The ease and efficiency with which conceptual rainfall runoff (CRR) models can be calibrated, as well as issues related to the uniqueness of their parameters, has received significant attention in literature. While several studies have tried to gain a better understanding of the underlying factors affecting these issues by examining the features of model error surfaces, this has generally been done in an ad-hoc fashion using lower-dimensional representations of higher-dimensional surfaces. In this paper, it is suggested that exploratory landscape analysis (ELA) metrics can be used to quantify key features of the error surfaces of CRR models, including their roughness and flatness, as well as their degree of optima dispersion throughout the surface. This enables key error surface features of CRR models to be compared in a consistent, efficient and easily communicable fashion for models with different combinations of attributes (e.g. model structure, catchment climate conditions, error metrics, and calibration data set lengths). Results from the application of ELA metrics to the error surfaces of 420 CRR models with different combinations of the above attributes indicate that increasing model complexity results in an increase in relative error surface roughness and relative optima dispersion and that, while increasing catchment wetness increases the relative roughness of error surfaces, it also decreases optima dispersion. This suggests that for the models considered in this study, optimisation efficiency is likely to decrease with increasing model complexity and catchment wetness, while optimisation difficulty is likely to increase and parameter uniqueness likely to decrease with model complexity and catchment dryness. While implications for choice of model complexity will need further work, this study highlights the potential value of the proposed approach to understanding the calibration efficiency, difficulty and parameter uniqueness of conceptual rainfall runoff models.

中文翻译：

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使用适应度景观指标提高对概念降雨径流模型的校准效率、难度和参数唯一性的理解


校准概念降雨径流（CRR）模型的简便性和效率，以及与其参数独特性相关的问题，已在文献中受到广泛关注。虽然一些研究试图通过检查模型误差曲面的特征来更好地理解影响这些问题的根本因素，但这通常是使用高维曲面的低维表示以临时方式完成的。在本文中，建议使用探索性景观分析（ELA）指标来量化 CRR 模型误差表面的关键特征，包括它们的粗糙度和平坦度，以及它们在整个表面上的最佳分散程度。这使得 CRR 模型的关键误差表面特征能够以一致、高效且易于沟通的方式与具有不同属性组合（例如模型结构、流域气候条件、误差度量和校准数据集长度）的模型进行比较。将 ELA 度量应用于具有上述属性的不同组合的 420 个 CRR 模型的误差表面的结果表明，增加模型复杂性会导致相对误差表面粗糙度和相对最佳离散度的增加，并且在增加流域湿度的同时，会增加相对误差表面粗糙度和相对最佳离散度。误差表面的粗糙度，它也会降低最佳色散。这表明，对于本研究中考虑的模型，优化效率可能会随着模型复杂性和流域湿度的增加而降低，而优化难度可能会随着模型复杂性和流域干燥度的增加而增加，参数唯一性可能会降低。 虽然模型复杂性选择的影响需要进一步的工作，但本研究强调了所提出的方法在理解概念降雨径流模型的校准效率、难度和参数唯一性方面的潜在价值。