Nonlinear mixed effect modelling for improved estimation of water retention and infiltration parameters

Accurate estimation of soil hydraulic functions is an important topic in soil physics and hydrology. Soil scientists and hydrologists use experimental data to derive parameters of the hydraulic functions, and when measurements are not available they utilise pedotransfer functions. In all of the current methods, there is a lack of consideration for environmental covariates in the parameter estimation process. This paper presents nonlinear mixed effects (NLME) approach that incorporates various sources of information to make parameter estimates for population and individual-sites at the same time. Using likelihood approximations, NLME allows structured covariance matrices and estimated parameters to vary over sample-points thus giving more accurate description of the magnitudes and sources of inter-individual variations. This approach was used to estimate the hydraulic parameters from infiltration and water retention measurements that incorporate information about soil degradation. The performance of NLME was compared to: (i) average parameters obtained by considering whole dataset as one group and (ii) individual treatment of each sample-point independently. The best performance was achieved with NLME that gave the lowest residual standard error for the Philip’s infiltration and the van Genuchten’s water retention function. By including sampling structure and covariates in the parameter estimation process, NLME offers opportunity to study the mechanisms or factors producing a particular hydrologic response from different parts of the watershed. This information can be used for targeting recommendations in watershed management.