Estimation of Traveltime and Longitudinal Dispersion in Streams in West Virginia

Abstract

Traveltime and dispersion data are important for understanding and responding to spills of contaminants in waterways. The U.S. Geological Survey (USGS), in cooperation with West Virginia Bureau for Public Health, Office of Environmental Health Services, compiled and evaluated traveltime and longitudinal dispersion data representative of many West Virginia waterways. Traveltime and dispersion data were not available for streams in the northwestern part of the State. Compiled data were compared with estimates determined from national equations previously published by the USGS. The evaluation summarized procedures and examples for estimating traveltime and dispersion on streams in West Virginia.

National equations developed by the USGS can be used to predict traveltime and dispersion for streams located in West Virginia, but the predictions will be less accurate than those made with graphical interpolation between measurements. National equations for peak concentration, velocity of the peak concentration, and traveltime of the leading edge had root mean square errors (RMSE) of 0.426 log units (127 percent), 0.505 feet per second (ft/s), and 3.78 hours (h). West Virginia data fit the national equations for peak concentration, velocity of the peak concentration, and traveltime of the leading edge with RMSE of 0.139 log units (38 percent), 0.630 ft/s, and 3.38 h, respectively. The national equation for maximum possible velocity of the peak concentration exceeded 99 percent and 100 percent of observed values from the national data set and West Virginia-only data set, respectively. No RMSE was reported for time of passage of a dye cloud, as estimated using the national equation; however, the estimates made using the national equations had a root mean square error of 3.82 h when compared to data gathered for this study.

Traveltime and dispersion estimates can be made from the plots of traveltime as a function of streamflow and location for streams with plots available, but estimates can be made using the national equations for streams without plots. The estimating procedures are not valid for regulated stream reaches that were not individually studied or streamflows outside the limits studied.

Rapidly changing streamflow and inadequate mixing across the stream channel affect traveltime and dispersion, and reduce the accuracy of estimates. Increases in streamflow typically result in decreases in the peak concentration and traveltime of the peak concentration. Decreases in streamflow typically result in increases in the peak concentration and traveltime of the peak concentration. Traveltimes will likely be less than those determined using the estimating equations and procedures if the spill is in the center of the stream, and traveltimes will likely be greater than those determined using the estimating equations and procedures if the spill is near the streambank.

First posted December 5, 2013