Quantifying and Accounting for Uncertainty

Abstract

This chapter deals with a wide range of issues with a common theme: coping with uncertainty. To this end, we look at the sources of uncertainty and the types of errors we need to deal with. We then explore methods for identifying these errors and for incorporating them into our predictions. This chapter extends our discussion on these topics in chapter 1, the discussion in chapter 3 on estimation under conditions of uncertainty, and image simulation using MC techniques. A comprehensive treatment of uncertainty needs to address two different types of errors. The first type is the model error, which arises from incorrect hypotheses and unmodeled processes (Gaganis and Smith, 2001), for example, from poor choice of governing equations, incorrect boundary conditions and zonation geometry, and inappropriate selection of forcing functions (Carrera and Neuman, 1986b). The second type of error is parameter error. The parameters of groundwater models are always in error because of measurement errors, heterogeneity, and scaling issues. Ignoring the effects of model and parameter errors is likely to lead to errors in model selection, in the estimation of prediction uncertainty, and in the assessment of risk. Parameter error is treated extensively in the literature: once a model is defined, it is common practice to quantify the errors associated with estimating its parameters (cf. Kitanidis and Vomvoris, 1983; Carrera and Neuman, 1986a, b; Rubin and Dagan, 1987a,b; McLaughlin and Townley, 1996; Poeter and Hill, 1997). Modeling error is well recognized, but is more difficult to quantify. Let us consider, for example, an aquifer which appears to be of uniform conductivity. Parameter error quantifies the error in estimating this conductivity. Modeling error, on the other hand, includes elusive factors such as missing a meandering channel somewhere in the aquifer. This, in essence, is the difficulty in determining modeling error; parameter error can be roughly quantified based on measurements if one assumes that the model is correct, but modeling error is expected to represent all that the measurements and/or the modeler fail to capture. To evaluate model error, the perfect model needs to be known, but this is never possible.