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Are Models Too Simple? Arguments for Increased Parameterization

机译：模型太简单了吗？关于增加参数化的争论

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摘要

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.
机译：人们应该毫无疑问地接受模型应该尽可能简单的想法。但是，过多的简化和简化可能会降低模型的效用。模型通常是用来预测的。然而，无论是（1）校准数据是否可以约束模拟的预测值，还是（2）校准参数的数量和类型与关键预测可能依赖的水力特性细节相对应，它们通常都以校准为参数设置参数。通过校准过程估算的参数化通常受到校准参数数量小于观测数量的限制。这种限制主要源于校准和计算能力的历史限制；我们在这里辩称，现在可以使用更好的方法和计算能力，并且应该变得更加广泛地使用。为此，将两种模型校准方法进行了对比：（1）基于建模者先验定义的少量均匀参数区域的传统方法，以及（2）正规化反演，其中比传统方法包含更多的参数。我们讨论正则化反演的一些优点，重点是可以从校准数据中获得的更多见解。我们使用推理来提出这些问题，我们认为这对建模者具有常识吸引力。不需要数学知识就可以遵循我们的论点。但是，我们在附录中提供了方程式，以说明传统模型校准和正则化反演方法之间的根本差异。

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