Scaling of Hydraulic Functions in Heterogeneous Soil Using Nonlinear Least Squares Minimization Method

Presenting soil heterogeneity precisely in various spatial scales is the main key to simulate water and solute transport through it. The method described by Richards is mostly used to study water flow through vadose zone. It requires spatial representation of hydraulic functions and water retention relationship in the soil. To represent the spatial relationship of soil hydraulic functions, scaling approach is being used since the last few decades. In this study, a simple scaling method using nonlinear least squares minimization technique has been used to scale soil matric potential, hydraulic conductivity as well as simultaneous scaling of soil matric potential and hydraulic conductivity data. Simultaneous scaling is necessary as it reduces the volume of data by producing a single set of scale factors for hydraulic functions in a heterogeneous soil. Van Genuchten’s semi-empirical expressions were used in this study to parameterize soil hydraulic functions. Results showed that correlation coefficient from raw and descaled data was superior when soil matric potential and hydraulic conductivity data were scaled separately than simultaneously. Improvement of correlation coefficient in simultaneous scaling can be obtained by adding more weight to the soil matric potential data than unsaturated hydraulic conductivity data, which enhances the overall correlation coefficient in simultaneously scaling. Statistical analysis of the scale factors showed that they are lognormally distributed. Scale factors calculated by solving simple equations obtained using the method described in this study can be used to simulate water movement through heterogeneous soil conditions using HYDRUS model.