U.S. Geological Survey
Water-Resources Investigations Report 00-4113

Estimated Flow-Duration Curves for Selected Ungaged Sites in the Cimarron and Lower Arkansas River Basins in Kansas

By Seth E. Studley

Prepared in cooperation with the
KANSAS DEPARTMENT OF HEALTH AND ENVIRONMENT

Cowskin Creek near Wichita, Kansas, November 1998.
(photograph by Dennis Lacock, USGS)

CONTENTS

Abstract
Introduction
Description of Furness Method
Use of Miscellaneous Measurements
Existing Streamflow Information at Ungaged Sites
Collection of Base-Flow Measurements
Construction of Estimated Flow-Duration Curves
Summary and Conclusions
References
Appendix A. Estimated flow-duration curves and tables for 16 ungaged sites in the Cimarron and lower Arkansas River Basins in Kansas
Appendix B. Site descriptions for 16 ungaged sites in the Cimarron and lower Arkansas River Basins in Kansas
Appendix C. Miscellaneous streamflow measurements made during 1999 at 16 ungaged sites in the Cimarron and lower Arkansas River Basins in Kansas

FIGURES

Map showing:

Figure 1. Location of selected ungaged sites, concurrently measured, long-term, continuous-record streamflow-gaging stations, and miscellaneous streamflow-measurement sites in the Cimarron and lower Arkansas River Basins in Kansas used for estimation of flow-duration curves
Figure 2. Geographic variation of mean streamflow in Kansas
Figure 3. Percentage duration of mean streamflow in Kansas
Figure 4. Ratios of 1-percent-duration streamflow to mean streamflow adjusted to drainage area of 500 square miles in Kansas

Figure 5. Graph showing relation between drainage area and ratio of 1-percent-duration streamflow to mean streamflow
Figure 6. Map showing ratios of 50-percent-duration streamflow to mean streamflow adjusted to drainage area of 500 square miles in Kansas
Figure 7. Graph showing relation between drainage area and 50-percent-duration streamflow to mean streamflow
Figure 8. Map showing percentage duration of appreciable flow adjusted to drainage area of 500 square miles in Kansas
Figure 9. Graph showing relation between drainage area and duration of appreciable flow
Figure 10. Map showing average slopes of flow-duration curves adjusted to drainage area of 500 square miles in Kansas
Graph showing:
Figure 11. Relation between drainage area and average slope of flow-duration curve
Figure 12. Comparison of estimated flow-duration curve with computed flow-duration curve for 1968-98 for Little Arkansas River at Valley Center
Figure 13. Improvement of estimated flow-duration curve by use of low-flow measurements for Little Arkansas River at Valley Center

Graph showing estimated flow-duration curve for 1968-98 for site:
Figure 14. 07142650, Peace Creek near Sylvia
Figure 15. 07142860, Cow Creek near Claflin
Figure 16. 07143660, Turkey Creek near Buhler
Figure 17. 07144037, Emma Creek 3 miles north and 0.75 mile west of Sedgwick
Figure 18. 07144080, Sand Creek 3 miles north and 2 miles east of Sedgwick
Figure 19. 07144545, Cowskin Creek near Oatville
Figure 20. 07145220, Smoots Creek near Murdock
Figure 21. 07148100, Grouse Creek near Dexter
Figure 22. 07148110, Silver Creek at Highway 166 east of Arkansas City
Figure 23. 07148200, Mule Creek near Wilmore
Figure 24. 07148600, Medicine Lodge River at Sun City
Figure 25. 07148900, Elm Creek at Medicine Lodge
Figure 26. 07149590, Sandy Creek near Waldron
Figure 27. 07149605, Little Sandy Creek near Corwin
Figure 28. 07151670, Bluff Creek south of Anthony
Figure 29. 07157900, Cavalry Creek at Coldwater

TABLE

Table 1. Selected ungaged sites and concurrently measured, long-term, continuous-record, streamflow-gaging stations in the Cimarron and lower Arkansas River Basins in Kansas used for estimation of flow-duration curves

The use of firm, trade, or brand names in this report is for identification purposes only and does not constitute endorsement by the U.S. Geological Survey

Abstract

INTRODUCTION

One method for estimating flow-duration curves is outlined in Furness (1959) and in Searcy (1959). Furness (1959) applied the method to sites with drainage areas between 100 and 3,000 miî. The drainage-area limits were used because of the lack of long-term data for sites with drainage areas less than 100 miî or more than 3,000 miî. Also, most of the basins in Kansas with drainage areas of more than 3,000 miî are regulated and cannot be related to natural flow conditions. There are now (1999) several continuous-record streamflow-gaging stations in Kansas that have less than 100 miî of drainage area and that have enough data available for testing the Furness method. One of the stations (Cow Creek near Claflin, station 07142860, fig. 1) is used in this report and serves as an example of how the Furness method works for ungaged sites with drainage areas less than 100 miî.

A 1.5-year study by the USGS, done in cooperation with the Kansas Department of Health and Environment (KDHE) to fulfill a part of the Kansas State Water Plan, was begun in January 1999 to test and refine the Furness method for estimating flow-duration curves for ungaged sites and to present estimated flow-duration curves for 16 selected ungaged sites in the Cimarron and lower Arkansas River Basins in Kansas. The specific study objectives were to:

1. Test and, if necessary, refine the Furness method by generation of an estimated flow-duration curve for a long-term, continuous-record, streamflow-gaging station and compare the estimated curve with the computed curve for that station.
2. Evaluate existing streamflow information for the ungaged sites for the verification and (or) refinement of the estimated flow-duration curve.
3. Collect several, low- to medium-streamflow measurements at 16 selected ungaged sites and concurrently at respective nearby, long-term, continuous-record, streamflow-gaging stations.
4. Construct estimated flow-duration curves for the selected ungaged sites using the Furness method and the streamflow measurements.

The streams that need estimated flow-duration curves were chosen on the basis of the Clean Water Act's required 303d list developed by KDHE. The ungaged sites on those streams were chosen by USGS personnel on the basis of accessibility to the stream, suitability of the site for streamflow measurement, and availability of historic streamflow data. In this report, ungaged sites are those sites that currently (1999) do not have continuous stage-recording equipment even though they may have some historical data available. Figure 1 shows the location of the 16 ungaged sites, 8 long-term, continuous-record, streamflow-gaging stations used to correlate ungaged-site streamflows to flow-duration percentages, 4 miscellaneous streamflow-measurement sites, and the station used to test the Furness method (07144200). Table 1 lists the ungaged sites and the concurrent, long-term, continuous-record, streamflow-gaging stations used for estimation of flow-duration curves.

A period of record from 1968 through 1998 was used for this study of flow durations in the Cimarron and lower Arkansas River Basins because, in the years since Furness developed the method for estimating flow-duration curves, changes in farming practices, the number of lakes and ponds, population, and land use have caused significant changes in the long-term flow-duration curves. By using 1968-98 streamflow records, the duration curves can be used to describe current flow conditions on the streams, from which planners can more accurately assess the availability of streamflow for future uses. Also, this period is long enough to include equal periods of both drought and flood conditions.

The purpose of this report is to present the results of a test of the Furness method for the estimation of flow-duration curves at a long-term, continuous-record, streamflow-gaging station and to present estimated flow-duration curves for selected ungaged sites in the Cimarron and lower Arkansas River Basins in Kansas (fig. 1, table 1). These estimated duration curves will be used by KDHE as part of the State's Water Plan to help ensure a safe and clean water supply for Kansans. From a national perspective, the methods and results presented in this report could have wide applicability for water-supply and water-quality assessments for sites where little or no streamflow data have been collected. The estimated flow-duration curves can provide a basis for evaluating streamflow on ungaged streams for water-power studies, stream-contamination studies, and other water-quality studies.

DESCRIPTION OF FURNESS METHOD

The method used in this study to estimate flow-duration curves (Furness, 1959, p. 186-211) uses maps and graphs to identify six unique factors of flow duration for ungaged sites. The factors are: (1) mean streamflow (fig. 2) and percentage duration of mean streamflow (fig. 3), (2) ratio of 1-percent-duration streamflow to mean streamflow (figs. 4 and 5), (3) ratio of 0.1-percent-duration streamflow to 1-percent-duration streamflow, (4) ratio of 50-percent-duration streamflow to mean streamflow (figs. 6 and 7), (5) percentage duration of appreciable (0.10 ft/s) streamflow (figs. 8 and 9), and (6) average slope of the flow-duration curve (variability index) (figs. 10 and 11). The maps and graphs in Furness (1959) were originally created using streamflow data for 1921-56. In 1983, the maps were updated by Jordan (1983, p. 15-30) using an additional 20 years of data (1957-76) (in figure 2, data from 1965-80 were used for stations west of 99 degrees longitude) and data from many additional streamflow-gaging stations (Carswell, 1982).

To test the method of estimating flow-duration curves, a long-term, continuous-record, streamflow-gaging station on the Little Arkansas River at Valley Center, Kansas (station 07144200, fig. 1), was used. This station has operated continually since October 1923, has a drainage area of 1,327 miî, and is located in Sedgwick County (fig. 1). Comparison of the estimated flow-duration curve with the computed flow-duration curve for this station provides a test of the method for estimating flow duration. The estimated factors were developed for figure 12 as follows:

Mean streamflow: From figure 2, the mean streamflow for the Little Arkansas River at Valley Center (station 07144200, fig. 2) is 0.35 (ft/s)/ miî or 0.35 x 1,327 = 464 ft/s. From figure 3, the percentage duration for mean streamflow for the Little Arkansas River at Valley Center (07144200, fig. 3) is 16 percent. The coordinates of mean streamflow are now defined and are plotted in figure 12 as 464 ft/s at 16-percent duration (point A).

1-percent-duration streamflow: From figure 4, the ratio of 1-percent-duration streamflow to mean streamflow for Little Arkansas River at Valley Center (station 07144200, fig. 4) is about 16. From figure 5, the adjustment from 500 to 1,327 miî is 0.96. The ratio of 1-percent-duration streamflow to mean streamflow is 16 x 0.96 = 15.36. Therefore, the 1-percent-duration streamflow is 15.36 x 464 ft/s = 7,127 ft/s. In figure 12 the 1-percent-duration point is plotted at 7,127 ft/s (point B).

0.1-percent-duration streamflow: Using the average ratio of 0.1-percent-duration streamflow to 1-percent-duration streamflow as calculated by Jordan (1983, p. 21), the value plotted in figure 12 for 0.1-percent duration is 7,127 x 3.1 = 22,100 ft/s (point C). If the Valley Center station were located west of 99÷ longitude, the 1-percent-duration streamflow would be multiplied by 5.7, instead of 3.1, to obtain the 0.1-percent-duration streamflow.

50-percent-duration streamflow: Figure 6 indicates that the ratio of 50-percent-duration streamflow to mean streamflow for the Valley Center station (07144200, fig. 6) is about 0.15, and figure 7 shows that the adjustment to 1,327 miî is 1.21; therefore, the 50-percent-duration streamflow is 0.15 x 1.21 x 464 = 84 ft/s as plotted in figure 12 (point D).

Duration percentage of appreciable flow: "Appreciable flow" is the name given by Furness (1959) to represent a streamflow of 0.10 ft/s. This value of streamflow was important because, for many years, this was the smallest non-zero streamflow value reported in most streamflow records. Figure 8 shows that the percentage duration of 0.10 ft/s adjusted to 500 miî at the Valley Center station (07144200, fig. 8) is about 99 percent. To find the duration of appreciable flow for 1,327 miî in figure 9, a point representing 99-percent duration and a drainage area of 500 miî was plotted. Following the diagonal line to 1,327 miî of drainage area, the percentage duration of 0.10 ft/s was found to be about 99.6 percent. In figure 12, the point is plotted as 0.10 ft/s at the 99.6-percent duration (point E). If an estimated duration curve is to be developed for a site where appreciable flow occurs more than 99 percent of the time, as in this example, the value of the duration of appreciable flow is ignored, and the curve is developed using the other five factors.

Average slope of the duration curve: The average slope of the duration curve is a graphical approximation of the variability index, which is the standard deviation of the logarithms of the stream discharges (Furness, 1959, p. 202-204, figs. 147 and 148). On a duration curve that fits the log-normal distribution exactly, the variability index is equal to the ratio of the discharge at the 15.87-percent-duration point to the discharge at the 50-percent-duration point. Because duration curves usually do not exactly fit the log-normal distribution, the average-slope line is drawn through an arbitrary point, and the slope is transferred to a position approximately defined by the previously estimated points.

Figure 10 provides an average slope of about 0.55 for a 500-miî drainage area for the Valley Center station (07144200, fig. 10). Figure 11 shows an adjustment of 0.91 for 1,327 miî of drainage area. Thus, the average slope for the Valley Center station is 0.55 x 0.91 = 0.50. The average-slope line is plotted in figure 12 by drawing a straight line between a point defined by 0.50 times the height of one log cycle, or about 3,300 ft/s on the 1,000-to-10,000 cycle, plotted at 15.87-percent duration and a point at 1,000 ft/s at 50-percent duration. Because the Valley Center station has appreciable flow more than 95 percent of the time, the average-slope line defines the average slope of the duration curve from 5- to 95-percent duration. If the duration percentage of appreciable flow is less than 95 percent, then the average-slope line defines a line for 1/19 to 19/19 times the duration percentage of appreciable flow. For example, if the duration percentage of appreciable flow is 93 percent, then the slope is applied to the area of the curve between 4.9- and 93-percent duration.

Using five of the six factors plotted in figure 12 (point E is ignored), duration-curve estimation was attempted for the Little Arkansas River at Valley Center. A smooth curve was drawn through the four estimated points, keeping in mind the average slope and the duration range for which that slope applies. After the estimated duration curve was drawn, a line parallel to the average-slope line was drawn to verify that the average slope of the estimated duration curve, between the limits of 5- and 95-percent duration, is close to the estimated slope from the map. The final curve is the estimated duration curve for the station, shown as a dashed line in figure 12. The computed duration curve for the station for 1968-98 is shown as a solid line. The agreement between the estimated duration curve and the computed duration curve for the Little Arkansas River at Valley Center is close. Accuracy may be improved with the use of low- to medium-flow measurements made at the Valley Center station and correlating them with the durations at a nearby, long-term, continuous-record, streamflow-gaging station.

If additional accuracy for the estimated duration curve is needed, the area under the curve is computed, and then the solution for the mean discharge is found using the method described by Furness (1959, p. 179). Then, if necessary, the curvature of the upper part of the estimated curve is revised to obtain the desired agreement between the area under the curve and the mean discharge.

The estimated duration curve for Cow Creek near Claflin, station 07142860 (fig. 15, appendix A at the end of this report), is an example of how the Furness method may be applied to sites with drainage areas less than 100 miî. The Claflin station has a drainage area of 43.4 miî and has 15 years of continuous streamflow data from 1967-81. The computed duration curve and estimated duration curve for this site are plotted using discharge per square mile, which is the duration discharge divided by the drainage area. The estimated duration points and streamflow measurements define an estimated curve that closely resembles the computed duration curve for the 1967-81 period. From this example, it appears that the Furness method is applicable to smaller drainage-area sites when miscellaneous low-flow discharge measurements are used.

USE OF MISCELLANEOUS MEASUREMENTS

An example of how discharge measurements at ungaged sites are used to improve the estimated duration curve is shown in figure 13. The estimated curve that was developed in figure 12 shows a close approximation to the actual duration curve for 1968-98. The part of the duration curve that is the most difficult to estimate is the low-flow part, and with the use of some miscellaneous low-flow measurements, this part of the curve can be verified or improved. A retrieval of data stored in NWIS for the Valley Center station provided 62 measurements, dating back to 1987, with discharges less than 84 ft/s, which is the estimated 50-percent-duration discharge. Of those 62 measurements, 49 were made when the stream appeared to represent base-flow conditions (no apparent surface runoff). These 49 discharge values were correlated with mean daily streamflow values from the Little Arkansas River at Alta Mills station (07143665, fig. 1). The duration percentages for each daily discharge value then were taken from the 1968-98 duration curve for the Alta Mills station and assigned to the same day's discharge value for the Valley Center station (07144200, fig. 1). The measurements were plotted in figure 13 at the correlated duration percentages acquired from the Alta Mills station. The measurements indicate that the low-flow part of the curve should be shifted to the right and also extended beyond 95-percent duration to 99.8-percent duration as shown by the blue line in figure 13. The extended estimated duration curve appears reasonable when compared to the computed 1968-98 duration curve for the site.

Tests were performed on all of the other concurrently measured streamflow-gaging stations listed on the right in table 1. Although the results are not shown in this report, they were similar to those for the Little Arkansas River at Valley Center station. The estimated curves were fairly accurate in the high-flow part of the curve and less accurate in the low-flow part of the curve when compared with the computed duration data for 1968-98. The computed curves for the concurrently measured stations listed on the right in table 1 were all improved when low-flow discharge measurements were correlated with nearby stations for 1968-98.

EXISTING STREAMFLOW INFORMATION AT UNGAGED SITES

COLLECTION OF BASE-FLOW MEASUREMENTS

CONSTRUCTION OF ESTIMATED FLOW-DURATION CURVES

The estimated flow-duration curves for the 16 selected ungaged sites are presented in appendix A. In most cases, the low-flow part of the curves have been modified from the originally estimated curve on the basis of streamflow measurements. Appendix B provides the site descriptions for the 16 ungaged sites, and Appendix C provides a listing of the miscellaneous streamflow measurements made at the 16 ungaged sites during 1999. The curves have been presented in discharge per square mile of drainage area so that they may used for sites on the same stream that are near the estimated site. To use the curve at a different site, multiply the discharge per square mile value of the curve by the drainage area of the desired site to obtain the discharge for the site. Care should be taken not to use the estimated duration curves at sites too far away because other factors may affect the duration curve at the estimated site that may not affect the flow duration at a different site on the same stream. It is more accurate to estimate a flow-duration curve for the intended site rather than trying to use the estimated curve for a different site on the same stream.

SUMMARY AND CONCLUSIONS

REFERENCES

APPENDICES

APPENDIX A. Estimated flow-duration curves and tables for 16 ungaged sites in the Cimarron and lower Arkansas River Basins in Kansas
Graph showing estimated flow-duration curve for 1968-98 for site:
Figure 14. 07142650, Peace Creek near Sylvia
Figure 15. 07142860, Cow Creek near Claflin
Figure 16. 07143660, Turkey Creek near Buhler
Figure 17. 07144037, Emma Creek 3 miles north and 0.75 mile west of Sedgwick
Figure 18. 07144080, Sand Creek 3 miles north and 2 miles east of Sedgwick
Figure 19. 07144545, Cowskin Creek near Oatville
Figure 20. 07145220, Smoots Creek near Murdock
Figure 21. 07148100, Grouse Creek near Dexter
Figure 22. 07148110, Silver Creek at Highway 166 east of Arkansas City
Figure 23. 07148200, Mule Creek near Wilmore
Figure 24. 07148600, Medicine Lodge River at Sun City
Figure 25. 07148900, Elm Creek at Medicine Lodge
Figure 26. 07149590, Sandy Creek near Waldron
Figure 27. 07149605, Little Sandy Creek near Corwin
Figure 28. 07151670, Bluff Creek south of Anthony
Figure 29. 07157900, Cavalry Creek at Coldwater

 

APPENDIX B

APPENDIX C