基于MCMC方法的概念性流域水文模型参数优选及不确定性研究
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摘要
概念性流域水文模型不仅在水循环研究领域有着重要的地位,在与水循环相关的其它领域也发挥着越来越重要的作用。无论是水文与水资源、环境和生态等重大问题的决策,还是防洪抗旱等均离不开水文模型的支撑。概念性流域水文模型的预报精度与模型结构及模型参数取值密切相关,因此,如何选取适用于指定研究区域的模型结构及模型参数是确保概念性流域水文模型预报精度的重要前提。鉴于此,本文在研究模型结构适用性的基础上,针对复杂非线性流域水文模型参数优选问题的难解性,引入融合马尔可夫链蒙特卡罗方法的优化算法,系统开展了模型参数优选、参数不确定性及模型输出的不确定性等研究,主要研究内容和结论如下：
(1)选取RRMT中9个降雨.径流模型组合,并采用SCE-UA优化算法及3个模型评价目标函数,对长江流域的岷江、嘉陵江及乌江流域开展模型结构适用性研究。根据模型结构的复杂度以及模型的预报能力对模型结构进行综合评价,选出适用于指定研究区域的模型结构。
(2)在系统研究SCEM-UA算法基础上,采用自适应Metropolis采样替代SCEM-UA算法中的Metropolis-annealing采样,提出了新的SCEAM-UA算法,该算法能在每一次迭代过程后自适应地调整协方差和接受率策略。通过实例研究发现,SCEAM-UA算法较好地克服了“早熟收敛”问题,搜索性能要优于传统SCEM-UA算法。此外,基于改进SCEAM-UA算法采样,对岷江、嘉陵江及乌江流域CMD-3PAR模型参数进行了敏感性分析,为模型参数的准确取值奠定基础。
(3)从算法的搜索效率、求解质量、算法稳定性等方面对SCE-UA、SCEM-UA、SCEAM-UA、DE-MC及DREAM等算法进行了比较分析,得出：DREAM和SCEAM-UA算法的优化性能优于DE-MC和SCEM-UA算法。在分析比较不同算法的性能基础上,初步建立了流域水文模型参数优选方法的评价指标体系,为选择高效的流域水文模型参数优选算法提供了科学依据。此外,对RRMT的优化模块进行拓展开发,嵌入新的SCEM-UA、SCEAM-UA、DE-AM、DREAM及MODREAM等算法,进一步增强了RRMT优化模块的功能。
(4)将DREAM算法应用于岷江、嘉陵江及乌江流域CMD-3PAR模型的参数优选,研究发现：DREAM算法能有效推求模型参数后验分布,适用于参数先验信息较少的复杂流域水文模型参数优选及不确定性分析。在DREAM算法基础上引入多目标优化思想,综合考虑水量平衡、水文特征曲线、洪峰流量等水文过程的不同要素,提出了一种基于改进适应度分配策略和外部存档方案的多目标DREAM算法,并以岷江、嘉陵江及乌江流域为例,对CMD-3PAR模型进行了自动参数优选,通过对比单目标优选与多目标优选结果发现：MODREAM算法可在较短时间内生成大量的非劣解供决策者评价优选,更能反映流域实际水文特征,使得模型计算流量与实测流量过程更加吻合,优于传统的单目标DREAM算法。
综上所述,融合MCMC方法的优化算法能较好地处理复杂非线性流域水文模型参数优选问题,适用于模型参数后验分布的推求,给流域水文模型参数优选的不确定性研究带来了广阔的前景。
The conceptual hydrological model not only plays an important role in research area in relation to hydrological cycle but also plays an increasing role in other areas related with hydrological cycle. Decision-making for major issues with respect to hydrology and water resources, environment, ecology, as well as flood control and drought prevention cannot be made without the support of hydrological model. Simulation accuracy of conceptual hydrological model is highly related with model structure and model parameters, therefore, appropriate selection of model structure and model parameters should be highlighted to ensure the performance of conceptual hydrological models for the specific research areas. A systematic research on assessment of model structure and parameter optimization based on Markov chain Monte Carlo method is carried out, focusing on uncertainty analysis of model structure, parameter and model output. The main contents and research results are as follows:
(1) The applicability of nine rainfall-runoff models selected from RRMT has been tested on three catchments in the Yangtze River basin (Min River, Jialing River and Wu River Basin), using the SCE-UA optimization algorithm and three performance criteria which measure different aspects of the system behavior. A comprehensive assessment of model structures is given with regard to model complexity and model performance. The model structure with the highest ranking score is proposed as potentially the most suitable for rainfall-runoff simulation in the Min River, Jialing River and Wu River Basin.
(2) The Metropolis-annealing scheme in the SCEM-UA algorithm is replaced with a new strategy of adaptive Metropolis sampling, herein forming a new SCEAM-UA algorithm. The newly developed SCEAM-UA algorithm adaptively updates the covariance strategy and acceptance rate during sampling. The case studies show that SCEAM-UA algorithm counters the problem of premature convergence, and the search performance is better than the traditional SCEM-UA algorithm. In addition, sensitivity analysis of model parameters are carried out based on the sampling from SCEAM-UA algorithm for the Min River, Jialing River and Wu River Basin, which can lay good foundation for uncertainty analysis of model parameter.
(3) SCE-UA, SCEM-UA, SCEAM-UA, DE-MC and DREAM are compared in aspects of search efficiency, solution quality and stability, the results indicate that DREAM and SCEAM-UA algorithm have better performance than DE-MC and SCEM-UA algorithm. Assessment index system of selecting parameter optimization methods for complex hydrological models is established on the basis of intercomparison on different algorithms, from which appropriate selection of parameter optimization method can therefore benefit. In addition, the optimization module of RRMT is further developed, embedded with SCEM-UA, the newly developed SCEAM-UA, DE-AM, DREAM and MODREAM, further enhancing the function of RRMT optimization module.
(4) DREAM algorithm is applied in the CMD-3PAR parameter optimization, which is shown to be capable of inferring the posterior distribution of model parameters and solving the parameter optimization problem and uncertainty analysis for complex hydrological models. Moreover, a new Multi-objective DREAM algorithm with emphasis on overall consideration of water balance, characteristic of hydrographs and peak flow, is proposed based on the concept of modified fitness assignment and external archive strategy, and is illustrated with case studies of parameter optimization of CMD-3PAR hydrological model for the Min River, Jialing River and Wu River Basin. The results show that MODREAM is capable of generating a lot of non-dominated solutions with wide and uniform distribution for decision-makers and is better than the single objective DREAM in achieving accurate simulation of hydrographs and seeking the real hydrological characteristics of the River Basin.
In summary, traditional optimization method combined with MCMC algorithm can readily cope with the complex nonlinear parameter optimization problems of hydrological model. Moreover, it is capable of inferring the posterior distribution of model parameters, bringing a broad prospect for the uncertainty analysis of model parameter.
(1)选取RRMT中9个降雨.径流模型组合,并采用SCE-UA优化算法及3个模型评价目标函数,对长江流域的岷江、嘉陵江及乌江流域开展模型结构适用性研究。根据模型结构的复杂度以及模型的预报能力对模型结构进行综合评价,选出适用于指定研究区域的模型结构。
(2)在系统研究SCEM-UA算法基础上,采用自适应Metropolis采样替代SCEM-UA算法中的Metropolis-annealing采样,提出了新的SCEAM-UA算法,该算法能在每一次迭代过程后自适应地调整协方差和接受率策略。通过实例研究发现,SCEAM-UA算法较好地克服了“早熟收敛”问题,搜索性能要优于传统SCEM-UA算法。此外,基于改进SCEAM-UA算法采样,对岷江、嘉陵江及乌江流域CMD-3PAR模型参数进行了敏感性分析,为模型参数的准确取值奠定基础。
(3)从算法的搜索效率、求解质量、算法稳定性等方面对SCE-UA、SCEM-UA、SCEAM-UA、DE-MC及DREAM等算法进行了比较分析,得出：DREAM和SCEAM-UA算法的优化性能优于DE-MC和SCEM-UA算法。在分析比较不同算法的性能基础上,初步建立了流域水文模型参数优选方法的评价指标体系,为选择高效的流域水文模型参数优选算法提供了科学依据。此外,对RRMT的优化模块进行拓展开发,嵌入新的SCEM-UA、SCEAM-UA、DE-AM、DREAM及MODREAM等算法,进一步增强了RRMT优化模块的功能。
(4)将DREAM算法应用于岷江、嘉陵江及乌江流域CMD-3PAR模型的参数优选,研究发现：DREAM算法能有效推求模型参数后验分布,适用于参数先验信息较少的复杂流域水文模型参数优选及不确定性分析。在DREAM算法基础上引入多目标优化思想,综合考虑水量平衡、水文特征曲线、洪峰流量等水文过程的不同要素,提出了一种基于改进适应度分配策略和外部存档方案的多目标DREAM算法,并以岷江、嘉陵江及乌江流域为例,对CMD-3PAR模型进行了自动参数优选,通过对比单目标优选与多目标优选结果发现：MODREAM算法可在较短时间内生成大量的非劣解供决策者评价优选,更能反映流域实际水文特征,使得模型计算流量与实测流量过程更加吻合,优于传统的单目标DREAM算法。
综上所述,融合MCMC方法的优化算法能较好地处理复杂非线性流域水文模型参数优选问题,适用于模型参数后验分布的推求,给流域水文模型参数优选的不确定性研究带来了广阔的前景。
The conceptual hydrological model not only plays an important role in research area in relation to hydrological cycle but also plays an increasing role in other areas related with hydrological cycle. Decision-making for major issues with respect to hydrology and water resources, environment, ecology, as well as flood control and drought prevention cannot be made without the support of hydrological model. Simulation accuracy of conceptual hydrological model is highly related with model structure and model parameters, therefore, appropriate selection of model structure and model parameters should be highlighted to ensure the performance of conceptual hydrological models for the specific research areas. A systematic research on assessment of model structure and parameter optimization based on Markov chain Monte Carlo method is carried out, focusing on uncertainty analysis of model structure, parameter and model output. The main contents and research results are as follows:
(1) The applicability of nine rainfall-runoff models selected from RRMT has been tested on three catchments in the Yangtze River basin (Min River, Jialing River and Wu River Basin), using the SCE-UA optimization algorithm and three performance criteria which measure different aspects of the system behavior. A comprehensive assessment of model structures is given with regard to model complexity and model performance. The model structure with the highest ranking score is proposed as potentially the most suitable for rainfall-runoff simulation in the Min River, Jialing River and Wu River Basin.
(2) The Metropolis-annealing scheme in the SCEM-UA algorithm is replaced with a new strategy of adaptive Metropolis sampling, herein forming a new SCEAM-UA algorithm. The newly developed SCEAM-UA algorithm adaptively updates the covariance strategy and acceptance rate during sampling. The case studies show that SCEAM-UA algorithm counters the problem of premature convergence, and the search performance is better than the traditional SCEM-UA algorithm. In addition, sensitivity analysis of model parameters are carried out based on the sampling from SCEAM-UA algorithm for the Min River, Jialing River and Wu River Basin, which can lay good foundation for uncertainty analysis of model parameter.
(3) SCE-UA, SCEM-UA, SCEAM-UA, DE-MC and DREAM are compared in aspects of search efficiency, solution quality and stability, the results indicate that DREAM and SCEAM-UA algorithm have better performance than DE-MC and SCEM-UA algorithm. Assessment index system of selecting parameter optimization methods for complex hydrological models is established on the basis of intercomparison on different algorithms, from which appropriate selection of parameter optimization method can therefore benefit. In addition, the optimization module of RRMT is further developed, embedded with SCEM-UA, the newly developed SCEAM-UA, DE-AM, DREAM and MODREAM, further enhancing the function of RRMT optimization module.
(4) DREAM algorithm is applied in the CMD-3PAR parameter optimization, which is shown to be capable of inferring the posterior distribution of model parameters and solving the parameter optimization problem and uncertainty analysis for complex hydrological models. Moreover, a new Multi-objective DREAM algorithm with emphasis on overall consideration of water balance, characteristic of hydrographs and peak flow, is proposed based on the concept of modified fitness assignment and external archive strategy, and is illustrated with case studies of parameter optimization of CMD-3PAR hydrological model for the Min River, Jialing River and Wu River Basin. The results show that MODREAM is capable of generating a lot of non-dominated solutions with wide and uniform distribution for decision-makers and is better than the single objective DREAM in achieving accurate simulation of hydrographs and seeking the real hydrological characteristics of the River Basin.
In summary, traditional optimization method combined with MCMC algorithm can readily cope with the complex nonlinear parameter optimization problems of hydrological model. Moreover, it is capable of inferring the posterior distribution of model parameters, bringing a broad prospect for the uncertainty analysis of model parameter.
引文
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