The field experiment was conducted at one flat dune foot in the Badain Jaran Desert (between 39°45′20″ N to 39°47′27″ N and 102°27′07″ E to 102°28′58″ E), in the northwest of the Alashan plateau in the western Inner Mongolia of China. The details on the field site and the observations made have been introduced by Zeng et al. . To apply the proposed model in the field, boundary conditions and forcing field had to be defined.
3.3.1. Boundary Conditions
 For this specific case, no ponding or surface runoff was considered. This means that the moisture flux out of the soil is always equal to evaporation minus precipitation.
where E(kg m−2 s−1) is the evaporation rate; P(m s−1) the precipitation rate. Considering the aerodynamic resistance and soil surface resistance to water vapor transfer from soil to atmosphere, the evaporation is expressed as [Camillo and Gurney, 1986]
where ρvs(kg m−3) is the water vapor density at the soil surface; ρva(kg m−3) the atmospheric vapor density; rs(s m−1) the soil surface resistance to water vapor flow; and ra(s m−1) the aerodynamic resistance. Equation (16) forms the surface boundary condition for moisture transport. Without taking ponding and surface runoff into consideration, soil surface was open to the atmosphere and the measured atmospheric pressure was adopted as the surface boundary condition for dry air transport in the soil. The measured soil surface temperature was set as the boundary condition for heat transport.
 In the Badain Jaran Desert, according to Gates et al. , the thickness of unsaturated zone ranges from less than 1 m in interdune areas to approximately 400 m in large dunes. In this study, the length of the soil column was set to be 5 m. The bottom boundary condition for the moisture equation was free drainage (unit hydraulic head gradient). Considering the diurnal variation scale, the temperature gradient and the air pressure gradient at the bottom of the column were specified to be zero. A one-dimensional setting was adopted in this study, predominantly considering the vertical interactive process between the atmosphere and the soil [Milly and Eagleson, 1980]. The initial soil matric head and soil temperature were determined by interpolating the measured values at midnight on 12 June 2008 between measurement depths. The initial soil air pressure was set according to the daily average atmospheric pressure during the selected 6 d period.
3.3.2. Meteorological Forcing Data
 In terms of finding a balance between computational efficiency and solution accuracy, the time step was required to be small enough for the moisture content and temperature not to exceed prescribed limits [Milly and Eagleson, 1980]. This meant that the time step was adjusted automatically during computing (1 to 1800 s). Accordingly, the time interval of the meteorological inputs was adjusted to match each new time step. In this study, the Fourier transform method was used to approximate the frequency domain representation of the meteorological forcing data, and continuously produced the forcing data.
 Figure 7 shows the measurement and the approximation of meteorological variables, including air temperature, relative humidity, wind speed, precipitation, atmospheric pressure, and soil surface temperature (Figures 7a–7f), measured in the Badain Jaran Desert at a height of 2 m above the soil surface, and at 30 min intervals. The 6 d data were chosen to include a rainfall event at the end of the first day of the selected period. Except for wind speed data fluctuating irregularly because of inherent randomness, the records of other variables showed clearly typical diurnal behavior.
Figure 7. Diurnal changes in meteorological variables: (a) air temperature, (b) relative humidity, (c) wind speed, (d) precipitation, (e) atmospheric pressure, and (f) surface temperature. They are recorded every 30 min from 13 to 19 June 2008. The solid lines are the approximation and the dots are the measurement.
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 Figure 7a shows that the average air temperature was 24.3°C 1 d before the rainfall and 20.4°C 1 d after. From that day on, the average air temperature increased to 28.7°C at the end of the selected period. As can be seen in Figure 7b, the average daily relative humidity was 0.31 before and 0.51 after rainfalls, followed by a 3 d gradual decrease to 0.14, with a slight increase on the final day to 0.21. As is seen in Figure 7e, the atmospheric pressure followed the same variation pattern as the relative humidity did. The daily average atmospheric pressure was 87528.8 Pa before and 87907.2 Pa after the precipitation. From the second day onwards, the average atmospheric pressure first decreased to 86791.3 Pa on the fifth day, and then increased again to 86753.21 Pa on the last day.
 Following van de Griend and Owe , the aerodynamic resistance (ra) and soil surface resistance (rs) was expressed as
where k is the von Karman constant (=0.41); U(m s−1) the measured wind speed at certain height; Zm(m) the height of wind speed measurement; d (m) the zero plane displacement (=0 for bare soil); Zom (=0.001 m) the surface roughness length for momentum flux; ψsm the atmospheric stability correction factor for momentum flux; Zoh (= 0.001 m) the surface roughness length for heat flux; ψsh the atmospheric stability correction factor for heat flux; rsl(=10 s m−1) the resistance to molecular diffusion across the water surface itself; a (=35.63) the fitted parameter; θmin (= 0.15 m−3 m3) the empirical minimum value above which the soil is able to deliver vapor at a potential rate; and θsur the soil water content in the topsoil layer.
3.3.3. Model Validation
 The field measurements of soil moisture and temperature described by Zeng et al. , were used to validate the proposed model. The soil temperature was measured at depths of 2, 5, 10, 20 and 50 cm by soil temperature profile sensor (STP01, Hukseflux Thermal Sensors B.V., Delft, Netherlands). According to Figure 8, there was reasonably good agreement between simulated and measured soil temperatures at different depths. The simulation matched the diurnal variations on most days. The underestimation occurring at 2 cm depth during the whole simulation period should partially be attributed to the Fourier-transformed surface temperature in Figure 7f. There were overestimations at other depths on some days. For example, overestimation occurred on day 1 at depths of 10, 20 and 50 cm, and on day 5 and 6 at depths of 10 and 20 cm. The simulations of temperature with and without considering airflow were compared in Figure 8. At the selected depths, there is no big difference between the two models. The root mean square errors (RMSEs) between the simulation (considering airflow) and the measurement are 4.135°C, 3.047°C, 3.667°C, 3.559°C and 1.532°C at the depth of 2, 5, 10, 20 and 50 cm, respectively. For the simulation without considering airflow, the RMSEs are 4.131°C, 3.031°C, 3.572°C, 3.394°C and 1.541°C at the selected depths.
Figure 8. Comparison between simulated (i.e., by model with and without considering airflow) and measured soil temperature during 13–19 June 2008, at selected depths: (top to bottom) 2 cm, 5 cm, 10 cm, 20 cm and 50 cm. The solid black line is the simulation with airflow, the solid gray line is the simulation without airflow, and the red open circle is the measurement.
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 The soil moisture was measured at a depth of 10, 20, 30, 40, and of 50 cm by soil water content profile sensor (EasyAG50, Sentek Pty. Ltd., Stepny, Australia). The quality of soil moisture measurement was quantitatively assessed and calibrated by Zeng et al. . A major concern with measuring soil moisture in sand was the temperature effect. The temperature had an effect on readings of the moisture sensors of 14.4% between 12°C and 45°C at 10 cm, of 13.9% between 11°C and 50°C at 20 cm, of 14% between 9°C and 51°C at 30 cm, of 13% between 9°C and 55°C at 40 cm, and of 15% between 8°C and 55°C at 50 cm. After calibration, the temperature effects at the depths of 10, 20, 30, 40, and 50 cm were reduced by 92%, 93%, 93.8%, 88%, and 82%, respectively [Zeng et al., 2009]. This ensured the quality of the measurements used to assess the model performance in simulating soil moisture variations.
 While the temperature simulation was in close agreement with the measurements, the soil moisture simulation was not, except for the depths of 10 cm and 50 cm (Figure 9). At a depth of 10 cm, the simulation captured the important trend, which was the response of soil moisture to the precipitation at the end of day 1. However, the measurements at depths 20, 30 and 40 cm did not follow the same trend as the simulation. This partially indicated that the parameters in soil hydraulic properties, assumed vertically homogeneous, were probably not correct. HYDRUS1D [Saito et al., 2006] was also used to simulate soil moisture and temperature variations. Results of this showed that agreement between measured and modeled soil moisture content was not achieved throughout the profile [Zeng et al., 2009]. Further investigation should be undertaken to quantify the heterogeneity of the sand at the field site.
Figure 9. Same as Figure 8 but for soil moisture content at selected depths: (top to bottom) 10 cm, 20 cm, 30 cm, 40 cm and 50 cm. The solid black line is the simulation with airflow, the solid gray line is the simulation without airflow, and the red open circle is the measurement.
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 Figure 9 shows also the simulation of soil water content without considering airflow. Compared to Figure 8, the discrepancy between the two models in simulating soil water content is more obvious. The RMSEs between the simulated (considering airflow) and the measured volumetric soil water content are 0.0052, 0.0218, 0.0232, 0.0268 and 0.0051 (m−3 m3) at the depth of 10, 20, 30, 40 and 50 cm. For the simulation without considering airflow, the RMSEs are 0.0189, 0.0089, 0.0114, 0.018 and 0.0068 (m−3 m3) at the selected depths. Except for the depth of 20, 30 and 40 cm, the model considering airflow performs closer to the field measurement than without airflow. However, at these less-good-match depths, the model with airflow does have a much more sensitive response to the rainfall event than without considering airflow. Even at the depth of 50 cm, clear response to the rainfall event is shown by the model with airflow, while not by the model without considering airflow.
3.3.4. Comparisons With Evaporation Measurement
 With boundary conditions and forcing data in place, the validated model was used to determine the surface evaporative flux, a crucial parameter subsequently affecting the atmospheric modeling. The observed evaporative flux was calculated from the latent heat flux recorded by a three-dimensional eddy covariance system (Campbell Scientific, Inc., Logan, UT) installed 2 m above the surface. The system consisted of a CSAT3 three-dimensional sonic anemometer and a KH20 krypton hygrometer. The CSAT3 measured wind speed in three dimensions at a frequency of 10 Hz, and with the same frequency the KH20 measured vapor pressure. With the high-frequency data from CSAT3 and KH20, the latent heat flux was obtained every 30 min. The sensible heat flux was also obtained by the eddy covariance system.
 Figure 10 shows the comparison between evaporation rates, calculated by the proposed model and the model excluding airflow (e.g., PdV model), and the actual measurements. The normalized root mean squared deviation (NRMSD) was used to quantify the simulation's goodness of fit. NRMSD was expressed as percentage, where lower values indicated better agreement between simulation and measurement.
 Except for the day immediately after rainfall (the second day), there was no big difference in the calculated evaporation rate, whether airflow was included or not. The NRMSDs for the selected simulation period were 13% and 14% for the proposed model and the no-air model, respectively. However, if only the second day was taken into account, the NRMSD of the proposed model was 16% and that of the no-air model 27%. This meant that in this field case the proposed model did improve the simulation and made it come closer to reality than the no-air model did. The significant improvement seen on the second day was mainly attributed to the moist soil immediately after the rainfall event. During the rest of the simulation period, the topsoil layer dried up, diminishing the advantage of including the airflow mechanism.