Performance Modeling of Storm Water Best Management Practices with Uncertainty Analysis

The performance of storm water best management practices (BMPs) contains many uncertainties that make predicting BMP performance difficult. The objective of this study is to build a BMP performance model that incorporates uncertainty analysis and to evaluate this model using observed total suspended solids (TSS) from detention basin data sets in the International Stormwater BMP Database. The representative storage-treatment performance model, the $k\mathrm{\text{-}}{C}^{*}$ model, was chosen to represent BMP performance. Its input parameters, influent event mean concentration (EMC) ($C_{\mathrm{in}}$), and the areal removal rate constant ($k$) are considered with the uncertainty analysis. To estimate the variance associated with $k$, the prediction interval method is applied to the linear regression equation relating hydraulic loading rate ($q$) to $k$. To estimate the variance of $C_{\mathrm{in}}$, observed $C_{\mathrm{in}}$ data in the BMP database are used. This study assumes that both $C_{\mathrm{in}}$ and $k$ can be represented by lognormal distributions. The probability density function of effluent EMC ($C_{\mathrm{out}}$) is estimated and compared with observed effluent data $C_{\mathrm{out}}$ for three cases: uncertainty in $C_{\mathrm{in}}$, uncertainty in $k$, and uncertainty in both $C_{\mathrm{in}}$ and $k$. This study applies three different uncertainty methods: the derived-distribution method (DDM), Latin hypercube sampling (LHS), and the first-order second-moment (FOSM) method. Results show that LHS is the most efficient method among the three to characterize the uncertainty of $C_{\mathrm{out}}$ in univariate or bivariate cases in the $k\mathrm{\text{-}}{C}^{*}$ model. Moreover, the uncertainty of $C_{\mathrm{out}}$, considering uncertainty in both $C_{\mathrm{in}}$ and $k$, contains all observed data within a 95% confidence interval.