A metamodel for stormwater detention basins design

The aim of storm basins is to protect urban areas against some predefined risk of exceeding a given value of downstream runoff, or a risk of overflow for a bounded storage capacity. This risk results from the combination of a natural hazard and hydraulic properties. The correct way to address this issue is to use a stochastic rainfall model, but it may require unavailable data and be cumbersome to use in the framework of an optimisation procedure. We give the end user a way to by-pass this step, by means of a metamodel. The problem is to calculate the parameters of the probability density function (pdf) of outputs as a function of the pdf of inputs and of the parameters of the dynamic deterministic system between inputs and outputs. We propose to apply a metamodel, which is a new way of designing approximate but generic derived distribution, based on conditional probabilities. For application to dimensioning of basins, the determination of the parameter(s) corresponding to an acceptable risk simply consists of solving an algebraic equation representing the metamodel. The methodology needs usual rainfall statistics and a specific parameter inferred from analysis of storms, or supposed to have a regional value.