A Stochastic Pollutant Load Model for the Design of Stormwater Detention Facilities

Abstract

A set of equations dependent on specified pollutant trap efficiency for computing storage capacity-treatment rate combinations of a stormwater detention system is provided. The equations are expressed in terms of the statistics of the runoff event variables: mean depth, duration, and interevent time. The hydrologic random variables are assumed to be independent and exponentially distributed. A mass balance equation is derived for the detention unit based on a first-order pollutant load model. With the aid of statistical derived distribution techniques, an expression for the expected pollutant washoff load is derived, which is further used to develop analytical storage/treatment isoquants for specified levels of pollutant trap efficiency. The isoquants are defined in terms of the design storage capacity, the treatment rate, the pollutant trap efficiency, and the runoff process statistics. A further extension of the model allows the derivation of equations for the estimation of the settling efficiency of pollutants of stored stormwater. The estimators for storage capacity-treatment rate are obtained from closed form expressions that, in addition, yield lower and upper bound estimates of the design variables. Illustrative examples using data for catchments in Minneapolis and Denver are provided.