defined to compute the evaporation from unsaturated soils. Notice that ρ vsat is the saturated water vapor concentration at the evaporative surface and depends on the temperature of the water that is evaporated.

Experimental Methods and Data Process
The experimental facility was installed on the terrace of the civil engineering building at the Universidad de Chile (supporting information Figure S1). The experimental facility is composed of two circular tanks 300 mm in diameter and 450 mm in height (tanks A and B), which were filled in the same way with 10.1029/2020WR028643

Water Resources Research
de AMESTI ET AL.
coarse sand with particle diameters between 0.5 and 1 mm. The water table depth is variable in tank A, which was fully saturated at the beginning of the experiments. Tank A was mounted on a balance that was used to measure the evaporation, and it has a piezometer to measure the depth to the water table.
Here, we define the water table depth as the depth at which the water pressure equates to the atmospheric pressure. In contrast, tank B was connected to a 150-mm diameter and 430-mm height Mariotte tank, which was used to maintain saturated conditions on the surface of tank B at all times. Both tank B and the Mariotte tank were mounted on balances to measure the evaporation rate of tank B, which indicates the potential evaporation. Continuous measurements of the mass of both tanks and the Mariotte tank were obtained with digital cameras that took images every hour during daylight. The use of blue dye can be used to identify the depth of the evaporative front (Assouline et al., 2014;Shokri et al., 2008).
Further instruments used during the experiments include two HOBO Pendant® Temperature/Light 64 K data logger thermistors to measure the soil temperature in both tanks every 10 min. These temperature measurements are representative of the average temperature in the soil upper layer (~2 cm). Similarly, one soil moisture sensor (Degacon Device GS1) was installed in tank A to record the average moisture in the soil upper layer (~3 cm), which was used to compute the degree of soil saturation. Finally, the air temperature, pressure, and relative humidity near the experimental facility were recorded every 10 min with a standard Campbell meteorological station.
In total, four experiments were conducted at 10.2, 6.4, 3.7, and 2.2 days of duration. Each of these experiments started with tank A filled with water, which evaporated over time.
With respect to the data process, the evaporation for the ith measurement was computed as the slope of the linear fit of the mass per unit of surface area of the tank as a function of time, using the seven measurements neighboring i. Mass observations were conducted every 1 h, and the 95% confidence interval of the slope was used to estimate the error of the observed evaporation. Evaporation under saturated conditions was computed using the total mass of tank B and the Mariotte tank, while the evaporation as a function of d was computed using the mass of tank A. The maximum evaporation of tank A was estimated as E max = E B , where E B is the evaporation of tank B computed with the slope of the mass as a function of time. Finally, the transfer velocity k t , which characterizes water vapor diffusion in the air, was determined as where ρ v∞ is computed with the measured air temperature, air pressure, and relative humidity and ρ B v sat is the saturated water vapor concentration using the soil temperature of tank B. Therefore, we assumed that the water temperature in tank B was the representative value for the water that is evaporated inside the soil of tank A.

Soil Properties
The soil properties were measured in the hydrogeology laboratory of the Hydraulic and Environmental Engineering Department of Pontificia Universidad Católica de Chile. These properties are as follows: Soil porosity (n) was measured with a balance, water, and a recipient that is capable of measuring volumes by adding dry soil to the recipient with water and measuring the displaced water to obtain the soil volume. Three different observations were made, obtaining n = 0.4 ± 0.006.
The saturated hydraulic conductivity of the soil (K W ) was measured using a constant-head permeameter (KSAT, METER Group, USA). Nine different measurements were made to characterize the soil, obtaining K W = 80 ± 12.5 m/day.
The capillarity region thickness, δ (Figure 1), is a key parameter whose actual value is uncertain. To estimate it, we used the soil water retention curve, which was measured in the laboratory with a HYPROP apparatus (METER Group, USA). The laboratory water retention curve was processed by fitting a line in the portion of the retention curve with larger gradients, and the intercept of this line with a saturation degree equal to 1 defines the point where the suction head is equal to the air-entry value, whereas the intercept with a saturation degree equal to 0 defines the evaporation plane. This adopted methodology is similar to the method used by Lehmann et al. (2008), who first fitted the curve of van Genuchten (1980) to the measurements and then used this fitted curve for determining the straight line that is intercepted to the saturation degree equal to 0 and 1. Alternatively, we also estimated δ based on the in situ measurements at the experimental facility for the water table depth and the water content that was measured with the soil moisture 10.1029/2020WR028643

Water Resources Research
de AMESTI ET AL. sensor in tank A. This information allows us for obtaining a pseudo retention curve that was processed in the same way as the laboratory retention curve for estimating δ. Finally, we define the depth d m , which is computed based on the mass of tank A, as the depth at which the air-water interface would exist if all of the liquid water in the tank were located below it. As a consequence, the capillary region thickness can be estimated as δ = d − d m , where d m is computed as follows: where A denotes the surface area of tank A, n is the soil porosity, ρ is the water density, M o denotes the initial mass of tank A, and M(t) is the mass of tank A measured with the balance at time t.

Capillary Region Thickness
The general overview of the measurements is shown in supporting information Text S1. As detailed in the soil properties subsection of the methods, the soil water retention curve and the in situ measurements in tank A were computed to characterize the capillary region thickness. Figure 2a shows the laboratory retention curve and the in situ measurements for the 10.2-day-long experiment. The corresponding values of δ were 172 and 85.6 mm. Furthermore, Figure 2a shows the capillary region thickness estimated as δ = d − d m , at which all the liquid water would be placed with a saturation degree equal to 1. The curves in Figure 2 show that important differences are obtained when the capillary region thickness is computed based on laboratory retention curve or in situ measurements. In particular, the in situ value of δ was smaller than that measured in the laboratory. The average value of δ obtained for all the in situ measurements was 100.1 ± 8.3 mm, and this value is used in this article to compute ξ = d − δ. Similarly, the thickness d − d m computed for the laboratory soil water retention curve was 156 mm, while d − d m computed for the in situ measurements was 89.9 ± 10.5 mm. The thickness d − d m is 90% of δ estimated based on the in situ measurements.
The different estimations of the capillary region thickness δ and d − d m are shown in Figure 2b, where it is observed that the δ estimated based on the mass of tank A initially grows until reaching a constant value that is larger than that based on the in situ measurements, but smaller than the δ value estimated with the laboratory water retention curve. The impact of the different values of δ on evaporation is given in the following section, while in the discussion we identify possible explanations for the different values of the water retention curves estimated in the laboratory and the in situ curve.

Dimensionless Number
For the same experiment shown in supporting information Figures S2 and 3 plots the time series of the computed variables that are used for validating the definition of the dimensionless number Π of Equation 7.

Water Resources Research
de AMESTI ET AL. Figure 3a shows the time series of evaporation from tanks A and B (gray and black dots, respectively), and Figure 3b plots the ratio E/E max , where E max was computed with Equation 10 and E corresponds to the evaporation from tank A. Evaporation from both tanks varies within the day in response to changes in the environmental conditions (temperature, air humidity, and wind speed). The maximum instantaneous values of evaporation were observed at noon, reaching values as high as 40 kg H2O /m 2 /day. As expected, the maximum evaporation was observed in tank B, which always had saturated conditions on the land surface. In contrast, the evaporation from tank A decreased over time in response to the deepening of the water table. The values of E/E max during the first days were larger than 0.9, whereas by the end of the experiment, E/E max had values smaller than 0.2. Finally, Figure 3c plots the time series of ξ for each one of the adopted methodologies, whose value varies between 0 and 10 cm, and Figure 3d plots the time series of the transfer velocity k t that report values in the range of 500 and 5,000 m/days.
The validation of the use of Π for computing E/E max is shown in Figures 3e-3h, where Figures 3e-3g plot the ratio E/E max as a function of the different variables required for evaluating Π, showing that none of the variables are solely able to explain the changes in the evaporation with respect to the maximum evaporation. However, once we plot E/E max as a function of Π (Figure 3h), it can be seen that all the data collapse into a single curve, which supports the use of this dimensionless number. Furthermore, to evaluate the use of the analytic expression of Equation 5 for quantifying this relationship between E/E max and Π, Figure 4a shows the direct comparison between the measured values of E max /E and Π for all four experiments, where Π was computed with ξ in situ , ξ lab , and d m , and D s ¼ Dθ 2:5 a =φ (Moldrup et al., 2000). Figure 4a shows that although the shape of the measurements follows the analytical solution of Equation 5 (black solid line), the measurements are shifted toward the right of the plot with respect to the analytic solution. This observation is particularly true for Π computed with ξ in situ and d m , while the use of Π computed with ξ lab presents a larger dispersion with respect to the analytical solution of Equation 5. The shift toward the right in the plot suggests that the dimensionless number Π can be corrected by a factor α such that the product αΠ is used in Equation 7, with α being a fitted dimensionless parameter. For D s ¼ Dθ 2:5 a =φ (Moldrup et al., 2000), the fitted values of α were α = 0.0149% ± 11%, 0.1128% ± 30%, and 0.011% ± 11% for the Π computed with ξ = d m , ξ lab , and ξ in situ , respectively. Similar results were obtained for the rest of the expressions tested for computing D s , with fitted values of α between 0.0103 and 0.0174 for ξ = d m , α between 0.078 and 0.1315 for ξ = ξ lab , and α between 0.008 and 0.013 for ξ = ξ in situ . The main results shown in Figure 4b are not sensitive to the specific model for computing D s .
Finally, Figures 4c-4e compare the measured evaporation from tank A with the predicted evaporation using Equation 7 and D s ¼ Dθ 2:5 a =φ. The errors in the cumulative evaporation for all the measurements were equal to 4%, 61%, and 1% for ξ = d m (Figure 4c), ξ lab (Figure 4d), and ξ in situ (Figure 4e). The disagreement between the measured and predicted evaporation using the laboratory water retention curve (ξ lab ) can be explained by the large value of δ = 172 mm so that the evaporation from tank B is predicted to be equal to the potential evaporation for a wider range of d, thus overestimating the actual evaporation. However, this explanation assumes that k t computed based on tank A is representative of the conditions in tank B, which may not be true as discussed below.

Dimensionless Number
We have presented and validated a theoretical background that links processes that occur at both sides of the land surface for computing the evaporation from unsaturated soils: the transport of water vapor from the land surface into the atmosphere and the molecular transport within the soil. The analysis led to a simple algebraic expression for computing evaporation from unsaturated soils (Equation 7), which depends on the dimensionless number Π = k t ξ/D s that quantifies the effect of soil transport processes in the soil with respect to transport from the land surface into the atmosphere (Figure 1b). For small values of Π, the evaporation from unsaturated soils approaches the potential evaporation and E can be computed with Equation 8 (E/E max → 1). This limit occurs not only when the water table is near the surface but also for large D s (e.g., sands or gravels) and small values of k t (e.g., during calm wind conditions). In contrast, when Π ≫ 1, E/E max ≈ 1/Π, such that the actual rate of evaporation is controlled by transport within the soil. Under these conditions, the evaporation can be computed with Equation 9 and is associated with large values of ξ (e.g., "deep" water table) or k t (e.g., during windy conditions) and small values of D s (e.g., clays).
The analysis that leads to Equation 7 considered steady state conditions, thus restricting the analysis to timescales larger than a characteristic time scale that is associated with the diffusion process of water vapor in the soil. This characteristic timescale, t*, can be estimated as the characteristic timescale that diffusion takes to act on length ξ, such that t* = ξ 2 /D s . For the experimental conditions presented in this article, the average and maximum values of t* were 9 and 25 min, respectively. These time steps are much smaller than those from the measurements (every 1 h). Therefore, temporal changes in the water vapor diffusion in the soil can be represented by a sequence of permanent states, each one described by Equation 7.
Our motivation for developing the simple expression of Equation 7 for computing the evaporation from unsaturated soils is that it simplifies the dynamic link between large-scale meteorological processes and basin-scale groundwater transport in the closed basins of the Altiplano region in the Andes Mountains of South America (Costelloe et al., 2009;de la Fuente & Meruane, 2017;Johnson et al., 2010;Suárez et al., 2020). In particular, groundwater in these closed basins upwells toward the terminal wetlands (oases in the desert) where it is completely evaporated; however, the amount of water that directly evaporates from the shallow aquifer is uncertain, and understanding how these unique ecosystems would behave in response to changes in the precipitation and the evaporation is necessary.

Fitted Dimensionless Parameter α
In this article, the dimensionless parameter α was needed to fit Equation 7 to the laboratory observations. The need for this adjustment suggests that the actual value of the adopted variables required for computing Π is uncertain. Since α < 1, it can be because k t estimated based on tank A is overestimated. In particular, Or et al. (2013) showed that the horizontal transport of water vapor can be a limiting factor for high evaporation rates and for coarse textured media. This microscopic phenomenon can be interpreted as an additional resistance to the vertical diffusion of water vapor that produces a smaller k t than what was measured in tank A. This additional resistance was reported for large values of k t and for stage 1 of evaporation (Or et al., 2013;Shahraeeni et al., 2012). If this is the case, additional resistance to the vertical diffusion of water vapor is needed to explain the observed rates of evaporation. The laboratory retention curve may be representative of our experiments, while the measured k t in tank A would not fully describe the transport process from the surface toward the atmosphere. To account for this extra resistance, Schlünder (1988) obtained a similar expression to our Equation 7 (E = E max /(1 + Φ)) where the dimensionless parameter, Φ, accounts for the additional resistance to the vertical diffusion associated horizontal transport of water vapor on the soil surface, whose value depends on the relative wetted surface area, among other factors.
However, it is important to note that an enhanced diffusion in soils has been previously reported by several authors since the midtwentieth century (Hernández-López et al., 2014;Philip & De Vries, 1957), and to account for these conditions, an enhanced factor is used, whose value ranges between 3 and 18. However, it is also important to note that Shokri et al. (2009) showed that the enhancement factor may not be needed if the correct dry region thickness, ξ, is used for computing evaporation based on the Fick's law. In the context of this article, the enhanced factor is equal to 1/α, and it takes different values depending on the used parametrization of D s and form for computing ξ. In particular, 1/α takes values between 30 and 75 for ξ = d m , values between 4 and 10 if ξ lab is used, and values between 41 and 102 if ξ in situ is used for computing Π. A first estimation suggests that these range of values of 1/α can also be explained by radial vapor diffusion, thus reducing the actual value of k t , as it was detailed in the previous paragraph.
In conclusion, despite the dimensionless number Π = k t ξ/D s and the expression of Equation 7 presented in this article being representative of the links between processes that occur on both sides of the land surface, further analysis is needed to elucidate the actual values of the dimensional variables k t , δ, and D s , particularly under field conditions (Suárez et al., 2020).

Water Retention Curves
In this article, we estimated the capillary region thickness based on simultaneous in situ measurements of the water content at the land surface and the depth of the atmospheric pressure isobar (the water table depth). These measurements gave us a pseudo retention curve that is different than the retention curve obtained in the laboratory, thus opening new research questions for understanding these differences and for developing methodologies in situ measurements of this key curve. First, for the in situ measurements consider a Lagrange approach that assumes that the water content at a certain height, ℓ, above the atmospheric pressure isobar does not depend on the depth of the atmospheric pressure isobar and is equal to the water content measured on the land surface when the atmospheric pressure isobar was at a depth ℓ below the land surface. This assumption may not always be true and detailed measurements of the water content at different elevations are needed. Second, the difference between the in situ measurements and the laboratory retention curve, as well as the observed changes in the water table depth observed in Figure S2 in the supporting information that showed that the water table raised during the day, suggests that there is a dynamic link between the piezometric head (water retention curve) and evaporation. Shokri and Salvucci (2011) and Sadeghi et al. (2012) noted that the groundwater evaporation must be supported by a vertical flow of liquid water within the capillary region that is described by Darcy's law, E = − K W (θ)∂h/∂z, where h is the pressure head and K W (θ) is the unsaturated hydraulic conductivity that depends on the water content (θ). Since K W does not depend on E, changes in the evaporation rate modify the vertical gradient of h that is steeper for large values of E. Therefore, as the evaporation in the experimental facility is larger than the evaporation in the laboratory apparatus used for measuring the laboratory retention curve, the differences between both retention curves may be explained by the evaporation itself. This dynamic link between the retention curve and evaporation also helps to explain the observed changes in the water table depth observed in Figure S2 of the supporting information, which showed that the water table was raised during the day. In particularly, the observations in Figure S2 may be due to thermal volumetric expansion/contraction associated with changes in the soil temperature; however, this can also be explained by temporal changes in the piezometric head (water retention curve) in response to changes in evaporation. Finally, it is important to note that the differences between in situ measurements and the laboratory retention curve can be due to the disturbance of the soil produced when collecting the sample that is analyzed in the laboratory. If this is the case, developing an in situ methodology for measuring the water retention curve may contribute to reducing this experimental error.
In future works, the dynamic link between evaporation and the retention curve should be studied in detail, as well as the advantages and disadvantages of using in situ simultaneous measurements of the soil humidity at the land surface and the depth of the atmospheric isobar (the water table depth) for estimating the capillary region thickness.

Summary
In this article we showed that the effect of water vapor diffusion within the soil on water evaporation from unsaturated soils can be quantified by the dimensionless number Π = k t ξ/D s . The results are sensitive to the depth of the evaporative plane ξ, the thickness of the capillary region, and the effective water vapor diffusion coefficient within the soil.