Maximum-likelihood estimation of unsaturated hydraulic parameters

Maximum-likelihood estimators properly represent measurement error, thus provide a statistically sound basis for evaluating the adequacy of a model fit and for finding the multivariate parameter confidence region. We demonstrate the advantages of using maximum-likelihood estimators rather than simple least-squares estimators for the problem of finding unsaturated hydraulic parameters.

Inversion of outflow data given independent retention data can be treated by an extension to a Bayesian estimator. As an example, we apply the methodology to retention and transient unsaturated outflow observations, both obtained on the same medium sand sample. We found the van Genuchten expression to be adequate for the retention data, as the best fit was within measurement error.

The Cramer–Rao confidence bound described the true parameter uncertainty approximately. The Mualem–van Genuchten expression was, however, inadequate for our outflow observations, suggesting that the parameters (α, n) may not always be equivalent in describing both retention and unsaturated conductivity.