This paper explores and combines implicit stochastic optimization (ISO) with copula functions to simulate long-term operating policies for a hydropower reservoir located in the Northeastern region of Brazil. Overall, ISO is considered as one of the most reliable techniques to derive long-term reservoir operating rules for reservoirs. This method employs a deterministic optimization model to estimate the optimal reservoir allocations under different inflow scenarios and later constructs operating rules for each month by relating the ensemble of the optimal releases, the initial storage volume and future inflow values. Those rules are generally established by fitting approaches including linear regression or nonlinear methods. This work illustrates the applicability to combine copulas with ISO to define reservoir operation policies based on a probabilistic procedure. Firstly, synthetic streamflow scenarios are simulated using a periodic vine copula model. Afterward, optimal release data are estimated by ISO for a set of inflow scenarios. Joint probability distribution functions based on copulas are constructed in order to forecast the expected release, conditioned to the initial reservoir volume and future inflows data. Results indicate that the proposed model represents a flexible approach to construct operating rules and derive long-term reservoir operating policies with low variability, allowing to reproduce different dependence structures of simulated data.

本文探索并结合了隐性随机优化（ISO）和copula函数，以模拟位于巴西东北部地区的水库的长期运行策略。总体而言，ISO被认为是得出油藏长期油藏运行规则的最可靠技术之一。该方法采用确定性优化模型来估计不同流入情景下的最优油藏分配，然后通过将最佳释放量，初始存储量和未来流入值的集合联系起来，为每个月构造作业规则。这些规则通常通过包括线性回归或非线性方法在内的拟合方法来建立。这项工作说明了将copula与ISO结合以基于概率过程定义储层运行策略的适用性。首先，使用周期性藤蔓copula模型来模拟合成流情景。之后，ISO针对一组流入方案估算最佳释放数据。构建了基于copulas的联合概率分布函数，以便根据初始储层容量和未来流入数据来预测预期释放量。结果表明，所提出的模型代表了一种灵活的方法来构造作业规则并导出具有低可变性的长期油藏作业策略，从而可以重现模拟数据的不同依赖性结构。之后，ISO针对一组流入方案估算最佳释放数据。构建了基于copulas的联合概率分布函数，以便根据初始储层容量和未来流入数据来预测预期的释放量。结果表明，所提出的模型代表了一种灵活的方法来构造作业规则并导出具有低可变性的长期油藏作业策略，从而可以重现模拟数据的不同依赖性结构。之后，ISO针对一组流入方案估算最佳释放数据。构建了基于copulas的联合概率分布函数，以便根据初始储层容量和未来流入数据来预测预期的释放量。结果表明，所提出的模型代表了一种灵活的方法来构造作业规则并导出具有低可变性的长期油藏作业策略，从而可以重现模拟数据的不同依赖性结构。