Unified diagnostic evaluation of physics-based, data-driven and hybrid hydrological models based on information theory (UNITE)

水文模型传统上依赖于物理定律和专业知识，编码在概念关系或偏微分方程中。然而，这种基于物理的模型往往结构过于僵化，产生模型结构误差，导致预测有偏差。最近，数据驱动的水文建模方法受到了人们的关注，因为它们直接提取数据中包含的信息，并且不受模型结构的限制。特别是深度学习方法在空间外推方面表现出较高的预测能力，但缺乏可解释性和变化条件下预测的理论基础。为了解决这个问题，已经出现了基于物理的数据驱动方法。通过注入专家知识，数据驱动模型获得了可解释性和预测技能。在这两个端元之间的建模连续体上，我们称任何这样的方法为“混合模型”。我们声称，将数据驱动与基于物理的建模相结合，还需要在统计评估层面上制定新的标准：我们需要方法上的进步，将基于物理的模型中的（缺乏的）信息和数据中的信息纳入同一规模。然而，迄今为止，专门针对混合动力车型性能定制的诊断工具还很缺乏。对于单个建模方法，已经建立的技能分数是存在的，但是如何处理混合模型还不清楚。正因为如此，人们几乎没有动力去建立和比较竞争的混合动力车型。然而，我们看到了在分析单个案例研究的真正可选模型集（在结构和建模类型上的变化，而不仅仅是参数化的细节）方面的巨大潜力，因为通过比较竞争模型结构的缺陷，我们可以了解到我们在系统理解和当前建模技能方面的最大差距。提出的项目目标是基于信息理论措施为混合模型开发一个统一的诊断评估框架（UNITE）。由于它的普遍性，信息论是一个合适的框架来分析和比较来自整个连续体和任何学科的模型。信息测度自然地从单一的情况扩展到多变量的情况，因此既包括少数输出变量的标准模型评价，也包括高维状态空间中模型轨迹的综合诊断评价。我们将重点放在明确旨在识别和比较模型内部机制的方法上，以促进科学理解和进步。无论最终模型处于模型连续体的哪个位置，这最终都会产生具有更好技能的更好模型。我们将在降雨径流建模的综合案例研究中测试和演示提出的工具箱。除此之外，该框架有望用于具有社会重要性的广泛科学学科中的任意类型的动态混合模型。

Hydrological models traditionally rely on physical laws and expert knowledge, encoded in conceptual relationships or partial differential equations. However, such physics-based models often suffer from a too rigid structure and produce model structural errors, resulting in biased predictions. Recently, data-driven approaches to hydrological modeling have gained attention, because they directly extract the information contained in the data and do not suffer from model structural limitations. Especially deep learning methods have demonstrated high predictive capability in spatial extrapolation, but lack interpretability and a theoretical foundation for prediction under changing conditions. To address this, physics-informed data-driven approaches have emerged. By infusing expert knowledge, data-driven models gain interpretability and prognostic skill. We call any such approach on the modeling continuum between these two end members “hybrid models”. We claim that merging data-driven with physics-based modeling requires also new standards on the level of statistical evaluation: we need methodological advances to bring (lack of) information in physics-based models and information in data to the same scale. However, diagnostic tools specifically tailored to the performance of hybrid models are lacking to date. Established skill scores exist for individual modeling approaches, but it is unclear how to treat hybrid models. Due to that, there is little motivation to set up and compare competing hybrid models. However, we see a huge potential in analyzing sets of truly alternative models (varying in structure and modeling type, not just details of parameterization) for individual case studies, because from comparing the deficits of competing model structures, we can learn the most about gaps in our system understanding and in our current modeling skill. The goal of the proposed project is to develop a unified diagnostic evaluation framework (UNITE) for hybrid models based on information-theoretic measures. Due to its generality, information theory is a suitable framework to analyze and compare models from the entire continuum, and from any discipline. Information measures naturally expand from single- to multivariate cases and thus encompass both standard model evaluation by few output variables and comprehensive diagnostic evaluation of model trajectories in high-dimensional state spaces. We put our focus on methods that explicitly aim to identify and compare model-internal mechanisms, in order to promote scientific understanding and progress. This will ultimately lead to better models with better skill, no matter on which position of the model continuum this final model is. We will test and demonstrate the proposed toolbox on a comprehensive case study of rainfall-runoff modeling. Thinking beyond, this framework is expected to be useful for arbitrary types of dynamic hybrid models in a broad range of scientific disciplines with societal importance.