Six myths about mathematical modeling in geomorphology
Six myths about mathematical modeling in geomorphology
复制标题
关于地貌学数学建模的六个误区
DOI：
10.1029/135gm06
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
V. Teles
中科院分区：
文献类型：
--
作者：
R. Bras;G. Tucker;V. Teles
翻译后摘要：地貌学家，地质学家和水文学家一直使用模型。不幸的是，在我们的领域中，模型主义者和实验主义者（或“观察主义者”）之间的人为分裂普遍存在。这种分裂是建立在偏见，误解和神话。数据和模型的滥用和错误表述使这种分裂永久化。在本文中，我们试图解决其中的六个神话，并主要用我们的经验来说明为什么我们认为数学模型是有用的和必要的贸易工具。首先，我们主张对“物理”模型的广义定义。机械式的严谨并不总是可能的，也不总是解决问题的最佳方法。第二，由于对现实的了解并不完全，核查是不可能的。我们可以努力对模型行为进行某种程度的确认，这种确认通常必须是统计的、分布的性质。第三，我们给出了一些例子，说明即使是未经证实的模型也可以成为有用的工具。第四，给出了被拒绝的模型的例子，在某种意义上说，“失败”，这提高了我们的知识，并导致我们的发现。第五，模型应该逐渐变得更加复杂，但这种复杂性通常会导致简单的结果。最后，最好的模型是那些输出挑战先入为主的想法。建模，包括数学建模，是现场研究人员和理论家的必要工具。
Abstract : 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.