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首页> 外文期刊>Journal of Hydrology >Analysis of the response surface of the objective function by the optimum parameter curve: how good can the optimum parameter values be?
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Analysis of the response surface of the objective function by the optimum parameter curve: how good can the optimum parameter values be?

机译：通过最佳参数曲线分析目标函数的响应面：最佳参数值有多好？

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This paper presents an optimum parameter curve as a visualisation of all the possible local and global peaks on the multidimensional response surface of the objective function associated with the calibration of hydrological models, coupled with an auxiliary curve called the search step index curve to facilitate analysis of the shape of the response surface. The construction of such an optimum parameter curve to analyse the response surface of a parametric model (conceptual or black-box) is directly prompted by the concept of equifinality embodied in the GLUE methodology of Beven and Binley, i.e. that there may be many parameter sets equally acceptable, in terms of near-equal model efficiency values, as simulators of the response of a watershed to rainfall. With the suggested methods, several numerical experiments have been conducted, firstly for a 2-parameter blackbox model (the Gamma function model), using synthetic error-free data for selected sets of parameter values, and secondly for a typical primitive conceptual rainfall-runoff model (the 9-parameter Wuhan-01 model), using the real data of three catchments. It is deduced that the goodness of the optimum parameter set estimated by optimisation is determined more by the shape of the response surface itself rather than by the optimisation methods used. It is also demonstrated that both multivariate normal distribution sampling and Markov chain sampling (the Metropolis algorithm) are more efficient in constructing the proposed optimum parameter curve than the method of uniform random sampling initially investigated for this purpose. (C) 2000 Elsevier Science B.V. All rights reserved. [References: 44]
机译：本文提出了一条最佳参数曲线，以可视化形式显示与水文模型校准相关的目标函数多维响应面上所有可能出现的局部和全局峰，并辅之以称为“搜索步骤索引曲线”的辅助曲线，以方便分析响应表面的形状。 Beven和Binley的GLUE方法论中体现的等价性概念直接提示了构建这种用于分析参数模型（概念或黑匣子）响应面的最佳参数曲线的方法，即可能存在许多参数集就模型效率值几乎相等而言，也可以接受，作为流域对降雨响应的仿真器。利用建议的方法，已经进行了一些数值实验，首先是针对2参数黑箱模型（Gamma函数模型），使用合成的无误差数据来选择参数值集，其次是典型的原始概念性降雨径流模型（9参数武汉01模型），使用三个流域的真实数据。可以推断出，通过优化估算出的最优参数集的优劣更多地取决于响应面本身的形状，而不是取决于所使用的优化方法。还证明了，与为此目的最初研究的均匀随机抽样方法相比，多元正态分布抽样和马尔可夫链抽样（Metropolis算法）在构建建议的最佳参数曲线方面更为有效。 （C）2000 Elsevier Science B.V.保留所有权利。 [参考：44]

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