Comparison of computationally frugal (linear) to expensive (nonlinear) methods for analyzing inverse modeling results

Methods for analyzing inverse modeling results can be separated into two categories: (1) linear methods, such as Cook’s D, which are computationally frugal and do not require additional model runs, and (2) nonlinear methods, such as cross validation, which are computationally more expensive because they generally require additional model runs. Depending on the type of nonlinear analysis performed, the additional runs can be the difference between 10’s of runs and 1000’s of runs. For example, cross-validation studies require the model to be recalibrated (the regression repeated) for each observation or set of observations analyzed. This can be computationally prohibitive if many observations or sets of observations are investigated and/or the model has many estimated parameters. A tradeoff exists between linear and nonlinear methods, with linear methods being computationally efficient, but the results being questioned when models are nonlinear. The trade offs between computational efficiency and accuracy are investigated by comparing results from several linear measures of observation importance (for example, Cook’s D, DFBETA’s) to their nonlinear counterparts based on cross validation. Examples from ground water models of the Maggia Valley in southern Switzerland are used to make comparisons. The models include representation of the stream-aquifer interaction and range from simple to complex, with associated modified Beale’s measure ranging from mildly nonlinear to highly nonlinear, respectively. These results demonstrate applicability and limitations of applying linear methods over a range of model complexity and linearity and can be used to better understand when the additional computation burden of nonlinear methods may be necessary.