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Dynamic control of flood-limited water level (FLWL) is an effective method to realize floodwater utilization, which can alleviate the contradiction between flood control and conservation during flood seasons. In this study, a method of identifying upper bound of FLWL is presented simultaneously considering pre-release for water supply in rainless period and pre-release for flood control in the early period of flood. A risk analysis framework considering continuous rainless-day forecast error and flood forecast error is established. An improved truncated Gaussian distribution to describe rainless-day forecast error is proposed, combined with normal distribution describing flood forecast error to derive the distribution of excess storage determined by the method of pre-release based on forecasts. Then risk assessment and decision making are conducted. The Xianghongdian Reservoir is selected for a case study. The results indicate that the allowable excess storage can be determined under a given acceptable risk by using this analytical method. Moreover, the excess storage decreases with the safety margin reserved for the downstream increasing under the same acceptable risk. [ABSTRACT FROM AUTHOR]

• Establishing a risk analysis model for multi-objective flood control operation of a complex reservoir system coupling multi-dimensional uncertainties. • Introducing the initial water level uncertainty to risk analysis for multi-reservoir operation. • Using copula theory to describe the correlation of the errors of reservoir initial water levels and the time-space correlation of flood forecast errors. Many uncertainties are involved in flood control operation of a multi-reservoir system and result in risks for the system. Risk analysis for reservoir flood control operation is essential for decision making. Traditional flood control risk analysis only takes flood forecast error as the main risk source, ignoring the influence of dynamic control of flood-limited water level on reservoir initial water level for flood regulation. In this study, the spatial correlation of reservoir initial water level errors and the spatiotemporal correlation of flood forecast errors are identified via copula function. A risk analysis model considering both upstream and downstream is established for multi-objective flood control operation of a complex reservoir system, coupling multi-dimensional uncertainties of reservoir initial water levels, flood forecast errors, reservoir capacity curve errors, reservoir discharge curve errors and river flood routing errors. The impact of multiple risk sources with spatiotemporal correlations on reservoir flood control operation is then evaluated and the competitive tradeoff between flood control risks in upstream and downstream analyzed. The model is applied to a mixed four-reservoir system in Pi River Basin in China. Results indicated that 1) there is a strong correlation between the reservoir initial water level errors in space and also between the flood forecast errors in space and time, which can be effectively described by copula function, and ignoring the correlations will underestimate the flood control risk; 2) the two objective values of upstream and downstream show a clear competitive relationship, and the solution that prefers one objective has low risk marginal benefit, thus choosing a compromise solution can balance risks; 3) coupling the initial water level uncertainty reduces the flood control risk caused by the flood forecast errors to a certain extent, but also lead to the increase of extreme risk loss. [ABSTRACT FROM AUTHOR]

• Proposed integrated flood risk identification, analysis, and diagnosis framework. • Characterized spatial-temporal dependent forecast uncertainties by Copula function. • Discovered the underestimation of risk when neglecting spatial-temporal dependences. • Constructed scenario-based risk diagnosis model to examine causes of risk. Uncertainties in flood forecasts that result from error propagation in meteorological–hydrological simulation processes present spatial and temporal dependences that are the principal sources of risk to real-time flood control in a multireservoir system. Risk analysis models that neglect such dependences potentially yield biased results regarding flood control operations. To enhance the accuracy of flood risk analysis and inform decision making regarding real-time flood control for a multireservoir system, this study proposed an integrated flood risk identification, analysis, and diagnosis model framework that incorporates the multidimensional dependences of forecast uncertainties. The framework includes an uncertainty identification model that uses the copula function to characterize the joint probability function of the mixed dependent uncertainties. It also incorporates a real-time flood risk analysis module that couples simulation and optimization to convert the complex multiobjective operation under uncertainty into a tractable model capable of flexibly evaluating individual and joint flood risks. The third component is a risk diagnosis module that calculates risk contributions using conditional probability, and identifies stable and vulnerable reservoirs within the system to alter operational decisions toward risk reduction. Methodologies were verified through application to a mixed four-reservoir system in the Pi River Basin, China. The principal findings were as follows. (1) Positive-dominated dependences of forecast uncertainties were identified because of error propagation through the meteorological and rainfall–runoff forecasts within the spatial and temporal continuity connection, and the copula function accurately described and quantified the multidimensional temporal and spatial dependences of the uncertainties. (2) In neglecting the spatial dependences of forecast uncertainties, the joint flood risk of the reservoir system was underestimated; in ignoring high-order temporal dependences, individual flood risk was underestimated owing to biased estimation in error variance. (3) Systematic reorganization of the operational strategies of diagnosed stable and vulnerable reservoirs could provide guidance for reduction and homogenization of flood risks. The proposed framework could be used to improve the accuracy of flood risk analysis and support reliable real-time flood control operation of a multireservoir system. [ABSTRACT FROM AUTHOR]