Two-copula based simulation for detention basin design

Abstract

This article presents a Monte Carlo simulation model based on Clayton copula to generate synthetic sequences of rainfall storms whose likelihood of occurrence is in consonance with historical records. These sequences are used as rainfall input data for the Storm Water Management Model to analyse a 3 km2 watershed in the city of Granada, Spain. The objective of our study is to estimate the optimal volume of a detention basin that would solve the problem created by a downstream combined sewer system (CSS), part of which is undersized and which cannot be enlarged without considerable cost. In this model, the synthetic rainfall sequences provide multiple inputs to the CSS model, which produce a range of model outputs. Risk-based analysis of these outputs helps to quantify the variability of the CSS response. As a result, our model enables decisions based on the comparison of expected outcomes and the costs of different choices. The rainfall storms are represented as a sequence of rectangular pulses, whose occurrences are driven by a Poisson process with a given arrival rate. Both storm durations and average storm intensities are fitted as Pareto distributions and the dependence between these variables is described using Clayton copula.