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Publications—Open-File Report 00–491

Statistical Approaches to Interpretation of Local, Regional, and National Highway-Runoff and Urban-Stormwater Data

By Gary D. Tasker and Gregory E. Granato

U.S. Geological Survey Open-File Report 00–491

Prepared in cooperation with the Federal Highway Administration. A Contribution to the National Highway Runoff Data and Methodology Synthesis.


This report is available in Portable Document Format (PDF):

OFR 00–491 (555 KB)  – 67 pages


Decision makers need viable methods for the interpretation of local, regional, and national-highway runoff and urban-stormwater data including flows, concentrations and loads of chemical constituents and sediment, potential effects on receiving waters, and the potential effectiveness of various best management practices (BMPs). Valid (useful for intended purposes), current, and technically defensible stormwater-runoff models are needed to interpret data collected in field studies, to support existing highway and urban-runoffplanning processes, to meet National Pollutant Discharge Elimination System (NPDES) requirements, and to provide methods for computation of Total Maximum Daily Loads (TMDLs) systematically and economically.

Historically, conceptual, simulation, empirical, and statistical models of varying levels of detail, complexity, and uncertainty have been used to meet various data-quality objectives in the decision-making processes necessary for the planning, design, construction, and maintenance of highways and for other land-use applications. Water-quality simulation models attempt a detailed representation of the physical processes and mechanisms at a given site. Empirical and statistical regional water-quality assessment models provide a more general picture of water quality or changes in water quality over a region. All these modeling techniques share one common aspect—their predictive ability is poor without suitable site-specific data for calibration.

To properly apply the correct model, one must understand the classification of variables, the unique characteristics of water-resources data, and the concept of population structure and analysis. Classifying variables being used to analyze data may determine which statistical methods are appropriate for data analysis. An understanding of the characteristics of water-resources data is necessary to evaluate the applicability of different statistical methods, to interpret the results of these techniques, and to use tools and techniques that account for the unique nature of water-resources data sets. Populations of data on stormwater-runoff quantity and quality are often best modeled as logarithmic transformations. Therefore, these factors need to be considered to form valid, current, and technically defensible stormwater-runoff models.

Regression analysis is an accepted method for interpretation of water-resources data and for prediction of current or future conditions at sites that fit the input data model. Regression analysis is designed to provide an estimate of the average response of a system as it relates to variation in one or more known variables. To produce valid models, however, regression analysis should include visual analysis of scatterplots, an examination of the regression equation, evaluation of the method design assumptions, and regression diagnostics. A number of statistical techniques are described in the text and in the appendixes to provide information necessary to interpret data by use of appropriate methods.

Uncertainty is an important part of any decisionmaking process. In order to deal with uncertainty problems, the analyst needs to know the severity of the statistical uncertainty of the methods used to predict water quality. Statistical models need to be based on information that is meaningful, representative, complete, precise, accurate, and comparable to be deemed valid, up to date, and technically supportable. To assess uncertainty in the analytical tools, the modeling methods, and the underlying data set, all of these components need be documented and communicated in an accessible format within project publications.





Basic Statistical Considerations

Classification of Variables

Characteristics of Water-Resources Data

Population Structure and Analysis


Regression Analysis

The Analytical Process

Linear Regression Methods

Nonlinear Regression Methods

Uncertainty, Quality Assurance, and Quality Control

Benchmarking of Analytical Tools

Uncertainty in Modeling Efforts

Uncertainty in Input Data



Appendix 1: Regression Tools

Appendix 2: Linear Regression Methods

Appendix 3: Nonlinear Regression Methods

Appendix 4: Uncertainty Analysis

Appendix 5: Region of Influence Method.

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Suggested Citation:
Tasker, G.D., Granato, G.E., 2000, Statistical Approaches to Interpretation of Local, Regional, and National Highway-Runoff and Urban-Stormwater Data: U.S. Geological Survey Open-File Report 00–491, 59 p.

For additional information write to:

USGS Massachusetts–Rhode Island Water Science Center
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Northborough, MA 01532

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