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Stochastic Empirical Loading and Dilution Model (SELDM)

Note: SELDM is now on version 1.0.1 Please use the new version on the software support page here

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The U.S. Geological Survey (USGS) and the Federal Highway Administration (FHWA) are currently cooperating in a national project to redesign the FHWA's highway-runoff quality planning model. The FHWA initiated the project to update the 1990 FHWA highway runoff quality model to reflect changes in runoff quality and to address the importance of upstream receiving-water concentrations for assessing the potential effects of runoff in these receiving waters. We developed the SELDM as a database application so that users can easily create and run highway-runoff simulations. SELDM simulates storm flows, concentrations, and loads. SELDM calculates the risk of exceeding water-quality criteria with and without user-defined BMPs. SELDM calculates annual runoff loads and is able to do a simple annual lake-loading analysis. We also developed national data sets for highway-runoff quality, precipitation, streamflow, runoff coefficients, and background water quality for use with the model. We developed these data sets so that users can easily select choices that represent the site a site of interest to use with the model. SELDM uses Monte-Carlo methods to quantify the effects of precipitation characteristics, streamflow, estimated runoff quantity and quality, and best management practices on the probability distribution of receiving-water concentrations. This web page will provide a catalog of reports and other information as these materials become available.

SELDM was developed in cooperation with the FHWA Office of Project Development and Environmental Review please see the: FHWA Natural Environment Web Page

This effort is an update of the FHWA 1990 model, which is now available here

This effort is an offshoot of the National Highway Runoff Water-Quality Data and Methodology Synthesis

Project Products
  Note: The CD-ROM image files are large and need to be saved to the user's computer to be used. Right-click the link and use the save as option.

NewRisley, J.C., and Granato, G.E., 2014, Assessing potential effects of highway runoff on receiving-water quality at selected sites in Oregon with the Stochastic Empirical Loading and Dilution Model (SELDM): U.S. Geological Survey Scientific Investigations Report 2014–5099, 74 p. Report On Line

This report provides case studies and examples to demonstrate stochastic-runoff modeling concepts and to demonstrate application of the model. Basin characteristics from six Oregon highway study sites were used to demonstrate various applications of the model. The highway catchment and upstream basin drainage areas of these study sites ranged from 3.85 to 11.83 acres and from 0.16 to 6.56 square miles, respectively. The upstream basins of two sites are urbanized, and the remaining four sites are less than 5 percent impervious.Concentrations and loads of cadmium, chloride, chromium, copper, iron, lead, nickel, phosphorus, and zinc were simulated at the six Oregon highway study sites by using statistics from sites in other areas of the country. Water-quality datasets measured at hydrologically similar basins in the vicinity of the study sites in Oregon were selected and compiled to estimate stormflow-quality statistics for the upstream basins. The quality of highway runoff and some upstream stormflow constituents were simulated by using statistical moments (average, standard deviation, and skew) of the logarithms of data. Some upstream stormflow constituents were simulated by using transport curves, which are relations between stormflow and constituent concentrations.Stochastic analyses were done by using SELDM to demonstrate use of the model and to illustrate the types of information that stochastic analyses may provide.Additional analyses using surrogate water-quality datasets for the upstream basin and highway catchment were provided for six Oregon study sites to illustrate the risk-based information that SELDM will produce. These analyses show that the potential effects of highway runoff on receiving-water quality downstream of the outfall depends on the ratio of drainage areas (dilution), the quality of the receiving water upstream of the highway, and the concentration of the criteria of the constituent of interest. These analyses also show that the probability of exceeding a water-quality criterion may depend on the input statistics used, thus careful selection of representative values is important.

Granato, G.E., 2014, Statistics for stochastic modeling of volume reduction, hydrograph extension, and water-quality treatment by structural stormwater runoff best management practices (BMPs): U.S. Geological Survey Scientific Investigations Report 2014–5037, 37 p. Report On Line

The U.S. Geological Survey (USGS) developed the Stochastic Empirical Loading and Dilution Model (SELDM) in cooperation with the Federal Highway Administration (FHWA) to indicate the risk for stormwater concentrations, flows, and loads to be above user-selected water-quality goals and the potential effectiveness of mitigation measures to reduce such risks. SELDM models the potential effect of mitigation measures by using Monte Carlo methods with statistics that approximate the net effects of structural and nonstructural best management practices (BMPs). In this report, structural BMPs are defined as the components of the drainage pathway between the source of runoff and a stormwater discharge location that affect the volume, timing, or quality of runoff. SELDM uses a simple stochastic statistical model of BMP performance to develop planning-level estimates of runoff-event characteristics. This statistical approach can be used to represent a single BMP or an assemblage of BMPs. The SELDM BMP-treatment module has provisions for stochastic modeling of three stormwater treatments: volume reduction, hydrograph extension, and water-quality treatment. In SELDM, these three treatment variables are modeled by using the trapezoidal distribution and the rank correlation with the associated highway-runoff variables. This report describes methods for calculating the trapezoidal-distribution statistics and rank correlation coefficients for stochastic modeling of volume reduction, hydrograph extension, and water-quality treatment by structural stormwater BMPs and provides the calculated values for these variables. This report also provides robust methods for estimating the minimum irreducible concentration (MIC), which is the lowest expected effluent concentration from a particular BMP site or a class 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. A database application and several spreadsheet tools are included in the digital media accompanying this report for further documentation of methods and for future use.

Granato, G.E., and Jones, S.C., 2014, The Stochastic Empirical Loading and Dilution Model (SELDM) for analysis of flows, concentrations, and loads of highway runoff constituents: in Compendium of Papers for the Transportation Research Board 93rd Annual Meeting, January 12-16, 2014, Washington, D.C., 19 p. Report On-Line Presentation On-Line

The Stochastic Empirical Loading and Dilution Model (SELDM) was developed by the U.S. Geological Survey in cooperation with the Federal Highway Administration (FHWA) to supersede use of the 1990 FHWA runoff-quality model. SELDM is designed to be a tool that can be used to transform disparate and complex scientific data into meaningful information about the risk for adverse effects of runoff on receiving waters, the potential need for mitigation measures, and the potential effectiveness of such measures for reducing these risks. SELDM is easy to use because much of the information and data needed to run SELDM are embedded in the model and are obtained by defining the location of the site of interest and five simple basin properties. Information and data from thousands of sites across the country were compiled to facilitate use of SELDM. Use of SELDM for doing the types of sensitivity analyses needed to properly assess water-quality risks are provided in a case study. For example, use of deterministic values to model upstream stormflows instead of representative variations in prestorm flow and runoff may substantially overestimate the proportion of highway runoff in downstream flows. Also, risks for total phosphorus excursions are substantially affected by the selected criteria and the modeling methods used. For example, if a single deterministic concentration rather than a stochastic population of values is used to model upstream concentrations, then the percentage of water-quality excursions in the downstream receiving waters may depend entirely on the selected upstream concentration.

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., CD–ROM.
Report On-Line Software On-Line

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 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.

CD-ROM
  USGS-TM-4C3.iso -- An ISO image of the CD-ROM with the model and supporting documentation (0.1 MB).
  USGS-TM-4C3.gi -- A gi image of the CD-ROM with the model and supporting documentation (0.1 MB).

Granato, G.E., 2012, Estimating basin lagtime and hydrograph-timing indexes used to characterize stormflows for runoff-quality analysis: U.S. Geological Survey Scientific Investigations Report 2012–5110, 47 p., with digital media Report On Line (3.5 MB).

A nationwide study to better define triangular-hydrograph statistics for use with runoff-quality and flood-flow studies was done by the U.S. Geological Survey (USGS) in cooperation with the Federal Highway Administration. Although the triangular hydrograph is a simple linear approximation, the cumulative distribution of stormflow with a triangular hydrograph is a curvilinear S-curve that closely approximates the cumulative distribution of stormflows from measured data. The temporal distribution of flow within a runoff event can be estimated using the basin lagtime, (which is the time from the centroid of rainfall excess to the centroid of the corresponding runoff hydrograph) and the hydrograph recession ratio (which is the ratio of the duration of the falling limb to the rising limb of the hydrograph). This report documents results of the study, methods used to estimate the variables, and electronic files that facilitate calculation of variables.

Ten viable multiple-linear regression equations were developed to estimate basin lagtimes from readily determined drainage basin properties using data published in 37 stormflow studies. Regression equations using the basin lag factor (BLF, which is a variable calculated as the main-channel length, in miles, divided by the square root of the main-channel slope in feet per mile) and two variables describing development in the drainage basin were selected as the best candidates, because each equation explains about 70 percent of the variability in the data. The variables describing development are the USGS basin development factor (BDF, which is a function of the amount of channel modifications, storm sewers, and curb-and-gutter streets in a basin) and the total impervious area variable (IMPERV) in the basin. Two datasets were used to develop regression equations. The primary dataset included data from 493 sites that have values for the BLF, BDF, and IMPERV variables. This dataset was used to develop the best-fit regression equation using the BLF and BDF variables. The secondary dataset included data from 896 sites that have values for the BLF and IMPERV variables. This dataset was used to develop the best-fit regression equation using the BLF and IMPERV variables.

Analysis of hydrograph recession ratios and basin characteristics for 41 sites indicated that recession ratios are random variables. Thus, recession ratios cannot be estimated quantitatively using multiple linear regression equations developed using the data available for these sites. The minimums of recession ratios for different streamgages are well characterized by a value of one. The most probable values and maximum values of recession ratios for different streamgages are, however, more variable than the minimums. The most probable values of recession ratios for the 41 streamgages analyzed ranged from 1.0 to 3.52 and had a median of 1.85. The maximum values ranged from 2.66 to 11.3 and had a median of 4.36.

Granato, G.E., 2010, Methods for development of planning-level estimates of stormflow at unmonitored sites in the conterminous United States: Washington, D.C., U.S. Department of Transportation, Federal Highway Administration, FHWA-HEP-09-005, 90 p. Report On Line (3.5 MB). Example Water-Quality Transport Curve Poster On Line (2.7 MB).

This report documents methods for data compilation and analysis of statistics for stormflows that meet data-quality objectives for order-of-magnitude planning-level water-quality estimates at unmonitored sites in the conterminous United States. Statistics for prestorm streamflow, precipitation, and runoff coefficients are used to model stormflows for use with the Stochastic Empirical Loading and Dilution Model (SELDM), which is a highway-runoff model. SELDM is designed to better quantify the risk of exceeding water-quality criteria as precipitation, discharge, ambient water quality, and highway-runoff quality vary from storm to storm. Summary statistics also may be used to help estimate annual-average water-quality loads. Streamflow statistics are used to estimate prestorm flows. Streamflow statistics are estimated by analysis of data from 2,873 U.S. Geological Survey streamgages in the conterminous United States with drainage areas ranging from 10 to 500 square miles and at least 24 years of record during the period 1960-2004. Streamflow statistics are regionalized using U.S. Environmental Protection Agency Level III nutrient ecoregions. Storm-event precipitation statistics are estimated by analysis of data from 2,610 National Oceanic and Atmospheric Administration hourly-precipitation data stations in the conterminous United States with at least 25 years of data during the 1965-2006 period. Storm-event precipitation statistics are regionalized using U.S. Environmental Protection Agency rain zones. Statistics to characterize volumetric runoff coefficients are estimated using data from 6,142 storm events at 306 study sites. Runoff coefficient statistics are not regionalized, but are organized by total impervious area. All of the geographic information system files, computer programs, data files, and regression results developed for this study are included on the CD-ROM accompanying this report.

CD-ROM
  FHWA-HEP-09-005.iso -- An ISO image of the CD-ROM with the database and supporting documentation (122 MB).
  FHWA-HEP-09-005.zip -- A compressed file containing the ISO image of the CD-ROM with the database and supporting documentation (70 MB).

Granato, G.E., and Cazenas, P.A., 2009, Highway-Runoff Database (HRDB Version 1.0)--A data warehouse and preprocessor for the stochastic empirical loading and dilution model: Washington, D.C., U.S. Department of Transportation, Federal Highway Administration, FHWA-HEP-09-004, 57 p. Report On Line (3 MB). Database-Design Map On Line (0.22 MB).

This report documents highway-runoff database (HRDB), which was developed to serve as a data warehouse for current and future highway-runoff data sets. The database can be used by transportation agencies and researchers as a data warehouse to document information about a data set, monitoring site(s), highway-runoff data (including precipitation, runoff, and event mean concentrations). The HRDB currently includes 37 tables with data for 39,713 event mean concentration (EMC) measurements (including over 100 water-quality constituents) from 2,650 storm events, monitored at 103 highway-runoff monitoring sites in the conterminous United States, as documented in 7 selected highway-runoff data sets. These data include the 1990 FHWA runoff-quality model data compilation and results from 6 other data sets collected during the period 1993–2005. The HRDB application, which is the graphical-user interface and associated computer code, can be used to facilitate estimation of statistical properties of runoff coefficients, runoff-quality statistics, and relations between water-quality variables in highway runoff from the available data. The database application facilitates retrieval and processing of the available data.

CD-ROM
  FHWA-HEP-09-004.iso -- An ISO image of the CD-ROM with the database and supporting documentation (73 MB).
  FHWA-HEP-09-004.zip -- A compressed file containing the ISO image of the CD-ROM with the database and supporting documentation (48 MB).

Note: The Washington State Department of Transportation (WSDOT) has issued a data advisory indicating that their data do not meet data-quality standards. The WSDOT advises HRDB users not to use the data designated as the WA2005 data set. These data will be removed from a future version of the HRDB.


Note: Version 1.0.0a of the HRDB was published with a with a new MA data set in a USGS report during 2010; that report is:
Smith, K.P., and Granato, G.E., 2010, Quality of stormwater runoff discharged from Massachusetts highways, 2005–07: U.S. Geological Survey Scientific Investigations Report 2009–5269, 198 p., Report and database on-line

Granato, G.E., Carlson, C.S., and Sniderman, B.S., 2009, Methods for development of planning-level stream-water-quality estimates at unmonitored sites in the conterminous United States: Washington, D.C., U.S. Department of Transportation, Federal Highway Administration, FHWA-HEP-09-003, 53 p. Report On Line (1.5 MB). Example Water-Quality Transport Curve Poster On Line (1.7 MB).

This report documents methods for data compilation and analysis of water-quality-transport curves that meet data-quality-objectives for order-of-magnitude planning-level estimates of stream-water quality at unmonitored sites in the 84 U.S. Environmental Protection Agency Level III nutrient ecoregions in the conterminous United States. The water-quality- transport curves developed in this analysis are intended for use with a stochastic data-generation algorithm, for use with a highway-runoff model designed to better quantify the risk of exceeding water-quality criteria as precipitation, discharge, ambient water quality, and highway-runoff quality vary from storm to storm. Transport curves are regression relations used to estimate constituent concentrations from measured or estimated water-discharge values. Three constituents, total phosphorus, total hardness, and suspended sediment, were selected for regression analysis to develop transport curves for each ecoregion. However, the data compilation and interpretation methods described herein may be used with other water-quality constituents. A total of 24,581 USGS surface-water-quality monitoring stations with drainage areas ranging from 0.002 to 1,140 square miles were identified in the conterminous United States and cataloged for retrieval of water-quality data. The number of paired water-discharge and water-quality samples for total phosphorus, total hardness, and suspended sediment concentrations was 246,403; 107,289; and 275,950, respectively. Examination of transport curves developed with these data indicate that these curves are appropriate models describing the underlying processes of washoff or dilution expected for each constituent, and that predictions made using these transport curves are comparable with published estimates for each water-quality constituent. All of the geographic information system files, computer programs, data files, and regression results developed for this study are included on the CD-ROM accompanying this report. The CD-ROM also contains a data directory with more than 1,876,000 paired discharge and water-quality measurements that include 21 other constituents commonly studied in highway- and urban-runoff studies.

CD-ROM
  FHWA-HEP-09-003.iso -- An ISO image of the CD-ROM with the database and supporting documentation (580 MB).
  FHWA-HEP-09-003.zip -- A compressed file containing the ISO image of the CD-ROM with the database and supporting documentation (275 MB).

Granato, G.E., 2009, Computer programs for obtaining and analyzing daily mean streamflow data from the U.S. Geological Survey National Water Information System Web Site: U.S. Geological Survey Open-File Report 2008–1362, 123 p. on CD-ROM, 5 appendixes. Report On Line Software On-Line

These programs may be used to get data from the USGS NWISWeb, calculate flow-duration statistics, do flow extension for short term or partial-record streamflow stations, calculate basic streamflow statistics, and creat batch input files for the USEPA DFLOW program.

These programs were used as part of this project to calculate streamflow statistics for 2,783 selected U.S. Geological Survey streamflow-gaging stations among U.S. Environmental Protection Agency Level III ecoregions.

Granato, G.E., 2006, Kendall-Theil Robust Line (KTRLine--version 1.0)—A visual basic program for calculating and graphing robust nonparametric estimates of linear-regression coefficients between two continuous variables: Techniques and Methods of the U.S. Geological Survey, book 4, chap. A7, 31 p. Report On-Line Software On-Line

The KTRLine program may be used to calculate parameters for robust, nonparametric estimates of linear-regression coefficients between two continuous variables. The Kendall-Theil robust line was selected because this robust nonparametric method is resistant to the effects of outliers and nonnormality in residuals that commonly characterize hydrologic data sets. The slope of the line is calculated as the median of all possible pairwise slopes between points. The intercept is calculated so that the line will run through the median of input data. A single-line model or a multisegment model may be specified. The KTRLine software is a graphical tool that facilitates development of regression models by use of graphs of the regression line with data and the regression residuals. The user may individually transform the independent and dependent variables to reduce heteroscedasticity and to linearize data. The program plots the data and the regression line. The program prints model specifications and regression statistics to the screen and saves the results to a user-specified output file in a format suitable for use with other programs.

The KTRLine program was used as part of this project to develop water-quality transport curves, relations between TSS and suspended sediment concentrations for highway runoff, relations between watershed area and pre-storm streamflow statistics and relations between the total-impervious fraction and runoff coefficient statistics of highway sites and upstream basins.

Granato, G.E., Cazenas, P.A., Jones, S.C., and Osterhues, Marlys, 2013, The Highway Runoff Database (HRDB) is a data warehouse and preprocessor for the new FHWA-USGS Stochastic Empirical Loading and Dilution Model (SELDM): Poster presented at 2013 International Conference on Ecology and Transportation-- Canyons, Crossroads, Connections Meeting Today's Transportation Ecology Challenges with Innovative Science & Sustainable Solutions, June 23-27, 2013 in Scottsdale, Arizona, Organized by the Center for Transportation and the Environment, Raleigh, North Carolina, 36 by 58 inches. Poster On-Line

The USGS, in cooperation with the FHWA developed the Highway Runoff Database (HRDB) as a data warehouse and preprocessor for the new Stochastic Empirical Loading and Dilution Model (SELDM). The HRDB is data rich. The latest version of the highway runoff database includes 54,384 event-mean concentrations (EMCs), from 4,186 storm events monitored at 117 study sites across the United States. The HRDB includes data for 194 highway-runoff constituents. Most of the constituents of greatest interest for highway-runoff characterization have more than 500 EMC samples in the database. The HRDB is easy to use. Data and statisics in the HRDB are readily available in easy-to-use formats with just a few mouse-clicks. Availability of this highway-runoff data in a standard format and the ease of use of the graphical user interface should provide information to improve highway-project delivery without compromising environmental protection.

For questions, comments, additions or suggestions contact:
Gregory Granato