In 2012, the U.S. Geological Survey and the Oregon Department of Transportation began a cooperative study to demonstrate use of the Stochastic Empirical Loading and Dilution Model (SELDM) for runoff-quality analyses in Oregon. SELDM can be used to estimate stormflows, constituent concentrations, and loads from the area upstream of a stormflow discharge site, from the site of interest and in the receiving waters downstream of the discharge. SELDM also can be used to assess the potential effectiveness of best management practices (BMP) for mitigating potential effects of runoff in receiving waters. Nominally, SELDM is a highway-runoff model, but it is well suited for analysis of runoff from other land uses as well.

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.

SELDM facilitates analysis by providing precipitation, pre-storm streamflow, and other variables by region or from hydrologically similar sites. In Oregon, there can be large variations in precipitation and streamflow among nearby sites. Therefore, spatially interpolated geographic information system data layers containing storm-event precipitation and pre-storm streamflow statistics specific to Oregon were created for the study using Kriging techniques.

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:

1. An analysis was done to demonstrate use of dilution factors as an initial reconnaissance tool for comparing relative risk among sites.
2. An analysis of hardness-dependent, water-quality criteria was done to illustrate the effects of variations in hardness and flow on the application and interpretation of such criteria. This analysis shows that hardness-dependent criteria can vary by an order of magnitude among storm events because hardness is diluted by stormflows.
3. An analysis of uncertainties in input and output values was done to demonstrate that properly selected robust datasets are needed to represent conditions at a site of interest. This analysis shows that the rate of water-quality exceedances that are measured or simulated may depend on sample size and the luck of the draw.
4. An analysis was done to demonstrate that SELDM and other Monte Carlo models may generate extreme values from input statistics, which may or may not be feasible based on physicochemical or hydrological limits.
5. An analysis of BMP modeling methods was done to demonstrate use of the model for estimating treatment requirements for meeting water-quality objectives.
6. An analysis of the use of grab sampling and nonstochastic upstream modeling methods was done to evaluate the potential effects on modeling outcomes.

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.