Validity of First‐Order Approximations to Describe Parameter Uncertainty in Soil Hydrologic Models

Model nonlinearity and parameter interdependence violate the use of a first‐order approximation to obtain exact confidence intervals of parameters in soil hydrologic models. In this study, the posterior distribution of parameters in soil water retention and hydraulic conductivity functions is examined using observed water retention data and a laboratory transient multistep outflow experiment. Parameter uncertainties obtained with traditional first‐order approximations and uniform grid sampling strategies were compared with those obtained using the Metropolis algorithm, a Markov Chain Monte Carlo (MCMC) sampler. A diagnostic measure, based on multiple sequences generated in parallel, was used to test whether convergence of the Metropolis sampler to the posterior distribution had been achieved. Most significantly, as the Metropolis algorithm can cope with rough response surfaces generated by the objective function used, it not only successfully infers the multivariate posterior probability distribution of the model parameters, but also provides valuable insights in parameter interdependence in the full parameter space.