Six Myths About Mathematical Modeling in Geomorphology.

摘要

Geomorphologists, geologists and hydrologists have always used models. Unfortunately an artificial schism between modelers and experimentalists (or 'observationalists') commonly exists in our fields. This schism is founded on bias, misinterpretation, and myth. The schism is perpetuated by misuse and mis-representation of data and models. In this paper we have tried to address six of those myths and illustrate, mostly with our experiences, why we think mathematical models are useful and necessary tools of the trade. First we argue for a broad definition of 'physical' models. Mechanistic rigor is not always possible or the best approach to problems. Second, verification is impossible given that reality is imperfectly known. We can strive for some level of confirmation of model behavior and this confirmation must generally be of statistical, distributional, nature. Third we give examples of how even unconfirmed models can be useful tools. Fourth, examples are given of rejected models, in a sense 'failures,' that have advanced our knowledge and led us to discoveries. Fifth, models should become progressively more complex, but this complexity commonly results in simple outcomes. Finally, the best models are those with outputs that challenge preconceived ideas. Modeling, including mathematical modeling, is a necessary tool of field researchers and theorists alike.