Statistical Methods for Simulating Structural Stormwater Runoff Best Management Practices (BMPs) With the Stochastic Empirical Loading and Dilution Model (SELDM)

Scientific Investigations Report 2020-5136
Prepared in cooperation with the Federal Highway Administration
By: , and 



This report documents statistics for simulating structural stormwater runoff best management practices (BMPs) with the Stochastic Empirical Loading and Dilution Model (SELDM). The U.S. Geological Survey developed SELDM and the statistics documented in this report in cooperation with the Federal Highway Administration to indicate the risk for stormwater flows, concentrations, and loads to exceed user-selected water-quality goals and the potential effectiveness of mitigation measures to reduce such risks. In SELDM, three treatment variables—hydrograph extension, volume reduction, and water-quality treatment—are simulated by using the trapezoidal distribution and the rank correlation with the associated runoff variables. This report describes methods for calculating the trapezoidal distribution statistics and rank correlation coefficients for these treatment variables and methods for estimating the minimum irreducible concentration (MIC), which is the lowest expected effluent concentration from a BMP site or a category of BMPs. These statistics are different from the statistics commonly used to characterize or compare BMPs; they are designed to provide a stochastic transfer function to approximate the quantity, duration, and quality of BMP effluent given the associated inflow values for a population of storm events.

Analyses for this study were done with data extracted from a modified copy of the December 2019 version of the International Stormwater Best Management Practices Database. Statistics for volume reduction, hydrograph extension, and water-quality treatment were developed with selected data. The medians of the best-fit statistics for selected constituents were used to construct generalized cumulative distribution functions for the three treatment variables. For volume reduction and hydrograph extension, selection of a Spearman’s rank correlation coefficient (rho) value that is the average of the median and maximum values for the BMP category may help generate realistic simulation results in SELDM. The median rho value may be selected to help generate realistic simulation results for water-quality treatment variables.

Water-quality treatment statistics, including trapezoidal ratios and MIC values, were developed for 51 runoff-quality constituents commonly measured in highway and urban runoff studies. Statistics were calculated for water-quality properties, sediment and solids, nutrients, major and trace inorganic elements, organic compounds, and biologic constituents.

Analysis of MIC values provides information to guide professional judgement for selecting values for simulating water quality at sites of interest. The MIC is a lower bound for BMP discharge concentrations and will therefore replace simulated BMP discharge concentrations below the selected value. A new method for estimating MIC values, the lognormal variate of inflow concentrations, was developed in this report and these statistics were calculated for individual constituents and constituent categories. Inflow quality is correlated to MIC values for some constituents, but regional soil concentrations were not strongly correlated to MIC values.

Suggested Citation

Granato, G.E., Spaetzel, A.B., and Medalie, L., 2021, Statistical methods for simulating structural stormwater runoff best management practices (BMPs) with the Stochastic Empirical Loading and Dilution Model (SELDM): U.S. Geological Survey Scientific Investigations Report 2020–5136, 41 p.,

ISSN: 2328-0328 (online)

Table of Contents

  • Acknowledgments
  • Abstract
  • Introduction
  • Methods
  • Results of Analyses
  • Summary
  • References Cited
  • Appendix 1. Water-Quality Treatment Statistics for Individual Constituents
Publication type Report
Publication Subtype USGS Numbered Series
Title Statistical methods for simulating structural stormwater runoff best management practices (BMPs) with the Stochastic Empirical Loading and Dilution Model (SELDM)
Series title Scientific Investigations Report
Series number 2020-5136
DOI 10.3133/sir20205136
Year Published 2021
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) New England Water Science Center
Description Report: 41 p.; 4 Tables; Data Release; Software Release
Online Only (Y/N) Y
Additional Online Files (Y/N) Y
Google Analytic Metrics Metrics page
Additional publication details