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

An increasingly attractive alternative to the direct measurement of soil hy draulic properties is the use of inverse procedures. We investigated the co nsequences of using different variables or combinations of variables from a mong pressure head, water content, and cumulative outflow on the estimation of hydraulic parameters by inverse modeling. We also looked at a new multi plicative formulation of the objective function which does not require weig hts for different variables. The inverse study combined a global optimizati on procedure, Sequential Uncertainty Fitting (SUFI), with a numerical solut ion of the one-dimensional variably saturated now equation. We analyzed mul tistep drainage experiments with controlled boundary conditions on two larg e lysimeters. Estimated hydraulic parameters based on different objective f unctions were all different from each other; however, a significance test o f simulation results based on these parameters revealed that most of the pa rameter sets produced simulation results that were statistically the same. Notwithstanding the significance test, ranking of the performances of the f itted parameters on the basis of the mean square error (MSE) statistic reve aled that they were highly conditional with respect to the variables and th e mathematical formulation of the objective function. To obtain statistical ly unconditional sets of parameters, we introduce and discuss the concept o f "parameter conditioning" instead of "parameter fitting". Parameter condit ioning identities a parameter domain such that when propagated in a stochas tic simulation, all or most of the measured points of a variable are within the 95% confidence interval of the Bayesian distribution of that variable.