U.S. Geological Survey WaterResources Investigations Report 024292
Prepared in cooperation with the KANSAS DEPARTMENT OF HEALTH AND ENVIRONMENT
Download this report as a PDF file (29 MB)
Download a free copy of
Acrobat Reader
Estimates of Median Flows for Streams on the Kansas Surface Water Register
By Charles A. Perry, David M. Wolock, and Joshua C. Artman
CONTENTS
PLATES  Not available online
 Map showing location of U.S. Geological Survey streamflowgaging stations and stream
segments on the Kansas Surface Water Register
 Map showing estimated median flows for downstream end of stream segments on the Kansas
Surface Water Register using the mostrecent 10 years of record (KSA analysis)
 Map showing estimated median flows for downstream end of stream segments on the Kansas
Surface Water Register using allavailable hydrology (AAH analysis)
FIGURES
15. Map showing:
Figure 1. Location of U.S. Geological Survey streamflowgaging
stations in Kansas and parts of surrounding States with 10 or more years of record
that were used to estimate median flows
Figure
2. Landsurface elevation in Kansas and parts of surrounding States
Figure
3. Average landsurface 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
regressionestimated median flows for (A) mostrecent 10 years of record (KSA) and (B)
allavailable hydrology (AAH) using Tobit analysis
Figure 7. Map showing median flow values for stream
segments in central Kansas estimated from regression equations and observed
streamflowgagingstation data for the mostrecent 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 streamflowgagingstation data for the
mostrecent 10 years of record (KSA) analysis
TABLES
Table 1. Streamflowgaging 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. Streamflowgaging 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 95percent confidence intervals
computed for streamflowgaging stations used in the interpolation procedure for the
mostrecent 10 years of record (KSA) and allavailable 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 mostrecent 10 years of record (KSA) and allavailable
hydrology (AAH) analyses
For additional information about ongoing studies in Kansas, please visit:
http://ks.water.usgs.gov/
The Kansas State Legislature, by enacting Kansas Statute KSA 82a2001 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 82a2001 et. seq., median flows were determined from U.S. Geological Survey
streamflowgagingstation data by using the mostrecent 10years of gaged data (KSA) for each
streamflowgaging station. Median flows also were determined by using gaged data from the
entire period of record (allavailable hydrology, AAH).
Leastsquares 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 regressionestimated 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 regressionestimated 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.
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
82a2001 et. seq. (see Appendix A) specifically mentions
median streamflow as one criterion for classifying streams. Current waterquality regulations
in Kansas apply numeric waterquality 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
waterquality criteria for the stream segments are based on assigned designated uses.
KSA 82a2001 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
streamflowgaging 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.
The purpose of this report is to document the methods and results of a study designed to
estimate the median flow (50percent 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 gagedlocation 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 drainagearea
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 geographicinformationsystem (GIS) database.
Two different statistical analysis were performed on uncontrolled flows measured at 149 gaging
stations. According to language in KSA 82a2001 et. seq., only the mostrecent 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 allavailable 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 surfacewater resources. Optimal reservoir operations,
legally distributed instream withdrawals, and waterquality 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 lowflow and flowduration studies for Kansas include an investigation by Furness
(1959) who developed a method for estimating flowduration curves for ungaged sites that was
based on regionalized flowduration data from 122 continuousrecord, streamflowgaging
stations with drainage areas of between 100 and 3,000 mi² for the period 192156. Maps
were developed showing a variety of statewide low and mean streamflow maps. Furness (1959)
also noted that the lowflow parts of the flowduration curves could be verified or improved
by relating baseflow measurements at the ungaged site to baseflow measurements at a nearby,
index streamflowgaging station.
Jordan (1983) updated the maps developed by Furness by including additional streamflowgaging
stations and data for the period 195776. Jordan's study included a map that depicted the
areas of Kansas where the median streamflow for a 500mi² 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 streamflowgaging stations as index stations. The results
of these two recent studies indicated that the Furness method continues to be a useful tool
for estimating flowduration 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 drainagearea
ratio method to compute streamflow characteristics for stream segments that had between 0.5
and 1.5 times the drainage area of streamflowgaging stations on the same stream. Many States
have used regression analysis to regionalize lowflow 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
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 twothirds 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 onethird of the State is more variable, with alternating hills and lowlands.
Landsurface elevations within the State range from about 700 ft above the North American
Vertical Datum of 1988 (NAVD 88) at the KansasOklahoma State line in southeast Kansas to
about 4,135 ft above the NAVD 88 at a point near the KansasColorado State line in western
Kansasa vertical difference of about 3,435 ft (fig. 2). The average landsurface slope for Kansas
(fig. 3)
using 30m grid elevation data is about 1.9 degrees.
Other physical characteristics affecting the flow characteristics of watersheds are the types
of soils and landuse and treatment practices within the basin. For example, with all other
factors being equal the lowflow 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 groundwater contribution to base flow of the stream.
The western twothirds of the State typically has soils of moderate to high permeability,
whereas the eastern onethird has soils of lower permeability. Landtreatment practices, such
as contour farming and construction of waterretention structures, can increase the amount of
infiltration of runoff to ground water, which ultimately returns to stream channels as base
flow. However, landtreatment practices are difficult to assess and apply to the various types
of basins statewide.
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 lowintensity 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 highintensity thunderstorms.
Watersheds in Kansas exhibit a wide range of climatic characteristics that affect streamflow.
Generally, precipitation varies in an eastwest direction, with little northsouth 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 streamflowgaging stations used in the regression analyses for
uncontrolled stream segments on the Kansas Surface Water Register is given in
table 1.
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
(parameterelevation 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 streamflowgaging stations used in the regression
analyses for uncontrolled stream segments are provided in table 1.
All basin characteristics were measured from digitalmap 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 drainagebasin 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.
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) 30year (196190) mean annual precipitation data (Daly and
others, 1997), (2) 30m gridded elevation data (U.S. Geological Survey, 1998) for determining
drainage area, mean basin slope, and mean basin elevation, and (3) STATSGO soilpermeability
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
thirtyone streamflowgaging 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
streamflowgaging 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.
The USGS has established standard methods for estimating flow duration (Searcy, 1959) for
streamflowgaging stations. The computer software programs IOWDM, ANNIE, and SWSTAT were used
to format input data, manage and display data, and complete the flowduration 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 flowduration
statistics for continuousrecord, streamflowgaging stations. The water year begins on October
1 and ends on September 30 of the following year. Daily mean flows for USGS streamflowgaging
stations in Kansas are available on the World Wide Web at http://waterdata.usgs.gov/ks/nwis/
A flowduration 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. Flowduration 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.
Flowduration analysis can be done by use of the USGS software described previously or by use
of commercially available statistical software.
Flowduration statistics are points along a flowduration curve. For example, the 99percent
duration streamflow is equaled or exceeded 99 percent of the time, whereas the 50percent
duration streamflow is equaled or exceeded 50 percent of the time. Strictly interpreted,
flowduration 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). Medianflow statistics
in this report were determined using the Loaiciga (1989) approach.
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
drainagearea ratio method and multiple linearregression analysis. The drainagearea ratio
method is most appropriate for use when the ungaged site is near a streamflowgaging station
on the same stream. Multiple linearregression analysis is used to obtain estimates for most
other ungaged sites.
The drainagearea 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 streamflowgaging 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 linearregression analysis is preferred over use of the
drainagearea ratio method. Guidelines have been provided for estimating peakflow 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 drainagearea 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 linearregression 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
linearregression equation takes the general form:
Y_{i} = b_{0} + b_{1}X_{1} + b_{2}X_{2}
+...+ b_{n}X_{n} + e_{i} ,
(1)
where Y_{i} is the value of the dependent variable for site i,
X_{1} to X_{n} are the n independent variables,
b_{0} to b_{n} are the n + 1 regressionmodel
coefficients, and e_{i} 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 e_{i} is constant and
independent of the values of X_{n}, (3) the e_{i} are normally
distributed for a Tobit regression, and (4) the e_{i} 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 Y_{i} = b_{0} + b_{1} log X_{1} +
b_{2} log X_{2} +...+ b_{n} log X_{n} + e_{i} .
(2)
The algebraically equivalent form when logarithmsbase 10 (log_{10}) are used in the
transformations, and the equation retransformed to original units is:
Y_{i} = 10^{b0}
(X_{1}^{b1})
(X_{2}^{b2})...
(X_{n}^{bn}) 10 ^{ei} ,
, or (3)
Y_{i} = 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
regressionlike 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 SPlus 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 regressionestimated 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
regressionestimated median flow. All observed and regressionestimated median flows have the
delta value added. The Chi^{2} is a measure of the fit of the Tobit model. The delta
value is varied until the Chi^{2} is maximized. The drainage area (DA) was divided by
1,000, the 30year 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 multicollinearity 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 regressionestimated 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 mostrecent 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
82a2001 criterion to use the mostrecent 10 years of streamflow data may mean that a new
analysis would be required every few years, and the resulting equation always would reflect
shortterm (less than10 years) climate variability.
The AAH analysis used allavailable streamflowdata 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 longterm 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 mostrecent 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.
In 1994, the Kansas Department of Health and Environment (KDHE) adopted the Reach File Version
2 (RF2) streamsegment 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 1:250,000scale 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
waterquality 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.
Drainage basins for each stream segment on the Kansas Surface Water Register were determined
in the GIS by converting the vector streamsegment coverage into a rastergrid 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 twodimensional space.
Mean values for climatic and basin characteristics were calculated for streamsegment drainage
basins using zonal statistics on basincharacteristic 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 basincharacteristic 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.
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 streamflowgaging station located either upstream or downstream from the
segment. These interpolation procedures use the previously defined drainagearea ratio method
and multiple linearregression 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. Medianflow
computations for controlled streamflowgaging stations, used in the interpolation of the KSA
and AAH analyses, are listed in table 4. Medianflow computations
for the uncontrolled streamflowgaging 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 mostrecent 10year median flow values
for those gages. Regression equations were developed in the section on "
Multiple LinearRegression Analyses". The numbers next to the stream segments are the
median flow values estimated from those regression equations. A comparison of the
streamsegment median flow values with the streamgage median values shows substantial "local"
differences between the streamsegment and streamgage values.
Figure 8 shows the effect of using the local
streamgage 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
regressionestimated 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 streamgage 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 streamflowgaging 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 13 in the back of this report. Plate 1 shows
the location of USGS streamflowgaging 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 mostrecent 10 years of data
(KSA analysis) were used. When allavailable 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
streamgage 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 95percent 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 95percent 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 gagingstation 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 95percent
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 82a2001 et. seq. and does not denote the level of accuracy of the
estimates.
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/streamflowstatistics. 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
countymap 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 popup
window as the cursor is placed over a stream segment.
The Kansas State Legislature, by enacting Kansas Statute 82a2001 et. seq. (KSA), has mandated
the selection of Kansas streams for waterquality 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.
Leastsquares multipleregression 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 streamflowgaging station data using the
mostrecent 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 allavailable 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
gagingstation 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.
Streamflowgagingstation 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 mostrecent 10 years of data
(KSA analysis) were used. When allavailable 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.

Arihood, L.D., and Glatfelter, D.R., 1991,
 Method for estimating lowflow characteristics of ungaged streams in Indiana: U.S.
Geological Survey WaterSupply Paper 2372, 18 p.

Bisese, J.A., 1995,
 Methods for estimating the magnitude and frequency of peak discharges of rural,
unregulated stream in Virginia: U.S. Geological Survey WaterResources Investigations
Report 944148, 70 p., 1 pl.

Choquette, A.F., 1988,
 Regionalization of peak discharges for streams in Kentucky: U.S. Geological Survey
WaterResources Investigations Report 884209, 105 p., 1 pl.

Cohn, T.A., 1988,
 Adjusted maximum likelihood estimation of the moments of lognormal population of Type
I censored samples: U.S. Geological Survey OpenFile Report 88350, 34 p.
v 
Daly, C., Neilson, R.P., and Phillips, D.L., 1994,
 A statisticaltopographic model for mapping climatological precipitation over
mountainous terrain: Journal of Applied Meteorology, v. 33, no. 2, p. 140158.

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. 1012.

Environmental Systems Research Institute, Inc., 1991,
 Understanding GISthe ARC/INFO method: Redlands, California, various pagination.

Flynn, K.M., Hummel, P.R., Lumb, A.M., and Kittle, J.L., Jr., 1995,
 User's manual for ANNIE, version 2, a computer program for interactive hydrologic
data management: U.S. Geological Survey WaterResources Investigations Report
954085, 211 p.

Furness, L.W., 1959,
 Kansas streamflow characteristicspart 1, Flow duration: Kansas Water Resources
Board Technical Report No. 1, 213 p.

Gebert, W.A., Graczyk, D.J., and Krug, W.R., 1987,
 Average annual runoff in the United States, 195180: U.S. Geological Survey
Hydrologic Investigations Atlas HA710, scale 1:7,500,000.

Inman, R.L., and Conover, W.J., 1983,
 A modern approach to statistics: New York, John Wiley, 497 p.

Johnson, C.G., 1970,
 A proposed streamflow data program for central New England: U.S. Geological Survey
OpenFile Report, 38 p.

Jordan, P.R., 1983,
 Kansas streamflow characteristicsmagnitude and frequency of low flows of
unregulated streams in Kansas, and estimation of flowduration curves for ungaged
sites: Kansas Water Office Technical Report No. 17, 55 p.

Judge, G.G., Griffiths, W.E., Hill, R.C., Lutkepohl, H., and Lee, T.C., 1985,
 Qualitative and limited dependent variable models, chapter 18, in The theory
and practice of econometrics: New York, Wiley, 1019 p.

Koltun, G.F., and Roberts, J.W., 1990,
 Techniques for estimating floodpeak discharges of rural, unregulated stream in Ohio:
U.S. Geological Survey Water Resources Investigations Report 894126, 68 p., 1 pl.

Koltun, G.F., and Schwartz, R.R., 1986,
 Multipleregression equations for estimating low flows at ungaged stream sites in
Ohio: U.S. Geological Survey WaterResources Investigations Report 864354, 39 p., 6
pls.

Ku, H.F., Randall, A.D., and MacNish, R.D., 1975,
 Streamflow in the New York part of the Susquehanna River Basin: New York State
Department of Environmental Conservation Bulletin 71, 130 p.

Loaiciga, H.A., 1989,
 Variability of empirical flow quantiles: Journal of Hydraulic Engineering, American
Society of Civil Engineers, v. 115, no. 1, p. 82100.

Lumb, A.M., Kittle, J.L., Jr., and Flynn, K.M., 1990,
 Users manual for ANNIE, a computer program for interactive\hydrologic analyses and
data management: U.S. Geological Survey WaterResources Investigations Report
894080, 236 p.

Lumia, Richard, 1991,
 Regionalization of flood discharges for rural, unregulated streams in New York,
excluding Long Island: U.S. Geological Survey WaterResources Investigations Report
904197, 119 p., 2 pls.

Male, J.W., and Ogawa, Hisashi, 1982,
 Low flow of Massachusetts streams: Amherst, Massachusetts, University of
Massachusetts, Water Resources Research Center Publication 125, 152 p.

MathSoft, 1999,
 SPLUS 2000 guide to statistics: Seattle, Washington, volumes I, II, and III, various
pagination.

Parker, G.W., 1977,
 Methods for determining selected flow characteristics for streams in Maine: U.S.
Geological Survey OpenFile Report 78871, 31 p.

Parrett, Charles, and Hull, J.A., 1985,
 Streamflow characteristics of mountain streams in western Montana: U.S. Geological
Survey WaterSupply Paper 2260, 58 p.

Putnam, J.E., Lacock, D.L., Schneider, D.R., and Carlson, M.D., 2001,
 Water resources data, Kansas, water year 2000: U.S. Geological Survey WaterData
Report KS001, 505 p.

Ries, K.G., and Friesz, P.I., 2000,
 Methods for estimating lowflow statistics for Massachusetts streams: U.S. Geological
Survey WaterResources Investigations Report 004135, 81 p.

Risley, J.C., 1994,
 Estimating the magnitude and frequency of low flows of streams in Massachusetts: U.S.
Geological Survey WaterResources Investigations Report 944100, 29 p.

Schoewe, W.H., 1949,
 The geography of Kansaspart 2, Physical geography: Transactions of the Kansas
Academy of Science, v. 52, no. 3, p. 261333.

Searcy, J.K., 1959,
 Flowduration curves, manual of hydrologypart 2. Lowflow techniques: U.S.
Geological Survey WaterSupply Paper 1542A, p. 133.

Studley, S.E., 2000,
 Estimated flowduration curves for selected ungaged sites in the Cimarron and Lower
Arkansas River Basins in Kansas: U.S. Geological Survey WaterResources
Investigations Report 004113, 43 p.

____2001,
 Estimated flowduration curves for selected ungaged sites in Kansas: U.S. Geological
Survey WaterResources Investigations Report 014142, 90 p.

Tobin, J., 1958,
 Estimation of relationships for limited dependent variables: Eonometrica, v. 26, p.
2436.

U.S. Department of Agriculture, 1994,
 State soil geographic (STATSGO) data base: Soil Conservation 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

Vogel, R.M., and Kroll, C.N., 1990,
 Generalized lowflow frequency relationships for ungaged sites in Massachusetts:
Water Resources Bulletin, v. 26, no. 2, p. 241253.

Wahl, K.L., and Wahl, T. L., 1995,
 Determining the flow of Comal Springs at New Braunfels, Texas, in Texas Water
'95: American Society of Civil Engineers, August 1617, 1995, San Antonio, Texas, p.
7786.

Wandle, S.W., Jr., and Randall, A.D., 1994,
 Effects of surficial geology, lakes and swamps, and annual water availability on low
flows of streams in central New England, and their use in lowflow estimation: U.S.
Geological Survey WaterResources Investigations Report 934092, 57 p.
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 660493839
Telephone: (785) 8323549
Fax: (785) 8323500
Email: cperry@usgs.gov
To request a paper copy of this report, email:
GSWKS_info@usgs.gov
