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SELDM: Stochastic Empirical Loading and Dilution Model - Software page

July 16, 2013

Note: to access the main SELDM page click here.



Granato, G.E., 2013, Stochastic empirical loading and dilution model (SELDM) version 1.0.0: U.S. Geological Survey Techniques and Methods, book 4, chap. C3, 112 p., on CD-ROM.       Full CD-ROM and Report On-Line

Granato, G.E., 2021, Stochastic Empirical Loading and Dilution Model (SELDM) software archive: U.S. Geological Survey software release,


The Stochastic Empirical Loading and Dilution Model (SELDM) is designed to transform complex scientific data into meaningful information about the risk of adverse effects of runoff on receiving waters, the potential need for mitigation measures, and the potential effectiveness of such management measures for reducing these risks. The U.S. Geological Survey developed SELDM in cooperation with the Federal Highway Administration to help develop planning-level estimates of event mean concentrations, flows, and loads in stormwater from a site of interest and from an upstream basin. Planning-level estimates are defined as the results of analyses used to evaluate alternative management measures; planning-level estimates are recognized to include substantial uncertainties (commonly orders of magnitude). SELDM uses information about a highway site, the associated receiving-water basin, precipitation events, stormflow, water quality, and the performance of mitigation measures to produce a stochastic population of runoff-quality variables. SELDM provides input statistics for precipitation, prestorm flow, runoff coefficients, and concentrations of selected water-quality constituents from National datasets. Input statistics may be selected on the basis of the latitude, longitude, and physical characteristics of the site of interest and the upstream basin. The user also may derive and input statistics for each variable that are specific to a given site of interest or a given area.

SELDM is a stochastic model because it uses Monte Carlo methods to produce the random combinations of input variable values needed to generate the stochastic population of values for each component variable. SELDM calculates the dilution of runoff in the receiving waters and the resulting downstream event mean concentrations and annual average lake concentrations. Results are ranked, and plotting positions are calculated, to indicate the level of risk of adverse effects caused by runoff concentrations, flows, and loads on receiving waters by storm and by year. Unlike deterministic hydrologic models, SELDM is not calibrated by changing values of input variables to match a historical record of values. Instead, input values for SELDM are based on site characteristics and representative statistics for each hydrologic variable. Thus, SELDM is an empirical model based on data and statistics rather than theoretical physiochemical equations.

SELDM is a lumped parameter model because the highway site, the upstream basin, and the lake basin each are represented as a single homogeneous unit. Each of these source areas is represented by average basin properties, and results from SELDM are calculated as point estimates for the site of interest. Use of the lumped parameter approach facilitates rapid specification of model parameters to develop planning-level estimates with available data. The approach allows for parsimony in the required inputs to and outputs from the model and flexibility in the use of the model. For example, SELDM can be used to model runoff from various land covers or land uses by using the highway-site definition as long as representative water quality and impervious-fraction data are available.


Version 1.1.1 was developed to allow SELDM to run within the 64-bit Microsoft Office® environment and add emerging contaminants including plastics, tire chemicals, and PFAS/PFOS.

SELDM Version: 1.1.0 - Version 1.1.0 Updated to add batch processing, changed the highway runoff duration used for upstream transport curves from the discharge duration which could vary from BMP to BMP to the runoff-concurrent duration and volume, and fixed a problem that allowed users to simulate a dependent variable in a lake analysis without the explanatory variable, which caused an error.

SELDM version - Update to change the database and code to modify a few items: (1.) Precipitation stations with latitudes on gridlines were not showing up in ecoregion statistics because of query. Tested ecoregions indicate that averages differ by less than 1% and medians differ by about 2.7% on average, but results are not significantly different at the 95% confidence interval. (2.) Ecoregion 13 and 80 both Northern Basin & Range. #13 should be Central Basin and Range #14 Should be Mojave/Southern Basin & Range. (3.) In Out.txt file, BMP output, change Irreducible Minimum Concentration to Minimum Irreducible Concentration. (4.) Added command DoEvents to run routine to reduce or eliminate "Not responding" messages while the model is running. (5.) Added full SELDM filename & Path to the out.txt file. (6.) Corrected problem in which copied analyses were created in default project directory. (7.) Fixed problems in load calculations for ng/L, pg/L, fg/L and other units. (8.) Added CalTrans TMDL constituents. July 24, 2018

SELDM version - Update to change the code so that copies of an analysis would use the Cunnane plotting position formula instead of the Blom plotting position formula. Each original analysis would use the Cunnane formula. Both plotting position formulas are correct, so analyses done with version 1.0.1 are not incorrect because of this difference. However, the two formulas produce slightly different exceedance percentiles and the manual provides information and equations for using the Cunnane plotting position formula. The change is in the Analysis form copy command code. June 1, 2016

SELDM version - Update to correct calculation of upstream and lake-basin transport curves. July 16, 2013

SELDM version - Initial release. March 27, 2013

System Requirements

SELDM is written in Visual Basic for Applications and therefore use is limited to Microsoft Windows operating systems. The graphical display forms require a screen resolution exceeding 1024 x 768 pixels.

Data Requirements

SELDM requires the latitude and longitude of the study site, the area, the imperviousness, the main channel length, main channel slope, and basin development factor for the highway site and the site of interest. SELDM also requires representative water-quality statistics for the site of interest and the upstream basin. Selected constituents have been pre-entered.


Support for this software will include upcoming on-line training sessions and classroom training at selected locations, limited software support, and compilation of suggested improvements. Only limited assistance can be provided for applying SELDM to specific problems, but the forthcoming training modules should be sufficient for most users.


Limited support is provided for correcting bugs and clarification of how the code is intended to work.

User Rights and Product Disclaimer

This software is a product of the U.S. Geological Survey, which is part of the U.S. Government. This software is freely distributed. There is no fee to download and (or) use this software. 

As a work of the United States Government, this USGS product is in the public domain ( within the United States. You can copy, modify, distribute, and perform the work, even for commercial purposes, all without asking permission. Additionally, USGS waives copyright and related rights in the work worldwide through CC0 1.0 Universal Public Domain Dedication ( ). 

This software has been approved for release by the U.S. Geological Survey (USGS). Although the software has been subjected to rigorous review, the USGS reserves the right to update the software as needed pursuant to further analysis and review. No warranty, expressed or implied, is made by the USGS or the U.S. Government as to the functionality of the software and related material nor shall the fact of release constitute any such warranty. Furthermore, the software is released on condition that neither the USGS nor the U.S. Government shall be held liable for any damages resulting from its authorized or unauthorized use. 

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

Publication Year 2013
Title SELDM: Stochastic Empirical Loading and Dilution Model - Software page
Product Type Software Release
Record Source USGS Digital Object Identifier Catalog