St. Elmaloglou
*, N. Malamos
Agricultural University of Athens, Department of Natural Resources and Agricultural Engineering, Laboratory of Agricultural Hydraulics, Iera Odos 75, 11855, Athens, Greece
Accepted 9 April 1999
Abstract
A simulation study of the soil moisture content under a prairie field, in Gembloux Belgium, by the use of the one-dimensional model SWAP93, was carried out. In order to determine the optimum relationship thatSmaxis following, two concepts of maximum water extraction rate were examined.
The first one assumed a linear variation of Smax with depth z and the second assumed a
homogeneous distribution ofSmaxwith depthz. Five statistical criteria were used to compare the
quality of simulation results, such as average error (AE), root mean square error (RMSE), root mean square (RMS), modeling efficiency (EF) and coefficient of residual mass (CRM). The differences between the criteria, showed that the assumption of the homogeneous distribution of Smax
throughout the soil profile resulted in a more accurate prediction of soil moisture content. The agreement between measured and simulated water content profiles, throughout the regarded period, was satisfactory for depths >30 cm. The deviation between simulated and experimental values for depth <30 cm could be explained by the influence from the cracks in the soil surface and wormholes that cause water losses and, consequently, underestimation of the experimental values.
#2000 Elsevier Science B.V. All rights reserved.
Keywords: Modeling; SWAP93; Prairie; Soil moisture content; Water extraction rate
1. Introduction
The development of mathematical models for soil±plant±atmosphere system has become the objective of extensive research during the last decades, mainly from soil
* Corresponding author. Tel.: +30-1-5294068; fax: +30-1-5294081.
E-mail address: [email protected] (S. Elmaloglou).
physicists, agricultural and hydraulics engineers. During this process a large number of models have been published, that range in their complexity from a simple transpiration model to a more comprehensive generic model involving the assimilation procedures of plants and the transient soil moisture flow equation.
Regarding water movement, many models use the Richards' equation to calculate soil-water flow (Nimah and Hanks, 1973a, b; Childs et al., 1977; Belmans et al., 1983; Radcliffe et al., 1986; Wagenet and Hutson, 1987; Lafolie, 1991; Clemente et al., 1994; Van den Broek et al., 1994).
Besides this approach, other models follow the daily water budgeting approach (Boisvert et al., 1992b) and the soil-water component of the crop growth models (Ritchie, 1985; Benson et al., 1992).
In this study the SWAP93 model, is used to simulate the water balance of a prairie field, assuming two concepts of maximum water extraction rate. This model originates from the model SWATR (Feddes et al., 1978), which was further developed by Belmans et al. (1983), Wesseling et al. (1991) and Van den Broek et al. (1994). The field was located in the area of Gembloux, Belgium, during the time period of 26/3/1976 to 28/6/1976.
2. Methodology
2.1. Soil physical properties
Field measurements for this research were obtained from a field study on prairie site in Gembloux, Belgium. A full description is given in Elmaloglou (1992). The soil on the study site is deep silt, with a relatively stable water table well below the 5 m depth. The data collection of the soil-water content (), was made by using a neutron probe, the calibration of which was performed for each one of the different soil layers. The water content measurements were taken within intervals of 10 cm to the depth of 180 cm and at least two times per week.
The soil matrix was divided in five layers, according to the results of the mechanical analysis, and the pF curves adopted in the laboratory, with Richard's apparatus, from the undisturbed specimens. The depth of each soil layer is shown in Table 1.
The pF curves, (Fig. 1), were produced by the `spline' function of the KTHETA program (Belmans, 1985). With the use of the same program the K± relations were extracted from the pF curves and also the saturated hydraulic conductivity (KS).
2.2. Crop development
Input data, adopted from the literature, are presented in Fig. 2 and consisted of values of leaf area index (LAI) and depth of the active roots.
The maximum thickness of the nonactive layer at the top of the soil profile was set to zero.
2.3. The model SWAP93
In the present study, the agro-hydrological model SWAP93 was used. For a detailed description of model assumptions and descriptions of the individual processes represented in the model the reader should refer to Smets et al. (1997). A brief description follows.
SWAP93 calculates the soil-water flow using an iterative solution of Richards' equation, based on the law of Darcy±Buckingham and the principle of mass conservation. In order to solve this equation, the soil hydraulic functions of each layer should be known. The root water uptake is described semi-empirically by a sink term, which is a function of the maximum root water uptake and the soil-water pressure head. Actual transpiration rate is set equal to root water uptake rate. The potential evapotranspiration, irrigation and precipitation determine the upper boundary conditions of the system. The model uses the formula of Ritchie (1972) for the calculation of potential soil evaporation. Based on general information from the literature, the previous formula was replaced by the Van Aelst formula (Van Aelst et al., 1988), and the calculated potential soil evaporation was reduced to the actual evaporation by taking the minimum of:
1. the potential evaporation rate;
2. the maximum soil-water flux in the top soil according to Darcy±Buckingham equation assuming a minimum allowed pressure head in the atmosphere; and
3. the empirical evaporation rate according to either Black et al. (1969) or Boesten and Stroosnijder (1986).
At the bottom of the system, boundary conditions can be described with various options, e.g., water table depth, flux to groundwater or free drainage (Wesseling et al., 1991).
2.4. Sink term
The sink term,S, is the function of maximum water extraction rateSmaxat depthzand
the water pressure head as:
S h;z a hSmax z
where(h) is a reduction factor that varies between zero and one (Fig. 3).
In order to determine the optimum relationship thatSmax is following, two different
scenarios were simulated (Fig. 4). The first one assumed a linear variation ofSmaxwith
depthzgiven by the formula (Hoogland et al., 1981):
Smaxaÿbjzj
Fig. 3. Schematic view of the dimensionless sink-term variable alpha (), as a function of the soil water pressure head,h.
whereais the maximum extraction rate at surface andb the reduction coefficient. The values of a and b were set to 0.007 and 0.00005, respectively. The second scenario assumed a homogeneous distribution ofSmaxwith depthz(Feddes et al., 1978), and the
value ofSmaxwas 0.005. The above values were based on information from the literature.
2.5. Statistical criteria
To evaluate the model's performance, several measures were used, such as average error (AE), root mean square error (RMSE), root mean square (RMS), modeling efficiency (EF) and coefficient of residual mass (CRM). The relationships, which describe these measures of analysis, are (Loague and Green, 1991):
AEX
wherePiare the predicted values,Oithe observed data,nthe number of samples andO
the mean of the observed data.
The AE, RMSE, RMS statistics have as lower limit the value of zero, which is the optimum value for them, as it is for CRM. The maximum and simultaneously the optimum value for EF is 1. Positive values of CRM indicate that the model underestimates the measurements and negative values indicate the model's tendency to overestimate (Hack-ten Broeke and Hegmans, 1995). If EF is less than zero, the model predicted values are worse than simply using the observed mean (Loague and Green, 1991).
3. Results and discussion
3.1. Soil moisture profiles
The simulations throughout the regarded period were very satisfying for depths >30 cm for both cases (Figs. 5 and 6). In case of homogeneousSmax(Fig. 5) there was a better
Fig. 5. Measured (symbols) and simulated (lines) water content profiles forSmax0.005, for Julian dates: 86, 111, 140, 161.
analysis results (Table 2). It should be noted that the deviation between simulated and experimental values for depth <30 cm, could be influenced from the cracks in the soil surface and wormholes that cause water losses and consequently underestimation of the experimental values.
Figs. 7 and 8 present the calculated and measured soil moisture content at depths of 20, 50 and 70 cm, respectively. The overall agreement is very good, but it is interesting to note the differences that occur at the start of the simulation. During this period, at the depth of 20 cm, the calculated water content was lower than the observed one, at 50 cm was higher and at 70 cm was also lower. One of the reasons that are responsible for that difference, is the rate of plant water extraction. Thus, we assumed that the sink term
S(h,z) as calculated by the model, was higher than the actual rate in the upper and lower layers, while lower in the middle one.
Table 2
Values of the statistical parameters used in comparison forSmax
Smax Depth (cm) AE (cm3/cm3) RMSE (%) RMS (%) EF CRM
0.007±0.00005|z| 20 ÿ0.008 10.64 2.35 0.830 0.038
50 0.006 2.50 0.69 0.951 ÿ0.022
70 ÿ0.002 3.72 1.13 0.757 0.006
0.005 20 ÿ0.004 8.43 1.86 0.899 0.017
50 0.004 2.07 0.57 0.967 ÿ0.015
70 ÿ0.003 3.09 0.94 0.848 0.009
Fig. 7. Comparison of simulated (lines) and measured (symbols) water content at 20, 50, 70 cm, for
As a consequence, the rate of water uptake by the whole root system, which is set equal to plant transpiration can be either overestimated or underestimated.
3.2. Statistical analysis
The discrepancy between measured and simulated soil moisture content is generally smaller withSmax0.005, than withSmax0.007ÿ0.00005|z|, as shown in Figs. 7 and
8. Root mean square error RMS and RMSE, (Table 2) are smaller in the first case and are generally small in both cases indicating little deviation between measured and simulated values. Also, in the first case, the values of modeling efficiency (EF) are greater than in the second, by a percentage that varies from 10.7% (70 cm depth) to 1.7% (50 cm depth). In addition, the values of coefficient of residual mass (CRM), are smaller than in the second case, by a percentage that varies from 123% (20 cm depth) to 33.3% (70 cm depth).
Based on the above analysis, it is apparent that we had better simulation results with constantSmax.
4. Conclusions
Soil moisture content and pressure head values were simulated by the SWAP93 model, using field data obtained in 1976 for grass crop in Gembloux, Belgium, for two different patterns of root water extraction. The agreement between measured and simulated soil
Fig. 8. Comparison of simulated (lines) and measured (symbols) water content at 20, 50, 70 cm, for
moisture content profiles, throughout the regarded period, was satisfactory for depths >30 cm. Differences between five statistical criteria calculated to assess the difference between measured and calculated values of against time, at three different depths, showed that the assumption of the homogeneous distribution ofSmaxthroughout the soil
profile resulted in a more accurate prediction of soil moisture content.
The small overall differences imply that the model is successful and can be a useful tool in predicting the different components of the soil-water balance of a prairie field.
Acknowledgements
The authors wish to thank Prof. S. Dautrebande (Agricultural University of Gembloux, Belgium) for providing the data concerning the soil physical characteristics and the meteorological data. Copy of the SWAP93 model, was obtained from Prof. J.G. Wesseling (DLO-Winard Staring Centre, Wageningen, Netherlands).
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