考虑水文预报不确定性的水库优化调度研究
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摘要
随着气象水文预报技术不断提高，充分利用水文预报成为提高水库系统效益的有效途径。基于水文预报进行水库调度时，如何处理预报不确定性是一个关键科学问题。水文预报的不确定性随着预见期的增加而增大，预见期太短则会导致决策信息不足，但预见期太长会导致决策可靠性降低。因此，有效预见期的确定是基于预报进行水库调度的另一个关键问题。本论文以不确定性条件下水库优化调度为研究对象，分析不同水库调度目标的经济学特性，提出针对特定问题的高效算法；分析预报不确定性随预见期的逐时演进特性，提出描述预报演进的通用模型；分析预报不确定性、预见期以外径流不确定性对当前决策的影响，提出确定有效预见期的准则。这三方面的研究，为有效利用水文预报信息改善水库调度决策提供了理论基础。论文主要包含以下三方面的研究内容：
（1）对水库调度目标经济特性进行分析，开发针对特定目标的高效调度算法。对于供水调度，基于边际效用递减推导调度决策与可用水量间的单调关系；对于发电调度，结合互补性，探讨调度决策与可用水量间的单调关系。根据调度决策单调性改进传统动态规划算法，提出供水调度的改进动态规划算法（IDP）、改进随机动态规划算法（ISDP）和发电调度的逐次改进动态规划算法（SIDP）。
（2）对预报不确定性进行分析，建立统计模型，描述预报不确定性逐时演进的特征。将总的预报不确定性分解为各时段的预报改进，描述和分析水文预报“预见期越长，预报不确定性越大”和“随着时间推进，预报不确定性趋于减小”的统计特征。一方面，对于理想的无偏、正态分布预报不确定性，通过理论分析，构建预报演进的鞅模型（MMFE）；另一方面，对于实际的有偏、非正态分布预报不确定性，结合正态分位数转换方法，建立预报演进的通用鞅模型（GMMFE）。
（3）对调度决策进行分析，综合预报不确定性、预见期以外径流不确定性对调度决策的影响，提出有效预见期（EFH）及其确定准则。研究发现：预见期较短时，调度决策主要受预见期以外径流不确定性影响，延长预见期能改进调度决策；预见期较长时，调度决策取决于预报不确定性，预见期延长导致更大的预报不确定性，反而不利于调度决策。通过确定水文预报的有效预见期，可以平衡预报不确定性、预见期以外径流不确定性的影响，实现调度决策不确定性的最小化。
Advances in weather forecasting, hydrologic modeling and hydro-climaticteleconnection relationships have improved hydrological forecasts considerably. Tocombine hydrological forecasts with optimization models provides a promisingapproach to improving reservoir system efficiency. Forecast uncertainty is a major issuein the use of hydrological forecasts in reservoir operation. On one hand, a short forecastmay not provide sufficient information; on the other hand, a long forecast can be toouncertain. As a result, effective forecast horizon is another important issue in reservoiroperation. The dissertation presents a systematic investigation of reservoir operationoptimization under hydrological uncertainty. Optimization models for reservoiroperation and statistical models for uncertainty analysis are set up, based on whicheffects of forecast uncertainty and hydrological uncertainty beyond forecast horizon onreservoir operation decisions are elaborated. The dissertation comprises three parts:
Firstly, optimization algorithms are developed based on examinations of reservoiroptimization models and monotonicity property of operation decisions. With the focuson objective function, for water supply problems, the monotonic relationship betweenrelease decision and water availability is derived from the property of diminishingmarginal utility; for hydropower problems, a similar monotonic relationship is derivedthrough formulations of the complementary relationship between release decisions andreservoir storage. The monotonic relationship enables improvements of conventionaldynamic programming. An improved dynamic programming (IDP) algorithm and animproved stochastic dynamic programming (ISDP) algorithm are developed for watersupply problems. A successive improved dynamic programming (SIDP) algorithm isdeveloped for hydropower problems.
Secondly, statistical models are set up to quantify and to simulate uncertaintyevolution in period-by-period updated hydrological forecasts. The model decomposestotal forecast uncertainty into forecast updates in intermediate periods and efficientlycaptures characteristics of forecast uncertainty, i.e.,“the longer the forecast horizon, thelarger the forecast uncertainty” and “forecast uncertainty reduces as time progresses”. Amartingale model of forecast evolution (MMFE) is set up to analyze unbiased andGaussian forecast uncertainties. In addition, biased and non-Gaussian characteristics of forecast uncertainties are illustrated based on real-world forecast data. To bridge the gap,a generalized marginal model of forecast evolution (GMMFE) integrating normalquantile transformation and MMFE is developed to simulate biased and non-Gaussianforecast uncertainties.
Thirdly, operation decisions are analyzed considering the joint effects of forecastuncertainty and hydrological uncertainty beyond forecast horizon. While a shortforecast may not provide sufficient information and a long forecast can be too uncertain,the concept of effective forecast horizon (EFH) is to balance the confidence and amountof forecast information. The analysis shows that when there is a short forecast horizon,uncertainty of operation decisions is dominated by hydrological uncertainty beyondforecast horizon and to prolong forecast horizon leads to improvement of operationdecisions. When the forecast horizon is long, uncertainty of operation decision is insteaddominated by forecast uncertainty and to prolong forecast horizon even goes againstimproving operation decisions. The selection of effective forecast horizon is to balancethe marginal effects of forecast uncertainty and hydrological uncertainty beyondforecast horizon, aiming to minimize the uncertainty of operation decision.
（1）对水库调度目标经济特性进行分析，开发针对特定目标的高效调度算法。对于供水调度，基于边际效用递减推导调度决策与可用水量间的单调关系；对于发电调度，结合互补性，探讨调度决策与可用水量间的单调关系。根据调度决策单调性改进传统动态规划算法，提出供水调度的改进动态规划算法（IDP）、改进随机动态规划算法（ISDP）和发电调度的逐次改进动态规划算法（SIDP）。
（2）对预报不确定性进行分析，建立统计模型，描述预报不确定性逐时演进的特征。将总的预报不确定性分解为各时段的预报改进，描述和分析水文预报“预见期越长，预报不确定性越大”和“随着时间推进，预报不确定性趋于减小”的统计特征。一方面，对于理想的无偏、正态分布预报不确定性，通过理论分析，构建预报演进的鞅模型（MMFE）；另一方面，对于实际的有偏、非正态分布预报不确定性，结合正态分位数转换方法，建立预报演进的通用鞅模型（GMMFE）。
（3）对调度决策进行分析，综合预报不确定性、预见期以外径流不确定性对调度决策的影响，提出有效预见期（EFH）及其确定准则。研究发现：预见期较短时，调度决策主要受预见期以外径流不确定性影响，延长预见期能改进调度决策；预见期较长时，调度决策取决于预报不确定性，预见期延长导致更大的预报不确定性，反而不利于调度决策。通过确定水文预报的有效预见期，可以平衡预报不确定性、预见期以外径流不确定性的影响，实现调度决策不确定性的最小化。
Advances in weather forecasting, hydrologic modeling and hydro-climaticteleconnection relationships have improved hydrological forecasts considerably. Tocombine hydrological forecasts with optimization models provides a promisingapproach to improving reservoir system efficiency. Forecast uncertainty is a major issuein the use of hydrological forecasts in reservoir operation. On one hand, a short forecastmay not provide sufficient information; on the other hand, a long forecast can be toouncertain. As a result, effective forecast horizon is another important issue in reservoiroperation. The dissertation presents a systematic investigation of reservoir operationoptimization under hydrological uncertainty. Optimization models for reservoiroperation and statistical models for uncertainty analysis are set up, based on whicheffects of forecast uncertainty and hydrological uncertainty beyond forecast horizon onreservoir operation decisions are elaborated. The dissertation comprises three parts:
Firstly, optimization algorithms are developed based on examinations of reservoiroptimization models and monotonicity property of operation decisions. With the focuson objective function, for water supply problems, the monotonic relationship betweenrelease decision and water availability is derived from the property of diminishingmarginal utility; for hydropower problems, a similar monotonic relationship is derivedthrough formulations of the complementary relationship between release decisions andreservoir storage. The monotonic relationship enables improvements of conventionaldynamic programming. An improved dynamic programming (IDP) algorithm and animproved stochastic dynamic programming (ISDP) algorithm are developed for watersupply problems. A successive improved dynamic programming (SIDP) algorithm isdeveloped for hydropower problems.
Secondly, statistical models are set up to quantify and to simulate uncertaintyevolution in period-by-period updated hydrological forecasts. The model decomposestotal forecast uncertainty into forecast updates in intermediate periods and efficientlycaptures characteristics of forecast uncertainty, i.e.,“the longer the forecast horizon, thelarger the forecast uncertainty” and “forecast uncertainty reduces as time progresses”. Amartingale model of forecast evolution (MMFE) is set up to analyze unbiased andGaussian forecast uncertainties. In addition, biased and non-Gaussian characteristics of forecast uncertainties are illustrated based on real-world forecast data. To bridge the gap,a generalized marginal model of forecast evolution (GMMFE) integrating normalquantile transformation and MMFE is developed to simulate biased and non-Gaussianforecast uncertainties.
Thirdly, operation decisions are analyzed considering the joint effects of forecastuncertainty and hydrological uncertainty beyond forecast horizon. While a shortforecast may not provide sufficient information and a long forecast can be too uncertain,the concept of effective forecast horizon (EFH) is to balance the confidence and amountof forecast information. The analysis shows that when there is a short forecast horizon,uncertainty of operation decisions is dominated by hydrological uncertainty beyondforecast horizon and to prolong forecast horizon leads to improvement of operationdecisions. When the forecast horizon is long, uncertainty of operation decision is insteaddominated by forecast uncertainty and to prolong forecast horizon even goes againstimproving operation decisions. The selection of effective forecast horizon is to balancethe marginal effects of forecast uncertainty and hydrological uncertainty beyondforecast horizon, aiming to minimize the uncertainty of operation decision.
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