Time of Travel in the White River

The time of travel data presented here were obtained by dye tracing. For this method, a soluble, fluorescent, and non-toxic dye was released into the river during a period of relatively steady streamflow. Concentrations of the dye were determined by means of a fluorometer at various points downstream. The time required for the peak concentration of dye to pass a downstream point approximates the average time it takes water molecules to travel the distance between the two points. (More information about dye-tracing methods for determining time of travel is given by Kilpatrick and Wilson, 1989.) Most of these data were collected in the late 1960's or early 1970's as part of a cooperative project between the Indiana Department of Natural Resources, the Indiana State Board of Health, and the U.S. Geological Survey (Eikenberry and Davis, 1976); some was collected in the 1980's for other projects. None has been collected recently. Jobson (1996) provides information on using time of travel information to estimate 1) the rate of movement of a contaminant through a river reach, 2) the rate of attenuation of the peak concentration of a conservative contaminant with time, and 3) the length of time for a contaminant plume to pass a point in a river.

The average time of travel for a stream reach varies inversely with streamflow. The relation can reasonably be represented by a straight line on logarithmic coordinates. Example relations for several reaches of the White River are shown below.

In arithmetic coordinates, the relation can be expressed as

where TOT is the time of travel, Q is the streamflow, and a and b are coefficients of the relation. An average reach velocity (V) for a given streamflow can be obtained by dividing the reach length (L) by the average time of travel

These equations can be used to obtain a reasonable approximation of the average time of travel and velocity for a reach within the range of the observed data used to estimate the coefficients of the relation. There can be a considerable amount of uncertainty in time of travel estimates obtained from these equations for streamflows outside of this range. In particular, the logarithmic linearity of the relation tends to not hold at large streamflows. This is evident in the relation obtained for the White River from Noblesville to 82nd Street in Indianapolis shown above. The time of travel measured at a streamflow of 5400 cubic feet per second is greater than would be expected based on the three measurements obtained at lower streamflows. There is also considerable uncertainty in extrapolating to very low flows, especially in impounded reaches.

The time required for a water molecule to travel the length of the White River can be considerable at low flows. Indiana experienced drought conditions during 1987-88. The period from mid-September until mid-November 1987 in particular was a time of very little runoff and relatively steady, low streamflow. Using the median streamflow recorded at U.S. Geological Survey streamflow gaging stations during this period and the estimating equations provided here, the average time required for a water molecule to travel from Winchester to Hazleton, a distance of 330 miles, was 1125 hours (47 days). Travel times are much slower in reaches upstream of Indianapolis than they are downstream. The average time of travel from Winchester to the Indianapolis Power and Light Company (IPL) Stout Generating Station dam in Indianapolis, a distance of 122 miles, was 810 hours while the time of travel from the IPL dam to Hazleton, a distance of 208 miles, was only 315 hours. Travel times are substantially longer in the upper reaches of the White River because a number of low-head dams slow the velocity of water. The average time of travel through central Indianapolis (from the Indianapolis Water Company Canal in Broad Ripple to the IPL dam), a distance of 16.9 miles, was 179 hours. In this short distance there are dams near Westfield Boulevard, near Kessler Boulevard, near 16th Street, near Oliver Street, and at the IPL Stout Generating Station.

A typical time of travel from Winchester to Hazleton is difficult to determine because a period of typical or normal streamflow rarely exists in the White River for the amount of time required for a water molecule to traverse the entire distance. As an example, however, the average time of travel from Winchester to Hazleton would be about 505 hours if the median streamflow (for the period 1949-1998) was occurring at all of the U.S. Geological Survey streamflow gaging stations. Under the same conditions, the average time of travel from Winchester to the IPL Stout Generating Station dam in Indianapolis would be about 350 hours while the time of travel from the IPL dam to Hazleton would be about 155 hours.

The time of travel data and the coefficients of the estimating equations (a and b) for the White River are given in the following web page. The equations provide an estimate of the time of travel in hours for streamflow in cubic feet per second. An estimate of the current time of travel in the river can be obtained by using the near real-time streamflow data for gaging stations on the White River. River miles shown are from Hoggatt (1975).

Time of Travel Data for the White River

REFERENCES

Eikenberry, S.E., and Davis, L.G., 1976, A technique for estimating the time of travel of water in Indiana streams: U.S. Geological Survey Water Resources Investigations Report 76-9, 39 p.

Hoggatt, R.E., 1975, Drainage areas of Indiana streams: Indianapolis, U.S. Geological Survey Report, 231 p.

Jobson, H.E., 1996, Prediction of Traveltime and Longitudinal Dispersion in Rivers and Streams: U.S. Geological Survey Water-Resources Investigations Report 96-4013, 69 p. (online version at URL http://water.usgs.gov/osw/pubs/disp/dispersion.html)

Kilpatrick, F.A., and Wilson, J.F., Jr., 1989, Measurement of time of travel in streams by dye tracing: U.S. Geological Survey Techniques of Water Resources Investigations Book 03, Chapter A9, 27 p. 27