A mathematical technique of estimating low-flow frequencies from base-flow measurements was evaluated by using data for streams in Indiana. Low-flow frequencies at low-flow partial-record stations were estimated by relating base-flow measurements to concurrent daily flows at nearby streamflow-gaging stations (index stations) for which low-flow- frequency curves had been developed. A network of long-term streamflow-gaging stations in Indiana provided a sample of sites with observed low-flow frequencies.Observed values of 7-day, 10-year low flow and 7-day, 2-year low flow were compared to predicted values to evaluate the accuracy of the method.
Five test cases were used to evaluate the method under a variety of conditions in which the location of the index station and its drainage area varied relative to the partial-record station. A total of 141 pairs of streamflow-gaging stations were used in the five test cases. Four of the test cases used one index station, the fifth test case used two index stations. The number of base-flow measurements was varied for each test case to see if the accuracy of the method was affected by the number of measurements used.
The most accurate and least variable results were produced when two index stations on the same stream or tributaries of the partial-record station were used. All but one value of the predicted 7-day, 10-year low flow were within 15 percent of the values observed for the long-term continuous record, and all of the predicted values of the 7-day, 2-year low-flow were within 15 percent of the observed values. This apparent accuracy, to some extent, may be a result of the small sample set of 15.
Of the four test cases that used one index station, the most accurate and least variable results were produced in the test case where the index station and partial-record station were on the same stream or on streams tributary to each other and where the index station had a larger drainage area than the partial-record station. In that test case, the method tended to over predict, based on the median relative error. In 23 of 28 test pairs, the predicted 7-day, 10-year low flow was within 15 percent of the observed value; in 26 of 28 test pairs, the predicted 7-day, 2-year low flow was within 15 percent of the observed value.
When the index station and partial- record station were on the same stream or streams tributary to each other and the index station had a smaller drainage area than the partial-record station, the method tended to under predict the low-flow frequencies. Nineteen of 28 predicted values of the 7-day, 10-year low-flow were within 15 percent of the observed values. Twenty-five of 28 predicted values of the 7-day, 2-year low flow were within 15 percent of the observed values.
When the index station and the partial- record station were on different streams, the method tended to under predict regardless of whether the index station had a larger or smaller drainage area than that of the partial-record station. Also, the variability of the relative error of estimate was greatest for the test cases that used index stations and partial-record stations from different streams. This variability, in part, may be caused by using more streamflow-gaging stations with small low-flow frequencies in these test cases. A small difference in the predicted and observed values can equate to a large relative error when dealing with stations that have small low-flow frequencies.
In the test cases that used one index station, the method tended to predict smaller low-flow frequencies as the number of base- flow measurements was reduced from 20 to 5. Overall, the average relative error of estimate and the variability of the predicted values increased as the number of base-flow measurements was reduced.
|Title||Evaluation of a Method of Estimating Low-Flow Frequencies from Base-Flow Measurements at Indiana Streams|
|Authors||John Thomas Wilson|
|Publication Subtype||USGS Numbered Series|
|Series Title||Water-Resources Investigations Report|
|Record Source||USGS Publications Warehouse|
|USGS Organization||Indiana Water Science Center|