U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2015–5031

Prepared in cooperation with the Arkansas Department of Environmental Quality, 

Southwestern Energy, the Arkansas Natural Resources Commission, and 

the Arkansas Game and Fish Commission

Dry Season Mean Monthly Flow and Harmonic Mean Flow 

Regression Equations for Selected Ungaged Basins in 

Arkansas
 
Dry Season Mean Monthly Flow and 

Harmonic Mean Flow Regression Equations 

for Selected Ungaged Basins in Arkansas

By Brian K. Breaker

Prepared in cooperation with the Arkansas Department of Environmental Quality, 

Southwestern Energy, the Arkansas Natural Resources Commission, and 

the Arkansas Game and Fish Commission

Scientific Investigations Report 2015–5031

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2015

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as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Breaker, B.K., 2015, Dry season mean monthly flow and harmonic mean flow regression equations for selected 

ungaged basins in Arkansas: U.S. Geological Survey Scientific Investigations Report 2015–5031, 25 p., http://dx.doi.

org/10.3133/sir20155031.

ISSN 2328-0328 (online)
iii

Contents

Abstract ..........................................................................................................................................................1

Introduction ....................................................................................................................................................1

Purpose and Scope .............................................................................................................................2

Previous Studies ..................................................................................................................................2

Methods of Analysis for Data from U.S. Geological Survey Continuous-Record Streamflow 

Gages .................................................................................................................................................2

Basin Characteristics ..........................................................................................................................2

Regression Techniques .......................................................................................................................4

Dry Season Mean Monthly Flow Data .............................................................................................5

Harmonic Mean Flow Data ................................................................................................................5

Regionalization of Harmonic Mean Flow Data ...............................................................................5

Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations .........................7

Limitations ......................................................................................................................................................9

Summary .......................................................................................................................................................11

Selected References ..................................................................................................................................11

Appendix 1. U.S. Geological Survey Streamflow Gages Used for Regression Analysis 

for Dry Season Mean Monthly Flow and Harmonic Mean Flow ...............................15

Appendix 2. Definitions of Basin Characteristics Evaluated as Response Variables for 

Inclusion in the Regression Analysis .............................................................................19

Appendix 3. Dry Season Mean Monthly Flow, Harmonic Mean Flow, and Explanatory 

Variable Values for Final Regression Equations ..........................................................21

Figures

1. Map showing U.S. Geological Survey streamflow gages used for dry season 

mean monthly flow and harmonic mean flow regressions ...................................................3

2. Map showing physiographic sections of Arkansas ...............................................................6

Tables

1. Range of basin characteristic values used to develop dry season mean monthly 

flow and harmonic mean flow regression equations for unregulated streams in 

Arkansas .......................................................................................................................................4

2. Regression equations and ancillary regression diagnostics for dry season mean 

monthly flow estimation in Arkansas .......................................................................................8

3. Regression equations and ancillary regression diagnostics for harmonic mean 

flow estimation in two regions identified in Arkansas ..........................................................8

4. Values needed to determine the 90-percent prediction intervals for estimates 

obtained from regression equations using covariance matrices in Arkansas ...............10
iv

Conversion Factors

Inch/Pound to International System of Units

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2

) 259.0 hectare (ha)

square mile (mi2

) 2.590 square kilometer (km2) 

Flow rate

cubic foot per second (ft3

/s) 0.02832 cubic meter per second (m3/s)

million gallons per day (Mgal/d) 0.04381 cubic meters per second (m3

/s)

Hydraulic gradient

foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)

Datum

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Abbreviations

ADEQ Arkansas Department of Environmental Quality

EPA U.S. Environmental Protection Agency

GIS Geographic Information System

MLR multiple-linear-regression

NPDES National Pollutant Discharge Elimination System

NRMSE normalized root mean square error

NWIS National Water Information System

OLS ordinary-least-squares

PBIAS percent bias

QAH harmonic mean flow

R2 coefficient of determination

RSE residual standard error

USGS U.S. Geological Survey

WLS weighted-least-squares
Dry Season Mean Monthly Flow and Harmonic Mean Flow 

Regression Equations for Selected Ungaged Basins in 

Arkansas

By Brian K. Breaker

Abstract

The U.S. Geological Survey, in cooperation with the 

Arkansas Department of Environmental Quality, Southwestern 

Energy, the Arkansas Natural Resources Commission, and the 

Arkansas Game and Fish Commission, developed regression 

equations for estimation of dry season mean monthly flows 

and harmonic mean flows that are representative of natural 

streamflow conditions at selected ungaged basins in Arkansas. Observed values of dry season mean monthly flow and 

harmonic mean flow computed from daily-mean flow data 

were used with basin characteristics to identify significant 

explanatory variables for multiple-linear-regression equations to estimate predicted values of dry season mean monthly 

flow and harmonic mean flow. Five dry season mean monthly 

flow regression equations and two harmonic mean flow 

regression equations were developed using dry season mean 

monthly flows and harmonic mean flows established for 91 

and 93 U.S. Geological Survey continuous-record streamflowgaging stations, respectively. The dry season in Arkansas 

is defined as the months of July through November for this 

study. For harmonic mean flow calculations and regression 

equations, the study area is composed of the SpringfieldSalem Plateaus (Arkansas and Missouri), Boston Mountains, 

Arkansas Valley, Ouachita Mountains (Arkansas and Oklahoma), and West Gulf Coastal Plain (Arkansas) physiographic 

sections. All continuous-record streamflow-gaging stations 

used to compute dry season mean monthly flows were located 

within Arkansas. 

Equations for two regions were found to be statistically 

significant for developing regression equations for estimating harmonic mean flows at ungaged basins; thus, equations 

are applicable only to streams in those respective regions in 

Arkansas. Regression equations for dry season mean monthly 

flows are applicable only to streams located throughout 

Arkansas. All regression equations are applicable only to 

unaltered streams where flows were not significantly affected 

by regulation, diversion, or urbanization. The median number 

of years used for dry season mean monthly flow calculation was 43, and the median number of years used for harmonic mean flow calculations was 34 for region 1 and 43 for 

region 2. 

Introduction

Water use in the State of Arkansas was estimated to be 

about 11,500 million gallons per day in 2010 (A.L. Pugh 

and Terrance W. Holland, U.S. Geological Survey, written 

commun., 2014). Groundwater and surface-water sources 

comprised 69 percent and 31 percent, respectively, of total 

water use. Total water use increased in Arkansas by 435 

percent between 1965 and 2010 (A.L. Pugh and Terrance W. 

Holland, U.S. Geological Survey, written commun., 2014). 

As population and agriculture in Arkansas continue to 

increase, more stress is placed on streams in the State. The 

Arkansas Department of Environmental Quality (ADEQ) 

protects and regulates water resources of Arkansas through 

various programs (http://www.adeq.state.ar.us/Default.htm) 

involving permitting. Through issuance of National Pollutant 

Discharge Elimination System (NPDES) permits, the ADEQ 

is responsible for ensuring waters of the State of Arkansas 

are suitable for sustaining diverse biological communities 

and do not simultaneously pose threats to human health. The 

NPDES permits are required for industrial, municipal, or 

other facilities that discharge treated wastewater directly to 

surface waters. The U.S. Environmental Protection Agency 

(EPA) recommends that the long-term harmonic mean flow 

be used for assessing potential human health effects because 

it provides a more conservative estimate than the arithmetic 

mean flow. The harmonic mean flow is determined by taking 

the reciprocal of the mean value of the reciprocal of individual values.

The U.S. Geological Survey (USGS), in cooperation 

with the ADEQ, Southwestern Energy, the Arkansas Natural 

Resources Commission, and the Arkansas Game and Fish 

Commission, developed regional regression equations for 

estimation of dry season mean monthly flows and harmonic 

mean flows that are representative of natural streamflow 

conditions, defined as streamflows that are not affected by 

regulation, diversion, or urbanization (referred to hereinafter 

as unaltered) at ungaged basins in Arkansas. A continuousrecord streamflow-gaging station (referred to hereinafter 

as a streamflow gage) is a location on a stream where gage 

height is recorded continuously and for which daily-mean 

streamflow is computed (Funkhouser and others, 2008). 
2 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas

Dry season mean monthly flows and harmonic mean flows 

are routinely needed for ungaged streams for water-quality 

regulation, stream-related structural design, wastewater management, and stream-hazard identification. These two streamflow statistics, in particular, are useful for setting criteria for 

wastewater-treatment plant effluent and allowable pollutant 

loads to meet water-quality standards for human health criteria, irrigation, recreation, and wildlife conservation. For the 

estimation of these two statistics at ungaged streams, regional 

regression equations were developed using statistical relations 

that exist between streamflow data collected at streamflow 

gages and geologic, climatic, physical, and statistical variables 

for watersheds that contribute flow to a streamflow gage (Eash 

and Barnes, 2012). 

Purpose and Scope

The purpose of this report is to present regression 

equations for estimation of dry season mean monthly flows 

and harmonic mean flows (QAH) at ungaged basins in 

Arkansas. Dry season mean monthly flows and QAH computed from USGS streamflow gages are also presented. 

Equations developed during this study also are intended for 

delivery in the USGS StreamStats program (U.S. Geological 

Survey, 2012a,b). The StreamStats program allows users to 

select a point on a stream in an interactive map and then automatically delineates the watershed for that point and computes 

selected statistics for the watershed (Eash and Barnes, 2012). 

The StreamStats program will provide users the ability to 

estimate dry season mean monthly flow, QAH, and associated 90 percent prediction intervals for ungaged streams in 

Arkansas.

Previous Studies

Six studies have been conducted for estimation of lowflow characteristics in Arkansas beginning with Hines (1965). 

The most recent study by Funkhouser and others (2008) used 

data collected through the 2005 water year, defined as the 

period from October 1 of a given year to September 30 of the 

following year designated by the calendar year in which it 

ends. Previous reports for low-flow statistics in Arkansas 

have focused primarily on development of regional regression 

equations for low-flow frequencies, such as the 7-day, 2-year 

low flow (Q7,2) and the 7-day,10-year low flow (Q7,10). No 

previous studies in Arkansas have developed regional regression equations to estimate dry season mean monthly flow or 

QAH. 

Methods of Analysis for Data from U.S. 

Geological Survey Continuous-Record 

Streamflow Gages

Data used for this report are from 113 streamflow gages 

in Arkansas, Oklahoma, and Missouri (fig. 1); however, 

streamflow gages from neighboring States were used only for 

QAH because explanatory variables used in regression equations for dry season mean monthly flow were spatially limited 

to within Arkansas. Streamflow gages from neighboring 

States were used to improve the representativeness of QAH 

and basin characteristics found in the Arkansas border areas 

and to provide better estimates of the error of the regression 

equations for ungaged sites near the Arkansas border. Streamflow gages located on unaltered streams (fig. 1; app. 1) with a 

minimum of 15 water years of daily-mean flows were initially 

selected for evaluation in the study. However, some gages with 

12 water years of daily-mean flow data were added to enhance 

the spatial distribution of streamflow gages used to develop 

regression equations. Daily-mean flow data collected through 

the 2013 water year were retrieved for the 113 streamflow 

gages from the USGS National Water Information System 

(NWIS) database (U.S. Geological Survey, 2001).

Basin Characteristics

For this study, 47 basin characteristics (app. 2) were 

evaluated as potential explanatory variables for use in regression equations for estimating dry season mean monthly flow 

and QAH. The geographic information system (GIS) derived 

characteristics were selected to represent the varying geologic, 

climatic, physical, and statistical properties of the watersheds 

for the 113 streamflow gages. 
Methods of Analysis for Data from U.S. Geological Survey Continuous-Record Streamflow Gages 3

Figure 1. U.S. Geological Survey streamflow gages used for dry season mean monthly flow and harmonic mean flow regressions. 

ARKANSAS

LOUISIANA

TEXAS

OKLAHOMA

TENNESSEE

MISSISSIPPI

MISSOURI

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92#

Harmonic mean flow region 1

Harmonic mean flow region 2

Shaded relief derived from U.S. Geological Survey

 National Elevation Dataset, 10-meter grid (2011)—

 Elevation data for basins in Arkansas used for analysis 

 and regionalization of dry season mean monthly flow 

 and harmonic mean flow

Selected U.S. Geological Survey streamflow gage

 used for analysis and regionalization of dry

 season mean monthly flow and harmonic 

 mean flow in Arkansas with map identification

 number (appendix 1)

EXPLANATION

0 20 40 60 80 100 KILOMETERS

0 20 40 60 80 100 MILES

95° 94° 93° 92° 91° 90°

37°

36°

35°

34°

33°

Base from the U.S. Geological Survey digital data, 2011, 1:100,000

USA Contiguous Albers Equal Area Conic USGS version

North American Datum 1983
4 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas

Regression Techniques

Ordinary-least-squares (OLS) regressions were used 

to develop initial multiple-linear-regression (MLR) equations that were used for the initial analysis of streamflow 

data. Final equations for regional regressions were developed 

using weighted-least-squares (WLS) regressions. Logarithmic 

transformations (base 10) were used on all response variables 

(mean monthly flow and QAH) and tested for select explanatory variables (table 1) for the final regression equations. 

Logarithmic transformations were applied based on graphical 

comparisons of response variables and explanatory variables. 

Only drainage area was log transformed for the final regression equations. Other transformations were used for select 

explanatory variables (percent Ordovician and Mississippian) 

as necessary to increase linearity between the response variable and explanatory variables. The response variable was 

assumed to be a linear function of the explanatory variables.

MLR equations followed the general form

Yi = b0 + b1X1 + b2X2 + ··· + bnXn + ei (1)

where

Yi is the response variable for site i,

X1 to Xn are the n explanatory variables for site i,

b0 to bn are the n + 1 regression model coefficients, 

and

ei is the residual error for site i.

A base-10 logarithmic transformation of the MLR has the 

form of

logYi = b0 + b1logX1+ b2logX2 + ··· + bnlogXn + ei (2)

where

log is the base-10 logarithmic transformation of 

the variable.

The algebraic equivalence of equation 2 after transformation 

back to its original units is

0 1 2

1 2 1 0 10 b b b bn ei Y X X X i = ... n (3)

Tasker (1980) reported that OLS regression assumes that 

the time-sampling variance in the response-variable estimates 

is the same for each streamflow gage used in the analysis. As 

a result, this would imply that all observations of the response 

variable are equally reliable. This assumption is not always 

satisfied in hydrologic regressions because of the reliability of 

the record available for computation of the response variable 

based on the length of the observed streamflow record (Tasker, 

1980; Eash and Barnes, 2012). The WLS regression adjusts for 

the variation in the reliability of the response-variable estimates by using a weight for each streamflow gage to account 

for differences in the period of record available for computation of the response variable (Eng and others, 2009; Eash and 

Barnes, 2012). 

Table 1. Range of basin characteristic values used to develop dry season mean monthly flow and harmonic mean flow regression 

equations for unregulated streams in Arkansas.

[Slope1085, slope of channel in feet per mile between points at 10 and 85 percent of the longest flow path from the outlet]

Dry season mean monthly streamflow

Drainage area Mean dry season total runoff

Minimum First 

quartile Median Mean Third quartile Maximum Minimum First quartile Median Mean Third quartile Maximum

4.1 89.0 241 464 528 7,350 3.6 4.0 4.3 4.3 4.6 5.6

Harmonic mean flow region 1

Drainage area Base-flow index Slope1085

Minimum

First 

quartile

Median Mean

Third 

quartile

MaximumMinimum

First 

quartile

Median Mean

Third 

quartile

MaximumMinimum

First 

quartile

Median Mean

Third 

quartile

Maximum

8.0 99.8 304 779 784 7,350 0.3 0.4 0.5 0.5 0.5 0.7 2.0 7.2 9.2 15.1 17.2 95.8

Harmonic mean flow region 2

Drainage area Base-flow index Percent Ordovician and Mississippian

Minimum

First 

quartile

Median Mean

Third 

quartile

MaximumMinimum

First 

quartile

Median Mean

Third 

quartile

MaximumMinimum

First 

quartile

Median Mean

Third 

quartile

Maximum

4.1 83.0 210 341 410 2,090 0.1 0.2 0.2 0.3 0.3 0.4 0.0 0.0 6.0 24.8 47.0 100
Methods of Analysis for Data from U.S. Geological Survey Continuous-Record Streamflow Gages 5

Candidate regressions were selected for WLS by testing all possible combinations of the 42 explanatory variables 

(app. 2) using the allReg() function contained within the

“USGSwsStats” package (Lorenz, 2013b) for R, an integrated 

suite of software facilities for data manipulation, calculation, 

and graphical display (R Core Team, 2014). The best candidate regression equations were selected based on the lowest 

values of Mallow’s Cp and analysis of multicollinearity using 

the variance inflation factor (Helsel and Hirsch, 2002). The 

WLS regressions were repeatedly performed in R (R Core 

Team, 2014) to reduce the number of explanatory variables to 

those significant at the 95-percent confidence interval. Regression diagnostics, including residual standard error, coefficient 

of determination (R2), multicollinearity, Cook’s D, leverage, 

and graphical relations (Helsel and Hirsch, 2002), were used 

to evaluate the performance of WLS regressions.

Dry Season Mean Monthly Flow Data

Daily-mean streamflow data for 91 USGS streamflow gages were used to compute monthly-mean flows. A 

mean monthly flow is computed as the arithmetic mean of 

all monthly-mean flows for a given month of the year for a 

selected period of record for a streamflow gage. A monthlymean flow is computed as the arithmetic mean of the dailymean flows for a given month of the year. Regression analysis 

was performed with ensembles for five critical, dry season 

months, July through November. 

Five regression equations were developed for the calculation of dry season mean monthly flows during the months of 

July through November. All five equations contain at least one 

significant explanatory variable (table 1) derived from a previous runoff study in Arkansas (Pugh and Westerman, 2014). 

The median number of years of record used for calculation 

of dry season mean monthly flow at the 91 streamflow gages 

was 43 (app. 1). Equations for estimation of dry season mean 

monthly flow are applicable only at ungaged, unaltered stream 

locations in Arkansas.

Harmonic Mean Flow Data

Equations for two regions were found to be statistically 

significant for developing regression equations for estimating 

harmonic mean flow at selected ungaged basins in Arkansas. 

Of the 93 streamflow gages used for QAH (fig. 1; app. 1), 33 

and 60 streamflow gages were used for the first and second 

regions, respectively. The median number of years of data 

used for QAH calculations in the WLS regression analysis was 

34 for region 1 and 43 for region 2 (app. 1). The WLS regression equations used to estimate QAH are applicable only to 

ungaged, unaltered streams in region 1 and region 2.

For QAH calculations (app. 3), the study area is composed of the Springfield-Salem Plateaus (Arkansas and 

Missouri), Boston Mountains, Arkansas Valley, Ouachita 

Mountains (Arkansas and Oklahoma), and West Gulf Coastal 

Plain (Arkansas) physiographic sections (fig. 2). A QAH value 

was calculated for all streamflow gages used in the regression 

equations using the USGS "DVstats" package (Lorenz, 2013a) 

in R software (R Core Team, 2014), which is based on the 

EPA’s computer program for estimating design flows for use 

in water-quality studies (DFLOW) (Rossman, 1990b). The 

QAH statistic generally is smaller than the arithmetic mean 

statistic, gives more weight to lower flows, and is corrected 

for daily flow values of zero (Rossman, 1990a). The QAH is 

calculated as

1

nz 1

nz nz

t N

i

i

N N QAH N

= Q

       =               ∑

(4)

where

Qi is the daily mean streamflow, in cubic feet per 

second,

Nnz is the number of nonzero days, and

Nt is the total number of Qi values.

If Nnz equals Nt, QAH is equal to the reciprocal of the mean of 

the reciprocals of all Qi. 

Regionalization of Harmonic Mean Flow Data

Regionalization is a statistical framework used to estimate statistics at ungaged stream locations from statistics 

calculated at USGS streamflow gages (Ries, 2007). Regionalization techniques are used because streamflow statistics can 

vary substantially between regions because of differences in 

geology, climate, and physical characteristics. Regionalization 

of low-flow statistics in Arkansas was first attempted by Hines 

(1965). Subsequently, Ludwig and Tasker (1993) divided the 

western two-thirds of Arkansas into three low-flow regions of 

well sustained and poorly sustained low flow. Minor changes 

were made to the existing low-flow statistical regions by 

Funkhouser and others (2008) attributable to enhanced GIS 

capabilities for spatial data processing. No regional methods 

for mean flow estimation have been developed for Arkansas 

prior to this study.

Streamflow gages used for QAH were located on streams 

in Arkansas, Oklahoma, or Missouri. An initial OLS regression was performed on all gages selected for inclusion in a 

statewide regression analysis. Residuals from the statewide 

OLS regression were spatially analyzed and indicated the need 

for equations in two regions. 
6 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas

Figure 2. Physiographic sections of Arkansas.

ARKANSAS

LOUISIANA

TEXAS

OKLAHOMA

TENNESSEE

MISSISSIPPI

MISSOURI

Physiographic section (Fenneman, 1946)

 Arkansas Valley

Boston Mountains

East Gulf Coastal Plain

Mississippi Alluvial Plain

Osage Plains

Ouachita Mountains

Springfield-Salem Plateaus

West Gulf Coastal Plain

EXPLANATION

0 20 40 60 80 100 KILOMETERS

0 20 40 60 80 100 MILES Base from the U.S. Geological Survey digital data, 2011, 1:100,000

USA Contiguous Albers Equal Area Conic USGS version

North American Datum 1983

95° 94° 93° 92° 91° 90°

37°

36°

35°

34°

33°
Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations 7

Region 1 includes a small part of Arkansas that is located 

exclusively in the northern part of the State (fig. 1), mostly 

in the Springfield-Salem Plateaus (figs. 1 and 2). The region 

is underlain by a series of limestone and dolomite units and 

therefore exhibits numerous karst features that affect regional 

hydrology and groundwater/surface-water interaction (Ludwig 

and Tasker, 1993). Streams in region 1 often are sustained 

by numerous springs. The well-sustained flows from numerous springs are indicative of a regional source of water that is 

supplemented during extended periods of precipitation by a 

local component of groundwater recharge (Ludwig and Tasker, 

1993). 

Region 2 includes the rest of the State excluding the Mississippi Alluvial Plain. The northern part of region 2 (fig. 1) 

includes the Boston Mountains, Arkansas Valley, Ouachita 

Mountains, and parts of the Springfield Plateau physiographic 

sections (fig. 2; Fenneman, 1946). Region 2 is underlain or 

mantled by consolidated rocks consisting primarily of sandstones and shales. The primary porosity and permeability of 

these sandstones and shales have been greatly reduced by 

compaction and deep burial; therefore, only limited amounts 

of groundwater are available from secondary openings including joints and fractures. The fractures, however, do not supply 

the base flows of streams to the extent that numerous springs 

do in region 1 (Ludwig and Tasker, 1993).

The southern part of region 2 is located in the West Gulf 

Coastal Plain physiographic section, which is underlain by 

unconsolidated deposits composed of sand, silt, and clay. The 

streams in the southern part of region 2 generally do not have 

sustained base flow because (1) the stream channels are not 

incised deeply enough to intercept the water table, and (2) the 

surficial deposits typically have low permeability and porosity 

(Ludwig and Tasker, 1993).

Dry Season Mean Monthly Flow and 

Harmonic Mean Flow Regression 

Equations

Observed values of dry season mean monthly flows and 

QAH (app. 3) computed from daily-mean flow data were 

used with basin characteristics (app. 2) to identify significant 

explanatory variables (table 1) for multiple-linear-regression 

equations (tables 2 and 3) to estimate predicted values of dry 

season mean monthly flows and QAH. Predicted values were 

compared to observed values to evaluate the performance of 

the WLS regression equations. The widely used residual standard error (RSE) and adjusted correlation coefficient (Helsel 

and Hirsch, 2002) diagnostics of the regression analysis are 

provided for their respective regression equations (tables 2 and 

3). Normalized root mean square error (NRMSE) and percent 

bias (PBIAS) were additional metrics computed for all of the 

regression equations. Values for normalized root mean square 

error ranged from 33.6 to 38.4 percent for dry season mean 

monthly flow (table 2) and from 29.2 to 45.8 percent for QAH 

(table 3). The NRMSE is computed as

( )

( )

2

1

1

100

N

i i i

i

predicted observed N NRMSE

sd observed

= −

=

∑

(5)

where

sd is standard deviation,

N is the total number of comparisons, and

i is the individual value.

and PBIAS as

( ) 1

1

100

N

i i i

N

i i

predicted observed PBIAS

observed

=

=

− = ∑

∑ (6)

Of the 47 basin characteristics (app. 2), 5 were found 

to be significant explanatory variables for dry season mean 

monthly flow and QAH regressions for regions 1 and 2: 

(1) drainage area; (2) base-flow index; (3) slope 1085; the 

stream slope computed as the change in elevation in feet 

between points at 10 and 85 percent of the length in miles 

of the longest flow path from the outlet, divided by length 

between the points; (4) mean dry season total runoff; and 

(5) percent Mississippian and Ordovician surficial geology 

(app. 3). An example regression equation for QAH for region 

2 is:

logQAH = A + blogDA + cOM + dBFI (7)

where

log is the base-10 logarithmic transformation of 

the variable,

QAH is the harmonic mean flow,

A is the intercept,

DA is the drainage area, in square miles,

OM is the percent Ordovician and Mississippian 

surficial geology divided by 100 + 1,

BFI is the base-flow index, and

b, c, and d are the coefficients of regression for the 

basin characteristics used as explanatory 

variables,

Or, in the algebraic equivalence of equation 7, the regression 

equation can be transformed back to the original units

QAH = 10A(DA)b10c(OM) 10d(BFI) (8)
8 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas

Table 3. Regression equations and ancillary regression diagnostics for harmonic mean flow estimation in two regions identified in 

Arkansas.

[QAH, harmonic mean flow; DRNAREA, drainage area; BFI, base flow index; Slope1085, slope of channel in feet per mile between points at 10 and 85 percent 

of the longest flow path from the outlet; ORDOMISS, percent surficial geology Ordovician and Mississippian rocks divided by 100 plus 1; RSE, residual 

standard error; R2, correlation coefficient; NRMSE, normalized root mean square error; PBIAS, percent bias]

Regression equation

Number of 

streamflow 

gages used to 

develop equation

RSE Adjusted R2 NRMSE 

(percent)

PBIAS 

(percent)

Weighted-least-squares regression equation for region 1

QAH=10-2.733DRNAREA1.320102.690(BFI)100.0150(Slope1085) 33 0.233 0.93 29.2 -0.8

Weighted-least-squares regression equation for region 2

QAH=10-3.654DRNAREA1.022101.132(ORDOMISS)102.431(BFI) 60 0.295 0.82 45.8 -4.6

Table 2. Regression equations and ancillary regression diagnostics for dry season mean monthly flow estimation in Arkansas.

[DRNAREA, drainage area; DryTotRun, mean dry season total runoff; RSE, residual standard error; R2, correlation coefficient; NRMSE, normalized root mean 

square error; PBIAS, percent bias]

Regression equation 

Number of 

streamflow 

gages used 

to develop 

equation

RSE Adjusted 

R2

NRMSE 

(percent)

PBIAS 

(percent)

Weighted-least-squares regression equation for July mean monthly streamflow

July=10-1.441DRNAREA1.022100.229(DryTotRun) 91 0.198 0.89 34.1 -1.1

Weighted-least-squares regression equation for August mean monthly streamflow

August=10-1.921DRNAREA1.092100.250(DryTotRun) 91 0.262 0.84 38.4 -1.2

Weighted-least-squares regression equation for September mean monthly streamflow

September=10-1.556DRNAREA0.975100.274(DryTotRun) 91 0.197 0.88 33.6 -0.2

Weighted-least-squares regression equation for October mean monthly streamflow

October=10-0.902DRNAREA0.929100.174(DryTotRun) 91 0.193 0.87 35.6 0.3

Weighted-least-squares regression equation for November mean monthly streamflow

November=10-0.446DRNAREA0.865100.179(DryTotfRun) 91 0.180 0.87 35.0 1.0
Limitations 9

Limitations

The final regression equations are applicable only to 

streams in Arkansas that are unaltered. The range of values 

for explanatory variables used to develop the final regression 

equations for this report is listed in table 1. A measure of the 

uncertainty associated with the regression of dry season mean 

monthly flows and QAH is the prediction interval. A prediction interval is the probability that the actual value of the estimated statistic will be within a specific margin of error (Helsel 

and Hirsch, 2002). For a 90-percent prediction interval, the 

true streamflow statistic has a 90-percent probability of being 

within the margin of error. The following equation described 

by Eash and Barnes (2012), which is modified from Tasker 

and Driver (1988), can be used to compute the 90-percent 

prediction interval for the true value of a streamflow statistic 

for an ungaged site:

Q Q QT T

< < (9)

where

Q is the dry season mean monthly flow or QAH 

predicted for the ungaged site from the 

regression equation, and T is computed as

( ) /2, 10 a n p i t S

T −     = (10)

where

t

(α/2,n˗t) is the critical value from the student’s 

t-distribution at alpha level α (α=0.10 for 

the 90-percent prediction intervals; critical 

values may be obtained in many statistics 

textbooks (Iman and Conover, 1983),

n – p is the degree of freedom with n streamflow 

gages included in the regression analysis 

and p parameters in the equation (the 

number of explanatory variables plus one), 

and

Si is the standard error of prediction for site i

and is computed as

Si= [MEV + XiUX'i]0.5 (11)

where

MEV is the mean squared error from WLS 

regression equations developed for this 

study using a user-defined weighting 

matrix;

Xi is the row vector for the streamflow gage 

i, starting with the number 1, followed 

by the logarithmic values of the basin 

characteristics used in the regression;

U is the covariance matrix for the annual or 

seasonal regression coefficients; and

X'i is the matrix algebra transpose of the Xi

(Ludwig and Tasker, 1993; Ries and Friesz, 

2000).

The XiUX′i in equation 11 also is referred to as the 

sampling error variance. The values of t

(α/2,n˗p)

 and U needed to 

determine prediction intervals for estimates obtained by the 

regression equations in tables 2 and 3 are listed in table 4. 
10 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas

Table 4. Values needed to determine the 90-percent prediction intervals for estimates obtained from regression equations using 

covariance matrices in Arkansas.

[t(α/2,n-p), the critical value from Students t-distribution for the 90-percent probability used in equation 10; MEV, regression model error variance used in equation 

11; U, covariance matrix as used in equation 10; logDA, log 10 transformed drainage area; DryTotRun, mean dry season total runoff; BFI, base-flow index; 

Slope1085, slope of channel in feet per mile between points at 10 and 85 percent of the longest flow path from the outlet; OM, percent surficial geology 

Ordovician and Mississippian divided by 100 plus 1]

Response variable t

(α/2,n-p) MEV U

July mean monthly streamflow 1.8467 0.0452 (Intercept) logDA DryTotRun

(Intercept) 1.15185673 -0.09291594 -0.20827625

logDA -0.09291594 0.03838950 -0.00044198

DryTotRun -0.20827625 -0.00044198 0.04785087

August mean monthly streamflow 1.6063 0.0700 (Intercept) logDA DryTotRun

(Intercept) 1.15185673 -0.09291594 -0.20827625

logDA -0.09291594 0.03838950 -0.00044198

DryTotRun -0.20827625 -0.00044198 0.04785087

September mean monthly streamflow 1.7944 0.0457 (Intercept) logDA DryTotRun

(Intercept) 1.15185673 -0.09291594 -0.20827625

logDA -0.09291594 0.03838950 -0.00044198

DryTotRun -0.20827625 -0.00044198 0.04785087

October mean monthly streamflow 1.9042 0.0474 (Intercept) logDA DryTotRun

(Intercept) 1.15185673 -0.09291594 -0.20827625

logDA -0.09291594 0.03838950 -0.00044198

DryTotRun -0.20827625 -0.00044198 0.04785087

November mean monthly streamflow 2.2257 0.0381 (Intercept) logDA DryTotRun

(Intercept) 1.15185673 -0.09291594 -0.20827625

logDA -0.09291594 0.03838950 -0.00044198

DryTotRun -0.20827625 -0.00044198 0.04785087

Harmonic mean flow region 1 1.6937 0.0641 (Intercept) logDA BFI Slope 1085

(Intercept) 2.58006150 -0.32751084 -3.01763726 -0.01798169

logDA -0.32751084 0.15093641 -0.24450775 0.00403552

BFI -3.01763726 -0.24450775 7.31182381 0.00878366

Slope1085 -0.01798169 0.00403552 0.00878366 0.00024154

Harmonic mean flow region 2 0.6311 0.0966 (Intercept) logDA OM BFI

(Intercept) 0.87816120 -0.22420424 -0.16063462 -0.45994120

logDA -0.22420420 0.12259160 -0.00073796 -0.30059200

OM -0.16063460 -0.00073796 0.18825272 -0.28469990

BFI -0.45994120 -0.30059202 -0.28469990 6.22702050
Selected References 11

Summary

The U.S. Geological Survey (USGS), in cooperation with 

the Arkansas Department of Environmental Quality (ADEQ), 

Southwestern Energy, the Arkansas Natural Resources Commission, and the Arkansas Game and Fish Commission, developed 

regression equations for estimation of dry season mean monthly 

flows and harmonic mean flows (QAH) that are representative 

of natural streamflow conditions at selected ungaged basins in 

Arkansas. Observed values of dry season mean monthly flow 

and QAH computed from daily-mean flow data were used with 

basin characteristics to identify significant explanatory variables 

for multiple-linear-regression equations to estimate predicted 

values of dry season mean monthly flow and QAH. These two 

streamflow statistics are routinely needed for ungaged streams 

for water-quality regulation, stream-related structural design, 

wastewater management, and stream-hazard identification. Dry 

season mean monthly flow and QAH are useful for setting criteria for wastewater-treatment plant effluent and allowable pollutant loads to meet water-quality standards for human health 

criteria, irrigation, recreation, and wildlife conservation. 

Five dry season mean monthly flow regression equations 

and two QAH regression equations were developed using dry 

season mean monthly flow and QAH established for 91 and 

93 USGS continuous-record streamflow gaging stations, respectively. The dry season in Arkansas is defined as the months of 

July through November. For QAH calculations and regression 

equations, the study area is composed of the Springfield-Salem 

Plateaus (Arkansas and Missouri), Boston Mountains, Arkansas 

Valley, Ouachita Mountains (Arkansas and Oklahoma), and 

West Gulf Coastal Plain (Arkansas) physiographic sections. All 

streamflow-gaging stations used to compute dry season mean 

monthly flows were located within Arkansas. Continuousrecord streamflow-gaging stations used for this study had a 

minimum of 12 water years of daily-mean flow data. Basin 

characteristics that included geologic, climatic, physical, and 

statistical variables were computed for each basin. 

The median number of years used for dry season mean 

monthly flow calculation was 43. Regression equations for 

mean monthly flow were applicable only to stream sites located 

throughout Arkansas. The regression equations for dry season 

mean monthly flow and QAH are applicable only to unaltered 

streams where flows were not significantly affected by regulation, diversion, or urbanization.

Equations for two regions were found to be statistically 

significant for developing regression equations for estimating 

QAH at ungaged basins in Arkansas. Of the 93 continuousrecord streamflow-gaging stations used for QAH, 33 and 60 

streamflow-gaging stations were used for the first and second 

regions, respectively. The median number of years of data used 

for QAH calculations in the weighted-least-squares regression 

analysis was 34 for region 1 and 43 for region 2. The weightedleast-squares regression equations used to estimate QAH were 

applicable only to streams in their respective regions, region 1 

and region 2.

Residual standard error, adjusted correlation coefficient, 

normalized root mean square error, and percent bias were used 

to evaluate the performance of the regression equations developed for this study. Values for normalized root mean square 

error ranged from 33.6 to 38.4 percent for dry season mean 

monthly flow and from 29.2 to 45.8 percent for QAH. Equations developed during this study also are intended for delivery 

in the USGS StreamStats program. StreamStats will provide 

users the ability to estimate dry season mean monthly flow, 

QAH, and 90 percent prediction intervals for ungaged streams 

in Arkansas. 

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Appendixes 1–3 

Table 1–1. U.S. Geological Survey streamflow gages used for regression analysis for dry season mean monthly flow and harmonic mean flow.—Con[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in the column heading for 

Map 

identification 

number

Dry season 

mean 

monthly 

streamflow 

(ft3/s)

Harmonic 

mean 

flow 

region 1 

(ft3/s)

Harmonic 

mean 

flow 

region 2 

(ft3/s)

USGS 

site 

number

USGS station name

Latitude 

(decimal 

degrees)

Longitude 

(decimal 

degrees)

Begin 

date

1 ü -- -- 07047600 Tyronza River near Tyronza, Ark. 35.505082 -90.380101 10/01/1942 ü -- -- 07047942 L’Anguille River near Colt, Ark. 35.144722 -90.878056 10/01/1973 ü -- -- 07047950 L’Anguille River at Palestine, Ark. 34.972778 -90.885556 10/01/1944 ü -- ü 07048000 West Fork White River at Greenland, Ark. 35.982906 -94.172622 10/01/194

5 ü -- ü 07048600 White River near Fayetteville, Ark. 36.073056 -94.081111 10/01/196

6 ü -- ü 07048800 Richland Creek at Goshen, Ark. 36.104167 -94.007500 10/01/199

7 ü -- ü 07049000 War Eagle Creek near Hindsville, Ark. 36.200000 -93.855000 10/01/195

8 ü -- ü 07050000 White River at Beaver, Ark. 36.472293 -93.765472 10/01/190

9 ü -- ü 07050500 Kings River near Berryville, Ark. 36.427222 -93.620833 10/01/193

10 ü -- ü 07053207 Long Creek at Denver, Ark. 36.389444 -93.315833 10/01/199

11 ü -- ü 07053250 Yocum Creek near Oak Grove, Ark. 36.454444 -93.356111 10/01/199

12 -- ü -- 07053810 Bull Creek near Walnut Shade, Mo. 36.717750 -93.206806 10/01/19913 -- ü -- 07054080 Beaver Creek at Bradleyville, Mo. 36.779639 -92.907278 10/01/19914 ü -- ü 07055646 Buffalo River near Boxley, Ark. 35.938889 -93.405000 10/01/199

15 ü -- ü 07055875 Richland Creek near Witts Spring, Ark. 35.797222 -92.928889 10/01/199

16 ü -- ü 07056000 Buffalo River near St. Joe, Ark. 35.983056 -92.747222 10/01/193

17 ü -- ü 07056515 Bear Creek near Silver Hill, Ark. 35.940000 -92.713333 01/22/199

18 ü -- ü 07057000 Buffalo River near Rush, Ark. 36.117294 -92.554607 10/01/192

19 -- ü -- 07057500 North Fork River near Tecumseh, Mo. 36.623028 -92.248139 10/01/19420 -- ü -- 07058000 Bryant Creek near Tecumseh, Mo. 36.627222 -92.306056 10/01/194

21 -- ü -- 07058500 North Fork River at Tecumseh, Mo. 36.587611 -92.288856 10/01/19222 ü ü -- 07060710 North Sylamore Creek near Fifty Six, Ark. 35.991667 -92.213889 10/01/196

23 -- ü -- 07065495 Jacks Fork at Alley Spring, Mo. 37.148167 -91.443083 10/01/19924 -- ü -- 07066000 Jacks Fork at Eminence, Mo. 37.154083 -91.358167 10/01/19225 -- ü -- 07068000 Current River at Doniphan, Mo. 36.622003 -90.847623 10/01/19226 -- ü -- 07068510 Little Black River below Fairdealing, Mo. 36.631724 -90.575393 10/01/19827 ü ü -- 07069000 Black River at Pocahontas, Ark. 36.254167 -90.970278 10/01/198

28 ü ü -- 07069305 Spring River at Town Branch Bridge at Hardy, Ark. 36.313611 -91.482778 10/01/200

29 ü ü -- 07069500 Spring River at Imboden, Ark. 36.205556 -91.171667 10/01/193

30 -- ü -- 07070500 Eleven Point River near Thomasville, Mo. 36.784780 -91.492084 10/01/195

Appendix 1Table 1–1. U.S. Geological Survey streamflow gages used for regression analysis for dry season mean monthly flow and harmonic mean flow.[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in the column heading for 
Table 1–1. U.S. Geological Survey streamflow gages used for regression analysis for dry season mean monthly flow and harmonic mean flow.—Con[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in the column heading for 

Map identi- fication number Dry season mean monthly streamflow (ft3/s) Harmonic mean flow region 1 (ft3/s) Harmonic mean flow region 2 (ft3/s) USGS site number USGS station name Latitude (decimal degrees) Longitude (decimal degrees) Begin date 

31 -- ü -- 07071500 Eleven Point River near Bardley, Mo. 36.648694 -91.200833 10/01/19232 ü ü -- 07072000 Eleven Point River near Ravenden Springs, Ark. 36.346389 -91.114167 10/01/192

33 ü ü -- 07072500 Black River at Black Rock, Ark. 36.102500 -91.097778 10/01/192

34 ü ü -- 07073000 Strawberry River near Evening Shade, Ark. 36.098959 -91.608474 10/01/193

35 ü ü -- 07073500 Piney Fork at Evening Shade, Ark. 36.080626 -91.610974 10/01/193

36 ü ü -- 07074000 Strawberry River near Poughkeepsie, Ark. 36.111111 -91.449444 10/01/193

37 ü -- ü 07075000 Middle Fork of Little Red River at Shirley, Ark. 35.656667 -92.292778 10/01/193

38 ü -- ü 07075300 South Fork of Little Red River at Clinton, Ark. 35.586944 -92.451389 10/01/196

39 ü -- ü 07075500 South Fork Little Red River near Clinton, Ark. 35.566744 -92.383490 10/01/193

40 ü -- -- 07077380 Cache River at Egypt, Ark. 35.857500 -90.933056 10/01/19641 ü -- -- 07077500 Cache River at Patterson, Ark. 35.269722 -91.236389 10/01/19242 ü -- -- 07077555 Cache River near Cotton Plant, Ark. 35.035556 -91.322500 10/01/19843 ü -- -- 07077950 Big Creek at Poplar Grove, Ark. 34.555656 -90.845669 10/01/19744 -- ü -- 07189000 Elk River near Tiff City, Mo. 36.631461 -94.586889 10/01/19345 -- ü -- 07189540 Cave Springs Branch near South West City, Mo. 36.547297 -94.618000 10/01/19946 -- ü -- 07189542 Honey Creek near South West City, Mo. 36.548889 -94.683611 10/01/19947 ü ü -- 07191160 Spavinaw Creek near Maysville, Ark. 36.364523 -94.551330 10/01/200

48 ü ü -- 07191179 Spavinaw Creek near Cherokee City, Ark. 36.342024 -94.587720 10/01/200

49 -- ü -- 07191220 Spavinaw Creek near Sycamore, Okla. 36.334722 -94.641389 10/01/19650 ü ü -- 07194800 Illinois River at Savoy, Ark. 36.103056 -94.344444 10/01/197

51 ü ü -- 07195400 Illinois River at Highway 16 near Siloam Springs Ark. 36.144722 -94.494722 10/01/197

52 ü ü -- 07195430 Illinois River South of Siloam Springs, Ark. 36.108611 -94.533333 10/01/199

53 ü ü -- 07195800 Flint Creek at Springtown, Ark. 36.256111 -94.433611 10/01/196

54 -- ü -- 07195855 Flint Creek near West Siloam Springs, Okla. 36.216111 -94.605278 10/01/19755 ü ü -- 07196900 Baron Fork at Dutch Mills, Ark. 35.880000 -94.486389 10/01/195

56 -- ü -- 07197360 Caney Creek near Barber, Okla. 35.785091 -94.856340 10/01/19957 ü -- ü 07247000 Poteau River at Cauthron, Ark. 34.918889 -94.299444 10/01/193

58 -- -- ü 07247500 Fourche Maline near Red Oak, Okla. 34.912599 -95.155799 10/01/193

59 ü -- ü 07249400 James Fork near Hackett, Ark. 35.162500 -94.406944 10/01/195

60 -- -- ü 07249413 Poteau River near Pama, Okla. 35.165653 -94.653002 10/01/198

61 ü -- ü 07249500 Cove Creek near Lee Creek, Ark. 35.722306 -94.407992 10/01/195

62 -- -- ü 07249985 Lee Creek near Short, Okla. 35.517222 -94.464167 10/01/193
Table 1–1. U.S. Geological Survey streamflow gages used for regression analysis for dry season mean monthly flow and harmonic mean flow.—Con[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in the column heading for 

Map 

identification 

number

Dry season 

mean 

monthly 

streamflow 

(ft3/s)

Harmonic 

mean 

flow 

region 1 

(ft3/s)

Harmonic 

mean 

flow 

region 2 

(ft3/s)

USGS 

site 

number

USGS station name

Latitude 

(decimal 

degrees)

Longitude 

(decimal 

degrees)

Begin 

date

63 ü -- ü 07250000 Lee Creek near Van Buren, Ark. 35.494533 -94.449659 10/01/193

64 -- -- ü 07250935 Jones Creek at Winfrey, Ark. 35.735833 -94.103056 10/01/200

65 ü -- ü 07251000 Frog Bayou near Mountainburg, Ark. 35.660361 -94.149094 10/01/193

66 ü -- ü 07252000 Mulberry River near Mulberry, Ark. 35.576944 -94.015278 10/01/193

67 ü -- -- 07252500 Sixmile Creek subwatershed 6 near Chismville, 

Ark.

35.208989 -93.878247 10/01/195

68 ü -- -- 07253000 Sixmile Creek at Chismville, Ark. 35.220925 -93.939091 10/01/19569 ü -- -- 07253500 Sixmile Creek near Branch, Ark. 35.248703 -93.974647 10/01/195

70 ü -- -- 07255000 Sixmile Creek at Caulksville, Ark. 35.301478 -93.854366 10/01/19571 ü -- -- 07255500 Hurricane Creek near Branch, Ark. 35.350572 -93.934392 10/01/19572 ü -- ü 07256000 Hurricane Creek near Caulksville, Ark. 35.346889 -93.863058 10/01/195

73 ü -- ü 07256500 Spadra Creek at Clarksville, Ark. 35.468333 -93.463056 10/01/195

74 ü -- ü 07257000 Big Piney Creek near Dover, Ark. 35.549525 -93.158508 10/01/195

75 ü -- ü 07257006 Big Piney Creek at Highway 164 near Dover, Ark. 35.505833 -93.181389 10/01/199

76 ü -- ü 07257500 Illinois Bayou near Scottsville, Ark. 35.466389 -93.041111 10/01/194

77 ü -- ü 07258500 Petit Jean River near Booneville, Ark. 35.106944 -93.923611 10/01/193

78 ü -- ü 07259500 Petit Jean River near Waveland, Ark. 35.104813 -93.631582 10/01/193

79 ü -- ü 07260000 Dutch Creek at Waltreak, Ark. 34.986944 -93.613056 10/01/194

80 ü -- ü 07260500 Petit Jean River at Danville, Ark. 35.058611 -93.395556 10/01/191

81 ü -- ü 07261000 Cadron Creek near Guy, Ark. 35.298611 -92.403889 10/01/195

82 ü -- ü 07261500 Fourche LaFave River near Gravelly, Ark. 34.872500 -93.657222 10/01/193

83 ü -- ü 07262500 Fourche LaFave River near Nimrod, Ark. 34.950646 -93.154623 10/01/193

84 ü -- ü 07263000 South Fourche LaFave River near Hollis, Ark. 34.911944 -93.056111 10/01/194

85 ü -- ü 07263295 Maumelle River at Williams Junction, Ark. 34.876111 -92.774444 10/01/198

86 ü -- -- 07264000 Bayou Meto near Lonoke, Ark. 34.736667 -91.915833 10/01/19587 -- -- ü 07337900 Glover River near Glover, Okla. 34.097607 -94.902167 10/01/196

88 ü -- ü 07339500 Rolling Fork near DeQueen, Ark. 34.047500 -94.412778 10/01/194

89 ü -- ü 07340300 Cossatot River near Vandervoort, Ark. 34.380000 -94.236389 10/01/196

90 ü -- ü 07340500 Cossatot River near DeQueen, Ark. 34.045000 -94.212500 10/01/194

91 ü -- -- 07341000 Saline River near Dierks, Ark. 34.096111 -94.085000 10/01/19692 ü -- -- 07349430 Bodcau Creek at Stamps, Ark. 33.366791 -93.522399 10/01/19393 ü -- ü 07356000 Ouachita River near Mount Ida, Ark. 34.610000 -93.697500 10/01/194

94 ü -- ü 07356500 South Fork Ouachita River at Mount Ida, Ark. 34.560375 -93.636026 10/01/194
Table 1–1. U.S. Geological Survey streamflow gages used for regression analysis for dry season mean monthly flow and harmonic mean flow.—Con[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in the column heading for 

Map identi- fication number Dry season mean monthly streamflow (ft3/s) Harmonic mean flow region 1 (ft3/s) Harmonic mean flow region 2 (ft3/s) USGS site number USGS station name Latitude (decimal degrees) Longitude (decimal degrees) Begin date 

95 ü -- -- 07359800 Caddo River near Alpine, Ark. 34.266763 -93.362681 10/01/19396 ü -- ü 07360200 Little Missouri River near Langley, Ark. 34.311667 -93.899722 10/01/199

97 ü -- ü 07360800 Muddy Fork Creek near Murfreesboro, Ark. 34.083443 -93.752128 10/01/194

98 ü -- ü 07361000 Little Missouri River near Murfreesboro, Ark. 34.048721 -93.720183 10/01/192

99 ü -- ü 07361500 Antoine River at Antoine, Ark. 34.038889 -93.418056 10/01/195

100 ü -- ü 07361600 Little Missouri River near Boughton, Ark. 33.878163 -93.304616 10/01/193

101 ü -- ü 07362100 Smackover Creek near Smackover, Ark. 33.375278 -92.776667 10/01/196

102 ü -- ü 07362500 Moro Creek near Fordyce, Ark. 33.792222 -92.333333 10/01/195

103 ü -- ü 07362587 Alum Fork Saline River near Reform, Ark. 34.797500 -92.933889 10/01/198

104 ü -- ü 07363000 Saline River at Benton, Ark. 34.567778 -92.610278 10/01/195

105 ü -- ü 07363300 Hurricane Creek near Sheridan, Ark. 34.319541 -92.344597 10/01/196

106 ü -- ü 07363400 Hurricane Creek below Sheridan, Ark. 34.228611 -92.372500 10/01/200

107 ü -- ü 07363500 Saline River near Rye, Ark. 33.700833 -92.025833 10/01/193

108 ü -- -- 07364133 Bayou Bartholomew at Garrett Bridge, Ark. 33.866389 -91.656111 10/01/198109 ü -- -- 07364150 Bayou Bartholomew near McGehee, Ark. 33.627778 -91.445833 10/01/193

110 ü -- -- 07364185 Bayou Bartholomew near Portland, Ark. 33.235556 -91.535556 10/01/199

111 ü -- ü 07365800 Cornie Bayou near Three Creeks, Ark. 33.038056 -92.940556 10/01/195

112 ü -- ü 07365900 Three Creeks near Three Creeks, Ark. 33.067082 -92.884050 10/01/195

113 ü -- -- 07369680 Bayou Macon at Eudora, Ark. 33.100278 -91.254444 10/01/198
Appendix 2 19

Appendix 2. Definitions of Basin Characteristics Evaluated as Response 

Variables for Inclusion in the Regression Analysis

Appendix 2

Annual precipitation, in inches, is the average annual precipitation for the drainage basin as computed from PRISM 

(Prism Climate Group, 2012) data for 1951–2011.

August average precipitation, in inches, is the basin average for the month of August averaged from PRISM (Prism 

Climate Group, 2012) data for 1981–2010.

Average basin elevation, in feet, is the average elevation of 

the basin as determined from the National Elevation Dataset 

(U.S. Geological Survey, 2011) 10 meter grid.

Base flow Index (BFI), dimensionless, is the mean ratio of 

base flow to annual streamflow from the USGS kriged BFI 

grid (Falcone and others, 2010) as an averaged value for the 

basin.

Basin perimeter distance, in miles, is the distance around the 

boundary of the basin.

Basin shape factor, dimensionless, is the ratio of the total 

drainage area to the basin length.

Drainage area, in square miles, is the area measured in a horizontal plane that is enclosed by a drainage divide.

Forest, in percent, calculated from the National Land Cover 

Database as the percentage of the basin that is mixed forested 

(Jin and others, 2013).

July average precipitation, in inches, as a basin average 

for the month of July averaged from PRISM (Prism Climate 

Group, 2012) data for 1981–2010.

Longest flow path length, in miles, is the maximum flow 

distance within a basin from the start of overland flow to the 

outlet.

Maximum basin elevation, in feet, is the maximum elevation 

of the basin computed from the National Elevation Dataset 

(U.S. Geological Survey, 2011) 10 meter grid.

Mean annual groundwater runoff, in inches, is the portion 

of the total runoff at the outlet from seepage of water from the 

ground into a stream channel as computed from geographic 

information system (GIS) grid from Pugh and Westerman 

(2014).

Mean annual precipitation 1951–2011, in inches, at the 

basin outlet is the average annual precipitation as determined from PRISM (Prism Climate Group, 2012) data for 

1951–2011.

Mean annual precipitation 1971–2000, in inches, at the 

basin centroid and averaged for the basin is the average annual 

precipitation as determined from PRISM (Prism Climate 

Group, 2012) data for 1971–2000.

Mean annual surface runoff, in inches, is the portion of the 

total runoff at the outlet that travels over the land surface into 

the stream channel as computed from GIS grid data from Pugh 

and Westerman (2014).

Mean annual total runoff, in inches, is the total runoff at the 

outlet that travels over the land surface and from seepage of 

water from the ground into the stream channel as computed 

from GIS grid data from Pugh and Westerman (2014).

Mean dry season groundwater runoff, in inches, is the 

portion of the total runoff at the outlet from seepage of water 

from the ground into a stream channel for the months of June 

through November as computed from GIS grid data from Pugh 

and Westerman (2014).

Mean dry season precipitation, in inches, is the average 

precipitation for the months of July through November averaged over the drainage basin as computed from PRISM (Prism 

Climate Group, 2012) data for 1951–2011.

Mean dry season surface runoff, in inches, is the portion of 

the total runoff at the outlet that travels over the land surface into the stream channel for the months of June through 

November as computed from GIS grid data from Pugh and 

Westerman (2014).

Mean dry season total runoff, in inches, is the total runoff at 

the outlet that travels over the land surface and from seepage of water from the ground into the stream channel for the 

months of June through November as computed from GIS grid 

data from Pugh and Westerman (2014).

Mean wet season groundwater runoff, in inches, is the portion of the total runoff at the outlet from seepage of water from 

the ground into a stream channel for the months of December 

through May as computed from GIS grid data from Pugh and 

Westerman (2014).

Mean wet season precipitation, in inches, is the average 

precipitation for the months of December through June averaged over the drainage basin as computed from PRISM (Prism 

Climate Group, 2012) data 1951–2011.

Mean wet season surface runoff, in inches, is the portion 

of the total runoff at the outlet that travels over the land 

surface into the stream channel for the months of December 

through May as computed from GIS grid data from Pugh and 

Westerman (2014).

Mean wet season total runoff, in inches, is the total runoff at 

the outlet that travels over the land surface and from seepage of water from the ground into the stream channel for the 

months of December through May as computed from GIS grid 

data from Pugh and Westerman (2014).

Minimum basin elevation, in feet, is the maximum elevation 

of the basin computed from the National Elevation Dataset 

(U.S. Geological Survey, 2011) 10 meter grid.

November average precipitation, in inches, as a basin average for the month of November averaged from PRISM (Prism 

Climate Group, 2012) data for 1981–2010.
20 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas

October average precipitation, in inches, as a basin average for the month of October averaged from PRISM (Prism 

Climate Group, 2012) data for 1981–2010.

Outlet elevation, in feet, is the elevation at the gage location 

computed from the National Elevation Dataset (U.S. Geological Survey, 2011) 10 meter grid.

Percent Cretaceous (K), is the percentage of the basin in 

which Cretaceous sedimentary rocks dominate the surface of 

the basin as computed from GIS grid data created by Reed and 

Bush (2005).

Percent Paleozoic (lPz), is the percentage of the basin in 

which lower Paleozoic sedimentary rocks dominate the surface of the basin as computed from GIS grid data created by 

Reed and Bush (2005).

Percent Mississippian, is the percentage of the basin in 

which Mississippian-age rocks dominate the surface of the 

basin as computed from GIS grid data from Haley and others 

(1993). 

Percent Middle Paleozoic (mPz), is the percentage of the 

basin in which Middle Paleozoic sedimentary rocks dominate 

the surface of the basin as computed from GIS grid data created by Reed and Bush (2005).

Percent Ordovician, is the percentage of the basin in which 

Ordovician-age rocks dominate the surface of the basin as 

computed from GIS grid data from Haley and others (1993).

Percent Ordovician and Mississippian, is the percentage of 

the basin in which Mississippian and Ordovician-age rocks 

dominate the surface of the basin as computed from GIS grid 

data from Haley and others (1993).

Percent Paleogene (pgT), is the percentage of the basin in 

which Paleogene sedimentary rocks dominate the surface of 

the basin as computed from GIS grid data created by Reed and 

Bush (2005).

Percent Quaternary (Q), is the percentage of the basin in 

which Quaternary deposits dominate the surface of the basin 

as computed from GIS grid data created by Reed and Bush 

(2005).

Percent Upper Paleozoic (uPz), is the percentage of the basin 

in which Upper Paleozoic sedimentary rocks dominate the 

surface of the basin as computed from GIS grid data created 

by Reed and Bush (2005).

Percent Middle Proterozoic (Yv), is the percentage of the 

basin in which Middle Proterozoic volcanic rocks dominate 

the surface of the basin as computed from GIS grid data created by Reed and Bush (2005).

Relief, in feet, is the maximum basin elevation minus the 

minimum basin elevation computed from the National Elevation Dataset (U.S. Geological Survey, 2011) 10 meter grids.

September average precipitation, in inches, as a basin average for the month of September averaged from PRISM (Prism 

Climate Group, 2012) data for 1981–2010.

Slope, in feet per mile, of the longest flow path through the 

basin.

Slope 1085, in feet per mile, is the stream slope computed as 

the change in elevation between points at 10 and 85 percent of 

length along the longest flow path from the outlet, determined 

by GIS, divided by length between the points.

Soil Permeability, in inches per hour, is the rate at which 

water flows through soil as computed from STATe Soil 

GeOgraphic (STATSGO) grid data (Schwarz and Alexander, 

1995; U.S. Department of Agriculture, 2001).

Soil hydrologic group, dimensionless, percentage of drainage 

basin in hydrologic soil group as computed from STATe Soil 

GeOgraphic (STATSGO) grid data (Schwarz and Alexander, 

1995; U.S. Department of Agriculture, 2001).

Streamflow-variability Index, dimensionless, is a measure 

of the steepness of the slope of a streamflow duration curve as 

computed at the outlet.

Sum of stream lengths for basin, in miles, is the total length 

of all streams in the basin combined.

Urban, percent, calculated from the National Land Cover 

Database as the percentage of the basin that is urban (Jin and 

others, 2013).
Table 3–1. Dry season mean monthly flow, harmonic mean flow, and explanatory variable values for final regression equations.—Continued [USGS, U.S. Geological Survey; ft3/s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent of the longest flow path from the outlet; mi2, squa

in., inches; --, gage was not used for the regression in the column heading for that station; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma]

USGS site 

number USGS station name

Mean 

monthly 

streamflow for 

July 

(ft3/s)

Mean 

monthly 

streamflow for 

August 

(ft3/s)

Mean 

monthly 

streamflow for 

September 

(ft3/s)

Mean 

monthly 

streamflow for 

October 

(ft3/s)

Mean 

monthly 

streamflow for 

November 

(ft3/s)

Harmonic 

mean 

flow 

(ft3/s)

Baseflow 

index

Drainage 

area 

(mi2)

Ordovic

and 

Missis

pian 

(perce

07047600 Tyronza River near Tyronza, Ark. 244 174 165 148 368 -- 0.25 332 0 

07047942 L’Anguille River near Colt, Ark. 265 284 440 332 625 -- 0.30 534 0 

07047950 L’Anguille River at Palestine, Ark. 412 442 587 374 671 -- 0.31 788 0 

07048000 West Fork White River at Greenland, Ark. 28 26 22 37 100 1.44 0.30 83.0 10 

07048600 White River near Fayetteville, Ark. 114 52 148 255 579 11.5 0.31 399 21 

07048800 Richland Creek at Goshen, Ark. 69 20 44 55 99 4.22 0.34 140 28 

07049000 War Eagle Creek near Hindsville, Ark. 129 68 70 130 199 25.0 0.33 265 36 

07050000 White River at Beaver, Ark. 660 508 408 649 976 143 0.43 1,250 48 

07050500 Kings River near Berryville, Ark. 213 116 154 209 534 39.1 0.34 529 70 

07053207 Long Creek at Denver, Ark. 37 14 30 95 74 6.52 0.38 103 79 

07053250 Yocum Creek near Oak Grove, Ark. 29 21 31 24 45 14.4 0.36 52.6 100 

07053810 Bull Creek near Walnut Shade, Mo. -- -- -- -- -- 11.9 0.38 196 0 

07054080 Beaver Creek at Bradleyville, Mo. -- -- -- -- -- 69.9 0.38 298 0 

07055646 Buffalo River near Boxley, Ark. 14 10 26 38 93 1.28 0.26 58.8 7 

07055875 Richland Creek near Witts Spring, Ark. 25 12 31 42 120 1.18 0.29 67.3 1 

07056000 Buffalo River near St. Joe, Ark. 238 164 226 340 960 118 0.34 828 50 

07056515 Bear Creek near Silver Hill, Ark. 26 18 42 38 73 11.1 0.34 78.5 47 

07057000 Buffalo River near Rush, Ark. 405 230 243 354 729 179 0.35 1,020 58 

07057500 North Fork River near Tecumseh, Mo. -- -- -- -- -- 484 0.58 562 100 

07058000 Bryant Creek near Tecumseh, Mo. -- -- -- -- -- 255 0.53 569 100 

07058500 North Fork River at Tecumseh, Mo. -- -- -- -- -- 752 0.50 1,160 0 

07060710 North Sylamore Creek near Fifty Six, Ark. 11 10 16 21 47 8.82 0.33 8.4 100 

07065495 Jacks Fork at Alley Spring, Mo. -- -- -- -- -- 101 0.47 304 0 

07066000 Jacks Fork at Eminence, Mo. -- -- -- -- -- 232 0.50 404 0 

07068000 Current River at Doniphan, Mo. -- -- -- -- -- 1,920 0.55 2,050 0 

07068510 Little Black River below Fairdealing, Mo. -- -- -- -- -- 75.4 0.51 194 0 

07069000 Black River at Pocahontas, Ark. 3,410 2,620 2,470 2,580 3,700 3,180 0.51 4,860 66 

Appendix 3Table 3–1. Dry season mean monthly flow, harmonic mean flow, and explanatory variable values for final regression equations.[USGS, U.S. Geological Survey; ft3/s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent of the longest flow path from the outlet; mi2, squar

in., inches; --, gage was not used for the regression in the column heading for that station; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma]
Table 3–1. Dry season mean monthly flow, harmonic mean flow, and explanatory variable values for final regression equations.—Continued [USGS, U.S. Geological Survey; ft3/s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent of the longest flow path from the outlet; mi2, squa

in., inches; --, gage was not used for the regression in the column heading for that station; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma] USGS site number USGS station name Mean monthly stream- flow for July (ft3/s) Mean monthly stream- flow for August (ft3/s) Mean monthly stream- flow for Septem- ber (ft3/s) Mean monthly stream- flow for October (ft3/s) Mean monthly stream- flow for November (ft3/s) Harmonic mean flow (ft3/s) Base- flow index Drainage area (mi2) Ordovic

and Missis

pian (perce

07069305 Spring River at Town Branch Bridge at Hardy, Ark. 598 500 578 754 814 575 0.49 845 100 

07069500 Spring River at Imboden, Ark. 766 579 618 686 1,170 718 0.50 1,160 100 

07070500 Eleven Point River near Thomasville, Mo. -- -- -- -- -- 19.3 0.51 358 100 

07071500 Eleven Point River near Bardley, Mo. -- -- -- -- -- 491 0.65 784 100 

07072000 Eleven Point River near Ravenden Springs, Ark. 834 685 634 625 875 734 0.52 1,120 100 

07072500 Black River at Black Rock, Ark. 5,150 4,080 3,940 4,130 6,730 4,990 0.47 7,350 76 

07073000 Strawberry River near Evening Shade, Ark. 82 43 61 58 181 32 0.47 215 99 

07073500 Piney Fork at Evening Shade, Ark. 29 19 29 27 74 7.55 0.37 99.8 100 

07074000 Strawberry River near Poughkeepsie, Ark. 186 123 168 193 407 138 0.42 472 100 

07075000 Middle Fork of Little Red River at Shirley, Ark. 64 83 103 201 423 5.21 0.28 302 15 

07075300 South Fork of Little Red River at Clinton, Ark. 28 19 60 102 242 3.05 0.28 148 0 

07075500 South Fork Little Red River near Clinton, Ark. 112 153 90 213 467 2.92 0.27 317 0 

07077380 Cache River at Egypt, Ark. 472 457 490 422 800 -- 0.32 691 2 

07077500 Cache River at Patterson, Ark. 528 448 493 481 911 -- 0.29 1,030 1 

07077555 Cache River near Cotton Plant, Ark. 670 776 633 655 1,100 -- 0.30 1,160 1 

07077950 Big Creek at Poplar Grove, Mo. 150 203 198 186 491 -- 0.32 374 0 

07189000 Elk River near Tiff City, Mo. -- -- -- -- -- 199 0.46 853 100 

07189540 Cave Springs Branch near South West City, Mo. -- -- -- -- -- 3.12 0.46 8.0 100 

07189542 Honey Creek near South West City, Mo. -- -- -- -- -- 16.0 0.46 48.7 100 

07191160 Spaviw Creek near Maysville, Ark. 53 36 33 43 38 29.3 0.46 88.8 100 

07191179 Spaviw Creek near Cherokee City, Ark. 77 33 77 79 164 35.4 0.46 103 100 

07191220 Spaviw Creek near Sycamore, Okla. -- -- -- -- -- 33.1 0.48 132 100 

07194800 Illinois River at Savoy, Ark. 77 33 77 79 164 30.5 0.41 167 74 

07195400 Illinois River at Highway 16 near Siloam Springs Ark. 377 268 386 307 409 258 0.43 509 89 

07195430 Illinois River South of Siloam Springs, Ark. 460 271 350 368 507 282 0.43 568 90 

07195800 Flint Creek at Springtown, Ark. 9.7 7.5 8.5 11 17 6.01 0.48 14.9 100 

07195855 Flint Creek near West Siloam Springs, Okla. -- -- -- -- -- 14.6 0.48 56.8 0 

07196900 Baron Fork at Dutch Mills, Ark. 17 7.9 21 28 54 2.26 0.31 41.1 58 
Table 3–1. Dry season mean monthly flow, harmonic mean flow, and explanatory variable values for final regression equations.—Continued[USGS, U.S. Geological Survey; ft3/s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent of the longest flow path from the outlet; mi2, squa

in., inches; --, gage was not used for the regression in the column heading for that station; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma]

USGS site 

number USGS station name

Mean 

monthly 

streamflow for 

July 

(ft3/s)

Mean 

monthly 

streamflow for 

August 

(ft3/s)

Mean 

monthly 

streamflow for 

September 

(ft3/s)

Mean 

monthly 

streamflow for 

October 

(ft3/s)

Mean 

monthly 

streamflow for 

November 

(ft3/s)

Harmonic 

mean 

flow 

(ft3/s)

Baseflow 

index

Drainage 

area 

(mi2)

Ordovic

and 

Missis

pian 

(perce

07197360 Caney Creek near Barber, Okla. -- -- -- -- -- 23.8 0.38 90.2 100 

07247000 Poteau River at Cauthron, Ark. 61 25 53 112 269 3.27 0.18 204 0 

07247500 Fourche Maline near Red Oak, Okla. -- -- -- -- -- 1.17 0.14 120 0 

07249400 James Fork near Hackett, Ark. 49 11 31 74 149 2.55 0.20 147 0 

07249413 Poteau River near Pama, Okla. -- -- -- -- -- 70.5 0.20 1,780 0 

07249500 Cove Creek near Lee Creek, Ark. 22 10 11 13 24 0.85 0.25 34.8 11 

07249985 Lee Creek near Short, Okla. -- -- -- -- -- 3.16 0.24 434 0 

07250000 Lee Creek near Van Buren, Ark. 127 55 139 250 495 3.09 0.24 438 6 

07250935 Jones Creek at Winfrey, Ark. -- -- -- -- -- 0.74 0.23 20.5 0 

07251000 Frog Bayou near Mountainburg, Ark. 27 15 8.1 16 54 5.78 0.23 75.0 0 

07252000 Mulberry River near Mulberry, Ark. 125 73 102 190 501 4.68 0.25 374 0 

07252500 Sixmile Creek subwatershed 6 near Chismville, 

Ark.

1.6 0.7 0.82 0.51 3.7 -- 0.21 4.1 0 

07253000 Sixmile Creek at Chismville, Ark. 10 3.3 3.1 3.7 14 -- 0.20 23.8 0 

07253500 Sixmile Creek near Branch, Ark. 15 5.6 5.3 7.9 22 -- 0.20 36.3 0 

07255000 Sixmile Creek at Caulksville, Ark. 40 14 15 27 64 -- 0.19 103 0 

07255500 Hurricane Creek near Branch, Ark. 7.7 3.9 2.1 7.1 15 -- 0.21 17.7 0 

07256000 Hurricane Creek near Caulksville, Ark. 22 9.1 6.9 24 44 0.97 0.20 53.0 0 

07256500 Spadra Creek at Clarksville, Ark. 21 12 21 27 48 3.45 0.25 61.3 0 

07257000 Big Piney Creek near Dover, Ark. 69 40 51 134 393 3.97 0.27 273 3 

07257006 Big Piney Creek at Highway 164 near Dover, 

Ark.

101 57 119 166 422 2.28 0.25 297 3 

07257500 Illinois Bayou near Scottsville, Ark. 94 63 89 113 258 2.71 0.26 242 0 

07258500 Petit Jean River near Booneville, Ark. 62 30 57 80 194 1.21 0.18 241 0 

07259500 Petit Jean River near Waveland, Ark. 323 206 122 82 251 10.9 0.22 516 0 

07260000 Dutch Creek at Waltreak, Ark. 26 12 33 28 81 0.62 0.20 81.8 0 

07260500 Petit Jean River at Danville, Ark. 345 211 208 190 495 18.9 0.27 762 0 

07261000 Cadron Creek near Guy, Ark. 36 40 66 89 257 1.96 0.27 172 0 

07261500 Fourche LaFave River near Gravelly, Ark. 120 49 130 210 467 1.71 0.22 410 2 

07262500 Fourche LaFave River near Nimrod, Ark. 394 170 184 148 468 10.4 0.19 684 1 

07263000 South Fourche LaFave River near Hollis, Ark. 45 37 60 110 219 2.51 0.19 210 5 

07263295 Maumelle River at Williams Junction, Ark. 6.2 4.4 27 35 63 0.70 0.21 115 1 
Table 3–1. Dry season mean monthly flow, harmonic mean flow, and explanatory variable values for final regression equations.—Continued [USGS, U.S. Geological Survey; ft3/s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent of the longest flow path from the outlet; mi2, squa

in., inches; --, gage was not used for the regression in the column heading for that station; Ark., Arkansas; Mo., Missouri; Okla., Oklahoma] USGS site number USGS station name Mean monthly stream- flow for July (ft3/s) Mean monthly stream- flow for August (ft3/s) Mean monthly stream- flow for Septem- ber (ft3/s) Mean monthly stream- flow for October (ft3/s) Mean monthly stream- flow for November (ft3/s) Harmonic mean flow (ft3/s) Base- flow index Drainage area (mi2) Ordovic

and Missis

pian (perce

07264000 Bayou Meto near Lonoke, Ark. 55 50 81 76 253 -- 0.28 207 1 

07337900 Glover River near Glover, Okla. -- -- -- -- -- 3.69 0.18 320 0 

07339500 Rolling Fork near DeQueen, Ark. 87 56 108 114 256 4.71 0.18 183 88 

07340300 Cossatot River near Vandervoort, Ark. 80 28 72 123 206 34.8 0.23 89.1 80 

07340500 Cossatot River near DeQueen, Ark. 174 125 214 200 493 38.5 0.21 361 90 

07341000 Saline River near Dierks, Ark. 53 22 56 54 162 -- 0.21 120 90 

07349430 Bodcau Creek at Stamps, Ark. 78 19 31 50 69 -- 0.29 236 69 

07356000 Ouachita River near Mount Ida, Ark. 235 100 243 374 721 81.9 0.25 414 76 

07356500 South Fork Ouachita River at Mount Ida, Ark. 38 14 29 28 70 7.57 0.22 61.1 100 

07359800 Caddo River near Alpine, Ark. 159 92 127 146 401 -- 0.24 35.2 99 

07360200 Little Missouri River near Langley, Ark. 54 38 88 89 133 34.0 0.22 67.9 77 

07360800 Muddy Fork Creek near Murfreesboro, Ark. 50 12 72 60 133 1.88 0.19 120 50 

07361000 Little Missouri River near Murfreesboro, Ark. 486 453 425 311 460 36.6 0.21 382 57 

07361500 Antoine River at Antoine, Ark. 90 37 54 118 266 2.26 0.22 179 44 

07361600 Little Missouri River near Boughton, Ark. 652 487 628 489 1,180 84.7 0.23 1,070 41 

07362100 Smackover Creek near Smackover, Ark. 117 42 85 200 229 9.33 0.25 539 0 

07362500 Moro Creek near Fordyce, Ark. 48 22 55 97 104 1.14 0.23 241 7 

07362587 Alum Fork Saline River near Reform, Ark. 3.4 4.1 25 26 49 0.61 0.18 26.6 23 

07363000 Saline River at Benton, Ark. 150 130 307 281 677 52.1 0.23 549 83 

07363300 Hurricane Creek near Sheridan, Ark. 46 24 34 43 142 5.58 0.25 204 33 

07363400 Hurricane Creek below Sheridan, Ark. 58 58 110 270 217 4.80 0.27 262 25 

07363500 Saline River near Rye, Ark. 590 308 500 643 1,290 165 0.31 2,090 35 

07364133 Bayou Bartholomew at Garrett Bridge, Ark. 264 159 136 197 296 -- 0.35 401 0 

07364150 Bayou Bartholomew near McGehee, Ark. 225 169 174 213 369 -- 0.42 608 0 

07364185 Bayou Bartholomew near Portland, Ark. 495 281 424 644 682 -- 0.32 1,140 0 

07365800 Cornie Bayou near Three Creeks, Ark. 46 15 40 44 131 2.74 0.24 180 0 

07365900 Three Creeks near Three Creeks, Ark. 25 7.7 11 6.9 23 1.32 0.21 50.4 0 

07369680 Bayou Macon at Eudora, Ark. 235 136 127 149 141 -- 0.35 528 0 
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Breaker—Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas—SIR 2015–5031

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20155031