Are models too simple? Arguments for increased parameterization.

The idea that models should be as simple as possible is often accepted without question. However, too much simplification and parsimony may degrade a model's utility. Models are often constructed to make predictions; yet, they are commonly parameterized with a focus on calibration, regardless of whether (1) the calibration data can constrain simulated predictions or (2) the number and type of calibration parameters are commensurate with the hydraulic property details on which key predictions may depend. Parameterization estimated through the calibration process is commonly limited by the necessity that the number of calibration parameters be smaller than the number of observations. This limitation largely stems from historical restrictions in calibration and computing capability; we argue here that better methods and computing capabilities are now available and should become more widely used. To make this case, two approaches to model calibration are contrasted: (1) a traditional approach based on a small number of homogeneous parameter zones defined by the modeler a priori and (2) regularized inversion, which includes many more parameters than the traditional approach. We discuss some advantages of regularized inversion, focusing on the increased insight that can be gained from calibration data. We present these issues using reasoning that we believe has a common sense appeal to modelers; knowledge of mathematics is not required to follow our arguments. We present equations in an Appendix, however, to illustrate the fundamental differences between traditional model calibration and a regularized inversion approach.