Multiple inverse models for estimating soil hydraulic parameters based on field-scale moisture content observation

Abstract: Unsaturated zone hydrological processes played an important role between the processes of surface and groundwater hydrology. The Richards' equation was widely utilized to describe unsaturated zone flow due to its solid physical foundation. It was essential to know the parameters of this equation before simulation, and these parameters were also called as soil hydraulic parameters in this paper. Comparing with experimental methods, the inverse method was a more realistic way to obtain parameters. Universal Inverse Code (UCODE) using gradient-type minimization method provided users with flexibility in estimating parameters of forward models. However, there were many numerical methods to solve Richards' equation, and four representative numerical models discussed in this paper were Ross model, Picard-θ model, Picard-mix model and Picard-h model, respectively. It had been known that the Ross model was of the most computational efficiency, while Picard-h model may lead to serious mass balance problem. Based on the combination of UCODE and four numerical models of Richards' equation, four different inverse models of unsaturated flow were constructed in this paper to optimize three parameters of Richards' equation, i.e., Ks (Saturated Hydraulic Conductivity), α (Reciprocal of Air Entry Pressure) and n (Grain Size Distribution Parameter). In this paper, a ten days infiltration test was conducted in a 7.77 m ×29.38 m area located in Wuhan University Water Conservancy and Water Environmental Laboratory (China), and observed data was the soil water content measured by TRIME-PICO IPH system. Every 24 hours was as an irrigation-measurement period. The upper boundary flux Ra[L/T] changed with time. More specifically, Ra was 80 mm/d during the first 3 hours, while it was 0 mm/d in the last 21 hours. Before the infiltration test, Ks was measured directly by 29 double rings, and the others parameters were measured by centrifugal method (4 filled samples and 36 undisturbed samples). The parameters Ks and α significantly varied in space, while the variance of soil water content decreased with time due to uniform upper boundary in space. The measured soil hydraulic parameters were used as initial value, and then Ks, α and n were respectively estimated by the four inverse models based on the soil water content observed in the field scale. Several indexes, i.e. R2 (Coefficient of Determination), RMSE (Root Mean Squared Error), BIAS, IA (Index of Agreement), were used to evaluate the precision that the simulated model results matched the observed variables. By comparison of these indexes, the precision order of the four inverse models and measured parameters from high to low was as follows: Ross inverse model (RMSE: 0.0123), Picard-θ inverse model (RMSE: 0.0124), Picard-mix inverse model (RMSE: 0.0125), Picard-h inverse model (RMSE: 0.0128) and measured parameters (RMSE: 0.0138). The reason for the minimal differences of soil water content data simulated by the four models was that water retention curves (or unsaturated hydraulic conductivity curves) described by the four groups of optimized parameters were close to each other. Besides, the precision of the four inverse models were marginally improved with smaller grid size. In addition, the parameter equal finality was discussed in this paper. A group of parameters, by which RMSE is less than 0.0128 in this paper, can be called equivalent parameters. It can be noticed that the curves intersected in the soil water moisture interval where there were more observation values. The equal finality zone was defined as the envelopes of water retention curves or unsaturated hydraulic conductivity curves described by equivalent parameters. We discussed equal finality zones at three cases (RMSE≤0.128, RMSE≤0.128, RMSE≤0.125 and RMSE≤0.124) and pointed out that the width of equal finality zone became narrower with the demand of higher precision. The equal finality zone was also used to illustrate the fact that the precision of the filled samples were much higher than that of undisturbed samples.