Soil Science Society of America Journal 63:1608-1614 (1999)
© 1999 Soil Science Society of America
DIVISION S-1-SOIL PHYSICS
Estimation of Soil Evaporation Using the Differential Temperature Method
Guo Yu Qiua,
J. Ben-Asherb,
T. Yanoc and
K. Momiid
a Lab. of Environmental Plant Sci., National Inst. Environ. Studies, 16-2 Onogawa, Tsukuba, Ibaraki 305-0053, Japan
b The Jacob Blaustein Inst. for Desert Res., Ben-Gurion Univ., Sede Boqer Campus 84993, Israel
c Arid Land Research Center, Tottori Univ., 1390 Hamasaka, Tottori 680, Japan
d Dep. of Environ. Sci. and Technol., Kagoshima Univ., 21-24 Korimoto 1, Kagoshima 890, Japan
qiu.guoyu{at}nies.go.jp
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ABSTRACT
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Evaporation of soil water is a major water balance component during early growth stages of irrigated field crops, row crops with incomplete cover, and in soils with high water table. Quantification of soil evaporation can help in environmental and irrigation management. The objective is to develop a new method to estimate daily soil evaporation using differential measurements of temperature. A major advantage of this approach is that measurements of sensible heat flux can be replaced by those of surface temperature. An empirical coefficient was determined from integrated energy fluxes over daytime hours and mean daytime temperatures. It leads to a new soil evaporation transfer coefficient that can replace the aerodynamic resistance to calculate sensible heat flux. Experiments were conducted in a field with sandy soil that was irrigated with sprinklers and included a weighing lysimeter to measure actual evaporation. Measurements were of net radiation, soil heat flux over a wet and a reference air-dried soil, and air and surface temperatures of both soils. Regression between modeled and actual evaporation on a daily basis produced a slope of 1.05 and r2 = 0.9. Thirty days of cumulative model evaporation exceeded the measurements by 5%. The proposed coefficient can theoretically vary from 0 for wet soil to 1 for dry soil and can thus provide limits between 0 and potential evaporation. Actually, the coefficient increased from 0.2 to 0.8 in wet soil and from 0.8 to 1.0 in dry soil. The soil evaporation transfer coefficient was easy to measure, and it was sufficiently stable to adequately estimate soil evaporation.
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INTRODUCTION
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EVAPORATION OF SOIL WATER is a major water balance component during early growth stages of irrigated field crops, row crops with incomplete cover, and in soils with high water table. Quantification of soil evaporation can help in environmental and irrigation management. Estimation of evaporation from bare soil has recently been explored by using the energy balance method, and the microlysimeter method (Evett et al., 1994). Both methods have the advantage that the spatial variability of evaporation can be directly examined. Direct measurement of weight change due to surface evaporation from the microlysimeter is an important advantage. A disadvantage of the microlysimeter approach is that measurements are difficult and time consuming. The temperature-based energy balance method requires minimal measurement time and labor. Theoretical questions regarding parameter estimations are not completely solved; one example is the estimation of the aerodynamic resistance. The CONSERVB (Lascano and Van Bavel, 1986) and ENWATBAL computer codes (Lascano et al., 1987; Evett and Lascano, 1993; Qiu et al., 1999) use the general theory of surface soil temperature boundary conditions to develop an algorithm that estimates potential and actual evaporation from a bare soil by simulating a concurrent flow of water and heat. The simulation is laborious and requires extensive knowledge of soil hydraulic properties. Fox (1968) developed a technique to estimate evaporation from a bed of wet sand using wind speed and the difference between the daily maximum temperature of dry and wet sand. This technique is empirical because of the many assumptions and coefficients included. On the basis of Fox's work, Ben-Asher et al. (1983) and Evett et al. (1994) further verified and developed this technique, which was based on comparing the energy balance of a dry soil surface to that of a wet soil surface. Ben-Asher et al. (1983) used daytime mean wind speed and the difference between midday maximum soil surface temperatures of a reference dry soil and a wet soil to estimate evaporation, rendering the determination of two empirical coefficients in Fox's model unnecessary. Evett et al. (1994) re-evaluated the assumptions in Ben-Asher's model and wrote a new model to use half hourly temperatures and wind speed. Their derived equation was the best-fit aerodynamic resistance for dry soil, which showed that for their conditions (small containers), the aerodynamic resistance of dry soil was not dominated by wind speed. The model of Evett et al. (1994) is the only model known to rely on experimental results, and its successful implementation makes it imperative to further test the approach with intensive measurements of all the related parameters.
This study was executed in two major steps. First, experimental analysis led us to a modified equation for the differential temperature method. The modified equation was based on a soil evaporation transfer coefficient rather than on aerodynamic resistance. Secondly, we compared actual soil evaporation that was measured by a weighing lysimeter with evaporation estimated by the proposed differential model.
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Theory
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The basis for our discussion is the general energy balance equation:
 | (1a) |
On a dry soil without evaporation (LE = 0) Eq. [1a] becomes
 | (1b) |
where LE is the latent heat flux [E is the evaporative flux in kg m-2 s-1 and L is the latent heat of vaporization (2.4 MJ kg-1)], Rn is the net radiation at the soil surface, G is the soil heat flux (the rate at which heat is transferred into the soil profile), and H is the sensible heat flux between soil and atmosphere. All units are in J m-2 s-1. We employed the following sign convention values. Positive directions for Rn and G are toward the soil surface. Positive directions are taken as away from the soil for LE and H. The subscript "d" is for dry soil without evaporation (neglecting condensation and re-evaporation).
Two terms in Eq. [1] can be derived from the relationship between sensible heat flux and temperature as
 | (2a) |
 | (2b) |
where 
is air density (1.2 kg m-3), Cp is the specific heat of air (1010 J kg-1 K-1), ra is the exchange coefficient for sensible heat flux which is represented here as an aerodynamic resistance (s m-1), and T, Td, andTa are the respective wet soil surface, dry soil surface and air temperatures (K).
In Eq. [2a] and [2b], the aerodynamic resistance is the factor that is the least understood, and hence, it is more difficult to obtain for the estimation of sensible heat flux. Though ra can be estimated from physically based equations, laborious measurement is required to obtain it (Brutsaert, 1982) and there is no commonly accepted way to estimate it. For this reason we have conducted an empirical analysis of the data obtained from measurements over the two surfaces (wet and dry) in order to find an empirical variable related to the ratio between Eq. [2b] and [2a]:
 | (3) |
where 
, 
, and 
are the average daytime temperatures for the three subscripts. As shown in the results and discussion section, a linear regression analysis of Eq. [3] yielded the fact that the slope of rad/ra was near unity and its axial intercept was close to zero. Accordingly, in Eq. [1] we integrated the energy balance components over daytime hours (t), expressed 
Hdt in terms of Eq. [3] as
, and introduced it to Eq. [1a] in order to evaluate daily soil evaporation from
 | (4) |
As a matter of convention, for
we shall use the term soil evaporation transfer coefficient and assign to it the symbol ha. Equation [4] is a semi-empirical expression for the estimation of soil evaporation. The measurements that are required to calculate LE from Eq. [4] include four terms of energy fluxes (Rnd, Rn, Gd, and G) and three terms of temperature (T, Td, and Ta). Although Eq. [4] is still based on the differential temperature approach, more parameters must be measured in order to estimate LE by the proposed model than by the previous model (Evett et al., 1994), which requires only wind speed and the three temperature terms. The main advantage of Eq. [4] is that the soil evaporation transfer coefficient on Eq. [4] is very stable, ranging between zero and one. By comparison, ra can vary over an extremely wide range, even to four orders of magnitude (Brutsaert, 1982).
Analysis of Special Cases
Two special cases will now be examined. (i) The wet soil dries continuously until its surface water content is equal to the water content of the reference dry soil. Under this condition, we can get
. Consequently, ha = 1 and the two parts of the right hand side of Eq. [4] are equal to each other [i.e., (Rn - G) dt = (Rnd - Gd) dt]. Under this condition soil evaporation is zero, and as expected in Eq. [4], the LE dt is equal to zero. (ii) The second extreme condition is saturated soil, in which soil evaporation is controlled by atmospheric demand. Empirical models are often used to estimate soil evaporation under this condition. One of them was proposed by Priestley and Taylor (1972) to obtain daily potential evaporation.
 | (5) |
Equation [5] is usually applied to calculate mean values of LE over periods of a day or longer, where 
is the derivative of saturated vapor pressure with respect to air temperature (Pa K-1) and 
is the psychrometric constant (66 Pa K-1).
We shall examine this model and show that there is no major difference between Eq. [4] and [5] when soil is saturated. Equation [5] proved to be true for wind speed that is sufficient to mix soil and air vapors and to satisfy conditions of minimum potential evaporation (also referred to as equilibrium evaporation). Priestley and Taylor (1972) showed that during this stage of evaporation, the water vapor deficit is absent near the soil surface. Then the surface temperature of the wet soil is in equilibrium with air temperature (i.e.,
) and the second term in the right hand side of Eq. [4] is zero. Thus, Eq. [4] becomes an expression for potential evaporation from the saturated soil at its maximum rate given by LE dt = (Rn - G) dt. It should be emphasized that because the conditions of equilibrium evaporation in the sense of this analysis are hardly available, measuring the situation at which
is experimentally impossible and this analysis remains on the theoretical level. In the analysis to obtain Eq. [5] under conditions of equilibrium potential evaporation, the aerodynamic component was negligible. The aerodynamic component was also negligible in Eq. [4] under the same conditions. In spite of this similarity, Eq. [4] does not include the vapor pressure function /( + ) nor the empirical factor 1.26. To resolve this discrepancy we observed and showed that during midday, when evaporation is at its maximum, the product 1.26 /( + ) 
1 and Eq. [4] coincides with Eq. [5]. During these hours, as air temperatures vary from 25 to 35°C, /( + ) can vary from 0.747 to 0.824, and the product of these values with Priestley-Taylor factor (1.26 in Eq. [5]) approximates a value ranging from 0.93 to 1.03. Thus, for the theoretical case in which saturated soil surface evaporates at equilibrium potential evaporation at midday, our model complies with the model of Priestley-Taylor (1972). We can, therefore, conclude from the preceding that the proposed model is not dependent on aerodynamic resistance and provides consistent limits between no evaporation from a dry soil surface and potential evaporation from a saturated soil surface.
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Materials and methods
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The experiment was conducted on a 1-ha leveled field at the Arid Land Research Center, Tottori University, Japan (35°32'N; 134°13'E). The soil was Arenosol (silicious sand, Typic Udipsamment) with 96% sand. Porosity, field capacity, and wilting point were 0.4, 0.074, and 0.022 m3 m-3, respectively. Saturated hydraulic conductivity was 2.7 x 10-4 m s-1.
The study started on 5 May and continued until 4 June 1995. Irrigation was conducted by sprinklers between 2000 and 2200 h on 9, 16, 22, 26, and 29 May and 1 June. During each irrigation 13 mm water was applied and this was the only source of water for evaporation. Four reference air-dried soil samples were packed to the field bulk density (1430 kg m-3) in plastic pipes (one of 30 cm i.d., surface area 706 cm2, and 110 cm deep; and three of 20 cm i.d, surface area 314 cm2, and 55 cm deep). These cylinders were buried in the soil up to the field surface level, which is 5 m away from a weighing lysimeter. During irrigation they were covered with a sheet of polyethylene to prevent wetting and to assure that the soil remained dry. For the theoretical analysis we used data that were collected from the reference dry soil 2 wk after the experiment began in order to assure that data used for this analysis were collected from the reference dry soils only after the soils were thermally equilibrated. Actual evaporation from the wet soil was measured by a weighing lysimeter, which is described in Qiu et al. (1996a, 1996b). The lysimeter had a cylindrical shape with surface area of 1.77 m2, depth of 1.5 m, fetch of 50 m, resolution of 0.028-mm evaporation depth or equivalent 50-g weight change. The weighing lysimeter had a drainage system and drainage was conducted several times through the experimental period. Samples were recorded every 15 s and averaged every 30 min.
Net radiation over the wet surface was measured at a height of 2 m by an MS-45 Eko net radiometer (Eko Instruments, Tokyo). Solar radiation was measured at 2 m above the surface with MS-42 Eko solar radiation meter. The surface size of the reference dry soil was small and a special procedure was performed in order to measure net radiation from this surface. The first step of this procedure was the presentation of both Rnd and Rn in their energy balance forms: Rn = Rs(1 - 
) + Lin - Lout and Rnd = Rs(1 - d) + Lin - Ld,out, where Rs is the incoming short wave solar radiation; and d are albedos of wet soil surface and dry soil surface; and Lin and Lout are incoming and outgoing long wave radiation (units are J m-2 s-1). The second step was to determine the algebraic difference between Rnd and Rn to obtain Eq. [6], which was used to calculate Rnd:
 | (6) |
where
, 
is the Stefan Boltzmann constant (5.67 x 10-8 w m-2 K-4), 
is the emissivity (taken to be an average of 0.95), and = (d - w)e-kt (Gu et al., 1998). The maximum albedo on the dry reference is d = 0.35, the minimum albedo on the wet surface at saturation is w = 0.15, the extinction coefficient is k = 0.4, and t represent days after wetting of the surface. Using the above definitions, Rnd was calculated from Eq. [6] with Rs as the only additional measurement. All other parameters were known or taken in order to satisfy other measurements.
Surface temperature measurements were made with buried copper–constantan thermocouples. The thermocouples were covered with a 1-mm layer of sand to avoid heating by direct solar radiation and to replace the infrared thermometer (Evett et al., 1994). The temperature of the dry soil was measured with 12 replications and the temperature of the wet soil surface with 15 replications. Air temperature was measured with shielded thermocouples at height of 10 cm (five replications) and 20 cm (four replications). Soil heat flux was measured at a depth of 5 mm from the surface (assuming no heat storage above the plates) with five Eko-soil heat flux plates (type MF-9L). Two plates were placed in the dry soil and three in the wet soil.
The measurements were averaged and recorded on an automated data logging system every 30 min. Daily evaporation and all other energy balance components were calculated by integrating their diurnal curves, which were obtained from continuous measurements of three variables on each soil surface (temperature, soil heat flux, and net radiation), and two common variables Rs and air temperature. In order to test the empirical ratios of Eq. [3], we used the evaporation measured by the weighing lysimeter and calculated sensible heat flux integral (H dt in Eq. [3]) from the wet surface according to Eq. [1a] and for the dry surface according to Eq. [1b].
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Results and discussion
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Energy Exchange over Dry and Wet Soils
Figure 1
displays the behavior of daily integratedRn, H, and G over the wet and the reference dry soil during the study period from DOY (day of year) 142 through 149. Net radiation over the reference dry soil (Fig. 1a) was lower than that over the wet soil. The difference was more pronounced in the days that follow irrigation and was minimal as we approached the consecutive irrigation cycle. We can use Eq. [6] to further clarify the differences between Rn and Rnd by rewriting it as
 | (7) |
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Fig. 1 Comparison between daily energy exchange over wet and reference dry soil (a) net radiation; (b) soil heat flux; (c) sensible heat flux
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We see that Rn - Rnd was a direct consequence of time after irrigation (t) and wet surface temperature (T), which was increased and approached Td as t increased. At the irrigation day (t = 0) the terms on the right hand side of Eq. [7] were at maximum, and hence, the difference Rn - Rnd was also at its maximum, as shown in DOY 143 and 147 shortly after irrigation. Under stable climatic conditions without irrigation, the wet soil gradually became dry, the differences in albedo
approached their minimum, and the two surfaces became almost or absolutely identical, such that Rn - Rnd 0. This gradual process is well displayed in Fig. 1a from DOY 143 to 146 and from DOY 147 to 149.
Soil heat flux toward the wet soil (Fig. 1b) was significantly larger than the heat flux to the reference dry soil, especially during the days in which the irrigation cycle had started, as marked by the arrows. As time from the irrigation day proceeded, the difference between the two surfaces became smaller and in some days even negligible. Parts of the fluctuations in the reference soil heat flux were related to fluctuations of net radiation due to weather conditions. The amplitude of the heat flux to the wet soil was consistently larger than that for the reference soil. The larger soil heat flux toward the wet soil resulted from the larger water content in that soil, which is known to be associated with significant increase in its thermal conductivity. Thermal conductivity of sand increases very rapidly with increasing moisture content. In other words, wet soil is a relatively poor thermal insulator, and if even a little water is added, the effect of increased thermal conductivity largely dominates the effect the of thermal gradient that was larger in the dry soil than in the wet soil.
The sensible heat flux (Fig. 1c) showed similar trends of large differences after irrigation that gradually decreased with time, but more energy dissipated from the dry than the wet surface. Here the dominant factor was the strong thermal gradient that was generated at the dry soil surface because of its high surface temperature relative to the surface temperature of wet soil. Since there was no apparent difference in air temperature and aerodynamic resistances over the two surfaces, in Eq. [2] the dominant factor that affected the sensible heat flux from the dry soil was its surface temperature.
In Fig. 2
we selected one day to demonstrate the course of net radiation over the dry and the wet soils. The net radiation over the dry field (Fig. 2a) was smaller than over the wet field. Maximum differences were measured from 1000 to 1130 h, indicating that more energy was available for evaporation over the wet field than over the dry field, as already discussed above, for the daily sum. The difference became negligible when net radiation of both surfaces approached zero. As in the daily sum, soil heat flux (Fig. 2b) into the wet field was greater than the heat flux into the dry field because of greater thermal conductance of the wet soil.
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Fig. 2 Typical sampling day of (a) net radiation and (b) soil heat flux over the dry and the wet soil as a function of daytime hours
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The Correlation between ha and Hdt/Hddt
In order to test the plausibility of Eq. [3] we plotted ha and Hdt/Hddt as a function of time. The similarity between the two ratios can be seen in Fig. 3
. Both varied with irrigation sequence and climatic conditions. The fluctuations were between 0.4 and 0.9. The results of the linear regression analysis are given in Fig. 4
. In this figure we set the intercept of the trend line to zero because, theoretically, in Eq. [3] when
, the ratio Hdt/Hddt must also be zero. Under this restriction, the slope of the line in Fig. 4 was 1 and the coefficient of determination was r2 = 0.83. Results of this test indicated that ha and Eq. [4] can successfully replace the former models (Ben-Asher et al., 1983 and Evett et al., 1994) that were based on wind speed measurements. Thus, the analysis of the correlation between ha and Hdt/Hddt paved the way to introduce the modified differential temperature method for the estimation of daily soil evaporation.
Properties of the Soil Evaporation Transfer Coefficient
Figure 5a
displays the changes of surface temperatures with time after irrigation. Night values were not reported since they did not affect soil evaporation during daytime hours. Each daily cycle in Fig. 5 began at 800 h and ended at 1730 h. Shortly after irrigation (Day 0) when the surface of the wet field was wet, evaporation cooling resulted in the maximum differences between the wet and the dry soil surfaces. As time progressed, the difference between the surfaces reduced to a minimum 3 d after irrigation. The largest difference over all days was measured at 1200 h, while the smallest was measured in the afternoon. Though the difference between the three temperatures was small after sunset and before sunrise, during most of the evaporation hours the air temperature was lower than the temperature of the wet soil, and the temperature of the wet soil was lower than that of the reference dry soil. At the end of each day the temperature of the dry soil was slightly higher than that of the wet soil.
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Fig. 5 (a) The changes of surface temperatures with time after irrigation. (b) The soil evaporation transfer coefficient ha as a function of time after irrigation
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The corresponding ha is displayed in Fig. 5b. It can be seen that at the beginning of Day 0 ha was at its lowest (0.2). It gradually increased with temperature until it reached a maximum value of 0.8 with an average of 0.5. During the following day (Day 1), the starting value of the coefficient was 0.4 (greater than the starting value of Day 0), reaching a maximum of 1 at 1730 h. This maximum was reached during the following days, and it marked the upper limit of ha when surface temperatures of the reference dry soil and wet soil were equivalent and evaporation was reduced to zero. The average value of ha increased gradually from 0.5 to 0.7, to 0.8, and to 0.9. The high value of ha on Day 3 indicated negligible evaporation. It should also be noted that rapid changes of ha were due to the low water holding capacity of the sandy soil that dried quickly (usually faster than soils that are higher in silt, clay, and organic matter).
Toward the end of the daily evaporation, high values, 2ha units, were recorded. This was an isolated incident that occurred for a short time, associated with negative net radiation and soil heat fluxes and had negligible impact on total daily evaporation.
Calculated and Measured Evaporation
The cumulative evaporation (Fig. 6)
measured by the weighing lysimeter was consistently less than the evaporation calculated by the proposed method. The difference between the two cumulative lines in Fig. 6 was as high as 5%. We could not conclude from this study whether overestimation of measured evaporation is inherent in the proposed model nor whether similar overestimation would be observed under different soils and climatic conditions; however, an indication that overestimation by the differential temperature method may be negligible was obtained from the regression equation (graph not shown) of model results as a function of measured evaporation. The best fit line was Y = 1.046X + 0.018, r2 = 0.9. The slope close to 1 with a very small intercept indicated that the model generated reasonable quantitative results. Moreover, qualitatively, as can be further seen from Fig. 6, both curves show the cyclic fluctuations of evaporation. Shortly after irrigation (marked by arrows) when the wet soil was saturated, cumulative evaporation was controlled by the atmosphere and increased quickly. This trend continued for a short time (1 d) and then, following drying process of the wet soil, on both curves cumulative evaporation was controlled by the reduced soil water content and decreased gradually to its daily minimum, which appears as an intermediate asymptote between the two periods of irrigation.
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Fig. 6 Cumulative soil evaporation measured by a weighing lysimeter and calculated by the differential method as a function of time
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Analysis of Model Evaporation from Other Soils
Although application to other soils and climates were not yet studied, the basic principles of energy conservation on which the model was constructed authorize us to offer some preliminary predictions in order to demonstrate the possibility of using this model for other soils. In addition to the sandy soil, a dark, fine soil with large water holding capacity and low albedo is used for this purpose. Equations [4] and [7] and ha provide a simple description of the major factors that may be affected by the change of the soil type. The following four cases are examined. Case 1: The two soils are saturated and in both of them ha = 0. According to Eq. [4] and our previous analysis, under this condition evaporation is only limited by atmosphere demand, and soil types have no effect on evaporation. From this point of view, the model is consistent with the first constant evaporation stage (Hillel, 1981). Case 2: In both soils water depleted to its minimum such that ha = 1. According to our previous analysis, evaporation from both soils is zero. Cases 1 and 2, though they comply with the physical principles, are rarely encountered.
More realistic situations are the following two cases. Case 3: The two soils are unsaturated and have the same value of ha in Eq. [4]. Under these conditions, after the first stage of evaporation, the exponential extinction factor k in Eq. [7] dominates the process. Due to the lower water holding capacity of the sand and the higher water holding capacity of the fine, dark soil, the first phase is shorter on the sand. Because k of the sand (0.4) is larger than k of the fine textured soil (0.2, extracted from Gold and Ben-Asher, 1976), surface depletion on the sand soil is faster than on the fine, dark soil. Therefore, we predict that short time after irrigation, the term (d - w)e-kt on the sandy soil will be smaller than on the dark soil, even though (d - w) of the dark soil is smaller than that of the sand soil [for example, (d - w) = (0.30–0.15) when the water content of the dark clay soil was between 0.32 and 0.02, and (d - w) = (0.42–0.16) for the bright sand when water content was between 0.24 and 0.02 (Gold and Ben-Asher, 1976)]. The dominant role of k implies that Rn - Rnd is larger on the darker soil than on the bright sand. Therefore, according to the proposed model (especially Eq. [4]), daily evaporation from the darker soil is expected to be greater and the depletion with time is expected to be longer than from sand on a wide range of soil moisture conditions.
Case 4: The two soils are unsaturated but with variable ha under constant climatic conditions. Since ha is determined by soil surface temperature, the variation rate of ha is dictated by the ability of the soil to deliver water for cooling the surface. In other words, a large water holding capacity that characterizes the fine, dark soil type can maintain low surface temperature for a longer period than sand soil, which is characterized by small water holding capacity. It implies that ha is more stable for the hypothetical soil, which can produce small values for the rightmost side in Eq. [4] for a longer period and can further increase the evaporation from the hypothetical soil. The latter two cases demonstrate that the model predicts less evaporation from soils with high albedo. From this point of view, the model is consistent with the principles of energy conservation; however, it also demonstrated that albedo is only one of several factors affecting soil evaporation rate and that a rigorous treatment to account for differences in evaporation between soils is possible only if a comprehensive model capable of handling soil water and energy dynamic is employed.
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Summary
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In this study the basic concept of differential temperature measurements to estimate soil evaporation has been adapted. Evaporation was estimated from the temperature difference between wet soil and a reference dry soil in which evaporation was assumed negligible.
Two main changes are introduced to the modified model: (i) We did not use the Ben-Asher et al. (1983) approximation
 | (8) |
According to Eq. [8], the right hand term can be neglected in the energy balance equation because it is much smaller than the evaporation. Soil evaporation, then, was dependent only on the temperature variables and aerodynamic resistance functions. This approximation was associated with a maximum error of 9% in LE as measured by Evett et al. (1994). (ii) The aerodynamic functions were replaced by a soil evaporation transfer coefficient:
. The function ha determines the limits of soil evaporation between its maximum and minimum values. The lower limit (zero) is determined by available energy and the upper limit is determined by lack of water for evaporation.
These well defined boundaries in the new model are much less apparent in the models that are strongly linked to wind speed terms. The simplicity of ha renders it a useful tool that is simple to obtain for estimating soil evaporation, so quantitative information on soil evaporation may be obtained with considerably less measuring effort. The cumulative evaporation calculated by the model was in reasonably good agreement with the actual value, both qualitatively and quantitatively. Only three variables on each surface (temperature, soil heat flux, and net radiation), with incoming short wave radiation and air temperature as common variables, were used in order to obtain soil evaporation from a sandy soil. Although application to other soils and climates were not yet studied, the basic principles of energy conservation upon which the model was constructed authorize us to offer some preliminary predictions that have demonstrated that the method is consistent on other soils as well.
Received for publication November 9, 1998.
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REFERENCES
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TOP
ABSTRACT
INTRODUCTION
