U.S. Geological Survey
Water-Resources Investigations Report 00-4079

**CONVERSION FACTORS, ABBREVIATIONS, VERTICAL DATUM, AND DEFINITIONS**
Multiply	By	To obtain
cubic foot per second (ft/s)	0.02832	cubic meter per second
foot (ft)	0.3048	meter
foot per mile (ft/mi)	0.1894	meter per kilometer
inch (in.)	25.4	millimeter
inch per hour (in/h)	25.4	millimeter per hour
meter (m)	3.281	foot
mile (mi)	1.609	kilometer
square mile (miî)	2.590	square kilometer

Temperature can be converted to degrees Celsius (÷C) or
degrees Farenheit (÷F) by the equations:

÷C = 5/9(÷F - 32)
÷F = 9/5(÷C) + 32.

Vertical Datum
Sea Level: In this report, "sea level" refers to the National Geodetic Vertical Datum of 1929- a geodetic datum derived from a general adjustment of the first-order level nets of the United States and Canada, formerly called Sea Level Datum of 1929.

Definitions

Water year: In U.S. Geological Survey reports dealing with surface-water supply, water
year is the 12-month period, October 1 through September 30. The water year is designated
by the calender year in which it ends and which includes 9 of the 12 months. Thus the year
ending September 30, 1998, is called the "1998 water year."

CDA - Contributing-drainage area
G_g - Generalized skewness coefficient
G_s - Station skewness coefficient
GLS - Generalized least squares
IACWD - Interagency Advisory Committee on Water Data
Lat - Latitude
Lng - Longitude
P - Mean annual precipitation
RMSE - Root-mean-square error
S - Soil permeability
Sl - Main channel slope
STATSGO - State soil geographic data base
WLS - Weighted least squares

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

Peak streamflows were estimated at selected recurrence intervals (frequencies) ranging from 2 to 200 years using log-Pearson Type III distributions for 253 streamflow-gaging stations in Kansas. The annual peak-streamflow data, through the 1997 water year, were from streamflow-gaging stations with unregulated flow in mostly rural basins. A weighted least-squares regression model was used to generalize the coefficients of station skewness. The resulting generalized skewness equation provides more reliable estimates than the previously developed equation for Kansas.

A generalized least-squares regression model then was used to develop equations for estimating peak streamflows for sites without stream gages for selected frequencies from selected physical and climatic basin characteristics for sites without stream gages. The equations can be used to estimate peak streamflows for selected frequencies using contributing-drainage area, mean annual precipitation, soil permeability, and slope of the main channel for ungaged sites in Kansas with a contributing-drainage area greater than 0.17 and less than 9,100 square miles. The errors of prediction for the generalized least-squares-generated equations range from 31 to 62 percent.

INTRODUCTION

There is a continuing need for peak-streamflow information on Kansas streams. Information concerning frequency of peak streamflows in rural areas is vital to the safe and economic design of transportation drainage structures, such as bridges and culverts, and flood-control structures, such as dams, levees, and floodways. Effective flood-plain management programs and flood-insurance rates also are based on the analysis of peak-streamflow frequency.

A study of peak-streamflow frequencies was conducted by the U.S. Geological Survey in cooperation with the Kansas Department of Transportation. Much of the data used in this study, especially for many of the partial-record streamflow-gaging stations located on small streams, were collected by the U.S. Geological Survey (Putnam and others, 1998) as part of a cooperative program initiated with the Kansas Department of Transportation in 1956.

Purpose and Scope

The purpose of this report is to present results from an analysis of peak-streamflow frequencies for unregulated, mostly rural streams at streamflow-gaging stations with 10 or more years of record, and to present equations for determining peak-streamflow frequencies at ungaged sites in Kansas. This report includes data through the 1997 water year and supersedes previous U.S. Geological Survey reports that provide flood-frequency results and (or) techniques for Kansas streams.

The scope of the analyses included (1) determination of peak-streamflow frequencies for 253 streamflow-gaging stations in Kansas (fig. 1) using log-Pearson Type III techniques; (2) derivation of an equation to estimate the generalized skewness coefficients of the distribution of peak flows for each station, and (3) development of equations for relating the gaged, peak streamflow to respective physical and climatic characteristics and for estimating peak streamflows for selected recurrence intervals (frequencies) at ungaged, unregulated, mostly rural stream sites.

Previous Studies

Since 1960, seven studies have investigated various generalization techniques for estimating peak-streamflow frequencies for Kansas streams. Studies by Ellis and Edelen (1960), Irza (1966), Jordan and Irza (1975), and Clement (1987) analyzed peak-streamflow frequencies by using the available data and techniques to develop regression equations to estimate peak streamflows. Both Patterson (1964) and Matthai (1968) used the index-flood method, and Hedman and others (1974 used an active-channel-width concept to estimate the peak streamflow for selected recurrence intervals.

The generalization technique presented in this report incorporates the most recent analytical methods for estimating peak-streamflow frequency and is considered more reliable than those techniques previously reported for use with unregulated, rural streams in Kansas.

Acknowledgments

Some of the peak-streamflow data used in the flood-frequency analysis were collected through cooperative agreements between the U.S. Geological Survey and numerous Federal, State, and local government agencies, including: U.S. Army Corps of Engineers; Kansas Water Office; Kansas Department of Agriculture, Division of Water Resources; Arkansas River Compact Administration; Johnson County Department of Public Works; city of Hays; city of Wichita; city of Topeka; Hillsdale Lake Resource and Conservation District; U.S. Fish and Wildlife Service; and Kansas Department of Transportation.

FACTORS AFFECTING OCCURRENCE OF FLOODS

Flooding on small streams in Kansas is generally the result of very intense thunderstorms that affect almost all of the watershed and produce rainfall rates that exceed soil-infiltration rates. Within large watersheds, flooding generally is the result of prolonged rainfall that affects a major part of the total drainage basin. The prolonged rainfall eventually saturates the soil to the point that only a small part of the subsequent rainfall can infiltrate the soil. Physical constrictions in the stream channels, such as bridges or culverts, logs or ice jams, or backwater from high flows in other interconnected channels, can increase the depth of flooding. Kansas streams rarely experience flooding that results from snowmelt or dam failures.

Physical Characteristics

Physical characteristics within the respective watersheds have a pronounced effect on the nature of flooding. Watersheds with various basin and channel slopes, shapes, and drainage patterns have varying effects on the potential for flooding. For example, steep slopes tend to allow excess rainfall to move more rapidly away from the headwater areas but allow more rapid accumulation at downstream locations where flood conditions occur. Varying watershed shapes also cause different responses to excess rainfall. Long, narrow watersheds generally are less affected by small, isolated storms because usually only a part of the watershed receives intense rainfall. On the other hand, compact-shaped watersheds have a greater chance to be affected entirely by storms of comparable size, and the dendritic (tree-like) stream pattern facilitates more rapid concentration of runoff at or near the watershed's outlet; this increases the likelihood of downstream flooding.

Other physical characteristics affecting the flood potential of watersheds are the types of soils and land-use and treatment practices within the watershed. For example, the flood potential from watersheds with soils of low permeability (fig. 2) is greater than that from watersheds where highly permeable soils tend to allow greater infiltration and less runoff. Land-treatment practices, such as contour farming and construction of water-retention structures, can reduce the amount of rapid runoff to a stream system and thus reduce stream peaks.

Physiographically, Kansas is located almost entirely within the Interior Plains as described by Schoewe (1949). The hydrologic characteristics of the physiographic provinces within the Interior Plains are beyond the scope of this report, but the fact that there are significant variations denotes the complex nature of and difficulty in attempting to define flood-frequency relations across the State.

Generally, it has been accepted that the nature of flooding follows one of two patterns-one typical of the eastern one-third of the State and one typical of the western two-thirds. The arbitrary dividing line passes through Wichita and west of Junction City (locations shown in fig. 2). Crippen and Bue (1977) identified a similarly located boundary within the State when dividing the conterminous United States into flood regions for a study of maximum floodflows. The topography of the western two-thirds of the State is typical of the high plains region and is characterized by flat or gently sloping surfaces with little relief and soils of high permeability (fig. 2). The topography of the eastern one-third of the State is more variable, with alternating hills and lowlands having soils of low permeability (fig. 2).

Land-surface elevations within the State range from about 700 ft above sea level at the Kansas-Oklahoma State line in southeast Kansas to about 4,135 ft above sea level at a point near the Kansas-Colorado State line in western Kansas-a vertical difference of about 3,435 ft. Average basin slope for the 253 streamflow-gaging stations in Kansas is about 10 ft/mi.

Climatic Characteristics

The climate of Kansas is affected by the movement of frontal air masses over the open, inland plains, and seasonal precipitation extremes are common. About 70 percent of the mean annual precipitation falls from April through September. Precipitation during early spring and late fall occurs in association with frontal air masses that produce low-intensity rainfall of regional coverage. During the summer months, the weather is dominated by warm, moist air from the Gulf of Mexico or by hot, dry air from the Southwest. Summer precipitation generally occurs as high intensity thunderstorms.

Watersheds in Kansas exhibit a wide range of climatic characteristics that affect peak-streamflow frequency. Generally, the climatic characteristics vary in an east-west direction, with little north-south variation. The general climate of the western part of Kansas is semiarid with hot, dry summer months and cold, windy winter months. The eastern part of the State tends to be considerably more humid, with sultry summer months and cold winter months. Mean annual precipitation in the State varies from about 16 in. in the extreme western part to about 42 in. in the southeast (Daly and others, 1997) (fig. 3).

OCCURRENCE OF EXTREME FLOODS

Moderate flooding is an annual occurrence in Kansas; however, the State has experienced several extreme floods. Notably, the floods of 1951 in river basins of eastern and north-central Kansas were the result of a large storm system. Likewise, the floods that occurred on the Elk River during 1976 were extreme. The Great Bend area experienced extreme flooding during June 1981 when an isolated but very intense storm system produced up to 20 in. of rain during a 12-hour period (Clement and Johnson, 1982). Several storm systems during the summer of 1993 caused flooding in the Saline and Solomon River Basins of central Kansas (fig. 1) and all of the river basins in northeast and east-central Kansas. In 1995, intense storms caused widespread flooding in the eastern two-thirds of Kansas.

These are but a few of many floods that have been experienced on Kansas streams that are among the largest of floods recorded. The maximum observed discharges in relation to the respective contributing-drainage areas for the largest observed floods in Kansas are listed in table 1. The relation between maximum discharge and contributing-drainage area for the data presented in table 1 are depicted graphically in figure 4. Envelope curves have been drawn through the highest points for both eastern and western Kansas. No recurrence interval can be assigned to the curves although they represent peak discharges generally several times greater than those having 100-year recurrence intervals.

ESTIMATION OF PEAK-STREAMFLOW FREQUENCIES AT GAGING STATIONS ON UNREGULATED, RURAL STREAMS

Techniques from Bulletin 17B of the Interagency Advisory Committee on Water Data (1981) for estimating peak-streamflow frequency were used with annual maximum peak-streamflow data from 253 streamflow-gaging stations with 10 or more years of unregulated, rural peak-streamflow record. Unregulated, rural peak-streamflow record is defined as less than 10 percent of the basin is regulated by a dam or is impervious. The drainage areas for these stations ranged from 0.17 to 9,100 miî and extend into parts of Nebraska, Colorado, New Mexico, or Oklahoma for some stations. A summary of drainage-area distribution and average observed length of record per station for those stations used in the analysis is given in table 2. Peak streamflows for 2-, 5-, 10-, 25-, 50-, 100-, and 200-year recurrence intervals were calculated.

Log-Pearson Type III Techniques

In 1966, under the authority of House Document 465 (1966), the Interagency Advisory Committee on Water Data (IACWD) investigated various techniques for the analysis of peak-streamflow frequency and in 1967 recommended that the log-Pearson Type III frequency distribution be adopted as the standard technique to be used in Federal practice (U.S. Water Resources Council, 1967). Subsequently, the U.S. Water Resources Council conducted additional studies that resulted in improvements to the initial log-Pearson Type III technique. The improvements were reported in Bulletin 17B (Interagency Advisory Committee on Water Data, 1981).

The log-Pearson Type III technique transforms the arithmetic values of peak discharges to log values, then three statistics of the log values (mean, standard deviation, and skewness) are computed by the method of moments. The skewness coefficient is adjusted by weighting the computed station skewness with a generalized skew coefficient.

The reliability of the estimated peak-streamflow frequency is dependent on the assumption that the distribution to which the data are fit is correct and that the data are accurate and drawn from a representative sample of random and independent events. The length of the period used to compute the estimates of peak-streamflow frequencies and the variability of the data are the principal measures of the reliability. Generally, the longer the record the more reliable the estimates become because the size of the sampling error is proportional to the inverse of the square root of the length of the record.

Historical Peak Discharges and Outlier Thresholds

Many of the records of annual peak discharges at streamflow-gaging stations used in this study contained additional information relating to peak discharges that occurred before, during, or after the period of systematic record collection and represented maximum occurrences during an extended period. For example, it may be known that the maximum peak discharge recorded during the systematic record collection was the largest since a point in time before the beginning or after the ending of the recorded period. Likewise, a peak discharge that occurred outside of the period of systematic record may be known to be larger than any peak discharge that occurred during that period. This "historical data" can be used to make adjustments to the original distribution of the data by assigning a historical period of record that is longer than the systematic period, resulting in adjusted recurrence intervals of the annual maximum peak discharges.

Many drainage areas in Kansas, primarily western Kansas, have physical and climatic characteristics that can yield small annual peak streamflows. These small annual peak streamflows are considered low outliers if they are less than a certain threshold. The outlier thresholds identify data points that depart significantly from the trend of the remaining data, are defined by the IACWD (1981), and are accounted for in the analysis. In some situations, usually where there is more than one low outlier, the threshold appears too low. A visual inspection of the log-Pearson Type III distribution curve allows the analyst to observe the low-outlier threshold relative to the peak-discharge data set and adjust as deemed appropriate. Low-outlier thresholds were increased for 25 stations in Kansas to improve the fit of the data to the log-Pearson Type III distribution. Higher outliers were computed using the IACWD (1981) method.

Skew Coefficient

The IACWD (1981) recommends that the skewness coefficient computed from station records be weighted with a generalized skewness coefficient to reduce the bias caused primarily by records having relatively short lengths. The default method entails estimating the generalized skewness coefficient from a map showing lines of equal skewness for the entire United States (Interagency Advisory Committee on Water Data, 1981). The map showing generalized skewness coefficients of logarithms of annual peak streamflows is based on the skewness coefficients computed from station records collected through 1973 at 2,972 streamflow-gaging stations nationwide having 25 or more years of unregulated record and drainage areas less than 3,000 miî. The root-mean-square error (RMSE) between the isolines on the map and the station data for the entire country is 0.55.

Although using the IACWD (1981) map of generalized skewness probably improves most peak-streamflow frequency computations, the spatial position of the lines of equal skewness is subjective. The IACWD (1981) recommends that skewness coefficients be regionalized by one of three techniques-(1) averaging the station skewness coefficients within a specific area, (2) developing a local skewness map, or (3) relating the coefficients to predictor variables, such as physical and climatic characteristics of the drainage basins.

The greatest problem encountered when estimating the value of the skewness coefficient is the large error in results that are computed from short-term gaging-station records. A weighted least-squares (WLS) regression model was developed by Tasker and Stedinger (1986) to solve this problem. This WLS model weights the error variances on the basis of the length of the data record and variability in the data. The WLS model is well adapted for analysis of hydrologic data having variable accuracy because of the ability to separate the error of prediction into the sampling error and model error and to treat each error separately on the basis of length of the peak-streamflow record at the gaging station. The sampling error is a function of the length of the record and the degree of deviation from the average predictor variables. The model error, in this case, is the error associated with the formulation of the model. The error that can be expected when using the regression equation is the error of prediction, which includes both the sampling and model errors.

The WLS regression model weights each unbiased estimate of skewness on the basis of the length of the record of annual peak discharges. The technique relates the station skewness coefficient determined from the log-Pearson Type III distribution to one or more physical or climatic characteristics of the respective drainage basins. The result of the computations yields the coefficients and constants of a regression equation, as well as their significance to the equation. The resulting equation can be used to estimate the generalized skewness coefficient.

The WLS regression model in this report used station skewness computed from 253 streamflow-gaging-station records in Kansas as the dependent variable and several physical and climatic characteristics for each station as independent (predictor) variables. A summary of the results, including description and dimensions of the various physical and climatic characteristics for each gaging station used in the analysis, is provided in table 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h, 5i, 5j, 5k, 5l, 5m, 5n, 5o, and 5p.

The computation of the generalized skewness coefficient was limited to those stations having drainage areas no larger than 9,100 miî. The length of record for all stations was 11 or more years, and the value of station skewness ranged from -1.76 to 1.99. Contributing drainage area (CDA), latitude (Lat), and longitude (Lng) were the independent variables that yielded the best equation on the basis of the magnitude of the RMSE.

The equation used for estimating the generalized skewness coefficient at streamflow-gaging stations in Kansas is:

(1)

G_g = 1.191 + 0.0641 log₁₀(CDA) + 0.0935 (Lat) -0.0519 (Lng),

where

G_g = generalized skewness coefficient for the selected gaging station to be used in lieu of the IACWD Bulletin 17B map of generalized skewness (Interagency Advisory Committee on Water Data, 1981);
CDA = contributing-drainage area, in square miles;
Lat = latitude of the gaging station, in decimal degrees; and
Lng = longitude of the gaging station, in decimal degrees.

A weighted skewness coefficient used to compute the frequency of peak streamflows was the result of weighting estimates of the station skewness coefficient (G_s) and generalized skewness coefficient (G_g), where the weights were estimates as recommended in IACWD Bulletin 17B (1981, p. 12-13). In this case, the RMSE associated with the generalized skewness coefficient (G_g) is the error of prediction of the estimating equation. The RMSE is 0.19 for equation 1, whereas it is 0.35 in the most recent previously published peak-streamflow report for Kansas (Clement, 1987). Increased record length is most likely the reason the RMSE has improved.

Peak-Streamflow Frequencies at Gaging Stations

Using the unregulated annual peak streamflows recorded for 253 streamflow-gaging stations with lengths of record equal to or greater than 10 years, log-Pearson Type III distributions were fitted to the peak-streamflow data for each site. Adjustments then were made to account for data that represented low or high outliers and for historical data where necessary. Final estimates of peak-streamflow frequencies (table 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h, 5i, 5j, 5k, 5l, 5m, 5n, 5o, and 5p) were computed using the generalized skewness coefficients (G_g) obtained for each station using equation 1 and weighted with the station skewness coefficient (G_s) as recommended in IACWD Bulletin 17B (1981).

A study by Perry and Rasmussen (in press) points out that the effects of streamflow trends are not accounted for using the peak-streamflow frequency techniques in Bulletin 17B. Further investigation may be required to fully understand the effects of trends on peak streamflow and how to adjust the peak-streamflow analysis accurately. Peak-streamflow frequency analysis assumes a random sampling of a stable population of annual peak streamflows. If that population is not stable (that is, mean and standard deviations are not constant), it may be necessary to adjust the peak-streamflow data to obtain the best-fit peak-streamflow frequency analysis. However, the persistence of trends must be considered also.

REGRESSION EQUATIONS FOR ESTIMATION OF PEAK-STREAMFLOW FREQUENCIES AT UNGAGED SITES ON UNREGULATED, RURAL STREAMS

Regression Analysis

Although information concerning peak-streamflow frequencies is available at many streamflow-gaging-station locations in Kansas, often such information is needed at stream sites where insufficient or no data are available. Generalization of the peak-streamflow frequency information at gaging stations will facilitate estimates at ungaged sites. Multiple-regression analysis was used in this study to relate the peak streamflow at selected frequency intervals to various physical and climatic characteristics.

Research by Tasker and Stedinger (1989) indicates that generalized least squares (GLS) is appropriate for hydrologic regression. GLS regression takes into consideration the time-sampling error (length of record at each site) and the cross correlation of annual peak streamflows between sites.

The GLS regression model in this study used base-10 logarithmic transformation for both dependent and independent variables. The form of the model equation is:

(2)

log₁₀Q_t =log₁₀a + b₁log₁₀X₁+ b₂log₁₀X₂....+ b_nlog₁₀X_n,

which is equivalent to:

(3)

Q_t = 10^aX^b₁₁X^b₂₂....X^b_n_n,

where

Q_t is peak discharge for recurrence interval t, in years (dependent variable);
X₁ - X_n are physical and climatic characteristics (independent variables);
a is the regression constant; and
b₁ - b_n are the regression coefficients.

Selected Physical and Climatic Characteristics

The independent variables tested in the regression analysis were physical and climatic characteristics of each drainage basin. Initially, eight physical and climatic characteristics were tested: contributing-drainage area (CDA), mean annual precipitation (P), soil permeability (S), latitude and longitude, main channel length, main channel slope (Sl), basin slope, basin shape, and basin elevation.

In previous peak-streamflow frequency studies for Kansas, characteristics describing the physiography and climate of each drainage basin were calculated using rough approximations with paper maps. Depending on the scale of the map or the techniques used to calculate the characteristic, a variety of errors could occur. Some physical characteristics that possibly could improve the regression estimates were nearly impossible to calculate and either were estimated or ignored for the analysis.

For this study, ARC/INFO geographical information systems (GIS) software was used to estimate physical and climatic characteristics. Many spatial-data sets were available for this task, including: (1) 30-m gridded elevation data (U.S. Geological Survey, 1998) for determining the drainage-basin boundary, contributing-drainage area, basin slope, and mean basin elevation, (2) STATSGO soil-permeability data (U.S. Department of Agriculture, 1994), and (3) 30-year (1961-90) mean annual precipitation data (Daly and others, 1997). Drainage boundaries were determined using GIS for all 253 gaging stations used in the report. The drainage boundaries and the spatial-data sets just mentioned were used to calculate average physical and climatic characteristics for each basin (table 3).

Regression analysis relies on the assumption that independent variables are not closely interrelated. Violation of this rule generally results in regression coefficients that are unstable, and it becomes difficult to evaluate the interrelated variables' importance to the respective equations. Therefore, a simple cross-correlation matrix was computed for all independent variables and was used in the analysis to identify variables that might pose problems if included in the same analysis. Pairs of variables having correlation coefficients greater than 0.8 were considered closely interrelated, were evaluated further in the initial analysis, and only the more significant variable of the pair was included in the final analysis.

The ability of a regression equation to reliably estimate the peak streamflow having selected recurrence intervals at ungaged sites is measured by the error of prediction. The error of prediction is the measure of confidence in the estimated peak streamflow and describes the range within which an estimate would occur two-thirds of the time. Computed in logarithmic units, the RMSE, or the error of prediction, can be expressed as a percentage as shown in Hardison (1971). The percentages are unequal in the positive and negative directions. For example, the standard error of estimate of 0.17 logarithmic units represents errors of +48 and -32 percent; the average of the two percentages without regard to sign is 40 percent.

Regression Equation Results

Regression analysis was performed, and equations were developed for peak streamflow having recurrence intervals of 2, 5, 10, 25, 50, 100, and 200 years. The independent variables that most contribute to the explanation of the variance in the dependent variable (the peak streamflow) were CDA, P, Sl, and S. Table 4 gives the equations, the errors of prediction, and the equivalent years of record for each recurrence interval.

Attempts were made to improve the error of prediction for the regression equations by developing regional equations for smaller parts of the State. The first attempt was to divide the State along 97÷ longitude, similar to the division developed by Crippen and Bue (1977) as discussed earlier. Separate equations were developed for the gaging stations in the eastern and western divisions. The prediction error for the equations representing the eastern division decreased slightly, whereas the prediction error for the equations representing the western division increased.

Another attempt to reduce the prediction error was to group gaging stations according to drainage areas. The prediction errors for most of the equations developed for various groups tested were greater than the original error of prediction for equations developed from all 253 gaging stations. The best results were achieved when stations with contributing-drainage areas ranging from 30 to 9,100 miî were grouped together. Standard errors of prediction were reduced between 12 and 20 percent from predictions errors using all 253 stations. Standard error of prediction for equations developed for stations with contributing-drainage areas ranging from 0.17 to less than 30 miî were equal to or slightly greater than the standard errors for the equations developed using all the stations. The error of prediction for the most reliable equations ranged from 0.131 (31 percent) for the 10-year recurrence interval in large basins to 0.248 (62 percent) for the 200-year recurrence interval in small basins.

A direct statistical comparison of the equations from Clement (1987) to the equations from the current investigation is not possible because of differing data and groups of gages upon which the equations are based. Clement (1987) developed equations that were based on 218 gaging stations compared to the two groups of 91 and 164 gaging stations used in the current investigation. A review of the standard error of prediction of the equations indicates the errors in the 1987 study are generally about 15 percent less than those of the current investigation. However, separate regression analysis (not included in this report) was done using (1) peak streamflow record through 1903 for 237 gaging stations, (2) the same basin characteristics as in this investigation, and (3) the same drainage-area grouping as described in this investigation. The standard errors of prediction of the resulting equations are about 13 percent greater than those for the equations presented in this report.

Hardison (1971) related prediction error and streamflow variability to equivalent years of record. The equivalent years of record is the number of years of streamflow record necessary to provide an estimate equal in accuracy to the regression equation. The accuracy of the regression equations for unregulated, rural streams, expressed in average equivalent years of record, is summarized in table 4.

Use of Regression Equations

The GLS regression equations shown in table 4 may be used to estimate the peak streamflow for specific recurrence intervals (frequencies) at ungaged sites by determining the values of the physical and climatic characteristics relative to the site and substituting the values into the respective equations. The values for contributing-drainage area (CDA) can be determined from digital data using GIS or paper topographic maps. The values for mean annual precipita-tion (P) and soil permeability (S) can be determined from digital data using GIS or from figures 2 or 3. Both P and S are areal averages for the entire drainage area. Main channel slope (Sl) can be measured and calculated from topographic maps.

The equations shown in table 4 were developed using data from streams located in rural basins, whose contributing-drainage areas ranged from 0.17 to 9,100 miî, during periods of record when flows were unregulated. Therefore, the equations should not be used to estimate peak streamflow if the watershed is not predominately rural, if the contributing-drainage area is smaller than 0.17 miî or larger than 9,100 miî, or if streamflow is affected by regulation.

SUMMARY

Estimates of peak streamflow for selected frequencies were computed by using observed annual peak-streamflow data collected through the 1997 water year for streamflow-gaging stations located on unregulated rural streams in Kansas with 10 or more years of record. Log-Pearson Type III distributions were fitted to the observed annual peak-streamflow data for each streamflow-gaging station by using techniques recommended by the Interagency Committee on Water Data. Peak streamflows for 2-, 5-, 10-, 25-, 50-, 100-, and 200-year recurrence intervals were calculated.

A weighted least-squares (WLS) regression model was used to estimate a generalized skew coefficient for all the stations in this analysis. The WLS regression model used station skew coefficients computed from 253 streamflow-gaging-station records in Kansas as the dependent variable and several physical and climatic characteristics for each station as independent (predictor) variables in a regression equation. The root-mean-square error (RMSE) for this equation (0.19) decreased from a RMSE of 0.35 for a previously developed equation.

Regression equations then were developed to compute peak streamflows for ungaged sites at selected recurrence intervals by using generalized least-square regression to relate peak streamflow at gaging stations to physical and climatic characteristics. The significant independent variables in the regression equations were contributing-drainage area, mean annual precipitation, average soil permeability, and slope of the main channel. Standard error of prediction did not improve when the State was divided into eastern and western areas. The standard error of prediction for the regression equations was smallest when the group of 253 streamflow-gaging stations was divided into two groups on the basis of contributing-drainage area. Standard error of prediction for equations developed for stations with contributing-drainage areas greater than 0.17 and less than 30 miî were equal to or slightly greater than the standard errors for the equations developed using all the stations. Standard errors of prediction for equations developed for stations with contributing-drainage areas between 30 and 9,100 miî were reduced between 12 and 20 percent from predictions errors using all 253 stations. The errors of prediction for all the generated equations ranged from 31 to 62 percent.

SELECTED REFERENCES

: Clement, R.W., 1987, Floods in Kansas and techniques for estimating their magnitude and frequency on unregulated streams: U.S. Geological Survey Water-Resources Investigations Report 87-4008, 50 p.
: Clement, R.W. and Johnson, D.G., 1982, Flood of June 15, 1981, in Great Bend and vicinity, central Kansas: U.S. Geological Survey Water-Resources Investigations Report 82-4123, 12 p.
: Crippen, J.R., and Bue, C.D., 1977, Maximum floodflows in the conterminous United States: U.S. Geological Survey Water-Supply Paper 1887, 52 p.
: Daly, C., Taylor, C.H., and Gibson, W.P., 1997, The PRISM approach to mapping precipitation and temperature, in Reprints of 10th Conference on Applied Climatology, Reno, Nevada: American Meteorological Society, p. 10-12.
: Ellis, D.W., and Edelen, G.W., Jr., 1960, Kansas streamflow characteristics, part 3, Flood frequency: Kansas Water Resources Board Technical Report No. 3, 221 p.
: Hardison, C.H., 1969, Accuracy of streamflow characteristics, in Geological Survey Research, 1969: U.S. Geological Survey Professional Paper 650-D, p. D210-D214.
: _____1971, Prediction error of regression estimates of streamflow characteristics at ungaged sites, in Geological Survey Research, 1971: U.S. Geological Survey Professional Paper 750-C, p. C228-C236.
: Hedman, E.R., Kastner, W.M., and Hejl, H.R., 1974, Kansas streamflow characteristics-part 10, Selected streamflow characteristics as related to active-channel geometry of streams in Kansas: Kansas Water Resources Board Technical Report No. 10, 21 p.
: Hershfield, D.M., 1961, Rainfall frequency atlas of the United States: U.S. Department of Commerce, Weather Bureau Technical Paper 40, 115 p.
: House Document 465, 1966, A unified national program for managing flood losses, 89th Congress, 2d session: U.S. Government Printing Office, 47 p.
: Interagency Advisory Committee on Water Data, 1981, Guidelines for determining flood flow frequency: Washington, D.C., Bulletin 17B of the Hydrology Committee, 28 p.
: Irza, T.J., 1966, Preliminary flood-frequency relations for small streams in Kansas: Lawrence, Kansas, U.S. Geological Survey open-file report, 19 p.
: Jennings, M.E., Thomas, W.O., and Riggs, H.C., 1994, Nationwide summary of U.S. Geological Survey regional regression equations for estimating magnitude and frequency of floods for ungaged sites, 1993: U.S. Geological Survey Water-Resources Investigation Report 94-4002, 196 p.
: Jordan, P.R., and Irza, T.J., 1975, Kansas streamflow characteristics-magnitude and frequency of floods in Kansas, unregulated streams: Kansas Water Resources Board Technical Report No. 11, 34 p.
: Matthai, H.F., 1968, Magnitude and frequency of floods in the United States-part 6B, Missouri River Basin below Sioux City, Iowa: U.S. Geological Survey Water-Supply Paper 1681, 636 p.
: Patterson, J.L., 1964, Magnitude and frequency of floods in the United States-part 7, Lower Mississippi River Basin: U.S. Geological Survey Water-Supply Paper 1691, 636 p.
: Perry, C.A., and Rasmussen, T.J., in press, Trends in annual peak flows of selected streams in central Great Plains: Journal of the American Water Resources Association.
: Putnam, J.E., Lacock, D.L., Schneider, D.R., Carlson, M.D., and Dague, B.J., 1998, Water resources data, Kansas, water year 1997: U.S. Geological Survey Water-Data Report KS-97-1, 445 p.
: Schoewe, W.H., 1949, The geography of Kansas-part 2, Physical geography: Transactions of the Kansas Academy of Science, v. 52, no. 3, p. 261-333.
: Tasker, G.D., and Stedinger, J.R., 1986, Regional skew with weighted LS regression: Journal of Water Resources Planning and Management, v. 112, book 2, p. 225-237.
: -- 1989, An operational GLS model for hydrologic regression: Journal of Hydrology, v. 111, p. 361-375.
: U.S. Department of Agriculture, 1994, State soil geographic (STATSGO) data base: Soil Conservation Service Miscellaneous Publication 1462, 37 p.
: U.S. Geological Survey, 1998, National elevation data base: Sioux Falls, South Dakota, National Mapping Division EROS Data Center, accessed June 6, 1998, at URL http://edcwww2.cr.usgs.gov/ned/ned.html
: U.S. Water Resources Council, 1967, A uniform technique for determining flood flow frequency: Washington, D.C., Bulletin 15 of the Hydrology Committee, 15 p.

Photographs

Cimarron River near Elkhart, May 3, 1999. View upstream from left bank.
Photograph by Craig Dare, USGS.

Arkansas River near Coolidge, May 6, 1999. View downstream from right bank.
Photograph by Craig Dare, USGS.

Cow Creek near Hutchinson, July 22, 1999. View upstream from left bank.
Photograph by Mike Holt, USGS.

Kansas River at Wamego, July 1993. View upstream from left bank.
Photograph by Charles Perry, USGS.

For additional information, please write or call:

U.S. Geological Survey
4821 Quail Crest Place
Lawrence, KS 66049-3839
Telephone: (785) 842-9909
FAX: (785) 832-3500
email:

GS-W-KS_info@usgs.gov

U.S. Geological Survey Water-Resources Investigations Report 00-4079

PDF file (size 7 KB)

Estimation of Peak Streamflows for Unregulated Rural Streams in Kansas

CONTENTS

FIGURES

TABLES

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

U.S. Geological Survey
Water-Resources Investigations Report 00-4079