贝叶斯概率水文预报系统及其应用研究
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摘要
论文结合国家“973”和国家自然科学基金资助项目,在详尽综述国内外流域水文模型、洪水预报系统以及水文预报不确定性研究进展的基础上,着重研究并探讨了概念性流域水文模型参数优选技术以及贝叶斯概率水文预报系统的建模与应用。论文主要结论和创新点如下:
(1) 综述了国内外概念性流域水文模型参数优选技术的研究现状,介绍并比较了常用的参数优选方法;着重探讨了目标函数及其组合求解技术,深入研究了多目标参数自动优选问题的参数解空间。实例研究结果表明:多目标参数自动优选方法能综合考虑水文过程的各要素,优于传统的单目标参数优选结果。
(2) 介绍了贝叶斯预报处理器(BPF)和水文不确定性处理器(HUP),分别对其进行了实例研究。引入平稳序列的线性AR模型与线性扰动模型(LPM)对HUP的先验分布与似然函数作了改进。改进的HUP结构简单,避免了正态分位数转化,降低了由于选取、优选各变量边缘分布函数而产生的误差,并且较HUP的预报精度有一定提高。
(3) 综述了国内外定量降水预报方法的研究进展及其与水文模型的耦合途径,分析研究了一个定量降水预报不确定性处理器(PUP)。在此基础上,提出并建立了三峡水库区间流域随机降水模型,选用最近邻相似法模拟降水量的时段分配系数。将所建随机降水模型与区间洪水预报模型相耦合,分析得到区间流域定量降水预报不确定性的解析解。实例研究结果表明,耦合模型可提高三峡水库区间流域的洪水预报精度,并提供了待预报流量的区间估计。
(4) 比较分析了基于预见期降水信息的水文不确定性处理器(PD-HUP)。建立了贝叶斯概率水文预报系统以分析水文预报不确定性对预报结果的影响,利用全概率公式将PD-HUP与所建三峡水库区间流域随机降水模型耦合起来,得到水文预报不确定性的解析解。选取三峡水库区间流域的水文、气象资料对所建系统进行检验与探讨,结果表明贝叶斯概率水文预报系统可显著提高预报精度,并提供了待预报流量的分布函数和区间估计。
(5) 提出了一个基于贝叶斯方法的实时洪水预报模型。该模型采用ARMA模型描述实测流量的先验分布,采用AR模型模拟预报残差的似然函数,并假定先验分布和似然函数均服从正态分布。根据贝叶斯公式综合得到后验分布函数,以其均值作为最终校正结果以发布洪水警报和防洪调度决策。实例研究结果表明:所建模型可显著提高预报精度,优于AR模型和递推最小二乘法(RLS),并提供了预报值的后验密度函数、区间估计等信息,实现了预报、校正与决策的有机耦合。
On the basis of reviewing of the hydrological model, flood forecasting system and hydrologic forecasting uncertainty in home and in abroad, the parameter calibration techniques for conceptual hydrological model and the probabilistic hydrologic forecasting system were studied and discussed in detail. This study was supported by the National Key Basic Research Program and the National Natural Science Foundation of China. The main results and innovation points of this thesis were summarized as follows:(1) After concisely reviewed the parameter calibration techniques for conceptual hydrological model, the parameter optimization algorithms were introduced and compared and the parameter space was analyzed deeply. The multi-objective functions and their combination as well as the solutions were also discussed in detail. It is found that automatic calibration using multiple objectives could consider of different aspects of the discharge hydrograph and has a better goodness-of-fit than that of the traditional single objective function.(2) The Bayesian processor of forecasting (BPF) and hydrologic uncertainty processor (HUP) were introduced and applied in the Baiyunshan basin and Three Gorges Reservoir (TGR) intervening basin, respectively. An autoregressive model and a linear perturbation model (LPM) were proposed to describe the Bayesian prior distribution and likelihood function of the HUP, respectively. The modified HUP is superior to current HUP that can not only avoid the normal quantile transform, but also can decrease the errors associated with the selection and calibration of the marginal distribution of the observed and simulated discharge. The application results show that the modified HUP can improve the flood forecasting accuracy.(3) The quantitative precipitation forecasting (QPF) and the coupling of the QPF with hydrologic model, and a precipitation uncertainty processor (PUP) were concisely reviewed and studied. A stochastic precipitation generator for TGR intervening basin was developed and the nearest neighbor bootstrapping regressive (NNBR) method was adopted to simulate the temporal disaggregation of the precipitation forecasts. The stochastic precipitation generator was coupled with the proposed flood forecasting model for TGR intervening basin and the analytic distribution of the quantitative precipitation forecasting uncertainty was obtained. It is shown that the coupling model could increase the flood forecasting precision and could also provide the interval estimation of the discharges to be forecasted.(4) A precipitation-dependent hydrologic uncertainty processor (PD-HUP) was studied and discussed. A probabilistic hydrologic forecasting system based on Bayesian method was developed to simulate the influence of flood forecasting accuracy corresponding to the predictive uncertainty, which is decomposed into quantitative precipitation forecasting uncertainty and hydrological model uncertainty. The PD-HUP and the proposed stochastic precipitation generator for TGR intervening basin were integrated together to get the predictive density function. By using the hydrologic and meteorological data of the TGR intervening basin, the proposed system was studied and discussed, it is shown that the proposed system not only can increase the forecasting precision, but also provide more useful information for flood control decision-making, such as the predictive distribution, interval estimation and so on.(5) A real-time flood-updating model based on the Bayesian method was proposed and developed. The ARMA model was used to describe the prior distribution of observed discharge and the AR model was adopted to simulate the likelihood function of forecasting error. Both the prior distribution and the likelihood function were assumed to be linear-normal distribution and they were integrated together to form a Bayesian posterior distribution, the mean values were treated as the finial results to issue flood warring and flood control decision-making. It is shown that the proposed model not only has a more superior forecasting precision than AR model and the recursive least-squares estimate (RLS) model, but also provides the posterior distribution of the discharge to be forecasted as well as the interval estimation, which could combine forecasting process and decision-making process together.
(1) 综述了国内外概念性流域水文模型参数优选技术的研究现状,介绍并比较了常用的参数优选方法;着重探讨了目标函数及其组合求解技术,深入研究了多目标参数自动优选问题的参数解空间。实例研究结果表明:多目标参数自动优选方法能综合考虑水文过程的各要素,优于传统的单目标参数优选结果。
(2) 介绍了贝叶斯预报处理器(BPF)和水文不确定性处理器(HUP),分别对其进行了实例研究。引入平稳序列的线性AR模型与线性扰动模型(LPM)对HUP的先验分布与似然函数作了改进。改进的HUP结构简单,避免了正态分位数转化,降低了由于选取、优选各变量边缘分布函数而产生的误差,并且较HUP的预报精度有一定提高。
(3) 综述了国内外定量降水预报方法的研究进展及其与水文模型的耦合途径,分析研究了一个定量降水预报不确定性处理器(PUP)。在此基础上,提出并建立了三峡水库区间流域随机降水模型,选用最近邻相似法模拟降水量的时段分配系数。将所建随机降水模型与区间洪水预报模型相耦合,分析得到区间流域定量降水预报不确定性的解析解。实例研究结果表明,耦合模型可提高三峡水库区间流域的洪水预报精度,并提供了待预报流量的区间估计。
(4) 比较分析了基于预见期降水信息的水文不确定性处理器(PD-HUP)。建立了贝叶斯概率水文预报系统以分析水文预报不确定性对预报结果的影响,利用全概率公式将PD-HUP与所建三峡水库区间流域随机降水模型耦合起来,得到水文预报不确定性的解析解。选取三峡水库区间流域的水文、气象资料对所建系统进行检验与探讨,结果表明贝叶斯概率水文预报系统可显著提高预报精度,并提供了待预报流量的分布函数和区间估计。
(5) 提出了一个基于贝叶斯方法的实时洪水预报模型。该模型采用ARMA模型描述实测流量的先验分布,采用AR模型模拟预报残差的似然函数,并假定先验分布和似然函数均服从正态分布。根据贝叶斯公式综合得到后验分布函数,以其均值作为最终校正结果以发布洪水警报和防洪调度决策。实例研究结果表明:所建模型可显著提高预报精度,优于AR模型和递推最小二乘法(RLS),并提供了预报值的后验密度函数、区间估计等信息,实现了预报、校正与决策的有机耦合。
On the basis of reviewing of the hydrological model, flood forecasting system and hydrologic forecasting uncertainty in home and in abroad, the parameter calibration techniques for conceptual hydrological model and the probabilistic hydrologic forecasting system were studied and discussed in detail. This study was supported by the National Key Basic Research Program and the National Natural Science Foundation of China. The main results and innovation points of this thesis were summarized as follows:(1) After concisely reviewed the parameter calibration techniques for conceptual hydrological model, the parameter optimization algorithms were introduced and compared and the parameter space was analyzed deeply. The multi-objective functions and their combination as well as the solutions were also discussed in detail. It is found that automatic calibration using multiple objectives could consider of different aspects of the discharge hydrograph and has a better goodness-of-fit than that of the traditional single objective function.(2) The Bayesian processor of forecasting (BPF) and hydrologic uncertainty processor (HUP) were introduced and applied in the Baiyunshan basin and Three Gorges Reservoir (TGR) intervening basin, respectively. An autoregressive model and a linear perturbation model (LPM) were proposed to describe the Bayesian prior distribution and likelihood function of the HUP, respectively. The modified HUP is superior to current HUP that can not only avoid the normal quantile transform, but also can decrease the errors associated with the selection and calibration of the marginal distribution of the observed and simulated discharge. The application results show that the modified HUP can improve the flood forecasting accuracy.(3) The quantitative precipitation forecasting (QPF) and the coupling of the QPF with hydrologic model, and a precipitation uncertainty processor (PUP) were concisely reviewed and studied. A stochastic precipitation generator for TGR intervening basin was developed and the nearest neighbor bootstrapping regressive (NNBR) method was adopted to simulate the temporal disaggregation of the precipitation forecasts. The stochastic precipitation generator was coupled with the proposed flood forecasting model for TGR intervening basin and the analytic distribution of the quantitative precipitation forecasting uncertainty was obtained. It is shown that the coupling model could increase the flood forecasting precision and could also provide the interval estimation of the discharges to be forecasted.(4) A precipitation-dependent hydrologic uncertainty processor (PD-HUP) was studied and discussed. A probabilistic hydrologic forecasting system based on Bayesian method was developed to simulate the influence of flood forecasting accuracy corresponding to the predictive uncertainty, which is decomposed into quantitative precipitation forecasting uncertainty and hydrological model uncertainty. The PD-HUP and the proposed stochastic precipitation generator for TGR intervening basin were integrated together to get the predictive density function. By using the hydrologic and meteorological data of the TGR intervening basin, the proposed system was studied and discussed, it is shown that the proposed system not only can increase the forecasting precision, but also provide more useful information for flood control decision-making, such as the predictive distribution, interval estimation and so on.(5) A real-time flood-updating model based on the Bayesian method was proposed and developed. The ARMA model was used to describe the prior distribution of observed discharge and the AR model was adopted to simulate the likelihood function of forecasting error. Both the prior distribution and the likelihood function were assumed to be linear-normal distribution and they were integrated together to form a Bayesian posterior distribution, the mean values were treated as the finial results to issue flood warring and flood control decision-making. It is shown that the proposed model not only has a more superior forecasting precision than AR model and the recursive least-squares estimate (RLS) model, but also provides the posterior distribution of the discharge to be forecasted as well as the interval estimation, which could combine forecasting process and decision-making process together.
引文
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