Inverse Solution of Soil-Water Transport Model Parameters Using Response Surface Methodology

Soil hydraulic properties influence crop yield, soil fertility, and soil water status. While the laboratory or direct methods of measuring hydraulic properties are accurate, they are expensive, time consuming, and may not represent in-situ properties. On the other hand, model-based inverse solution procedures or indirect methods of estimating soil hydraulic conductivity (K) relate primary model variables such as volumetric water content (theta) and soil water suction (psi) to K and the soil-water characteristic curve. In this study, an inverse solution technique was developed to determine saturated soil hydraulic conductivity (K(s), cm h -1 ) and plant conductance to water uptake (C, m -1 min -1 ) under field conditions using a 1-D water transport model. The soil water content data (theta) were measured at 12 locations and at several depths at each location within the root zone in two different alfalfa checks using access tubes (each 1.5 m deep) and a neutron moisture probe. The inverse solution process utilized the measured soil moisture conditions in the alfalfa checks between two successive irrigations. In this study, the soil water retention curve was assumed to be of the form described by van Genuchten. The water contents at upper (0.225 m) and lower (1.2 m) depths provided the boundary conditions (BCs) needed for the model. The water content readings immediately following the irrigation event (i.e., t = 0) were used as the initial condition (IC). The model was solved to develop third-order orthogonal response surfaces over a range of model parameters (K(s) and C). Moreover, a multiple linear regression technique was used to empirically relate experimental theta to the depth and time of measurements. The response surface solutions were then optimized against the empirical surface to seek the optimum values of K(s) and C. The parameters estimated by the inverse solution technique were found to be unique and robust, and they predicted experimentally observed soil water data very well (R 2 > 0.95 and slope = 1:1 for most of the cases). These parameters, known from the inverse solution technique, were used to estimate the amount of deep percolation beyond the root zone depth for all cases.