Improved Inverse Modeling by Separating Model Structural and Observational Errors

Abstract

A practical formal likelihood function (L) is developed to separate model structure errors and observation errors by the separation of correlated and uncorrelated model residuals. L overcomes the time-consuming problem of likelihood functions proposed by previous studies, and combines the Mean Square Error (MSE) and first-order Auto-Regression (AR(1)) models. For comparison of the effect of different error models, MSE, AR(1), and L are used as efficiency criteria to calibrate the three-dimensional variably saturated ground-water flow model (MF2K-VSF) based on the soil tank seepages of rainfall–runoff experiments. Results of L are nearly the same as those of AR(1) due to negligible observational errors. Although all calibrated models well mimic the seepage discharges, MF2K-VSF with MSE cannot capture the groundwater level and soil suction processes because of the considerable autocorrelation of model residuals owing to model inadequacies (e.g., neglect of the soil moisture hysteresis), which obviously violates the statistical assumption of MSE. By contrast, L accounts for the model structural errors and thus enhances the reliability of hydrological simulations.