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Abstract

Bare soil evaporation was measured with the eddy-covariance method at the Selhausen field site. The site has a distinct gradient in soil texture, with a considerably higher stone content at the upper part of the field. We investigated the effect of different soil properties in the upper and lower parts of the field on evaporation using eddy covariance (EC) measurements that were combined with a footprint model. Because only one EC station was available, simultaneous evaporation measurements from the two field parts were not available. Therefore, measurements were put into the context of meteorologic and soil hydrologic conditions. Meteorologic conditions were represented by the potential evaporation, i.e., the maximum evaporation that is determined by the energy available for evaporation. The influence of precipitation and soil hydrologic conditions on the actual evaporation rate was represented by a simple soil evaporation model. The amount of water that could be evaporated at the potential rate from the lower part of the field was found to be large and considerably larger than from the upper part of the field. The difference in evaporation led to threefold larger predicted percolation or runoff in the upper than the lower part of the field. Simulations using the Richards equation were able to reproduce the differences in evaporation between the lower and upper parts of the field and relate them to the different groundwater table depths in the two parts of the field.

Through a combination of eddy covariance measurements with a footprint model and potential and actual evapotranspiration calculations, the spatial variability of bare soil evaporation at the field scale was observed. Using soil water flow modeling, this variability was linked to variations in the depth of the water table from the soil surface in the sloping field plot.

The exchange of water between the soil and the atmosphere plays an important role in the partitioning of radiation energy into latent and sensible heat fluxes and is therefore an important output variable in models that predict land-surface–atmosphere interactions (Maxwell and Kollet, 2008). As a consequence, soil moisture influences the air temperature (Koster et al., 2006) and plays an important role in the occurrence of heat waves, for instance in central Europe (Schär et al., 2004). It is expected that in the future, the transition zone between a humid and semiarid climate will shift northward in Europe, which will increase the sensitivity of the summer air temperature with respect to soil moisture content in large parts of Europe. This is expected to result in an increased variability of the summer temperature (Seneviratne et al., 2006b).

Soil moisture content also influences the precipitation amount. Eltahir (1998) explained that a wetter soil will result in a larger total flux of heat from the soil surface into the atmospheric boundary layer because the increase in the latent heat flux is larger than the reduction in the sensible heat flux. Altogether, this will result in shallower but moister atmospheric boundary layers, leading to an increased likelihood of localized convective storms (Eltahir, 1998). Schär et al. (2004) illustrated, in a sensitivity experiment with a regional climate model, that the European summer precipitation is strongly influenced by the soil moisture content. Betts (2004) showed, on the basis of calculations with global circulation models, that for certain regions on the Earth, an increased sensitivity of precipitation amount to soil moisture content can be expected. These regions are preferentially located in the transition zone between an arid and a humid climate, where evapotranspiration is at least part of the year controlled by the soil.

Nevertheless, these model-based studies have important limitations because the calculation of the precipitation amount in climate models is strongly parameterized. Moreover, verifying feedback mechanisms between soil moisture content and precipitation amount in an experimental setup is very difficult. Soil moisture content has a relatively long memory, which is increased by the mentioned positive feedback mechanisms between the soil moisture content and weather conditions. It has been shown that this memory effect can be used for improving seasonal weather predictions in some regions, for instance southern Europe (Seneviratne et al., 2006a).

Spatiotemporal soil moisture dynamics in global circulation models (GCMs) is modeled on the basis of a very coarse discretization. Soil moisture content is constant across a (large) grid cell and soil properties like water holding capacity often do not show any spatial variability in GCMs. Knowledge about the role of sub-grid-scale spatial variability of soil moisture content in weather conditions is limited. It is known, however, that the spatial variability of the soil moisture content will result in differential heating (i.e., spatially variable sensible heat fluxes). Many studies using large eddy simulation have shown that differential heating may create a mesoscale circulation and strongly impacts the flow structure of the atmospheric boundary layer (Mahrt et al., 1994). Observations confirm the existence of such mesoscale circulation systems induced by surface heterogeneity (Rabin et al., 1990). A mesoscale circulation will develop for horizontal heterogeneity scales that are larger than the boundary layer height (50 m−2 km, typically around 1 km) (Shen and Leclerc, 1995). This is a much smaller scale than the grid cells of current global or regional circulation models.

This argument is based on large eddy simulations with a “dry” atmosphere and does not include the thermodynamic role of water vapor in the atmosphere, which will have an additional effect. Lynn et al. (1998) used a cloud-resolving model to simulate deep moist convection over a surface with heterogeneous soil moisture contents. They found that heterogeneity is able to trigger moist convection and pointed out that an important parameter is the spatial correlation length of the soil moisture content. Also, Shao et al. (2001) and Ament and Simmer (2006) illustrated in a study with a high-resolution mesoscale atmospheric model the importance of sub-grid-scale heterogeneity and an improved parameterization of it. Although in this study we looked at latent heat fluxes related to variability at scales smaller than the boundary layer height, it is expected that the observed spatial variability of latent and sensible heat fluxes at this smaller scale will also occur at somewhat larger scales.

Besides its importance for atmospheric processes, the exchange of water between the soil and the atmosphere plays an even more critical role in soil hydrologic processes and processes that are linked to water fluxes in the soil, such as leaching processes. This is motivated by the fact that the water that is available for deep percolation and leaching is the rest term of precipitation and evapotranspiration. Small relative errors in the estimation of evapotranspiration therefore result in large relative errors in the estimated deep percolation. Currently, little is known about the spatial variability of groundwater recharge because the amount of in situ data from, for example, lysimeters is limited and not available at a high spatial resolution. A better understanding of the groundwater recharge mechanism (which asks for a better understanding of the evapotranspiration process) is increasingly important because recharge will be impacted by climate change and, in many regions, aquifer storage will (further) decline, yielding increased water stress (Bouraoui et al., 1999; Brouyere et al., 2004; Woldeamlak et al., 2007; Goderniaux et al., 2009).

These points illustrate the importance of the coupling between the soil and atmosphere, its dependence on soil moisture, and the spatial variability of soil moisture. It must, however, be stressed that soil moisture is not the primary state variable that defines the exchange of water and energy between the land surface and the atmosphere. It is, rather, the energy status of the water in the soil, or water potential, and the hydraulic conductivity of the soil that control water fluxes between the soil and the atmosphere. Both the water potential and the hydraulic conductivity are related to the soil water content but this relation depends on soil properties and is spatially variable.

In this study, we focused on the effect of soil properties on evaporation from a bare soil surface in a field with a distinct gradient in soil texture. At this scale, evaporation rates can be measured using the EC method (e.g., Sumner and Jacobs, 2005), which can be combined with a footprint model to determine the source of the measured vapor flux (Schmid, 2002); however, a single EC station cannot measure evaporation rates from the different parts of the field simultaneously. The evaporation measurements that are obtained from different parts of the field therefore cannot be compared directly. To compare the evaporation measurements, these measurements must be interpreted using a model that predicts the evaporation rate at each point in time. The objective of this study was to develop a procedure to compare evaporation measurements from different parts of a field site. Making use of this procedure, the effect of within-field variability in soil properties on evaporation rates was investigated. Finally, we investigated whether the evaporation rates that were observed could be reproduced by a soil water flow model that uses the Richards equation to describe water flow.

Materials and Methods

Calculation of Potential Evaporation

The potential evaporation, Ep (mm h−1), from bare soil was calculated with an hourly time step using the FAO method (Allen et al., 1998).The FAO method first calculates the potential evapotranspiration, ETo (mm h−1), from a grass reference surface using a modified Penman–Monteith equation (Allen et al., 1998, p. 74, Eq. [53]): 
\begin{eqnarray*}&&\mathrm{ET}_{o}{=}\\&&\frac{0.408{\Delta}(R_{\mathrm{n}}{-}G){+}\mathrm{{\gamma}}[37/(T{+}273)]u_{2}(e_{\mathrm{s}}{-}e_{\mathrm{a}})}{{\Delta}{+}\mathrm{{\gamma}}(1{+}0.34u_{2})}\end{eqnarray*}
[1]
where Δ (kPa °C−1) is the slope of the saturation vapor pressure curve, Rn (MJ m−2 h−1) is the net radiation at the grass surface, G (M J m−2 h−1) is the soil heat flux density, γ (kPa °C−1) is the psychrometric constant, T (°C) is the air temperature, u2 (m s−1) is the wind speed at 2 m above ground level, es (kPa) is the saturation vapor pressure, and ea (kPa) is the actual vapor pressure. All input variables are mean hourly values. The value of es is calculated as (Allen et al., 1998, p. 36, Eq. [11]) 
\[e_{\mathrm{s}}{=}0.6108\mathrm{exp}\left(\frac{17.27T}{T{+}237.3}\right)\]
[2]
Given relative humidity, RH (dimensionless), measurements, the ea is determined as (Allen et al., 1998, p. 74, Eq. [54]) 
\[e_{\mathrm{a}}{=}e_{\mathrm{s}}\mathrm{RH}\]
[3]
The slope of the saturation vapor pressure curve, Δ, is calculated as (Allen et al., 1998, p. 37, Eq. [13]) 
\[{\Delta}{=}\frac{4098e_{\mathrm{s}}}{(T{+}237.3)^{2}}\]
[4]
The psychrometric constant, γ, is given by (Allen et al., 1998, p. 32, Eq. [8]) 
\[\mathrm{{\gamma}}{=}0.665{\times}10^{{-}3}P\]
[5]
where P (kPa) is the atmospheric pressure. Because the effect of atmospheric pressure on potential evapotranspiration is generally small, a constant, average value can be used for that purpose. This can be estimated from (Allen et al., 1998, p. 31, Eq. [7]) 
\[P{=}101.3\left[\frac{293{-}0.0065Z}{293}\right]^{5.26}\]
[6]
where Z (m) is the elevation above sea level. The soil heat flux density, G, is approximated as (Allen et al., 1998, p. 55, Eq. [45–46]) 
\[G{=}\left\{\begin{array}{ll}0.1R_{\mathrm{n}}&\mathrm{during}{\,}\mathrm{daylight}{\,}\mathrm{periods}\\0.5R_{\mathrm{n}}&\mathrm{during}{\,}\mathrm{nighttime}{\,}\mathrm{periods}\end{array}\right.\]
[7]
Finally, evapotranspiration from the reference grass surface, ETo, is related to the potential evaporation from bare soil, Ep, in the “energy limited” stage by use of an empirical coefficient (Allen et al., 1998, p. 263, Eq. [7–1]): 
\[E_{\mathrm{p}}{=}1.15\mathrm{ET_{o}}\]
[8]
The value 1.15 represents increased evaporation potential, which is mainly due to the low albedo of wet soil (Allen et al., 1998, p. 263). Equation [8] does not account for differences in soil color or soil surface roughness between different soils so that the potential evaporation is defined for a reference wet soil surface.
For the first time period under investigation (May 2007–July 2007), we used the measured air temperature (2 m), relative humidity (2 m), wind speed (30 m), and the duration of sunshine from a nearby weather station (Forschungszentrum Jülich, 50°54′36″ N, 6°24′34″ E) to calculate the potential bare soil evaporation The wind speed measured at 30 m above ground level was converted to wind speed at standard height (2 m) assuming a logarithmic wind speed profile (Allen et al., 1998, p. 56, Eq. [47]): 
\[u_{2}{=}u_{z}\frac{4.87}{\mathrm{ln}(67.8z{-}5.42)}\]
[9]
where z (m) is the height of the measurement above ground level and uz (m s−1) is the measured wind speed at height z. The net radiation was estimated from the sunshine duration following the procedure given in Allen et al. (1998, p. 45–53).

For the second time period under investigation (May 2008–July 2008), directly measured wind speed at the standard height of 2 m, u2, soil heat flux density, G, and net radiation, Rn, were used from a second nearby weather station (Selhausen, 50°52′18″ N, 6°27′1″ E) to calculate the potential bare soil evaporation.

Measurement of Actual Evaporation using the Eddy Covariance Method

Actual evaporation, E (mm h−1 ∼ 3.6 g m−2 s−1), is measured with the EC method, which requires fast (≥10 s−1) measurements of the vertical component of the wind vector w (m s−1) and water vapor density ρv (kg m−3) in the atmospheric surface layer. After a correction for the difference between the measured density fluctuations and the desired specific humidity fluctuations (Webb et al., 1980), the vertical turbulent flux of water vapor at the measurement location is given by the fundamental EC equation: 
\[E{=}\frac{{\sum}_{k{=}1}^{N}(w_{k}{-}{\bar{w}})(\mathrm{{\rho}}_{\mathrm{v}k}{-}\mathrm{{\rho}}_{\mathrm{v}})}{N{-}1}\]
[10]
where N is the number of raw measurements contributing to one eddy covariance averaging block. Given the additional requirements of approximately stationary conditions and well-developed turbulence, this vertical turbulent flux represents a weighted average of the surface flux in the upwind environment of the measurement equipment. The weighting function describing the contribution of each surface unit to the measured flux can be estimated by a footprint model (for an overview, cf. Schmid, 2002).

Here, we used an EC station close to the center of the Selhausen field site and a footprint model to assign values of E for half hours with appropriate meteorologic conditions either to the upper (high stone content) or lower part of the field (Fig. 1 ). The field has a surface of 59 by 195 m. The soil at the site was kept bare since September 2006 and was regularly treated with herbicides to keep it free from weeds. Every year the soil was harrowed in spring. In this field, there is a strong gradient in stone content, which ranges from 60% in the topsoil of the upper part of the field to 4% in the lower part of the field. The average texture of the fine soil and the stone content in the upper and lower parts of the plot are given in Table 1 .

The EC station consists of a CSAT3 3-D Sonic Anemometer (Campbell Scientific, Logan, UT) for the measurement of the wind vector and temperature fluctuations required for the Webb et al. (1980) correction, and a Li7500 open-path infrared gas analyzer (Li-Cor, Lincoln, NE) for the measurement of water vapor density fluctuations. Both instruments are operated at a measurement height of 1.45 m at a distance from each other of 0.15 m, and logged at a speed of 20 s−1, eliminating the known signal transmission delay between the two instruments during the logging process.

Eddy Covariance Flux Processing and Footprint Modeling

The calculation of fluxes was performed with self-developed software, the processing steps of which have been tested against those of the established packages TK2 (Mauder and Foken, 2004, p. 45) and ECpack (van Dijk et al., 2004, p. 99). For our study, we first applied a spike test (Vickers and Mahrt, 1997) to the raw data with a tolerance of 3.5 standard deviations, a cross-correlation synchronization between the spatially separated instruments for w and ρv (Mauder and Foken, 2004, p. 45), deletion of Li7500 data in case a diagnostic value implemented by the manufacturer indicated strong obstruction of the measurement path (e.g., by rain), and linear detrending (van Dijk et al., 2004, p. 99) on a half-hourly basis.

The statistics average, variance, and covariance (cf. Eq. [10]) were accepted if more than 90% of valid raw data were present in a half-hour block and were subjected to a double rotation (Kaimal and Finnigan, 1994), correction for frequency response (revised after Moore, 1986), for the difference between sonic temperature statistics and those of air temperature (Schotanus et al., 1983), and for density fluctuations (Webb et al., 1980).

To discriminate the time blocks mainly representing the surface flux of the lower part of the test site, the upper half, and mixed footprint conditions from each other, we estimated the footprint geometry with the analytical model of Kormann and Meixner (2001). The model implementation of Neftel et al. (2008) was used to calculate the relative contribution of the upper and lower parts as a function of wind direction, wind speed, friction velocity, Obukhov parameter, and crosswind variance. The E fluxes of half-hourly time blocks were assigned to the upper part of the field if its relative contribution was 70% or more and to the lower part if 10% or less, and vice versa for the lower part. Half hours not fulfilling these requirements due to wind directions around north–northwest or south–southeast, as well as those indicating an inappropriate turbulence data source for the footprint model by implausible roughness lengths estimated by the model (Neftel et al., 2008) of 0.4 m or more, were discarded.

Calculation of the Actual Evaporation using a Simple Soil Evaporation Model

The model of Boesten and Stroosnijder (1986) was used to calculate the evaporation from a bare soil surface as a function of the potential evaporation rate, the precipitation, and the soil hydrologic status. This model assumes a reservoir of soil moisture that can be evaporated at a potential rate. When this reservoir is depleted, the evaporation rate decreases by the square root of the cumulative potential evaporation rate and the soil water reservoir is further depleted. The soil water reservoir is refilled by precipitation and a bookkeeping of the amount of water lost by cumulative evaporation and the input from rainfall is used to evaluate the status of the soil water reservoir that can be evaporated at the potential rate. Cumulative evaporation from the soil reservoir during a drying cycle after the soil water reservoir was completely filled with water is given by 
\[{\sum}\mathrm{Ea}{\Delta}t{=}{\sum}\mathrm{Ep}{\Delta}t{\,}\mathrm{if}{\sum}\mathrm{Ep}{\Delta}t{\leq}\mathrm{{\beta}}^{2}\]
[11]
 
\[{\sum}\mathrm{Ea}{\Delta}t{=}\mathrm{{\beta}}\sqrt{{\sum}\mathrm{Ep}{\Delta}t}{\,}\mathrm{if}{\,}{\sum}\mathrm{Ep}{\Delta}t{>}\mathrm{{\beta}}^{2}\]
[12]
where β (m0.5) is a soil parameter, ΣEaΔt is the amount of water that is lost due to evaporation from the soil reservoir since it was last completely filled, and ΣEpΔt represents the amount that would be potentially lost from the soil reservoir due to potential evaporation since it was last completely filled.
If precipitation, Prec, occurs, the amount of water that is lost from the soil reservoir is updated as follows. When the precipitation during a time step Δt = ti+1ti is smaller than the potential evaporation rate during that time step, then it is assumed that this precipitation is evaporated and the cumulative potential loss from the soil reservoir is updated as 
\begin{eqnarray*}&&({\sum}\mathrm{Ea}{\Delta}t)^{i{+}1}{=}({\sum}\mathrm{Ep}{\Delta}t)^{i}\\&&{+}\mathrm{Ep}{\Delta}t{-}P_{\mathrm{rec}}{\Delta}t\end{eqnarray*}
[13]
The amount of water that is lost from the soil reservoir until time ti+1 since it was last completely filled with water, (ΣEaΔt)i+1, is calculated from Eq. [11] and [12] using (ΣEpΔt)i+1 (Eq. [13]). The calculated actual evaporation, Ea, during Δt is equal to the amount of water that is lost from the soil reservoir between time ti and ti+1 at the precipitation rate: 
\[\mathrm{Ea}{=}\frac{({\sum}\mathrm{Ea}{\Delta}t)^{i{+}1}{-}({\sum}\mathrm{Ea}{\Delta}t)^{i}}{{\Delta}t}{+}P_{r\mathrm{ec}}\]
[14]
When the precipitation rate is larger than the potential evaporation, then the actual evaporation is equal to the potential evaporation and the amount of the precipitation that is not evaporated fills up the soil water reservoir: 
\begin{eqnarray*}&&({\sum}\mathrm{Ea}{\Delta}t)^{i{+}1}{=}\mathrm{max}\left[({\sum}\mathrm{Ea}{\Delta}t)^{i}\right.\ \\&&\left.\ {-}(P_{\mathrm{rec}}{-}\mathrm{Ep}){\Delta}t;0\right]\end{eqnarray*}
[15]
Because the initial soil water content was not known at the start of the evaporation measurement campaign, a warm-up period of at least 1 mo was used for the simulation of the actual evaporation rates. Using a longer warm-up period did not lead to different predictions of the actual evaporation.

Calculation of the Actual Evaporation using the Richards Equation

We also tested whether the measured evaporation rate could be predicted using the more physically based Richards equation for water flow in variably saturated soils: 
\[\frac{{\partial}\mathrm{{\theta}}(h)}{{\partial}t}{=}\frac{{\partial}}{{\partial}z}\left[K(h)\left(\frac{{\partial}h}{{\partial}z}{+}1\right)\right]\]
[16]
where θ is the volumetric soil water content, h (m) is the matric potential head, K(h) (m s−1) is the unsaturated hydraulic conductivity, and z is the vertical coordinate. To model evaporation from a bare soil, a mixed soil surface boundary condition is used. When the matric potential head is above a certain threshold head, hcrit, the Richards equation is solved for a prescribed flux at the soil surface, which is equal to the potential evaporation rate. When the matric potential head becomes smaller than hcrit, the boundary condition at the soil surface is switched to a constant-head boundary condition and the actual evaporation rate at the soil surface is obtained by calculating the flux for the given matric potential head at the soil surface. A similar mixed boundary condition is used to simulate infiltration when rainfall occurs: 
\begin{eqnarray*}&&{-}K(h)\left(\frac{{\partial}h}{{\partial}z}{+}1\right)\left|_{z{=}0}\right.{=}E_{\mathrm{p}}{-}P_{\mathrm{rec}}\\&&\mathrm{when}{\,}h_{\mathrm{crit}}{<}h{<}0\\&&\mathrm{else}{\,}h\left|_{z{=}0}\right.{=}h_{\mathrm{crit}}\\&&\mathrm{or}{\,}h\left|_{z{=}0}\right.{=}0\end{eqnarray*}
[17]
where hcrit = −100,000 cm.
For the bottom boundary condition, we considered three different cases. In the first case, a soil profile of 100-cm depth with a unit hydraulic gradient at the bottom of the profile was considered: 
\[\left(\frac{{\partial}h}{{\partial}z}{+}1\right)\left|_{z{=}{-}100{\,}\mathrm{cm}}\right.{=}1\]
[18]
This condition assumes that the soil profile is not replenished by upward water flow from below the 100-cm depth and is often used to simulate soil water balances in soils with deep groundwater tables. In the second case, a 400-cm-deep soil profile with a water table at 400-cm depth was assumed. Based on groundwater level measurements in a piezometer close to the field site, this groundwater level is representative for the lower part of the field. In a third case, an 800-cm-deep soil profile with a groundwater level at 800-cm depth was considered. This groundwater level is representative for the upper part of the field, which is 4 m higher than the lower part. The Richards equation was solved numerically using the HYDRUS software (Šimůnek et al., 2008, p. 330) and a spatial discretization of 1 cm. Similarly to the simple soil evaporation model, a warm-up period was used. The initial condition was a uniform pressure head of −100 cm, which corresponds with the field capacity of the soil.

For the parameterization of the soil hydraulic functions, we also considered three cases. In the first case, the water retention, θ(h), and hydraulic conductivity, K(h), curves were described by the Mualem–van Genuchten (van Genuchten, 1980) functions. The parameters of these functions were derived from water retention curves that were measured in small soil samples (100 cm3) from the lower part of the field. The saturated hydraulic conductivity, Ks, was derived from inverse modeling using soil water content measurements at various depths in the soil profile (Table 2 ).

The Mualem–van Genuchten parameterization is based on a capillary network model of the pore space and does not account for film flow in pore crevices. An underestimation of this film flow may lead to a considerable underestimation of the unsaturated soil hydraulic conductivity under dry soil conditions (Tuller and Or, 2001, 2005) and may therefore lead to an underestimation of the amount of water that can be evaporated from the soil profile (Goss and Madliger, 2007). To investigate the effect film flow could have on the simulated bare soil evaporation, we considered, in a second case, a hydraulic conductivity curve that represents the effect of film flow on the unsaturated hydraulic conductivity. From Tuller and Or (2001), we inferred that film flow starts to have an important impact on the unsaturated hydraulic conductivity for pressure heads smaller than −1000 cm and that the decrease in hydraulic conductivity between h = −1000 cm and h = −10,000 is about a factor of 10. Similar to Peters and Durner (2008), we used a simple description of the hydraulic conductivity curve to account for film flow and assumed a linear dependence between logK(h) and log(−h) for h < −1000 cm. The adaption to the hydraulic conductivity that we made to account for film flow is shown in Fig. 2 .

The hydraulic parameters given in Table 2 were derived from soil samples that were nearly gravel free and that were taken from the lower part of the field. Due to the high gravel content, it was impossible to take undisturbed soil samples from the upper part of the field. In a third case, we estimated the hydraulic parameters of the upper part of the field by rescaling the hydraulic functions that were derived for the lower part of the field. Based on the texture of the fine soil fraction (Table 1), we assumed that the hydraulic properties of the fine soil fraction in the upper and lower parts of the field were similar and we rescaled the saturated water content and saturated hydraulic conductivity by the volumetric fraction of the fine soil material, fV: 
\[f_{\mathrm{v}}{=}\frac{(1{-}f_{\mathrm{G,gravel}}){\rho}_{\mathrm{b,fines}}^{{-}1}}{(1{-}f_{\mathrm{G,gravel}}){\rho}_{\mathrm{b,fines}}^{{-}1}{+}f_{\mathrm{G.gravel}}{\rho}_{\mathrm{s,gravel}}^{{-}1}}\]
[19]
where fG,gravel is the gravimetric gravel content (0.4 for the upper part of the plot), ρb,fines is the bulk density of the dry fine soil (1.65 g cm−3), and ρs,gravel is the mass density of the gravel (2.65 g cm−3). The obtained scaling factor fV was 0.71.

Results

The precipitation rate, potential evaporation, and the EC-measured evaporation during the two measurement campaigns are shown in Fig. 3 . Because only the EC measurements for which the footprint was in the upper or lower part of the field were retained, the EC measurements cover only 23% of the entire measurement campaign. For 14% of the measurement campaign, measurements from the lower part of the field were obtained, whereas measurements from the upper part of the field cover 9% of the measurement campaign. The periods when measurements were obtained from one part of the field were rather contiguous and not interrupted by measurements from the other part of the field. As a consequence, it is nearly impossible to make a direct comparison of evaporation rates that were measured at nearly the same time in the two parts of the plot.

In Table 3 , the cumulative precipitation and the average and cumulative potential evaporation, as well as EC-measured and calculated evaporation, are given for different time periods. Because the two EC measurement campaigns took place during late spring and early summer, the total amount of precipitation during the two campaigns, 422 mm, was smaller than the cumulative potential evaporation, 585.9 mm, during these campaigns. Because only a certain amount of the water that is stored in the soil can be evaporated at a potential evaporation rate, however, the actual evaporation rate during the measurement campaign was expected to be smaller than the potential evaporation rate. We calculated the actual Ea for a reference soil with β = 6 mm0.5, which was a first guess of an average β value for the field plot. For the reference soil, the calculated cumulative actual evaporation, 387.9 mm, is lower than the cumulative potential evaporation and also lower than the cumulative precipitation so that there was a precipitation excess during the measurement campaigns.

The cumulative potential evaporation during the period that was covered by EC measurements was 193.9 mm, which is 33% of the total cumulative potential evaporation during the campaign. This percentage is larger than the percentage of the campaign duration that was covered by EC measurements (23%), which goes along with a larger mean potential evaporation rate during periods when EC measurements were available than during the entire measurement campaign. Time periods with low wind speeds, which go along with lower evaporation rates and larger footprints, were not considered because of the criterion that the footprint should be at least 70% within one of the two field parts.

The mean potential evaporation rate for measurements with a footprint in the lower part of the field was larger than for measurements with a footprint in the upper part of the field. The difference between the EC-measured mean evaporation rate in the lower and upper parts of the field could therefore partly be explained by differences in atmospheric demand, which was apparently, on average, higher for measurements from the lower than from the upper part of the field. The actual evaporation rate from a soil, however, is not only determined by the atmospheric demand, which is quantified by the potential evaporation rate, but depends also on the soil hydraulic conditions or the availability of soil moisture that can be evaporated. This water availability depends on the precipitation events and soil hydraulic properties, which were summarized in our simplified model by the water reservoir, i.e., β2, that can be evaporated at a potential rate. Simulations of the actual evaporation for a reference soil indicate that the mean actual evaporation rate should, in fact, be higher for the times when evaporation rates were measured from the upper part of the field than from the lower part of the field. The EC measurements from the upper part of the field were apparently obtained soon after a rainfall event so that the soil would still be sufficiently wet to evaporate at a higher rate. On the other hand, measurements from the lower part of field seem to correspond with drier soil conditions that occurred later after precipitation events. As a consequence, the mean actual evaporation, when EC measurements were available, should have been higher for the upper than for the lower part of the field despite the lower atmospheric demand or potential evaporation rate. This clearly points to the importance of the soil hydrologic conditions when comparing EC evaporation measurements from different footprints. Because the measured evaporation showed the opposite difference from the simulated actual evaporation rates for the upper and lower parts of the field, the soil properties between the two footprints must be significantly different. The soil in the lower part of the field seems to be capable of storing a larger amount of water that can be evaporated at a potential rate than the soil in the upper part of the field.

To achieve an agreement between the predicted and EC-measured cumulative evaporation, the β parameter was changed for the upper and lower parts of the field to 4 and 12 mm0.5, respectively. Figure 4 shows the cumulated measured and predicted actual evaporation and the cumulated potential evaporation for the upper and lower parts of the field. Because the measured evaporation rates were not continuous, the cumulated evaporations do not correspond with a total cumulated evaporation during a certain uninterrupted time period. They rather represent the cumulative amount of evaporation during time periods when measurements were available. Using an adapted model parameter for the upper and lower parts of the field plot, the course of the measured cumulative evaporation was fairly well reproduced by cumulative evaporation rates that were predicted by the simple water balance model. The simple soil water model predicted fairly well when the actual evaporation started to deviate from the potential evaporation, i.e., after approximately 10 mm of cumulated evaporation for the upper and 40 mm of cumulated evaporation for the lower parts of the plot. Note that these values do not correspond with and should be smaller than the soil moisture reservoir that can be evaporated at a potential rate, i.e., β2, because the cumulated measured evaporation rates do not include evaporation during periods when no data were obtained. Furthermore, the soil water reservoir might have been partially depleted at the start of the measurement campaign. Also, after the onset of the deviation between the potential and actual cumulated evaporation, the predicted and measured cumulated actual evaporation rates corresponded fairly well. For the reference soil, the onset of the deviation between cumulated actual and potential evaporation was predicted to occur much earlier than observed in the lower part of the field. In the upper part of the field, the reference soil overestimated the actual cumulated evaporation.

In Fig. 5 the predicted evaporation is plotted vs. the EC-measured evaporation for the two parts of the plot. For comparison, the potential evaporation is also plotted vs. the EC-measured evaporation. This plot illustrates that the relation between the predicted and measured instantaneous evaporation rate is affected by noise. The coefficient of determination was defined as 
\[R^{2}{=}1{-}\frac{{\sum}(\mathrm{Ea}{-}\mathrm{EEC})^{2}}{{\sum}(\mathrm{EEC}{-}\mathrm{\overline{EEC}})^{2}}\]
[20]
where
\(\overline{EEC}\)
is the average of the EC measurements. The value of R2 was 0.25 for the lower and 0.56 for the upper parts of the field. The difference between Ea and EEC may be due to (i) an incorrect prediction of the difference between the potential and actual evaporation, which is related to the soil evaporation model and its parameterization, (ii) an incorrect prediction of the potential evaporation, or (iii) measurement errors or noise in the EC measurements. The random error of EC-measured turbulent fluxes is considerable and dependent on the flux magnitude, which can also be seen in Fig. 5 (Richardson et al., 2006). The latter two error sources could be quantified by comparing the measured and predicted evaporation during time periods when the model predicts a potential evaporation rate. For measurements during time periods of potential evaporation, R2 was 0.24 for the lower and 0.58 for the upper parts of the field. For the period when the predicted evaporation rate was smaller than the potential evaporation, R2 was 0.50 and 0.63 for the lower and upper parts of the field, respectively. Because the R2 values for the periods with potential evaporation were similar to the R2 values for the entire data set, the noise in the relation between predicted and measured evaporation was mainly caused by measurement errors and by errors in estimation of the potential evaporation. The mean difference between EC-measured and potential evaporation during periods of potential evaporation was −0.006 and −0.016 mm h−1 for the upper and lower parts of the plot, respectively, which corresponds with 3 and 14% of the mean evaporation during these periods. A further indicator for measurement errors might be the occasional occurrence of EC measurements with apparent negative evaporation fluxes (Fig. 5). Most of these negative fluxes occurred during the night, however, when bare soil can take up small amounts of vapor from the atmosphere because of dew condensation or hygroscopicity, and all of them are within a physically plausible range for these processes (Graf et al., 2004, 2008).

An analysis of the EC-measured evaporation rates indicated that the control of the soil on the evaporation rate differed considerably between the upper and lower parts of the field. To investigate the impact this difference could have on the soil water fluxes, the simple soil evaporation model was run for a period of 2 yr with potential evaporation and precipitation data. From the difference between cumulative precipitation and actual evaporation, the amount of runoff and leaching in the two parts of the field was estimated (Table 4 ). The stronger control of the soil on the evaporation rate in the upper part of the field had, in relative terms, a large impact on the amount of water that was lost from the upper part of the field due to leaching and runoff. This loss was almost a three times larger than in the lower part of the field. This indicates that a process such as contaminant leaching, which is driven by a precipitation surplus, may vary considerably at the field scale due to variations in actual soil evaporation. Variations in leaching have been attributed mainly to water flow variability that resulted from water redistribution at the soil surface or within the soil profile due to soil heterogeneity. These results illustrate that, at a larger scale, variations in evaporation may also become an important factor for leaching variability and may lead to considerably larger contaminant load to the groundwater at locations with reduced evaporation.

In Table 5 , the cumulated evaporation at the end of the measurement period that was simulated by the Richards equation for the lower and upper parts of the field and for different lower boundary conditions and soil hydraulic functions is given. In Fig. 6 , cumulated potential, measured, and simulated evaporation by the Richards model for the upper and lower parts of the field are shown. For each part of the field, simulations that considered soil hydraulic conditions for each of the two parts are shown. By comparing these simulations, the effect of the soil hydraulic conditions on the simulated evaporation rate in one part of the field can be evaluated directly.

For the same hydraulic functions, the simulated evaporation rate was always lower for the free-drainage boundary condition at the 100-cm depth than for a groundwater table at the 400- or 800-cm depth. This indicates that water flow in the soil below the 100-cm depth is still relevant for evaporation at the soil surface.

In the lower part of the field, the cumulative evaporation was predicted well for a free-drainage boundary condition at the 100-cm depth and a hydraulic conductivity curve that accounts for film flow. For a groundwater table at the 400- or 800-cm depth, however, the hydraulic conductivity curve that accounts for film flow led to a simulated evaporation rate that was equal to the potential evaporation rate. As a consequence, this model tended to overestimate the evaporation rate for lower boundary conditions that were more relevant for the field plot than a free-drainage boundary condition at the 100-cm depth. Using the Mualem–van Genuchten hydraulic functions, the cumulated evaporation rate decreased with increasing depth of the groundwater table. For a groundwater table depth of 4 m, the cumulated evaporation rate was slightly overestimated. For a deeper groundwater table and using hydraulic functions that accounted for a higher gravel content, which are conditions more relevant for the upper part of the field, the cumulated evaporation from the lower part of the field was underestimated considerably. This suggests that differences in evaporation between the upper and lower parts of the field may be attributed to the different depth of the groundwater table at the two locations. The simulation results also indicate that the large reservoir of water that can be evaporated at a potential rate from the lower part of the field may be related to the presence of a groundwater table at the 400-cm depth.

The cumulated evaporation from the upper part of the field that was simulated by the Richards model generally overestimated the measured cumulated EC evaporation. For a groundwater table at the 400-cm depth and hydraulic functions that do not account for the effect of the gravel content, which are conditions more relevant for the lower part of the plot, the simulated evaporation from the upper part of the plot was close to the potential evaporation. A deeper groundwater table and accounting for the gravel content led to a reduction of the simulated evaporation rate compared with the potential evaporation rate and therefore to a better prediction of the measured cumulated evaporation. It must be noted that we had no measurements of the hydraulic properties of the gravelly soil in the upper part of the field and neither did we have a detailed description of the 800-cm-deep soil profile that we considered in our simulations. From the geology of the site, it is known that the gravel content increases with depth but no quantitative information about the gravel content is available. As a consequence, there was considerable uncertainty about the hydraulic properties of the 800-cm profile in the upper part of the field. Another cause for a stronger reduction in the evaporation rate when the soil dries out could be a stronger increase in the albedo of the gravelly soil with decreasing soil moisture. The good agreement between the EC-measured evaporation and the potential evaporation rate during periods when the soil was sufficiently wet, however, indicates that the gravel content did not have a relevant impact on the soil albedo when the soil was wet.

Discussion and Summary

To interpret EC measurements of evaporation at heterogeneous sites, it is important that these measurements are put into context. Besides the spatial context or the footprint of the measurement, the temporal context of the measurement also needs to be considered. The temporal context includes both the temporal variability of the meteorologic conditions that determine the atmospheric demand for water as well as the soil hydrologic conditions that determine the availability of water for evaporation. Without considering these temporal contexts, comparisons between evaporation measurements from different footprints are meaningless. In our study, the soil hydrologic context varied considerably between the data sets from measurements with a footprint in the upper and lower parts of the field. The soil hydrologic context, in fact, inverted the difference in evaporation rate that would result from atmospheric demand.

When considering the meteorologic and soil hydrologic conditions, it became evident that the control of the soil on the evaporation rate was considerably different between the upper and lower parts of the field. This agrees with the different soil properties in the two parts of the field. The actual evaporation rates could be described relatively well by a simple soil evaporation model that was parameterized differently for the two parts of the field. The amount of water that could be evaporated at a potential rate was found to be considerably larger for the lower than for the upper part of the field. A water balance indicated that differences in evaporation between the lower and upper parts of the field plot led to large differences in deep percolation and runoff. This may have important consequences for the variability of transport processes at the field scale.

We found that from the lower part of the field, a reservoir of β2 = 144 mm could be evaporated at a potential rate. This is considerably larger than what was reported in other studies. For instance in the FAO guideline for computing crop evapotranspiration (Allen et al., 1998), a range of this reservoir between 2 mm for sandy soils and 12 mm for clayey soils is given. This range was based on measurements of soil evaporation from lysimeters just a few days after planting or sowing when crop transpiration is not important (Mutziger et al., 2005). A similar range was given by Boesten and Stroosnijder (1986), whereas Ventura et al. (2006) reported larger values up to 32 mm. It is important to mention that in these studies, the soil surface was disturbed and harrowed to prepare the seedbed just before the evaporation measurements started. In our study, the soil surface was left bare for a long time and was not harrowed or tilled shortly before the evaporation measurements started so that a crust was formed at the soil surface. Such a crust may create a capillary contact with the deeper soil and effectively dry out the soil.

Using simulations with a soil water flow model based on Richards' equation, the different control of the soil on the evaporation rate in the two parts of the plot could be linked to the shallower groundwater table in the lower than in the upper part of the field. The Richards equation does not, however, consider vapor flow, which enhances evaporation rates from drying soils. Because vapor flow is generally less effective at transporting water to the soil surface than liquid flow, vapor flow plays an important role only under dry soil conditions when the reservoir of water that can be evaporated at a potential rate is already depleted. As a consequence, vapor flow is not expected to be responsible for the long sustained potential evaporation rate from the lower part of the field. The higher gravel content in the upper part of the field reduced the evaporation but the effect of the gravel on the hydraulic properties and the simulated evaporation rate was considerably smaller than the effect of the groundwater table depth. The upward flow of water from deeper soil layers to the soil surface was crucial for explaining the large evaporation reservoir.

This confirms that soil management practices and processes that change the structure of the thin surface layer and disconnect the liquid water phase from the deeper soil can have a large impact on soil evaporation, especially in the presence of a shallow groundwater table. The depth of the groundwater table in the lower part of the field (4 m) falls within the range of depths, between 1 and 5 m, for which groundwater was found to have an important influence on the latent heat exchange between the land surface and the atmosphere (Kollet and Maxwell, 2008). This indicates that groundwater levels need to be considered for modeling land-surface–atmosphere interactions. It also implies that information about hydraulic properties of the subsoil or deeper vadose zone is required to describe the coupling between groundwater and land-surface processes. Because regional-scale information about soil properties, which is contained in soil maps and soil profile databases, focuses mainly on the top 1 m of the vadose zone, the hydraulic properties and their spatial distribution in the deeper vadose zone are not well known and uncertain. Further efforts to characterize the deeper vadose zone seem therefore useful, even for predicting land-surface–atmosphere interactions.

This research was supported by the German Research Foundation DFG (Transregional Collaborative Research Centre 32—Patterns in Soil–Vegetation–Atmosphere Systems: Monitoring, modelling and data assimilation). We thank Marius Schmidt and Karl Schneider from the University of Cologne for providing meteorologic data from the Selhausen test site and Axel Knaps for providing us with meteorologic data from the Forschungszentrum Jülich. A. Graf would like to thank the DFG for funding through the project GR 2687/3-1 “Links between local scale and catchment scale measurements and modelling of gas exchange processes over land surfaces.”