TESTING PROCEDURES FOR SPATIALLY DISTRIBUTED FLOW MODELS

Methods for testing, verifying, and validating predictive models of variably saturated groundwater flow are discussed. Specific procedures are introduced for measuring model complexity, assessing model consistency, and testing model validity. The discussion addresses numerical formulation, verification of internal consistency, benchmarking, groundtruth testing, performance measures, parameter estimation, hypothesis testing, and probabilistic induction. Verification of models includes tests of internal consistency and accuracy, like mass conservation and sensitivity to mesh size. Verification of codes also involves comparing results from the numerical model to analytical solutions, which are, however, limited in scope, and comparison with other numerical codes or 'benchmarking'. These aspects are illustrated using available three-dimensional codes developed by the authors. Recognizing the diversity of spatially distributed modeling approaches, we also propose measures of model complexity and of the amount of information inherent in model predictions. One of these measures is the spatial degree ot' freedom, a function of material and boundary heterogeneities in the model. Another one is the quantity of information or entropy, which depends also on precision. Several aspects of 'groundtruth' model validation using data from laboratory and field tests are discussed. Logical inference is used to distinguish model validation from refutation. Recognizing that full validation is not possible in practice, we formulate performance criteria to define the 'degree of validation'. Concepts and methods based on inductive calculus, Bayesian hypothesis testing, and maximum likelihood, are analyzed in some detail as alternative model validation strategies. Several examples of model testing are also discussed.