Operational medium range flood forecasting systems are increasingly moving towards the adoption of ensembles of numerical weather predictions (NWP), known as ensemble prediction systems (EPS), to drive their predictions. We review the scientific drivers of this shift towards such ‘ensemble flood forecasting’ and discuss several of the questions surrounding best practice in using EPS in flood forecasting systems. We also review the literature evidence of the ‘added value’ of flood forecasts based on EPS and point to remaining key challenges in using EPS successfully.

Ensemble flood forecasting: A review

Forecast uncertainty in real-time flood forecasting is the primary source of risk regarding reservoir flood control operation, affecting both reliability and safety of the entire system. Informing reservoir operation for real-time flood control coping with forecast uncertainty encourages overall robust control of risk probability, vulnerability, and resilience of upstream and downstream protection areas. Current stochastic programming models or chance constrained programming models (CCP) focuses on reducing either risk loss or vulnerability, thereby failing to ensure systematic control. This study established a robust multiobjective operation and risk decision-making model to inform reservoir operations. The proposed model includes three modules. First, a copula function was applied to capture multidimensional temporal dependences of forecast uncertainties, following which stochastic inflow scenarios were generated. Second, a robust multiobjective optimization (RMOO) model was established with the objectives of minimizing the probability of risk events, Conditional Value-at-Risk of risk loss (vulnerability) and the maximum sequential duration for both upstream and downstream areas. Then, an adaptive reference multiobjective evolutionary algorithm was used to solve the model and obtain noninferior solutions. Finally, the TOPSIS multicriteria decision-making method was introduced to select the compromise solution. Methodologies were verified by application to Xianghongdian reservoir, China. The main findings were as follows. (1) The copula function effectively captured the multidimensional positive temporal dependences of forecast uncertainties. (2) RMOO provided more widely distributed noninferior solutions than CCP, and performed better in lowering vulnerability of the system. (3) RMOO reduced the maximum release by 135.6 m3/s (7.33%) by increasing prerelease before the occurrence of flood peak. The proposed methodologies provide insights for supporting robust control of real-time operations of a reservoir system through simultaneous control of flood risk probability, vulnerability, and resilience. 

Robust multiobjective reservoir operation and risk decision-making model for real-time flood control coping with forecast uncertainty

• 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. 

Multi-objective risk analysis for flood control operation of a complex reservoir system under multiple time-space correlated uncertainties

Flood control operation is one of the effective measures to reduce flood risks. Since flood forecasting plays a critical role in real-time reservoir flood control operation, it is necessary to involve forecasting uncertainty in the optimal reservoir operation to inform decision-making. It has always been a difficult task to reduce flood risks by adjusting flood control strategies. To tackle this challenge, this study developed a multi-objective robust optimization methodology for real-time reservoir flood control operation, which mainly coped with forecast uncertainty. Three machine learning (ML) models, including back propagation neural network (BP), long short-term memory neural network (LSTM) and extreme learning machine (ELM) were adopted to forecast the short-term reservoir inflow. A stacking ensemble multi-ML model (SEM) was then applied to integrate the forecasting results of the above models. Furthermore, a multi-objective robust optimal operation model (MOROU) integrating both upstream and downstream safety was established to reduce flood risks and evaluate the impact of forecasting uncertainty on the reservoir operation. To maximize the efficiency of reservoir utilization, this study defined a new indicator of reservoir reserved capacity adaptation (RRCA) as one of the optimization indicators. To better solve the complex multi-objective problem, a scenario to point (STP) method was proposed for searching robust solutions of multi-objective optimization models. Methodologies were validated through an application to the Lishimen reservoir, China. Three main conclusions were derived from the study: (1) Three ML models performed well in flood forecasting with BP being slightly better than the other two, and the SEM method was found to be able to incorporate the characteristics of each model, outperforming the individual models; (2) MOROU showed a narrower distribution of flood risk both upstream and downstream and achieved an approximately 1.5% reduction in the maximum value of the highest water level; (3) RRCA was verified to enable to reduce the discharge flow by an average of 4.52% without occupying additional flood control reservoir capacity, confirming that it can be used as an optimization indicator to improve the utilization of the reservoir. The proposed method can provide robust strategies for real-time reservoir flood control under forecast uncertainty. 

Multi-objective robust optimization of reservoir operation for real-time flood control under forecasting uncertainty

Forecast errors of multiple information sources of a cascade hydropower system cause risks of water and energy supply in real-time operation. Mechanisms minimizing multiple risks with budgeted cost under oscillations of multiple forecast uncertainties through robust operation are not yet well-investigated. This study proposed a multiobjective robust optimization (RO) and decision-making framework comprising series of models for risk analysis, robust control, and decision making. The risk analysis model identifies and analyzes dependent risks that stem from forecast errors of supply and demand-side information by Copula functions. A RO model was established for minimizing risk probabilities, vulnerabilities of ecological protection, water and energy supply, as well as revenue loss from energy. Thereafter, a multiattribute decision-making model was incorporated for determining the compromise solution from competing non-dominated solutions. The proposed framework was applied to the cascade hydropower system of the Xiluodu, Xiangjiaba, Three Gorges project and Gezhouba reservoirs on the Yangtze River, China. The principal findings were as follows. (a) Addressing the singular forecast uncertainty of streamflow is inadequate to obtain robust solutions. (b) In a normal year, RO can reduce the average conditional value-at-risk of ecological water shortfall, consumptive water shortfall, and energy shortfall by 25.1%, 35.3%, and 16.5% than that of chance-constrained programming. (c) Multiple risks are dispersed through risk avoidance and hedging that reduces outflow variance and homogenizes mean outflow, lowering down efficiencies of energy production and water usage as a tradeoff. The proposed model framework could be applied to inform operation of cascade hydropower systems. 

Scenario‐Based Multiobjective Robust Optimization and Decision‐Making Framework for Optimal Operation of a Cascade Hydropower System Under Multiple Uncertainties

Dynamic long-term streamflow probabilistic forecasting model for a multisite system considering real-time forecast updating through spatio-temporal dependent error correction

Integrated real-time flood risk identification, analysis, and diagnosis model framework for a multireservoir system considering temporally and spatially dependent forecast uncertainties

The invention discloses a multi-station runoff medium-and-long-term rolling probability prediction method considering prediction uncertainty associated evolution characteristics. The method comprisesthe following steps: collecting and arranging long-series medium-and-long-term runoff data information of a basin where a station to be predicted is located, and selecting a proper prediction model tocarry out rolling simulation-prediction and analyze prediction error statistical characteristic parameters; coupling a Copula function to improve a yoke model so as to reflect the space-time correlation characteristic of the forecast error under the condition of considering the correlation evolution characteristic of the time history and the space dimension of the multi-station runoff forecast error; and randomly sampling the rolling forecast error scene sequence by adopting a Monte Carlo method, and superposing the rolling forecast error scene sequence on a single-value forecast result to obtain a rolling probability prediction scene sequence. The yoke model theory is improved to finely describe the medium-and-long-term runoff prediction error uncertainty associated evolution characteristics, so the prediction precision and reliability can be improved, and more accurate support information is provided for a water resource management decision.

Multi-station runoff medium-and-long-term rolling probability prediction method considering prediction uncertainty associated evolution characteristics

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Dynamic long-term streamflow probabilistic forecasting model for a multisite system considering real-time forecast updating through spatio-temporal dependent error correction

Integrated real-time flood risk identification, analysis, and diagnosis model framework for a multireservoir system considering temporally and spatially dependent forecast uncertainties

Multi-station runoff medium-and-long-term rolling probability prediction method considering prediction uncertainty associated evolution characteristics