Exploring Model Complexity for Column Experiments Using Model Selection Criteria

Abstract:

Selecting the reliable models for simulating column experiments is essential for the identification of processes governing contaminant transport. The aim of this work is to use model selection criteria (AIC, AICc, BIC and KIC) for exploring the most appropriate model to avoid over-complex and/or over-parameterized models. We consider five models of different levels of complexity, including the equilibrium and non-equilibrium convection dispersion models. The simplest model (CDE1) consists of the convection-dispersion equation, and only dispersivity is calibrated against column experiments. The most complex model (MIM2) is the mobile-immobile model with four parameters calibrated (with two parameters specifically for the model). The model selection criteria are used to evaluate the probabilities of the five models. It was found that using the full covariance matrix that consider residual correlation resolve the problem that the most complex model receives almost 100% model probability, which is not explainable by available data and knowledge. The model complexity is related to the various terms of the model selection criteria, and their relation is examined by physical understanding of the alternative models and the column experiments. The model selection criteria consider the goodness-of-fit statistics, number of model parameter, sensitivity to the model parameters, and uncertainty of the parameters. Considering these factors can prevent from occurring over-complexity and over-parameterization, when selecting the appropriate models for simulating column experiments. Cross-validation is conducted to confirm the conclusions drawn based on the model selection criteria.