Influence of Properly Weighting Soil-Water Retention Curve Data in Least Squares Analysis

The accurate prediction of soil hydraulic parameters is essential to simulate the transport of water, solutes and contaminants in soil, management of the agricultural water, management of production and in soil and water conservation. The least squares regression is the most common method applied for fitting the soil-water retention curve (SWRC) function to the observed data-points to optimize its parameters. However, the variance of SWRC data varies in different moisture content and therefore, unlike the wet-end of SWRC, the conventional unweighted regression method may not be sufficiently effective in estimating its dry-end (higher suctions). While, selected soil processes, such as soil moisture redistribution or transport of contaminants in soil occur in low soil moisture contents which correspond to the dry-end of the curve. Consequently, in fitting different hydraulic functions to SWRC, the accuracy of SWRC parameters would be improved in the low-moisture range content by determining the appropriate weights for data points. Accordingly, the objective of this study was to investigate the effect of properly weighting the SWRC data points on increasing the accuracy of the estimated soil hydraulic parameters. In this study, undistributed soil samples were collected from 20 cm soil depth with six replications. The SWRC of the samples were measured at suctions of 0 to 15000 cm. In order to fit the van Genuchten equation of SWRC on measured values of h(θ) and to estimate its hydraulic parameters through RETC code, the weighted least squares regression method was also used along with the conventional standard least squares regression method. For this purpose, some weights were assigned to the data points as the inverse of the variance of the measured volumetric soil water content in six replications, so that, the effect of the curve estimation error in low moisture contents were considered by assigning larger weights in the regression fitting. Finally, the accuracy of unweighted and weighted regression in the fitting of the SWRC model on the measured data was compared using statistical criteria and a suitable method for the averaging of hydraulic parameters was introduced. Comparison of the fitted hydraulic parameters by unweighted and weighted regression showed that the mean values of the residual water content (Ɵr), saturated water content (Ɵs) and α parameter (reciprocal of air-entry suction) in the weighted method were lower than the unweighted method, however the n parameter values obtained by the weighted method were higher than unweighted method. Reproduction of SWRC using the values hydraulic parameters estimated by either unweighted or weighted methods showed that the weighted method increases the accuracy of the estimation and reduces the percentage of point error in lower moisture contents (higher suctions) compared to the unweighted method. Although, the weighting method generally increased the error of SWRC estimation and decreased the correlation between estimated and observed moisture content. We found that, in both unweighted and weighted regression, the method II (averaging of volumetric water contents at different suctions and estimating hydraulic parameters) had a lower error in compression to method I (averaging of hydraulic parameters). However, in estimation of SWRC in lower moisture contents, the method I had lower point error than that of method II. The method I reduced the error percentage in the weighting method. Assigning proper weight to SWRC data points improves curve fitting in lower moisture range, which is very important in simulating redistribution of moisture or transfer of contaminants transport in the soil processes, particularly in arid and semi-arid conditions.