A stochastic approach to the flood control problem

We propose a stochastic model in conjunction with reliability analysis concepts to improve estimates for the protection volume that should be allocated in a reservoir to control a flood wave. In this approach, the inflow that reaches the reservoir during a flood is considered to be a load, and the reservoir capacity to control this flood is considered to be the resistance that the reservoir offers against the propagation of the flood. Here, the load and the resistance are modeled as a diffusion stochastic process, and the protection volume is determined via Itô's formula. In this scenario, an explicit formula for the failure risk is derived. The parameter inference is carried out by a Bayesian approach for a time discrete version of the load, and the estimates are obtained by using Monte Carlo Markov Chain Algorithms (MCMC). The maximum likelihood estimators are used in the comparison. The record utilized comprises nine years of daily inflow rates during flood periods that come to the Chavantes hydroelectric power plant (CHPP) in Southeast Brazil. The protection volumes estimated through the proposed model are compared to the volumes obtained by other existing methods.