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Scientific Investigations Report 2008–5112

Publications Warehouse SIR 2008–5112

Prepared in cooperation with the Kansas Department of Transportation

Precipitation-Frequency and Discharge-Frequency Relations for Basins Less than 32 Square Miles in Kansas

By Charles A. Perry

SIR2008-5112 Contents | Citation


Precipitation-frequency and discharge-frequency relations for small drainage basins with areas less than 32 square miles in Kansas were evaluated to reduce the uncertainty of discharge-frequency estimates. Gaged-discharge records were used to develop discharge-frequency equations for the ratio of discharge to drainage area (Q/A) values using data from basins with variable soil permeability, channel slope, and mean annual precipitation. Soil permeability and mean annual precipitation are the dominant basin characteristics in the multiple linear regression analyses.

In addition, 28 discharge measurements at ungaged sites by indirect surveying methods and by velocity meters also were used in this analysis to relate precipitation-recurrence interval to discharge-recurrence interval. Precipitation-recurrence interval for each of these discharge measurements were estimated from weather-radar estimates of precipitation and from nearby raingages. Time of concentration for each basin for each of the ungaged sites was computed and used to determine the precipitation-recurrence interval based on precipitation depth and duration. The ratio of discharge/drainage area (Q/A) value for each event was then assigned to that precipitation-recurrence interval.

The relation between the ratio of discharge/drainage area (Q/A) and precipitation-recurrence interval for all 28 measured events resulted in a correlation coefficient of 0.79. Using basins less than 5.4 mi2 only, the correlation decreases to 0.74. However, when basins greater than 5.4 and less than 32 mi2 are examined the relation improves to a correlation coefficient of 0.95.

There were a sufficient number of discharge and radar-measured precipitation events for both the 5-year (8 events) and the 100-year (11 events) recurrence intervals to examine the effect of basin characteristics on the Q/A values for basins less than 32 mi2. At the 5-year precipitation-/discharge-recurrence interval, channel slope was a significant predictor (r=0.99) of Q/A. Permeability (r=0.68) also had a significant effect on Q/A values for the 5-year recurrence interval. At the 100-year recurrence interval, permeability, channel slope, and mean annual precipitation did not have a significant effect on Q/A; however, time of concentration was a significant factor in determining Q/A for the 100-year events with greater times of concentration resulting in lower Q/A values. Additional high-recurrence interval (5-, 10-, 25-, 50-, and 100-year) precipitation/discharge data are needed to confirm these relations suggested above. Discharge data with attendant basin-wide precipitation data from precipitation-radar estimates provides a unique opportunity to study the effects of basin characteristics on the relation between precipitation recurrence interval and discharge-recurrence interval.

Discharge-frequency values from the Q/A equations, the rational method, and the Kansas discharge-frequency equations (KFFE) were compared to 28 measured weather-radar precipitation-/discharge-frequency values. The association between precipitation frequency from weather-radar estimates and the frequency of the resulting discharge was shown in these comparisons. The measured and Q/A equation computed discharges displayed the best equality from low to high discharges of the three methods. Here the slope of the line was nearly 1:1 (y=0.9844x0.9677). Comparisons with the rational method produced a slope greater than 1:1 (y=0.0722x1.235), and the KFFE equations produced a slope less than 1:1 (y=5.9103x0.7475). The Q/A equation standard error of prediction averaged 0.1346 log units for the 5.4-to 32-square-mile group and 0.0944 log units for the less than 5.4-square mile group. The KFFE standard error averaged 0.2107 log units for the less-than-30-square-mile equations. Using the Q/A equations for determining discharge frequency values for ungaged sites thus appears to be a good alternative to the other two methods because of this smaller error.

Posted August 2008

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Purpose and Scope

Previous Studies and Data Collection

Methods of Computing Discharge-Frequency Values

Rational Method

Kansas Discharge-Frequency Equations

Discharge/Drainage Area Method

Precipitation Frequency and Intensity

Discharge/Area (Q/A) Analyses

Existing Stream-Gage Information

Precipitation-/Discharge-Site Information



Supplemental Stream Gage Data

Precipitation/Discharge Sites

Precipitation-Recurrence Interval Determination

Precipitation-/Discharge-Frequency Distributions

Q/A Equations for Estimating Discharge-Frequency Values for Small Basins

Comparison of Equations Used to Estimate Discharge Frequency for Small Rural Basins with Precipitation-/Discharge-Frequency Measurements


References Cited


Perry, C.A., 2008, Precipitation-frequency and discharge-frequency relations for basins less than 32 square miles in Kansas: U.S. Geological Survey Scientific Investigations Report 2008–5112, 24 p.

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