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.

Bounding of Flow and Transport Analysis in Heterogeneous Saturated Porous Media: A Minimum Energy Dissipation Principle for the Bounding and Scale-Up

“…which demonstrates the Kelvin-type theorem that states the minimum total energy dissipation in the homogeneous system is always less than the dissipation that occurs for flow in any heterogeneous porous material occupying the same corresponding volume. Such minimum total dynamic energy dissipation ideas may seem more definitely indicated in the expanded inequality form provided by substituting Equations (6) and 7into Equations (13) and (14) and then combined with Equation 24to give:…”

“…This one-dimensional case provides a simple example to show how these conditions are satisfied. Assume a one-dimensional flow column of uniform cross-sectional area, A, and of total length, L, with the length along the column being denoted by, λ, where 0 ≤ λ ≤ L. Then Equation (27) becomes, using Equations (6) and 7:…”

“…A major difficulty in evaluating groundwater contaminant transport problems is our limited capacity to consider the full effects of subsurface material heterogeneity [2][3][4]. Unfortunately, the methods needed to completely characterize and model heterogeneous systems are impractical or not available [5,6]. Even as characterization methods gradually become more practical, time and costs for complete characterization of heterogeneous systems can still be prohibitive for most field problems.…”

Symmetrical Rank-Three Vectorized Loading Scores Quasi-Newton for Identification of Hydrogeological Parameters and Spatiotemporal Recharges

“…However, in previous studies, the establishment of a groundwater flow model has focused on hydrogeological parameter identification. The spatiotemporal patterns of pumpage and net recharge are mostly regarded as known [3][4][5][6][7][8][9][10][11][12][13][14][15]. If the pumpage and recharge spatiotemporal patterns are arbitrary, the calibrated model is subject to uncertainty [16].…”

The Use of River Flow Discharge and Sediment Load for Multi-Objective Calibration of SWAT Based on the Bayesian Inference

“…Many Pareto-based multi-objective calibration algorithms have been developed such as the multi-objective complex evolution (MOCOM) method [9], the multi-objective shuffled complex evolution metropolis algorithm (MOSCEM) [14], the nondominated sorting genetic algorithm (NSGA-II) [15], and the multi-algorithm genetically adaptive multi-objective method (AMALGAM) [16]. However, there are still some disadvantages in using these approaches: (1) they can only obtain the "Pareto front", rather than best fit results, so it still needs to convert the multi-objective values into a single value using the weighted sum principle for determination of the optimum solution [17]; (2) they are usually complex and time-consuming [10]; (3) they are difficult to estimate the parameter uncertainty because most parameter uncertainty analysis methods (such as Markov Chain Monte Carlo (MCMC) and Generalised Likelihood Uncertainty Estimation (GLUE)) are based on a single objective [18][19][20].…”