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Development of a Traveltime Prediction Equation for Streams in Arkansas

By Jaysson E. Funkhouser and C. Shane Barks

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Abstract

During 1971 and 1981 and 2001 and 2003, traveltime measurements were made at 33 sample sites on 18 streams throughout northern and western Arkansas using fluorescent dye. Most measurements were made during steady-state base-flow conditions with the exception of three measurements made during near steady-state medium-flow conditions (for the study described in this report, medium-flow is approximately 100-150 percent of the mean monthly streamflow during the month the dye trace was conducted). These traveltime data were compared to the U.S. Geological Survey’s national traveltime prediction equation and used to develop a specific traveltime prediction equation for Arkansas streams.

In general, the national traveltime prediction equation yielded results that over-predicted the velocity of the streams for 29 of the 33 sites measured. The standard error for the national traveltime prediction equation was 105 percent. The coefficient of determination was 0.78. The Arkansas prediction equation developed from a regression analysis of dye-tracing results was a significant improvement over the national prediction equation. This regression analysis yielded a standard error of 46 percent and a coefficient of determination of 0.74. The predicted velocities using this equation compared better to measured velocities.

Using the variables in a regression analysis, the Arkansas prediction equation derived for the peak velocity in feet per second was:

(Actual Equation Shown in report)

In addition to knowing when the peak concentration will arrive at a site, it is of great interest to know when the leading edge of a contaminant plume will arrive. The traveltime of the leading edge of a contaminant plume indicates when a potential problem might first develop and also defines the overall shape of the concentration response function.

Previous USGS reports have shown no significant relation between any of the variables and the time from injection to the arrival of the leading edge of the dye plume. For this report, the analysis of the dye-tracing data yielded a significant correlation between traveltime of the leading edge and traveltime of the peak concentration with an R2 value of 0.99. These data indicate that the traveltime of the leading edge can be estimated from:

(Actual Equation Shown in Report)

TABLE OF CONTENTS

CONTENTS ILLUSTRATIONS - Figure
  1. Map showing general location of sampling sites
  2. Diagram showing lateral mixing and longitudinal dispersion patterns and changes of concentration downstream from a single, midpoint, slug injection of tracer
  3. Definition sketch of time-concentration curves along a selected streamline resulting from an instantaneous dye injection
  4. Photograph showing injecting dye while wading across a stream
  5. Photograph showing injecting dye while boating across a stream
  6. Photograph showing injecting dye into a stream from a bridge
  7. Photograph showing lateral mixing of Rhodamine WT dye
  8. Photograph of the Self-Contained Underwater Fluorescence Apparatus (SCUFA)
  9. Plot showing relation between velocity predicted using the national traveltime prediction equation and observed velocity for Arkansas data set
  10. Plot showing the relation between velocity predicted using the Arkansas traveltime prediction equation and observed velocity for Arkansas data set
  11. Plot showing relation between traveltimes of leading edge and peak of dye cloud for the Arkansas data set
TABLES
  1. Sample sites and stream reaches used for traveltime study and their approximate locations in Arkansas
  2. Arkansas data used to evaluate the national traveltime prediction equation
  3. Ranges, means, and medians of explanatory variable values used to develop the Arkansas traveltime prediction equation



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