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1 This is a digital document from the collections of the Wyoming Water Resources Data System (WRDS) Library. For additional information about this document and the document conversion process, please contact WRDS at wrds@uwyo.edu and include the phrase Digital Documents in your subject heading. To view other documents please visit the WRDS Library online at: Mailing Address: Water Resources Data System University of Wyoming, Dept E University Avenue Laramie, WY Physical Address: Wyoming Hall, Room 249 University of Wyoming Laramie, WY Phone: (307) Fax: (307) Funding for WRDS and the creation of this electronic document was provided by the Wyoming Water Development Commission (

2 Estimating Streamflow from Concurrent Discharge Measurements Prepared for: Wyoming Water Development Commission By: 205 South Third Street Lander, Wyoming 82520

3 Estimating Streamflow from Concurrent Discharge Measurements Prepared for: Wyoming Water Development Commission By: Hugh Lowham, P.E., Thomas Wilkinson, J.J. Brown and Andrew Strike of 205 South Third Street Lander, Wyoming i

4 Table of Contents GLOSSARY... iv Introduction... 1 Purpose and Scope... 1 Concurrent Measurement Method... 2 Estimating Monthly Flows from Discharge Measurements... 2 Selection of Gaged Base Station... 2 Example - Marquette and Trout Creeks... 4 Comparison of different basin-characteristics relations for estimating flow... 9 Comparison of Unitized Flows Example - Sunlight Creek Arithmetic Ratio Method Regression Equation Based on Mid-month Measurements Use of Logarithmic Ratios Method Summary References List of Figures Figure 1. Locations of 14 USGS streamflow stations in mountainous areas of Wyoming 3 Figure 2. Unitized mean streamflows for 14 gaged perennial streams located in mountainous areas of Wyoming... 3 Figure 3. Location of selected streams and gaging stations in northwestern Wyoming... 4 Figure 4. Clearing section for measurement of Marquette Creek near Cody, Wyoming, downstream view, January 16, Figure 5. Discharge measurement of Trout Creek near Cody, Wyoming, downstream view, November 16, Figure 6. Ratios of measured flows on Marquette Creek to gaged daily mean flows on South Fork Shoshone River... 6 Figure 7. Graph showing ratios of measured flows on Trout Creek to gaged daily mean flows on South Fork Shoshone River... 7 Figure 8. Concurrent discharge data for Marquette Creek and South Fork Shoshone River... 8 Figure 9. Concurrent discharge data for Trout Creek and South Fork Shoshone River... 8 Figure 10. Unitized flows Figure 11. Daily mean discharge for USGS station Sunlight Creek, 1970 water year Figure 12. Daily mean discharge for USGS station South Fork Shoshone River, 1970 water year Figure 13. Concurrent discharges for Sunlight Creek and South Fork Shoshone River, 1970 water year ii

5 Figure 14. Daily mean discharge for USGS station Sunlight Creek, 1970 water year, with two additional measurements and average of measurements for months of May through August Figure 15. Concurrent discharge for Sunlight Creek and South Fork Shoshone River, 1970 water year, with additional measurements for May through August Figure 16. Concurrent discharge for Sunlight Creek and South Fork Shoshone River, water years, results of 24 measurements Figure 17. Concurrent and mean discharges for April List of Tables Table 1. Streamflow measurements for Marquette Creek, and daily mean flow for USGS streamflow gage South Fork Shoshone River... 6 Table 2. Streamflow measurements for Trout Creek and daily mean flow for USGS streamflow gage South Fork Shoshone River... 7 Table 3. Estimates of discharge for Marquette and Trout Creeks using various methodologies Table 4. Summary of records available for USGS streamflow stations Table 5. Assumed streamflow measurements for Sunlight Creek, and daily mean flow for USGS streamflow gage South Fork Shoshone River, 1970 water year Table 6. Summary of computed and actual gaged discharge for Sunlight Creek, using arithmetic ratios for 12 mid-month measurements, with straight-line interpolation between measurements Table 7, Summary of computed and actual gaged discharge for Sunlight Creek, using arithmetic ratio based on one mid-month measurement made during September Table 8. Summary of computed and actual gaged discharge for Sunlight Creek, using regression of 12 mid-month measurements, with equation applied to flow values Table 9. Summary of computed and actual gaged discharge for Sunlight Creek, using regression of 12 mid-month measurements, with equation applied to daily flow values Table 10. Summary of computed and actual gaged discharge for Sunlight Creek, using regression of mid-month measurements, with additional measurements for May through August, and applied to flows Table 11. Summary of computed and actual gaged discharge for Sunlight Creek, using regression of mid-month measurements, two years of data, with equation applied to flows Table 12. Summary of computed and actual discharges for USGS station Sunlight Creek, using logarithmic ratios Table 13. Summary of differences for the various procedures iii

6 GLOSSARY Cubic foot per second (ft 3 /s, or cfs) - Rate of discharge representing a volume of 1 cubic foot passing a given point during 1 second, equivalent to approximately 7.48 gallons per second, gallons per minute, or cubic meter per second. In a stream channel, a discharge of 1 cubic foot per second is equal to the discharge at a rectangular cross section, 1 foot wide and 1 foot deep, flowing at an average velocity of 1 foot per second. Daily mean discharge (flow) The mean discharge for a particular day, such as March 16, Discharge - The volume of fluid passing a point in a given period of time, commonly expressed in cubic feet per second, million gallons per day, gallons per minute, or seconds per minute per day. Drainage area - The drainage area of a stream at a specified location is that area, measured in a horizontal plane, which is enclosed by a drainage divide. Gaging station (gage) site on a stream, canal, lake, or reservoir where systematic observations of stage, discharge or other hydrologic data are obtained. For discharge of a stream, the term applies only to gaging stations where a continuous record of discharge is determined. Mean daily discharge (flow) The arithmetic mean of individual daily mean discharges for a particular day during a period of record, such as March 16 th for Mean discharge (flow) The arithmetic mean of individual mean discharges for a particular month during a period of record, such as March for Monthly mean discharge (flow) - The arithmetic mean of individual daily mean discharges for a particular month, such as of the 31 daily discharges of March Precipitation - Any or all forms of water particles that fall from the atmosphere, such as rain, snow, hail, and sleet. Runoff - That part of precipitation or snowmelt that appears in streams or surface-water bodies. Streamflow - The discharge of water in a natural channel. Water year A water year is defined as the 12-month period October 1 of one calendar year through September 30 of the following year. The water year is designated by the calendar year in which it ends. For example - the year ending September 20, 2007, is the 2007 water year. iv

7 Estimating Streamflow from Concurrent Discharge Measurements Introduction Sound management of stream-related projects requires decisions based on reliable flow information. Ideally, long-term records from streamflow gaging stations are available for each stream reach where data are desired, but this is rarely a reality. In cases where streamflow gage data are not available, it is possible to estimate streamflow at the site. Regional correlations of flow characteristics at gaged sites to various measured physical and climatic variables of drainage basins are often used to estimate streamflows when gage data are unavailable (Lowham, 1988; and Miselis, Wesche, and Lowham, 1999). This technique is commonly used in Wyoming to estimate flood flows and mean annual flows. Regional correlations are not as well suited for estimating of low flows because low flows are largely affected by localized geology which is difficult to quantify from regional map data (Riggs, 1972). This report details a method for estimating streamflows at ungaged sites in mountainous areas of Wyoming. Documentation and application of the technique was performed by as part of an instream flow study for the Wyoming Water Development Commission. Purpose and Scope The purpose of this report is to present an improved method for estimating flows of ungaged mountain streams in Wyoming. Mountainous areas are the main source of perennial flow in Wyoming. Interest in streamflow data for perennial mountain streams has increased with the recent rise in water rights filed for non-consumptive instream flows. The quantification of low flows from about October through April is most critical in the analysis of an instream flow request. This report describes the use of concurrent measurements to estimate streamflows in mountainous areas of Wyoming. Direct discharge measurements are taken at ungaged sites and are correlated with concurrent discharge data from a nearby gaging station. The relation between the measured and gaged data is used to translate long-term streamflow characteristics from the gaged site to the ungaged site and to produce an estimated streamflow record at the ungaged site for a given period of time (Riggs, 1969; Parrett and Cartier, 1990). Estimating streamflows in this manner is much less expensive than operating a gage and is far more accurate than an estimate made without direct discharge measurements. 1

8 Concurrent Measurement Method Estimating Monthly Flows from Discharge Measurements The concurrent measurement method is generally used to estimate flows. Measurements are made on the ungaged stream near the middle of the month to obtain estimates of the flows. A mid-month measurement generally will result in a more realistic estimate of flow than a measurement taken near the beginning or end of the month. Steps in the process are: 1. Select a representative gaged drainage that is preferably near the ungaged site where data are desired. The ungaged drainage should have physical and climatic characteristics similar to those of the gaged drainage. 2. Obtain mid-month discharge measurements at the ungaged site for 12 months. 3. Retrieve daily discharge data (daily mean discharge) from the gaged site records. Use the same days that measurements were obtained at the ungaged site. If the gaged site has been discontinued, the past records can still be used to estimate long-term flows, but concurrent mid-month discharge measurements will be necessary at the gaged site. 4. Estimate the desired flow values by relating the data for the ungaged and gaged sites. Examples of several different methods for determining the discharge estimates are provided in this report. Selection of Gaged Base Station It is important to select a gaged site with runoff characteristics similar to the ungaged site. Elevation and geology can greatly affect the magnitude of low flows, which are derived mainly from groundwater inflows. Figure 1 shows the locations of 14 U.S. Geological Survey (USGS) streamflow stations on perennial streams in mountainous areas of Wyoming. The hydrographs at these sites represent essentially natural flows, unaffected by storage or diversions. The unitized (divided by drainage area) mean flows for each station are plotted in Figure 2. This allows for a comparison of runoff per square mile for the various drainages. The variation between the individual hydrographs can be related to physiological conditions such as elevation, precipitation, surface geology, slope, and aspect. Variation in streamflows between sites from April through July is primarily due to elevation and the amount of snow available for runoff. The hydrograph for Dinwoody Creek shows relatively high unit runoff from July through September, likely due to glacial melt in the headwaters of the stream. Variation in streamflows during the lowflow months, October through April, is largely due to the influence of local surface geology. For example, flows in Box Elder Creek decrease as the stream crosses karst terrain. Loss of flow will also occur as a stream crosses glacial outwash or similar unconsolidated surface deposits. 2

9 Figure 1. Locations of 14 USGS streamflow stations in mountainous areas of Wyoming Stream flow (cfs/mi 2 ) Dinwoody Ck SF L. Wind River Shell Ck MF Powder River NF Powder River N. Brush Ck Encampment River Rock Ck Box Elder Ck Pine Ck Bear River Cache Ck 0.01 Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Figure 2. Unitized mean streamflows for 14 gaged perennial streams located in mountainous areas of Wyoming 3

10 Example - Marquette and Trout Creeks (2008) completed a feasibility study for instream flows on Marquette and Trout Creeks, which are located in the mountains of northwest Wyoming (Figure 3). Streamflow records for the USGS gage station South Fork Shoshone River were used to estimate flows on the ungaged streams. Mid-month streamflows were measured from June 2007 through May 2008 (Figures 4 and 5). Measured streamflow data for the ungaged instream flow sites are tabulated in Tables 1 and 2, along with the concurrent daily flows from the gaged site on South Fork Shoshone River. The ratios of direct discharge measurements at the ungaged sites to concurrent daily flows for South Fork Shoshone River are plotted in Figures 6 and 7. Also shown on Figures 6 and 7 are ratios using a separate set of measurements that were obtained by the Wyoming Game and Fish Department (WGFD) during 2004 (Dey and Annear, 2006). The WGFD data plot shows a pattern of ratios during May through August similar to those for measurements obtained by (2008). In general, the WGFD ratios are smaller than the Lowham ratios. The smaller ratios are probably due to the relatively greater spring and summer runoff that occurred for South Fork Shoshone River during 2004 versus Figure 3. Location of selected streams and gaging stations in northwestern Wyoming 4

11 Figure 4. Clearing section for measurement of Marquette Creek near Cody, Wyoming, downstream view, January 16, 2008 Figure 5. Discharge measurement of Trout Creek near Cody, Wyoming, downstream view, November 16,

12 Table 1. Streamflow measurements for Marquette Creek, and daily mean flow for USGS streamflow gage South Fork Shoshone River Measured Daily Mean Ratio of Marquette Cr/ Date Marquette Creek SF Shoshone River SF Shoshone R (cfs) (cfs) June 15, July 17, August 15, September 18, October 16, November 16, December 15, January 14, February 14, * March 15, April 15, May 16, * no measurement due to poor access conditions, an average of Jan and Mar values is used Lowham measurements Daily flow ratio May 17-Aug May 10-Jun 15-Jul WGFD measurements 2004 Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Figure 6. Ratios of measured flows on Marquette Creek to gaged daily mean flows on South Fork Shoshone River 6

13 Table 2. Streamflow measurements for Trout Creek and daily mean flow for USGS streamflow gage South Fork Shoshone River Measured Daily Mean Ratio of Trout Cr / Date Trout Creek SF Shoshone River SF Shoshone R (cfs) (cfs) June 15, July 17, August 15, September 18, October 16, November 16, December 15, January 14, February 14, March 15, April 15, May 16, Lowham measurements Daily flow ratio May 25-May 3-May 8-Jun 9-Jun 19-Aug 14-Jul 13-Jul WGFD measurements Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Figure 7. Graph showing ratios of measured flows on Trout Creek to gaged daily mean flows on South Fork Shoshone River The ratios of ungaged to gaged flows for both Marquette and Trout Creeks vary over the 12 month period of study. Much of the variation is likely caused by the nature of runoff from the relatively small drainages of the ungaged streams in relation to the large drainage of the South Fork Shoshone River. This variation highlights the importance of direct measurements. If flow estimates are based on only one or two measurements during the year, estimated flows will be inaccurate for many of the months. Concurrent discharge data for Marquette and Trout Creeks and South Fork Shoshone River are plotted in Figures 8 and 9. Trout Creek is a south-facing basin and runoff occurs earlier than on Marquette Creek, which is north-facing basin. Greater scatter in 7

14 the discharge measurements during low-flow months on Trout Creek is due to additional snowmelt and surface runoff during warm spells Discharge of Marquette Creek (cfs) 1.00 Dec-07 Jan-08 Mar-08 Nov-07 Feb-08 Apr-08 Aug-07 Sep-07 Oct-07 May-07 Jul-07 Jun Discharge of South Fork Shoshone River (cfs) Figure 8. Concurrent discharge data for Marquette Creek and South Fork Shoshone River Discharge of Trout Creek (cfs) Dec-07 Mar-08 Apr-08 Nov-07 Aug-07 Oct-07 Jan-08 Sep-07 Feb-08 May-08 Jul-07 Jun Discharge of South Fork Shoshone River (cfs) Figure 9. Concurrent discharge data for Trout Creek and South Fork Shoshone River 8

15 Comparison of different basin-characteristics relations for estimating flow The concurrent measurement method of estimating discharge requires mid-month discharge measurements. A full year is required to obtain all 12 mid-month measurements. Other methods exist for estimating streamflow based on data obtained from topographic maps, eliminating the necessity of site visits. Lowham (1988) developed the following equations to estimate mean annual flows using specific basin characteristics: Q a = A 1.01 (ELEV/1,000) 2.88, and Q a = A 0.93 PR 1.43 where Qa = mean annual flow, in cubic feet per second, A = contributing drainage area, in square miles, ELEV = mean basin elevation, in feet, and PR = average annual precipitation, in inches. Miselis, Wesche, and Lowham (1999) refined the procedure by developing discrete equations specific to each major mountain range in Wyoming. Equations were developed to estimate flows as well as annual flows. The following equations estimate mean flows and mean annual flows for streams in the Absaroka Mountains: Q a = A 1.15, Q Oct = A 1.07, Q Nov = A 1.16, Q Dec = A 1.28, Q Jan = A 1.31, Q Feb = A 1.30, Q Mar = A 1.17, Q Apr = A 1.08, Q May = A 1.13, Q June = A 1.19, Q July = A 1.19, Q Aug = A 1.11, and Q Sep = A 1.06 where Q Oct = mean flow, in cubic feet per second, for month designated. Table 3 summarizes estimated streamflows using the above equations for Marquette and Trout Creeks. The columns designated as A, B, and C are estimates based on mean annual flow, with flows calculated in proportion to the ratios of to annual flows for the gaged station South Fork Shoshone River. The column designated as D shows flow estimates based on equations for the respective months. The column designated as E shows estimates developed using the concurrent measurement method. 9

16 Table 3. Estimates of discharge for Marquette and Trout Creeks using various methodologies SF Shoshone River Marquette Creek Trout Creek A B C D E A B C D E Month Mean flow at station for water years (cfs) Ratio -Monthly flow/annual runoff/months (Qm/402/12) Lowham (1988), Qa equation using A and ELEV (cfs) Lowham (1988) Qa equation using A and PR (cfs) Miselis (1999) Qa equation using A (cfs) Miselis (1999) Qm equations using A (cfs) Lowham Engineering LLC (2008) using concurrent meas (cfs) Lowham (1988), Qa equation using A and ELEV (cfs) Lowham (1988) Qa equation using A and PR (cfs) Miselis (1999) Qa equation using A (cfs) Miselis (1999) Qm equations using A (cfs) Lowham Engineering LLC (2008) using concurrent meas (cfs) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep SUM 1.0 Mean A - Discharge estimates using equation for mean annual flow from Lowham (1988, p. 27) and applying ratios of mean flows from records for station B - Discharge estimates using equation for mean annual flow from Lowham (1988, p. 28) and applying ratios of mean flows from records for station C - Discharge estimates using equation for mean annual flow from Miselis, Wesche, and Lowham (1999, p. 97) and applying ratios of mean flows from records for station D - Discharge estimates using equations for mean flows from Miselis, Wesche, and Lowham (1999, p ) E Discharge estimates using mid-month concurrent discharge measurements, (2008, p. 11) Basin characteristics of Marquette Creek are: A = 2.1 mi 2, ELEV = 9,042 ft, PR = 20 inches Basin characteristics of Trout Creek are: A = 42 mi 2, ELEV = 8,428 ft, PR = 25 inches 10

17 HabiTech, Inc. (2004) analyzed instream flows of Marquette and Trout Creeks for the Wyoming Game and Fish Department. That analysis relied on the mean annual flow equation of Miselis, Wesche, and Lowham (1999). Monthly flows for each stream were then derived in proportion to streamflows for the gaged stream South Fork Shoshone River, similar to the examples in columns C of Table 3. Streamflow estimates using basin-characteristics equations (columns A-D) vary somewhat from estimates based on concurrent discharge measurements (column E). In general, the calculated estimates for Marquette Creek are less, and for Trout Creek are greater, than estimates based on the concurrent measurements. This disparity is the result of variation in the hydrologic characteristics of the ungaged streams relative to those of the gaged streams that were used in development of the regression models. The regression equations may not include all of the independent basin characteristics that significantly influence flows in the smaller drainages. The inclusion of additional independent variables, such as vegetation type and geology, could be explored to further refine the basin characteristics-based equations (Miselis, Wesche, and Lowham, 1999, p. 46). Comparison of Unitized Flows Figure 10 shows unitized flows for the gage station South Fork Shoshone River and the ungaged streams. The discharge values are divided by drainage area to calculate runoff per square mile. The graph illustrates the difference in the pattern of unit flows between these sites S.F. Shoshone R. mean ( ) S.F. Shoshone R. mean ( ) Marquette Ck mean ( ) Trout Ck mean ( ) Unit discharge (cfs /mi 2 ) Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Date Figure 10. Unitized flows 11

18 Example - Sunlight Creek Sunlight Creek and South Fork Shoshone River are gaged streams located near Cody (Figure 3). A summary of the available streamflow data is presented in Table 4. Table 4. Summary of records available for USGS streamflow stations USGS Station No. Name Drainage Area (mi 2 ) Period of Operation Record (water years) Sunlight Creek near , 29 Painter, WY S.F. Shoshone River near Valley, WY To illustrate the applicability of the concurrent measurement method, streamflows for Sunlight Creek were estimated using streamflow gage South Fork Shoshone River as a base station. Sunlight Creek was treated as if ungaged, and daily mean flows at mid-month were used as the measured discharges. A common base period of water years was used for the procedure, since both stations had records for that period. Water year 1970 was randomly selected as the 12-month period when measurements were made. The measured discharges were correlated to the gaged flow data for Shoshone River to determine flows. A summary of the data is presented in Table 5. The discharges for South Fork Shoshone River are adjusted to account for several small irrigation diversions upstream of the gage station. The adjusted discharges represent natural or virgin flows, unaffected by upstream storage or diversions. Table 5. Assumed streamflow measurements for Sunlight Creek, and daily mean flow for USGS streamflow gage South Fork Shoshone River, 1970 water year Assumed Measured Adjusted Daily Mean Ratio of Sunlight Creek/ SF Shoshone River Date Sunlight Creek SF Shoshone River (cfs) (cfs) 10/15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ The hydrographs of actual daily mean flows for water year 1970 on Sunlight Creek and South Fork Shoshone River are shown in Figures 11 and

19 Discharge (cfs) Daily mean discharges at mid-month 0 10/1/ /1/ /1/1969 1/1/1970 2/1/1970 3/1/1970 4/1/1970 5/1/1970 6/1/1970 7/1/1970 8/1/1970 9/1/1970 Figure 11. Daily mean discharge for USGS station Sunlight Creek, 1970 water year Discharge (cfs) Daily mean discharges at mid-month /1/ /1/ /1/1969 1/1/1970 2/1/1970 3/1/1970 4/1/1970 5/1/1970 6/1/1970 7/1/1970 8/1/1970 9/1/1970 Figure 12. Daily mean discharge for USGS station South Fork Shoshone River, 1970 water year 13

20 Sunlight Creek flows were estimated using several different modeling techniques in order to compare the different methods: o Use of arithmetic ratios (Table 5) of assumed measured flows for Sunlight Creek to the gaged daily mean flows of the base station South Fork Shoshone River. o Use of regression equations developed from the measured flows. The regression equations are based on the mid-month discharge data, and use flows of South Fork Shoshone River to estimate flows for Sunlight Creek. o Use of logarithmic ratios applied to measured flows to determine the discharge for the year of measurement (1970 water year) and again to determine the mean flows for the period of record ( water years). Arithmetic Ratio Method The mid-month ratios shown in Table 5 were used to estimate flows of Sunlight Creek. Two examples are shown. For the first example, 12 mid-month measurements are assumed. The ratio for each respective day is interpolated by a straight-line method from mid-month to mid-month. For example, the ratio (0.42) for estimating discharge for June 1 is determined by interpolation between the ratios for May 15 (0.36) and June 15 (0.53). Discharge for each day of the period from October 1, 1956 through September 30, 1971 is computed by multiplying the ratio by the discharge for South Fork Shoshone River. The flows are then determined by averaging the daily flows. For the second example, only one mid-month measurement is assumed during the month of September. Tables 6 and 7 summarize results for the two examples. Table 6. Summary of computed and actual gaged discharge for Sunlight Creek, using arithmetic ratios for 12 mid-month measurements, with straight-line interpolation between measurements Actual Assumed measured, 1970 water year Calculated mean, 1970 water year mean, 1970 water year Difference Calculated mean ( ) Actual mean ( ) Difference Date (cfs) (cfs) (cfs) (percent) (cfs) (cfs) (percent) October November December January February March April May June July August September

21 Table 6 summarizes estimates of the mean (1970 water year) and long-term mean ( water years) discharges for Sunlight Creek based on 12 discharge measurements. The differences between the actual gaged and computed flows are listed. The estimated long-term mean flows for the low-flow months of September through March are within 5 to 20 percent of the actual gaged flows. Estimates for the high-flow period are less accurate due to the variability of flow. Table 7, Summary of computed and actual gaged discharge for Sunlight Creek, using arithmetic ratio based on one mid-month measurement made during September Actual Assumed measured, 1970 water year Calculated mean, 1970 water year mean, 1970 water year Difference Calculated mean ( ) Actual mean ( ) Difference Date (cfs) (cfs) (cfs) (percent) (cfs) (cfs) (percent) October November December January February March April May June July August September Table 7 summarizes discharge estimates based on a ratio (0.46) for a single measurement, which was assumed to have been made during September. The estimate for the mean flow is relatively close for September. However, there is much greater variation in the mean flows than for the 12-measurement example. This illustrates the benefit of additional data for increased accuracy in estimating streamflows. Regression Equation Based on Mid-month Measurements Concurrent discharges for Sunlight Creek and the South Fork Shoshone River are plotted in Figure 13. The regression equation y = x was developed using 12 sets of mid-month discharges for the 1970 water year. The value x is the daily mean discharge for the base station South Fork Shoshone River, and y is the estimated daily mean discharge for Sunlight Creek. The equation is a power function, which plots as a straight line on a logarithmic scale graph. This is because hydrologic relationships, as with many other relationships in nature, adhere to straight-line relations after logarithmic transformation is done. The strong correlation coefficient (0.967) of the discharge data indicates similar runoff patterns between the two streams. Monthly flows for the base station South Fork 15

22 Shoshone River were used in the equation to estimate flows for Sunlight Creek. The results are summarized in Table Measured discharge of Sunlight Creek (cfs) 100 y = x R 2 = /15 5/15 10/15 11/15 4/15 12/15 2/15 3/15 1/15 8/15 6/15 7/ Adjusted gaged discharge of S.F. Shoshone River (cfs) Figure 13. Concurrent discharges for Sunlight Creek and South Fork Shoshone River, 1970 water year Table 8. Summary of computed and actual gaged discharge for Sunlight Creek, using regression of 12 mid-month measurements, with equation applied to flow values Assumed measured, 1970 water year Calculated mean, 1970 water year Actual mean, 1970 water year Difference Calculated mean ( ) Actual mean ( ) Difference Date (cfs) (cfs) (cfs) (percent) (cfs) (cfs) (percent) October November December January February March April Mau June July August September

23 As a comparison, the same equation was used to estimate daily flows (rather than flows) of Sunlight Creek. The daily flows were then summed to compute the values. Table 9 summarizes the results. There is little difference between results for the versus daily procedures. If only values are needed, the regression applied to the values is a relatively simple procedure that will provide sufficient accuracy. However, if daily values are needed to determine daily flow duration curves, then the application using daily flows should be used. Table 9. Summary of computed and actual gaged discharge for Sunlight Creek, using regression of 12 mid-month measurements, with equation applied to daily flow values Assumed measured, 1970 water year Calculated mean, 1970 water year Actual mean, 1970 water year Difference Calculated mean ( ) Actual mean ( ) Difference Date (cfs) (cfs) (cfs) (percent) (cfs) (cfs) (percent) October November December January February March April Mau June July August September The mid-month discharges shown in Figures 11 and 12 are a fairly accurate representation of the mean flows during low-flows months. However, discharges from May through July have a large range and are highly variable. During May and June, the mid-month measurements occur at troughs in the hydrograph. During May the mid-month measurement is relatively low compared to daily discharges during the latter part of the month. Although the correlation of discharges as shown in Figure 13 is strong, the mid-month measurements do not accurately represent the actual flows for the high-flow months. This is reflected in the differences shown in Table 8 for the highflow months. Twelve mid- measurements generally provide adequate data to estimate streamflows at an ungaged site and to evaluate the availability of low-flows. However, if a more accurate estimate of high flows or total runoff is needed, then additional measurements might be considered to refine the regression relation. A second test was conducted in an effort to improve the accuracy of discharge estimates for Sunlight Creek during the high runoff period. Two additional measurements are assumed for the 5 th and 25 th days of May through August (Figure 14). 17

24 Extra measurement Dischage (cfs) Average (3 measurements) 200 Mid-month measurement 0 10/1/ /1/ /1/1969 1/1/1970 2/1/1970 3/1/1970 4/1/1970 5/1/1970 6/1/1970 7/1/1970 8/1/1970 9/1/1970 Figure 14. Daily mean discharge for USGS station Sunlight Creek, 1970 water year, with two additional measurements and average of measurements for months of May through August The mid-month discharges plus the eight additional measurements for May through August are plotted in Figure 15. The regression equation y = x was developed using the expanded data set and flows of South Fork Shoshone River were used to estimate flows for Sunlight Creek. The results are summarized in Table

25 10000 Measured discharge of Sunlight creek (cfs) y = x R 2 = /15 10/15 4/15 12/15 2/15 1/15 3/15 9/15 5/15 8/15 8/ Adusted gaged discharge of S.F. Shoshone River (cfs) 8/5 5/5 6/15 7/25 7/15 7/5 5/25 6/5 6/25 Figure 15. Concurrent discharge for Sunlight Creek and South Fork Shoshone River, 1970 water year, with additional measurements for May through August Table 10. Summary of computed and actual gaged discharge for Sunlight Creek, using regression of mid-month measurements, with additional measurements for May through August, and applied to flows Assumed measured, 1970 water year Calculated mean, 1970 water year Actual mean, 1970 water year Calculated mean ( ) Actual mean ( ) Difference Difference Date (cfs) (cfs) (cfs) (percent) (cfs) (cfs) (percent) October November December January February March April May June July August September

26 Estimating flows using the regression equation with additional high-flow measurements resulted in less difference between the estimated and actual gaged flows for the high flow months. However, differences for the low flow months were generally greater. The additional data addressed the high-flow end of the regression relation, but resulted in a less-accurate estimation of low flows. A third test was made using mid-month measurements for two water years, The 24 measurements are plotted in Figure 16. The estimates calculated using the regression equation y = x are summarized in Table Measured discharge of Sunlight Creek (cfs) y = x R 2 = /71 9/70 8/70 4/71 10/70 10/69 5/70 11/70 2/71 11/69 3/71 4/70 12/69 1/71 12/702/70 3/70 1/70 6/70 5/ Adjusted gaged discharge of S.F. Shoshone River (cfs) 8/71 7/70 7/71 6/71 Figure 16. Concurrent discharge for Sunlight Creek and South Fork Shoshone River, water years, results of 24 measurements 20

27 Table 11. Summary of computed and actual gaged discharge for Sunlight Creek, using regression of mid-month measurements, two years of data, with equation applied to flows Assumed measured Calculated mean Actual mean Difference Calculated mean ( water years) Actual mean ( water years) Difference Date (cfs) (cfs) (cfs) (percent) (cfs) (cfs) (percent) 10/15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ /15/ Use of Logarithmic Ratios Method The previous section presented a description of regression relations used to estimate flows. As shown in Figures 14 through 16, the regression relation is represented by a single line that provides a best-fit to all of the collected data. Riggs (1969) presented a method for estimating flows that accounts for the variation that may occur from the straight line of the regression equation. The procedure uses ratios of the logarithms for each set of mid-month data to estimate the mean flows. Figure 17 is represents the procedure graphically. Rather than using one regression relation based on all of the mid-month measurements, the estimate of each flow is calculated using ratios of the logarithms of the data. This ratio is represented in Figure 17 by a 45-degree line through the mid-month data point for April. Separate ratios (or lines) are used for each month. This procedure allows for deviation from the main regression relation. The procedure adjusts the mid-month discharge to the mean discharge of the ungaged site, based on the ratio of the mean daily discharge to the 21

28 mean discharge of the gaged site. A similar adjustment is applied to estimate the long-term mean flow for each month. 100 Discharge of Sunlight Creek (cfs) Measured (22) Monthly Mean (21) 10 Daily Mean (75) Monthly Mean (70) Adjusted gaged discharge of S.F. Shoshone River (cfs) Figure 17. Concurrent and mean discharges for April 1970 Table 12 summarizes the data and estimates calculated using the procedure of logarithmic ratios. Column D lists mean discharge estimates; column F lists the mean discharge estimates. 22

29 Table 12. Summary of computed and actual discharges for USGS station Sunlight Creek, using logarithmic ratios A B C D E F Dates Sunlight Creek, assumed midmonth measurement, 1970 water year Antilog [loga/logb* logc] Antilog [logd/logc* loge] SF Shoshone River, midmonth daily discharge, 1970 water year SF Shoshone River, mean, 1970 water year Sunlight Creek, computed mean, 1970 water year SF Shoshone River, mean, water years Sunlight Ck, computed mean, water years Sunlight Ck, actual mean, water years mean difference (cfs) (cfs) (cfs) (cfs) (cfs) (cfs) (cfs) (percent) October November December January February March April May June July August September

30 Summary Ideally, streamflow data are obtained from continuous-recording streamflow gaging stations. If gaged data are not available for a site where information is needed, then it may be necessary to estimate flow characteristics. This report summarizes several different methods for estimating flows. If it is not practical or possible to visit the site, then flow can be estimated by using predictive relations such as those developed by Miselis, Wesche, and Lowham (1999). Greater accuracy can be attained using the concurrent-discharge method. For ungaged sites, streamflow data can be estimated by correlating 12 mid- direct flow measurements to concurrent gaging station records on a nearby stream. This technique is especially useful for estimating low flows. The concurrent-discharge methodology presented in this report was demonstrated by comparing estimated flows for Sunlight Creek, a gaged stream in northwestern Wyoming, to actual gaged data. Gaged daily flows at the middle of each month for the 1970 water year were used as direct measurements. These 12 mid- discharges were then related to the gaged record of the South Fork Shoshone River. Comparisons were made of the actual gaged versus estimated flows for the water years. Several different mathematical procedures for correlating flows from the gaged to ungaged site were demonstrated: 1. Arithmetic Ratios using 12 mid-month measurements, with interpolation between months to determine a ratio for each day. 2. Arithmetic Ratio assuming only one measurement was made, in September. 3. Regression Relation using 12 mid-month measurements, with estimates calculated using flow values. 4. Regression Relation using 12 mid-month measurements, with estimates calculated using daily flow values. 5. Regression Relation using 12 mid-month measurements, plus two additional measurements for the high-flow months of May-August, with estimates calculated using flow values. 6. Regression Relation using 24 mid-month measurements over a two-year period, with estimates calculated using flow values. 7. Logarithmic Ratios using 12 mid-month measurements, with estimates calculated using values. Table 13 summarizes the difference between the actual versus estimated mean flows. The percent difference for each flow was determined as: Percent difference = ((actual flow-estimated flow)/actual flow) X 100. The percent difference for each month, and the average of the absolute values of percent difference for each method, are shown in Table

31 Table 13. Summary of differences for the various procedures Dates Table 6 Table 7 Table 8 Table 9 Table 10 Table 11 Table 12 Sliding Ratio on Regression Regression Regression Regression Log ratios ratio on daily w/12 on w/12 on w/12 plus w/ 24 on on daily flows daily high-flow flows using Sept flows flows meas flows flows (percent) (percent) (percent) (percent) (percent) (percent) (percent) October November December January February March April May June July August September Absolute average Using regression of 12 measurements plus eight additional measurements during high flows yielded the lowest absolute average. However, the estimates for the low-flow months of October through March were generally less accurate than for the regression that used only 12 measurements. Each procedure, with the exception of using only a single measurement, produced results within 25 percent for the low-flow months of October through March. Regression relationships work well when a strong correlation exists between the ungaged and gaged streams. The sliding ratio and logarithmic ratio procedures work well when the ratios of discharges between the gaged and ungaged sites follow a similar pattern from year-to-year. Use of the sliding ratio or regression relation on daily flows has the advantage of providing summaries of daily flows if required for a particular investigation. Spreadsheet models were developed for potential users as part of this study. 25

32 References Dey, Paul D., and Annear, Thomas C., 2006, Trout Creek, Tributary to North Fork Shoshone River, Instream Flow Studies: Wyoming Game and Fish Department, Fish Division, Administrative Report, Project AW-CY-IF5-511, April Dey, Paul D., and Annear, Thomas C., 2006, Marquette Creek, Tributary to South Fork Shoshone River, Instream Flow Studies: Wyoming Game and Fish Department, Fish Division, Administrative Report, Project AW-CY-IF4-511, May HabiTech, Inc., 2004, Flow duration and flood frequency analyses for selected streams in the Shoshone River Basin, Wyoming: Prepared by HabiTech, Inc., Laramie, Wyoming, October 25, 2004 Lowham, H.W., 1988, Streamflows in Wyoming: U.S. Geological Survey Water- Resources Investigations Report , 2008, Marquette Creek and Trout Creek instream flow - Level I study: Prepared for Wyoming Water Development Commission, February 20, Miselis, D.V., Wesche, T.A., and Lowham, H.W., 1999, Development of hydrologic models for estimating streamflow characteristics of Wyoming s mountainous basins: Wyoming Water Resource Center Project Completion Report. Parrett, C., and Cartier, K.D., 1990, Methods for estimating streamflow characteristics at ungaged sites in western Montana: U.S. Geological Survey Water-Supply Paper 2365 Riggs, H.C., 1969, Mean streamflow from discharge measurements: International Association of Scientific Hydrology Bulletin XIV, no. 4, p Riggs, H.C., 1972, Low-flow investigations: U.S. Geological Survey Techniques of Water-Resources Investigations, Chapter B1, Book 4. 26