Uncertainty in estimation of soil hydraulic parameters by inverse modeling: Example lysimeter experiments

An increasingly attractive alternative to the direct measurement of soil hydraulic properties is the use of inverse procedures. We investigated the consequences of using different variables or combinations of variables from among pressure head, water content, and cumulative outflow on the estimation of hydraulic parameters by inverse modeling. We also looked at a new multiplicative formulation of the objective function which does not require weights for different variables. The inverse study combined a global optimization procedure, Sequential Uncertainty Fitting (SUFI), with a numerical solution of the one-dimensional variably saturated now equation. We analyzed multistep drainage experiments with controlled boundary conditions on two large lysimeters. Estimated hydraulic parameters based on different objective functions were all different from each other; however, a significance test of simulation results based on these parameters revealed that most of the parameter sets produced simulation results that were statistically the same. Notwithstanding the significance test, ranking of the performances of the fitted parameters on the basis of the mean square error (MSE) statistic revealed that they were highly conditional with respect to the variables and the mathematical formulation of the objective function. To obtain statistically unconditional sets of parameters, we introduce and discuss the concept of "parameter conditioning" instead of "parameter fitting". Parameter conditioning identities a parameter domain such that when propagated in a stochastic simulation, all or most of the measured points of a variable are within the 95% confidence interval of the Bayesian distribution of that variable.