Use of paired simple and complex models to reduce predictive bias and quantify uncertainty
Use of paired simple and complex models to reduce predictive bias and quantify uncertainty
复制标题
DOI：
10.1029/2011wr010763
复制
发表时间：
2011-12-28
影响因子：
5.4
通讯作者：
Christensen, Steen
中科院分区：
文献类型：
--
作者：
Doherty, John;Christensen, Steen
现代环境管理和决策是基于越来越复杂的数值模型的使用。这种模型的优点是允许表示复杂的过程和不同的系统属性分布，因为这些在任何特定的研究地点都是理解的。后者通常是随机表示的，这反映了对系统异质性特征的了解，同时也反映了对其空间细节的缺乏了解。然而，不幸的是，复杂的模型往往很难校准，因为它们的运行时间很长，有时数值稳定性也令人怀疑。在使用这样的模型时，对预测不确定性的分析也是一项困难的工作。这种分析必须反映出缺乏对空间水力特性细节的了解。同时，它必须受到这些细节的空间变异性的限制，这些细节产生于模型输出复制历史系统行为的观察的必要性。相比之下，简单模型的快速运行时间和一般的数值可靠性通常意味着良好的校准和复杂的校准约束不确定度分析方法的现成实施。然而，不幸的是，许多不确定性可能依赖的系统和过程细节在设计上从简单的模型中被省略了。这可能会导致低估与许多管理层兴趣预测相关的不确定性。本文件提出了一种方法，一方面试图克服与复杂模型和简单模型相关的问题，另一方面又允许获得它们各自提供的好处。它从子空间的角度对简化过程进行了理论分析，从而对模型简化的成本以及如何降低其中一些成本提供了见解。然后描述了一种配对模型使用的方法，通过该方法可以检测和校正简化模型的预测偏差，并可以量化校准后的预测不确定性。基于北欧和北美常见的地下水模拟环境的综合实例，对该方法进行了演示。
Modern environmental management and decision-making is based on the use of increasingly complex numerical models. Such models have the advantage of allowing representation of complex processes and heterogeneous system property distributions inasmuch as these are understood at any particular study site. The latter are often represented stochastically, this reflecting knowledge of the character of system heterogeneity at the same time as it reflects a lack of knowledge of its spatial details. Unfortunately, however, complex models are often difficult to calibrate because of their long run times and sometimes questionable numerical stability. Analysis of predictive uncertainty is also a difficult undertaking when using models such as these. Such analysis must reflect a lack of knowledge of spatial hydraulic property details. At the same time, it must be subject to constraints on the spatial variability of these details born of the necessity for model outputs to replicate observations of historical system behavior. In contrast, the rapid run times and general numerical reliability of simple models often promulgates good calibration and ready implementation of sophisticated methods of calibration-constrained uncertainty analysis. Unfortunately, however, many system and process details on which uncertainty may depend are, by design, omitted from simple models. This can lead to underestimation of the uncertainty associated with many predictions of management interest. The present paper proposes a methodology that attempts to overcome the problems associated with complex models on the one hand and simple models on the other hand, while allowing access to the benefits each of them offers. It provides a theoretical analysis of the simplification process from a subspace point of view, this yielding insights into the costs of model simplification, and into how some of these costs may be reduced. It then describes a methodology for paired model usage through which predictive bias of a simplified model can be detected and corrected, and postcalibration predictive uncertainty can be quantified. The methodology is demonstrated using a synthetic example based on groundwater modeling environments commonly encountered in northern Europe and North America.