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Kansas Water Science Center

U.S. Geological Survey
Water-Resources Investigations Report 02-4292
Prepared in cooperation with the
KANSAS DEPARTMENT OF HEALTH AND ENVIRONMENT

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Estimates of Median Flows for Streams on the Kansas Surface Water Register

By Charles A. Perry, David M. Wolock, and Joshua C. Artman

Photograph of

CONTENTS

PLATES - Not available online

  1. Map showing location of U.S. Geological Survey streamflow-gaging stations and stream segments on the Kansas Surface Water Register
  2. Map showing estimated median flows for downstream end of stream segments on the Kansas Surface Water Register using the most-recent 10 years of record (KSA analysis)
  3. Map showing estimated median flows for downstream end of stream segments on the Kansas Surface Water Register using all-available hydrology (AAH analysis)

FIGURES

    1-5. Map showing:
      Figure 1. Location of U.S. Geological Survey streamflow-gaging stations in Kansas and parts of surrounding States with 10 or more years of record that were used to estimate median flows
      Figure 2. Land-surface elevation in Kansas and parts of surrounding States
      Figure 3. Average land-surface slope in Kansas and parts of surrounding States
      Figure 4. Areas of equal average soil permeability in Kansas and parts of surrounding States
      Figure 5. Mean annual precipitation in Kansas and parts of surrounding States
    Figure 6. Graphs showing comparison of observed and regression-estimated median flows for (A) most-recent 10 years of record (KSA) and (B) all-available hydrology (AAH) using Tobit analysis
    Figure 7. Map showing median flow values for stream segments in central Kansas estimated from regression equations and observed streamflow-gaging-station data for the most-recent 10 years of record (KSA) analysis
    Figure 8. Map showing estimated median flow values for stream segments in central Kansas using interpolation procedures outlined in table 3 and observed streamflow-gaging-station data for the most-recent 10 years of record (KSA) analysis

TABLES

    Table 1. Streamflow-gaging stations and climatic and basin characteristics used in regression analyses of uncontrolled stream segments identifed on the Kansas Surface Water Register
    Table 2. Regression equations used to estimate median flows for uncontrolled stream segments on the Kansas Surface Water Register
    Table 3. Summary of interpolation procedures used to estimate median flow information for stream segments on the Kansas Surface Water Register
    Table 4. Streamflow-gaging stations and drainage areas used to interpolate median flows for controlled stream segments on the Kansas Surface Water Register
    Table 5. Estimated median flows with 95-percent confidence intervals computed for streamflow-gaging stations used in the interpolation procedure for the most-recent 10 years of record (KSA) and all-available hydrology (AAH) analyses
    Table 6. Stream segments on the Kansas Surface Water Register, CUSEGA numbers, stream names,and estimated median flows at downstream end of CUSEGA segments using the most-recent 10 years of record (KSA) and all-available hydrology (AAH) analyses

CONVERSION FACTORS AND ABBREVIATIONS

For additional information about ongoing studies in Kansas, please visit:
http://ks.water.usgs.gov/


Abstract

The Kansas State Legislature, by enacting Kansas Statute KSA 82a-2001 et. seq., mandated the criteria for determining which Kansas stream segments would be subject to classification by the State. One criterion for the selection as a classified stream segment is based on the statistic of median flow being equal to or greater than 1 cubic foot per second. As specified by KSA 82a-2001 et. seq., median flows were determined from U.S. Geological Survey streamflow-gaging-station data by using the most-recent 10-years of gaged data (KSA) for each streamflow-gaging station. Median flows also were determined by using gaged data from the entire period of record (all-available hydrology, AAH).

Least-squares multiple regression techniques were used, along with Tobit analyses, to develop equations for estimating median flows for uncontrolled stream segments. The drainage area of the uncontrolled gaging stations used in the regression analyses ranged from 2.06 to 12,004 square miles. A logarithmic transformation of the data was needed to develop the best linear relation for computing median flows. In the regression analyses, the significant climatic and basin characteristics, in order of importance, were drainage area, mean annual precipitation, mean basin permeability, and mean basin slope. Tobit analyses of KSA data yielded a root mean square error of 0.285 logarithmic units, and the best equations using Tobit analyses of AAH data had a root mean square error of 0.247 logarithmic units.

These equations and an interpolation procedure were used to compute median flows for the uncontrolled stream segments on the Kansas Surface Water Register. Measured median flows from gaging stations were incorporated into the regression-estimated median flows along the stream segments where available. The segments that were uncontrolled were interpolated using gaged data weighted according to the drainage area and the bias between the regression-estimated and gaged flow information. On controlled reaches of Kansas streams, the median flow information was interpolated between gaging stations using only gaged data weighted by drainage area.

Of the 2,232 total stream segments on the Kansas Surface Water Register, 30 percent of the segments had an estimated median streamflow of less than 1 cubic foot per second when the KSA analysis was used. When the AAH analysis was used, 40 percent of the segments had an estimated median streamflow of less than 1 cubic foot per second.

Introduction

The expected amount and historical range of flow in Kansas streams are important considerations for the classification, evaluation, and regulation of water supplies, recreation, aquatic life habitat, and pollution control within the State. Kansas Statute KSA 82a-2001 et. seq. (see Appendix A) specifically mentions median streamflow as one criterion for classifying streams. Current water-quality regulations in Kansas apply numeric water-quality criteria to the 2,232 stream segments listed on the Kansas Surface Water Register. The register is maintained by the Kansas Department of Health and Environment (KDHE) and is used to identify designated uses of stream segments. Numeric water-quality criteria for the stream segments are based on assigned designated uses.

KSA 82a-2001 et. seq. defines one criterion for a classified stream segment as having a median flow of 1 ft³/s or greater. Other criteria include whether a stream segment contains a wastewater discharge, contains threatened or endangered species, or has a cost/benefit ratio less than 1 where median streamflows are 0 ft³/s. Median flow statistics for stream segments are based on daily flow data collected by the U.S. Geological Survey (USGS) at 214 streamflow-gaging stations with 10 or more years of record located throughout Kansas and surrounding States (fig. 1). The current and historical streamflow information collected by the USGS provides a resource for estimating the expected amount and range of streamflow throughout the State. The measured streamflow record can be used to define statistics that summarize historical streamflow amounts at each stream gage. These statistics then can be related to the physical characteristics of the drainage basins that contribute to measured flow at the gage. Furthermore, a statistical model that is based on these relations can be used to estimate streamflow statistics for ungaged stream segments. Therefore, information on median flow characteristics is needed for streams in Kansas.

To address this need, a study of median flows for Kansas streams was conducted by the USGS in cooperation with KDHE. Streamflow data used in this study were collected by the USGS (Putnam and others, 2001) through other cooperative studies with various government agencies.

Purpose and Scope

The purpose of this report is to document the methods and results of a study designed to estimate the median flow (50-percent flow duration) for the downstream end of each stream segment listed on the Kansas Surface Water Register. Median flow for each stream segment was determined from gaged-location streamflow records or was estimated from statewide regression models. This report documents development of regression models to estimate median flow from climatic and basin characteristics. The report describes application of the drainage-area ratio method and the regression models to estimate the median flows for Kansas Surface Water Register stream segments, the interpolation of estimates for ungaged segments, and the Internet dissemination of results and a geographic-information-system (GIS) database.

Two different statistical analysis were performed on uncontrolled flows measured at 149 gaging stations. According to language in KSA 82a-2001 et. seq., only the most-recent 10 years of streamflow data for each gaging station were to be used for statistical analysis. This analysis was termed the KSA analysis. The entire period of record also was used for analysis of median flows, and this analysis was termed the all-available hydrology (AAH) analysis.

The information contained in this report can be used by State agencies and others to help in the effective management of Kansas surface-water resources. Optimal reservoir operations, legally distributed in-stream withdrawals, and water-quality concerns are issues directly linked to median streamflows. The methods described herein can be applied nationwide using USGS streamflow data that are available throughout the United States.

Previous Studies

Previous low-flow and flow-duration studies for Kansas include an investigation by Furness (1959) who developed a method for estimating flow-duration curves for ungaged sites that was based on regionalized flow-duration data from 122 continuous-record, streamflow-gaging stations with drainage areas of between 100 and 3,000 mi² for the period 1921-56. Maps were developed showing a variety of statewide low and mean streamflow maps. Furness (1959) also noted that the low-flow parts of the flow-duration curves could be verified or improved by relating base-flow measurements at the ungaged site to base-flow measurements at a nearby, index streamflow-gaging station.

Jordan (1983) updated the maps developed by Furness by including additional streamflow-gaging stations and data for the period 1957-76. Jordan's study included a map that depicted the areas of Kansas where the median streamflow for a 500-mi² basin was greater than 0.1 ft³/s.

Two studies by Studley (2000, 2001) evaluated the application of the Furness method to ungaged stream sites in Kansas using nearby streamflow-gaging stations as index stations. The results of these two recent studies indicated that the Furness method continues to be a useful tool for estimating flow-duration curves for ungaged sites and that the method could be used for sites with drainage areas less than 100 mi².

Many studies have been conducted to evaluate low flow from regression equations that relate low flow to basin characteristics. In a recent USGS study (Ries and Friesz, 2000), basin characteristics were determined from digital map data, and flow statistics were computed for individual stream segments using GIS techniques. Ries and Friesz (2000) used the drainage-area ratio method to compute streamflow characteristics for stream segments that had between 0.5 and 1.5 times the drainage area of streamflow-gaging stations on the same stream. Many States have used regression analysis to regionalize low-flow frequency statistics including New Hampshire, Rhode Island, and Vermont (Johnson, 1970); Pennsylvania and New York (Ku and others, 1975); Maine (Parker, 1977); Massachusetts (Male and Ogawa, 1982; Vogel and Kroll, 1990; Risley, 1994; Ries and Friesz, 2000); Montana (Parrett and Hull, 1985); Indiana (Arihood and Glatfelter, 1991); and central New England (Wandle and Randall, 1994).

FACTORS AFFECTING STREAMFLOW

Physical Setting

Physiographically, Kansas is located almost entirely within the Interior Plains as described by Schoewe (1949). A description of the hydrologic characteristics of the physiographic provinces within the Interior Plains is 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 flow characteristics across Kansas.

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. The topography of the eastern one-third of the State is more variable, with alternating hills and lowlands. Land-surface elevations within the State range from about 700 ft above the North American Vertical Datum of 1988 (NAVD 88) at the Kansas-Oklahoma State line in southeast Kansas to about 4,135 ft above the NAVD 88 at a point near the Kansas-Colorado State line in western Kansas-a vertical difference of about 3,435 ft (fig. 2). The average land-surface slope for Kansas (fig. 3) using 30-m grid elevation data is about 1.9 degrees.

Other physical characteristics affecting the flow characteristics of watersheds are the types of soils and land-use and treatment practices within the basin. For example, with all other factors being equal the low-flow potential from watersheds with soils of low permeability (fig. 4) is less than that from watersheds where highly permeable soils tend to allow greater infiltration and a greater ground-water contribution to base flow of the stream. The western two-thirds of the State typically has soils of moderate to high permeability, whereas the eastern one-third has soils of lower permeability. Land-treatment practices, such as contour farming and construction of water-retention structures, can increase the amount of infiltration of runoff to ground water, which ultimately returns to stream channels as base flow. However, land-treatment practices are difficult to assess and apply to the various types of basins statewide.

Climatic Characteristics

The climate of Kansas is affected by the movement various air masses of tropical and continental origin 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 streamflow. Generally, precipitation varies 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 more humid, with sultry summer months and cold, damp winter months. Mean annual precipitation, the major climatic factor affecting streamflow in the State, varies from about 16 in. in extreme western Kansas to about 42 in. in southeastern Kansas (Daly and others, 1997) (fig. 5). Mean annual precipitation at 149 streamflow-gaging stations used in the regression analyses for uncontrolled stream segments on the Kansas Surface Water Register is given in table 1.

Basin Characteristics

Basin characteristics used in the analyses were selected on the basis of their theoretical relation to differences in flow magnitudes of streams, results of previous studies in similar hydrologic environments, and on the ability to measure them. The basin characteristics considered in this report included drainage area, in square miles; mean basin elevation, in feet above NAVD 88; mean basin permeability, in inches; mean basin slope, in degrees; a Base Flow Index (Wahl and Wahl, 1995); mean annual runoff for hydrologic basins in the United States, in cubic feet per second (Gebert and others, 1987); and runoff from the PRISM model (parameter-elevation regressions on independent slope model), in cubic feet per second, using the mean annual precipitation grid for the United States developed by Daly and others (1994). The mean annual runoff reflects the difference between precipitation and evapotranspiration. Selected basin characteristics for the 149 streamflow-gaging stations used in the regression analyses for uncontrolled stream segments are provided in table 1.

All basin characteristics were measured from digital-map data using automated GIS procedures. The automated procedure was created using the AML programming language of the ARC/INFO GIS software (Environmental Systems Research Institute, Inc., 1991). The automated procedure determines the drainage-basin boundary at the gaging station or for the downstream end of a stream segment and creates a digital data layer of the basin boundary, then overlays the boundary on the other digital data layers to determine the other basin characteristics for the station or segment. The grid values then are averaged for the area within the drainage basin.

METHODS FOR ESTIMATING MEDIAN FLOWS

Climatic and basin characteristics were used in the analyses of median flows at gaged and ungaged sites on controlled and uncontrolled streams. For this study, ARC/INFO GIS software was used to estimate climatic and basin characteristics. Many spatial data sets were available for this task, including: (1) 30-year (1961-90) mean annual precipitation data (Daly and others, 1997), (2) 30-m gridded elevation data (U.S. Geological Survey, 1998) for determining drainage area, mean basin slope, and mean basin elevation, and (3) STATSGO soil-permeability data (U.S. Department of Agriculture, 1994).

The flow information was derived from 216 gaging stations in Kansas and the surrounding States with at least 10 years of streamflow record. Streamflow at 149 of the stations on uncontrolled stream segments were included in the regression analyses. The flows of uncontrolled stream segments are unaffected by storage and release from large upstream reservoirs. One hundred thirty-one streamflow-gaging stations in Kansas and 18 in surrounding States (four in Missouri, five in Nebraska, and nine in Oklahoma) measured uncontrolled flow. All available records through water year (October through September) 2000 were used to compute the streamflow statistics for these gaging stations. Names and descriptions of the streamflow-gaging stations used in measuring flow at uncontrolled sites are listed in table 1.

Three gaging stations in Kansas that measured uncontrolled flow and had at least 10 years of record were not included in the regression analyses. One station, Indian Creek at Overland Park (station 06893300), was not used because it is affected by extensive urbanization. Two other stations, Beaver Creek at Cedar Bluffs (station 06846500) and Paradise Creek near Paradise (station 06867500), were not used because streamflow statistics were not consistent with the other stations statistics.

Gaged Stream Sites

The USGS has established standard methods for estimating flow duration (Searcy, 1959) for streamflow-gaging stations. The computer software programs IOWDM, ANNIE, and SWSTAT were used to format input data, manage and display data, and complete the flow-duration statistical analyses (Lumb and others, 1990; Flynn and others, 1995). These programs are available on the World Wide Web at http://water.usgs.gov/software/surface_water.html

Daily mean flows for all complete water years of record were used to determine flow-duration statistics for continuous-record, streamflow-gaging stations. The water year begins on October 1 and ends on September 30 of the following year. Daily mean flows for USGS streamflow-gaging stations in Kansas are available on the World Wide Web at http://waterdata.usgs.gov/ks/nwis/

A flow-duration curve is a graphical representation of the percentage of time streamflows for a given time step (usually daily) are equaled or exceeded over a specified period (usually the complete period of record) at a stream site. Flow-duration curves usually are constructed by first ranking all of the daily mean discharges for the period of record at a gaging station from largest to smallest, next computing the probability for each value of being equaled or exceeded, then plotting the discharges against their associated exceedance probabilities (Loaiciga, 1989, p. 82). The daily mean discharges are not fit to an assumed distribution. Flow-duration analysis can be done by use of the USGS software described previously or by use of commercially available statistical software.

Flow-duration statistics are points along a flow-duration curve. For example, the 99-percent duration streamflow is equaled or exceeded 99 percent of the time, whereas the 50-percent duration streamflow is equaled or exceeded 50 percent of the time. Strictly interpreted, flow-duration statistics reflect only the period for which they are calculated; however, when the period of record used to compute the statistics is sufficiently long, the statistics often are used as an indicator of probable future conditions (Searcy, 1959). Median-flow statistics in this report were determined using the Loaiciga (1989) approach.

Ungaged Stream Sites

Estimates of streamflow statistics often are needed for sites on streams where no data are available. The two methods most commonly used to estimate statistics for ungaged sites are the drainage-area ratio method and multiple linear-regression analysis. The drainage-area ratio method is most appropriate for use when the ungaged site is near a streamflow-gaging station on the same stream. Multiple linear-regression analysis is used to obtain estimates for most other ungaged sites.

Drainage-Area Ratio Method

The drainage-area ratio method assumes that the streamflow at an ungaged site for the same stream is the same per unit area or at least responds in the same fashion as that at a nearby, hydrologically similar streamflow-gaging station used as an index. Drainage areas for the ungaged site and the index station are determined from topographic maps, digital elevation maps (DEMs), or by other GIS methods. Streamflow statistics are computed for the index station, then the statistics are divided by the drainage area to determine streamflows per unit area at the index station. These values are multiplied by the drainage area at the ungaged site to obtain estimated statistics for the site. This method is most commonly applied when the index gaging station is on the same stream as the ungaged site because the accuracy of the method depends on the proximity of the two sites and on similarities in drainage area and on other climatic and basin characteristics of the respective drainage basins.

Several researchers have provided guidelines as to how large the difference in drainage areas can be before use of multiple linear-regression analysis is preferred over use of the drainage-area ratio method. Guidelines have been provided for estimating peak-flow statistics, and usually the recommendation has been that the drainage area for the ungaged site should be within 0.5 and 1.5 times the drainage area of the index station (Choquette, 1988, p. 41; Koltun and Roberts, 1990, p. 6; Lumia, 1991, p. 34; Bisese, 1995, p. 13). One report (Koltun and Schwartz, 1986, p. 32) selected a range of 0.85 to 1.15 times the drainage area of the index station for estimating low flows at ungaged sites in Ohio. None of these researchers provided any scientific basis for use of these guidelines (R.E. Thompson, Jr., U.S. Geological Survey, written commun., 1999). In this report, the median flows at uncontrolled, ungaged locations are estimated by interpolation procedures using weighted drainage-area ratio from gaged sites and Tobit regression estimates at ungaged sites. No limit was placed on the ratios between the drainage area of the index station and the drainage area of the ungaged stream segment.

Multiple Linear-Regression Analyses

Multiple linear-regression analysis (regression analysis) has been used by the USGS and other researchers throughout the United States and elsewhere to develop equations for estimating streamflow statistics at ungaged sites. In regression analysis, a streamflow statistic (the dependent variable) for a group of gaging stations is related statistically to the climatic or basin characteristics of the drainage basins for the stations (the independent variables). This results in an equation that can be used to estimate the statistic for sites where no streamflow data are available.

Equations can be developed by use of several different regression analysis algorithms. The various algorithms use different methods to minimize the differences between the values of the dependent variable for the stations used in the analysis (the observed values) and the corresponding values provided by the resulting regression equation (the estimated or fitted values). Choice of one algorithm over another depends on the characteristics of the data used in the analysis and on the underlying assumptions for use of the algorithm. The multiple linear-regression equation takes the general form:

Yi = b0 + b1X1 + b2X2 +...+ bnXn + ei ,               (1)

where Yi is the value of the dependent variable for site i, X1 to Xn are the n independent variables, b0 to bn are the n + 1 regression-model coefficients, and ei is the error (difference between the observed and estimated values of the dependent variable) for site i. Assumptions for use of regression analysis are (1) equation 1 adequately describes the relation between the dependent and the independent variables, (2) the variance of the ei is constant and independent of the values of Xn, (3) the ei are normally distributed for a Tobit regression, and (4) the ei are independent of each other (Inman and Conover, 1983, p. 367). Tobit regression is discussed in the following paragraph. Regression analysis results must be evaluated to assure that these assumptions are met. Streamflow and basin characteristics used in hydrologic regression usually are log normally distributed; therefore, transformation of the variables to logarithms is usually necessary to satisfy regression assumption 3. Transformation results in a model of the form:

log Yi = b0 + b1 log X1 + b2 log X2 +...+ bn log Xn + ei .               (2)

The algebraically equivalent form when logarithms-base 10 (log10) are used in the transformations, and the equation retransformed to original units is:

Yi = 10b0 (X1b1) (X2b2)... (Xnbn) 10 ei , , or               (3)

Yi = 10 [b0 + b1 log X1 + b2 log X2 +...+ bn log Xn + ei ] .

To include zero values in a logarithmic transformation regression analysis, the Tobit regression was used. Tobit regression is a widely accepted method for estimating a regression-like model when there are adjusted data (Tobin, 1958; Judge and others, 1985). Adjusted data are data that are either censored or have had a discrete value delta (δ) added to them. Censored data are values below a threshold and are raised to the censoring value (for example, all values below 0.7 are raised to 0.7). Discrete values of delta (δ) are added to all data before transformation and then subtracted from the final regression model value. By applying these techniques, zero values of data can be transformed logarithmically. The Tobit procedure uses a maximum likelihood estimator. The Survival Regression Procedure in the S-Plus 2000 software package (MathSoft, 1999) was used in this study to fit the Tobit model.

A Tobit analysis was conducted on both the KSA and AAH data sets, and the resulting plots of observed versus regression-estimated values of median flow from the KSA and AAH data sets are shown in figures 6A and 6B. The graphs show the observed median flow plotted with the regression-estimated median flow. All observed and regression-estimated median flows have the delta value added. The Chi2 is a measure of the fit of the Tobit model. The delta value is varied until the Chi2 is maximized. The drainage area (DA) was divided by 1,000, the 30-year mean precipitation (PREC) was divided by 28, and the mean basin slope (SLOPE) was divided by 2 before the log transformation was made so that the log values were balanced between greater than and less than zero. This removed the multi-collinearity problems that occur when using squared values. The addition of the squares of log drainage area and log mean annual precipitation to the regression equation improved both KSA and AAH models substantially. The equations for regression-estimated median flow and uncertainty measures for KSA and AAH methods are listed in table 2. Only the 149 gages on uncontrolled streams with at least 10 years of record were used in the regression analyses. The drainage area of these gages ranged from 2.06 to 12,004 mi².

KSA and AAH analyses provided regression estimates that were different. The KSA analysis used the most-recent 10 years of data. For many of the stations in this report this period was 1990 to 2000. However, more than 50 percent of the stations had their last data recorded before 1990 and more than 40 percent before 1980. Climate variability becomes a factor when 10 years of record from an earlier period is compared with a later period. Application of the KSA 82a-2001 criterion to use the most-recent 10 years of streamflow data may mean that a new analysis would be required every few years, and the resulting equation always would reflect short-term (less than10 years) climate variability.

The AAH analysis used all-available streamflow-data records that were from 10 to 90 years in length. Use of the entire period of record, which averaged 35 years for the 149 stations, incorporated all of the knowledge about streamflow at a particular site. The climate of Kansas has gone through periods of wet and dry conditions, some of which have lasted longer than 10 years. The AAH analysis with its longer period of record incorporates long-term climate variability.

Although both sets of median flow data (KSA and AAH) have some nonoverlapping time periods, the analyses are still valid statistically. The different time periods cover different streamflow regimes ranging from wet to dry. Had the most-recent 10 years been interpreted as the period 1991 to 2000, the analysis would have been biased toward trends or cyclicity in the climate during that period. By using the different time periods of streamflow data for AAH analysis, this bias is removed. The increased number of sampled days of flow in the AAH data set makes it more robust than the KSA data set, which has a reduced number of sampled days.

Kansas Surface Water Register

In 1994, the Kansas Department of Health and Environment (KDHE) adopted the Reach File Version 2 (RF2) stream-segment coverage within the State of Kansas as the basic coverage for stream classification. RF2 was completed in the late 1980s by the U.S. Environmental Protection Agency (USEPA) by using the Feature File of the USGS Geographic Names Information System (GNIS) to add one new level of reach segments to the Reach File Version 1 (RF1) coverage. The source of RF1 (completed in 1982) was the USGS's 1:250,000-scale hydrography that was photographically reduced to a scale of 1:500,000 by the National Oceanic and Atmospheric Association (NOAA). In addition to the RF2 segments, other segments have been added by KDHE to the Kansas Surface Water Register primarily for the protection of aquatic life and other water-quality issues. The original RF2 coverage has almost 30,000 subsegments in Kansas. By combining subsegments, the number of total segments for which median flows were determined in this report was reduced to 2,232, which equals the number of segments listed in the current (2002) Kansas Surface Water Register. This number is about 900 more segments than the RF1 coverage. The Kansas Surface Water Register of June 1, 1999, is a public document and can be obtained from the World Wide Web at http://www.kdheks.gov/pdf/befs/register99.pdf. In addition to the 2,232 classified segments, there are segments that are unregulated that include lakes, tribal streams, and irrigation ditches. These segments were included in this report to complete the stream drainage pattern for the State. Each segment on the Kansas Surface Water Register is identified by a unique CUSEGA number (Appendix C, Table 6, at the end of this report). CUSEGA stands for catalog unit segment number alpha.

Because many of the stream basins in Kansas extend into the surrounding States, the data used for developing the Kansas Surface Water Register, which is based on the more detailed RF2, were joined with the national RF1 coverage that is available for Colorado, Missouri, Nebraska, and Oklahoma. This process was done by clipping the Kansas extent of the original RF1 stream coverage and replacing it with the more detailed version of the RF2 stream coverage. The two coverages were joined at the State boundaries for continuity. The line topology was reconfigured so that spatial relations between connecting stream segments (from and to nodes) were updated. Then the updated stream coverage was rechecked to correct any remaining digitizing errors including cycles, overshoots, and undershoots (that is, an arc that does not extend far enough to intersect another arc). Finally, the topology was checked for consistency (that is, all segments point downstream). All GIS analyses were performed using the Environmental Systems Research Institute (ESRI) ArcGIS and ArcInfo workstation.

A GIS database was used to manage and display the basin characteristics and estimated median flows for stream segments on the Kansas Surface Water Register. The relational database design facilitates identification and analysis of data unique to individual stream segments.

Basin Characteristics for Stream Segments

Drainage basins for each stream segment on the Kansas Surface Water Register were determined in the GIS by converting the vector stream-segment coverage into a raster-grid network with a raster size of 492 by 492 ft (150 by 150 m). Euclidean allocation was performed on the rasterized stream network to calculate for each cell the identity of the closest source or stream cell using the Euclidean distance. Euclidean distance is defined as the shortest length between two points in two-dimensional space.

Mean values for climatic and basin characteristics were calculated for stream-segment drainage basins using zonal statistics on basin-characteristic grids with Euclidean allocation zones. Zonal statistics were recorded in an attribute table and included the area and mean of the values of all cells in the basin-characteristic grids that belong to the same Euclidean zone. The climatic and basin characteristics computed included drainage area, mean annual precipitation, mean basin elevation, mean basin permeability, mean basin slope, a Base Flow Index (BFI), and the Gebert and PRISM flow model values. Output zonal statistics tables were relationally joined back to the original vector streams coverage so that each reach had an estimated value for each climatic and basin characteristic.

Estimates of Median Flows for Stream Segments

Different procedures were used to estimate median flow for each stream segment on the Kansas Surface Water Register depending on whether the segment was controlled or uncontrolled and whether there was a streamflow-gaging station located either upstream or downstream from the segment. These interpolation procedures use the previously defined drainage-area ratio method and multiple linear-regression equations and are summarized in table 3. The interpolation procedures outlined in table 3 for an ungaged segment between two gaged segments selects the upstream gage segment (if there is more than one) that has the largest drainage area. These procedures were applied to flow statistics developed for KSA and AAH analyses for each stream segment on the Kansas Surface Water Register. Median-flow computations for controlled streamflow-gaging stations, used in the interpolation of the KSA and AAH analyses, are listed in table 4. Median-flow computations for the uncontrolled streamflow-gaging stations, used in the interpolation of the KSA and AAH analyses, are listed in table 5 (Appendix B). The AAH median flow at gages representing controlled stream segments (those with large reservoirs upstream) was computed from the controlled period of record only. These records had to be at least 10 years in length during the period 1960 to 2000. Use of the 1960 to 2000 time period maintains a degree of consistency for comparison and interpolation of median flows between gaging stations on controlled segments.

Figure 7 shows part of a stream network and some stream gages in central Kansas. The numbers next to the stream gages are the most-recent 10-year median flow values for those gages. Regression equations were developed in the section on " Multiple Linear-Regression Analyses". The numbers next to the stream segments are the median flow values estimated from those regression equations. A comparison of the stream-segment median flow values with the stream-gage median values shows substantial "local" differences between the stream-segment and stream-gage values. Figure 8 shows the effect of using the local stream-gage median values to develop estimated median streamflow values by KSA analysis for the stream segments as outlined in table 3 and used in this report rather than only using the regression-estimated values. The local differences in estimated median flow values noted in figure 7 (regression estimates) are not as large in figure 8 (estimates derived in this report) because of the use of local stream-gage data. As a result, the interpolation procedure used in this report to develop median flow estimates appears to develop more accurate estimates than those that result from using only the regression equations.

The median flow information from streamflow-gaging stations and the regression equations from the KSA and the AAH analyses were used with the described interpolation procedures to generate a table of median flow values for the downstream end of stream segments on the Kansas Surface Water Register. The estimated median flow values for the KSA analysis and the AAH analysis are listed with their respective CUSEGA segment number in table 6 in Appendix C. In addition, three maps are provided on plates 1-3 in the back of this report. Plate 1 shows the location of USGS streamflow-gaging stations used in the interpolation procedure and Kansas Surface Water Register stream segments. Plate 2 shows estimated median flow values for each stream segment using the KSA analysis, and plate 3 shows estimated median flow values for each stream segment using the AAH analysis.

Of the 2,232 stream segments on the Kansas Surface Water Register, 30 percent of the segments had an estimated median flow of less than 1 ft³/s when the most-recent 10 years of data (KSA analysis) were used. When all-available data (AAH analysis) were used, which resulted in a regression equation with a lower level of uncertainty when compared to the KSA analysis, 40 percent of the stream segments had an estimated median flow of less than 1 ft³/s.

The uncertainty of the estimated median streamflows varies depending on the analysis used to determine the estimate for that segment. The greatest uncertainties exist for streams where no stream-gage information was available and only the regression estimates were used. For these segments, the uncertainty of the median flow estimate is the root mean square error of the regression estimate, which for the KSA analysis was 0.285 log units. This means that there is a 95-percent probability that the actual median flow for an estimate of 1 ft³/s is between 0.28 and 3.6 ft³/s (72 to 260 percent). For the AAH analysis, the root mean square error was 0.247 log units (table 2), which translates into a 95-percent probability that the actual median flow for an estimate of 1 ft³/s is between 0.33 and 3.04 ft³/s (67 to 204 percent). The lowest uncertainties exist for stream segments with gages near the downstream end of those segments. For these stream segments the uncertainty is a fraction of the uncertainty of the gaging-station flow measurement and rating process due to the central tendency of the median statistic. The average uncertainty for those segments with gages varies from 7.3 percent for the KSA data to 4.3 percent for the AAH data. The 95-percent confidence intervals for the gaged data used in the interpolation are listed in table 5 in Appendix B. Reporting estimated median values in table 6 and on plates 2 and 3 to three significant figures was done to conform with the intent of KSA 82a-2001 et. seq. and does not denote the level of accuracy of the estimates.

INTERNET DISSEMINATION OF RESULTS

This report and its associated figures, tables, appendices, plates, and the GIS database are available and can be downloaded from the World Wide Web at http://ks.water.usgs.gov/pages/streamflow-statistics. This web page is maintained by the USGS and has links to the GIS databbase described in this report in order to display the information on median flow by county for the State of Kansas. Estimated median flows from the KSA and AAH analyses are available for stream segments on the Kansas Surface Water Register. The county-map format includes county boundaries, State and Federal highways, and the stream segments for spatial reference. The estimated median flow values using the KSA and AAH analyses, indexed with their respective segment identifier number, are displayed as a pop-up window as the cursor is placed over a stream segment.

Summary

The Kansas State Legislature, by enacting Kansas Statute 82a-2001 et. seq. (KSA), has mandated the selection of Kansas streams for water-quality classification by the State. One criterion for selecting stream segments for classification is whether stream segments listed on the Kansas Surface Water Register have a median flow equal to or greater than 1 ft³/s. Therefore, information on median flow characteristics is needed for streams in Kansas. Daily streamflow information available for 214 gaging stations within Kansas and in adjacent States were used by the USGS in cooperation with KDHE to compute these statistics at gaged sites and to estimate these statistics at ungaged sites.

Least-squares multiple-regression techniques, along with Tobit analyses, were used to develop equations for estimating median flow (dependent variable) for ungaged, uncontrolled stream segments. Median flows were determined from streamflow-gaging station data using the most-recent 10 years of gaged data as defined by KSA analysis, and from the entire period of record, which is defined in this report as the all-available hydrology (AAH) analysis. Independent variables in the regression equations were the climatic and basin characteristics for streams flowing through Kansas. In the development of the regression equations, the significant climatic and basin characteristics, in order of importance, were drainage area, mean annual precipitation, mean basin permeability, and mean basin slope. Only the 149 gages on uncontrolled streams with at least 10 years of streamflow record were used in the regression analyses. The drainage area of these gages ranged from 2.06 to 12,004 mi².

A logarithmic transformation of the basin characteristics was needed to develop a linear relation for computing median flows. Because there were numerous zero values for median gaging-station flows, the Tobit regression was used to include those zero values in the regression. The resulting regression equations and an interpolation procedure were used to estimate median flows for the uncontrolled stream segments on the Kansas Surface Water Register.

Streamflow-gaging-station data were used to improve the quality of the estimates along the streams that had gages. Median flows for the segments that were uncontrolled were interpolated using gaged data weighted according to the drainage area and the bias between the regression estimate and gaged flow information. On controlled reaches of Kansas streams, the median flow information was interpolated between gaging stations by using only gaged data weighted by drainage area.

Of the 2,232 stream segments on the Kansas Surface Water Register, 30 percent of the segments had an estimated median flow of less than 1 ft³/s when the most-recent 10 years of data (KSA analysis) were used. When all-available data (AAH analysis) were used, which resulted in a regression equation with a lower level of uncertainty when compared to KSA analysis, 40 percent of the stream segments had an estimated median flow of less than 1 ft³/s.

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For additional information about ongoing studies in Kansas, please visit:
http://ks.water.usgs.gov

For additional information contact:

Charles A. Perry
U.S. Geological Survey
4821 Quail Crest Place
Lawrence, KS 66049-3839
Telephone: (785) 832-3549
Fax: (785) 832-3500
Email: cperry@usgs.gov

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