Abstract We define model-data interaction (MDI) as a two way process between models and data, in which on one hand data can serve the modeling purpose by supporting model discrimination, parameter refinement, uncertainty analysis, etc., and on the other hand models provide a tool for data fusion, interpretation, interpolation, etc. MDI has many applications in the realm of groundwater and has been the topic of extensive research in the groundwater community for the past several decades. This has led to the development of a multitude of increasingly sophisticated methods. The progress of data acquisition technologies and the evolution of models are continuously changing the landscape of groundwater MDI, creating new challenges and opportunities that must be properly understood and addressed. This paper aims to review, analyze and classify research on MDI in groundwater applications, and discusses several related aspects including: (1) basic theoretical concepts and classification of methods, (2) sources of uncertainty and how they are commonly addressed, (3) specific characteristics of groundwater models and data that affect the choice of methods, (4) how models and data can interact to provide added value in groundwater applications, (5) software and codes for MDI, and (6) key issues that will likely form future research directions. The review shows that there are many tools and techniques for groundwater MDI, and this diversity is needed to support different MDI objectives, assumptions, model and data types and computational constraints. The study identifies eight categories of applications for MDI in the groundwater literature, and highlights the growing gap between MDI practices in the research community and those in consulting, industry and government.

中文翻译：

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地下水研究中的模型-数据交互：方法、应用和未来方向回顾

摘要 我们将模型-数据交互（MDI）定义为模型和数据之间的双向过程，一方面数据可以通过支持模型判别、参数细化、不确定性分析等服务于建模目的，另一方面模型为数据融合、解释、插值等提供了工具。MDI 在地下水领域有很多应用，在过去的几十年里一直是地下水界广泛研究的主题。这导致了许多日益复杂的方法的发展。数据采集​​技术的进步和模型的演变不断改变地下水 MDI 的格局，创造必须正确理解和应对的新挑战和机遇。本文旨在回顾，对地下水应用中的 MDI 研究进行分析和分类，并讨论了几个相关方面，包括：(1) 基本理论概念和方法分类，(2) 不确定性的来源及其通常如何解决，(3) 地下水模型的具体特征和影响方法选择的数据，(4) 模型和数据如何相互作用以在地下水应用中提供附加值，(5) MDI 的软件和代码，以及 (6) 可能形成未来研究方向的关键问题。审查表明，地下水 MDI 有许多工具和技术，需要这种多样性来支持不同的 MDI 目标、假设、模型和数据类型以及计算约束。该研究确定了地下水文献中 MDI 的八类应用，