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
Scientific Investigations Report 2015–5031 Version 1.1, July 2015
U.S. Department of the Interior U.S. Geological Survey
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 Version 1.1, July 2015
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 First release: 2015 Revised: July 2015 (ver 1.1)
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Suggested citation: Breaker, B.K., 2015, Dry season mean monthly flow and harmonic mean flow regression equations for selected ungaged basins in Arkansas (ver. 1.1, July 2015): 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 Introduction
The U.S. Geological Survey, in cooperation with the Water use in the State of Arkansas was estimated to be Arkansas Department of Environmental Quality, Southwestern about 11,500 million gallons per day in 2010 (A.L. Pugh Energy, the Arkansas Natural Resources Commission, and the and Terrance W. Holland, U.S. Geological Survey, written Arkansas Game and Fish Commission, developed regression commun., 2014). Groundwater and surface-water sources equations for estimation of dry season mean monthly flows comprised 69 percent and 31 percent, respectively, of total and harmonic mean flows that are representative of natural water use. Total water use increased in Arkansas by 435 streamflow conditions at selected ungaged basins in Arkan- percent between 1965 and 2010 (A.L. Pugh and Terrance W. sas. Observed values of dry season mean monthly flow and Holland, U.S. Geological Survey, written commun., 2014). harmonic mean flow computed from daily-mean flow data As population and agriculture in Arkansas continue to were used with basin characteristics to identify significant increase, more stress is placed on streams in the State. The explanatory variables for multiple-linear-regression equa- Arkansas Department of Environmental Quality (ADEQ) tions to estimate predicted values of dry season mean monthly protects and regulates water resources of Arkansas through flow and harmonic mean flow. Five dry season mean monthly various programs (http://www.adeq.state.ar.us/Default.htm) flow regression equations and two harmonic mean flow involving permitting. Through issuance of National Pollutant regression equations were developed using dry season mean Discharge Elimination System (NPDES) permits, the ADEQ monthly flows and harmonic mean flows established for 91 is responsible for ensuring waters of the State of Arkansas and 93 U.S. Geological Survey continuous-record streamflow- are suitable for sustaining diverse biological communities gaging stations, respectively. The dry season in Arkansas and do not simultaneously pose threats to human health. The is defined as the months of July through November for this NPDES permits are required for industrial, municipal, or study. For harmonic mean flow calculations and regression other facilities that discharge treated wastewater directly to equations, the study area is composed of the Springfield- surface waters. The U.S. Environmental Protection Agency Salem Plateaus (Arkansas and Missouri), Boston Mountains, (EPA) recommends that the long-term harmonic mean flow Arkansas Valley, Ouachita Mountains (Arkansas and Okla- be used for assessing potential human health effects because homa), and West Gulf Coastal Plain (Arkansas) physiographic it provides a more conservative estimate than the arithmetic sections. All continuous-record streamflow-gaging stations mean flow. The harmonic mean flow is determined by taking used to compute dry season mean monthly flows were located the reciprocal of the mean value of the reciprocal of indi- within Arkansas. vidual values. Equations for two regions were found to be statistically The U.S. Geological Survey (USGS), in cooperation significant for developing regression equations for estimat- with the ADEQ, Southwestern Energy, the Arkansas Natural ing harmonic mean flows at ungaged basins; thus, equations Resources Commission, and the Arkansas Game and Fish are applicable only to streams in those respective regions in Commission, developed regional regression equations for Arkansas. Regression equations for dry season mean monthly estimation of dry season mean monthly flows and harmonic flows are applicable only to streams located throughout mean flows that are representative of natural streamflow Arkansas. All regression equations are applicable only to conditions, defined as streamflows that are not affected by unaltered streams where flows were not significantly affected regulation, diversion, or urbanization (referred to hereinafter by regulation, diversion, or urbanization. The median number as unaltered) at ungaged basins in Arkansas. A continuous- of years used for dry season mean monthly flow calcula- record streamflow-gaging station (referred to hereinafter tion was 43, and the median number of years used for har- as a streamflow gage) is a location on a stream where gage monic mean flow calculations was 34 for region 1 and 43 for height is recorded continuously and for which daily-mean region 2. 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 have focused primarily on development of regional regression are routinely needed for ungaged streams for water-quality equations for low-flow frequencies, such as the 7-day, 2-year regulation, stream-related structural design, wastewater man- low flow (Q7,2) and the 7-day,10-year low flow (Q7,10). No agement, and stream-hazard identification. These two stream- previous studies in Arkansas have developed regional regres- flow statistics, in particular, are useful for setting criteria for sion equations to estimate dry season mean monthly flow or wastewater-treatment plant effluent and allowable pollutant QAH. loads to meet water-quality standards for human health crite- ria, irrigation, recreation, and wildlife conservation. For the estimation of these two statistics at ungaged streams, regional regression equations were developed using statistical relations Methods of Analysis for Data from U.S. that exist between streamflow data collected at streamflow Geological Survey Continuous-Record gages and geologic, climatic, physical, and statistical variables for watersheds that contribute flow to a streamflow gage (Eash Streamflow Gages and Barnes, 2012). Data used for this report are from 113 streamflow gages in Arkansas, Oklahoma, and Missouri (fig. 1); however, Purpose and Scope streamflow gages from neighboring States were used only for QAH because explanatory variables used in regression equa- The purpose of this report is to present regression tions for dry season mean monthly flow were spatially limited equations for estimation of dry season mean monthly flows to within Arkansas. Streamflow gages from neighboring and harmonic mean flows (QAH) at ungaged basins in States were used to improve the representativeness of QAH Arkansas. Dry season mean monthly flows and QAH com- and basin characteristics found in the Arkansas border areas puted from USGS streamflow gages are also presented. and to provide better estimates of the error of the regression Equations developed during this study also are intended for equations for ungaged sites near the Arkansas border. Stream- delivery in the USGS StreamStats program (U.S. Geological flow gages located on unaltered streams (fig. 1; app. 1) with a Survey, 2012a,b). The StreamStats program allows users to minimum of 15 water years of daily-mean flows were initially select a point on a stream in an interactive map and then auto- selected for evaluation in the study. However, some gages with matically delineates the watershed for that point and computes 12 water years of daily-mean flow data were added to enhance selected statistics for the watershed (Eash and Barnes, 2012). the spatial distribution of streamflow gages used to develop The StreamStats program will provide users the ability to regression equations. Daily-mean flow data collected through estimate dry season mean monthly flow, QAH, and associ- the 2013 water year were retrieved for the 113 streamflow ated 90 percent prediction intervals for ungaged streams in gages from the USGS National Water Information System Arkansas. (NWIS) database (U.S. Geological Survey, 2001).
Previous Studies Basin Characteristics
Six studies have been conducted for estimation of low- For this study, 47 basin characteristics (app. 2) were flow characteristics in Arkansas beginning with Hines (1965). evaluated as potential explanatory variables for use in regres- The most recent study by Funkhouser and others (2008) used sion equations for estimating dry season mean monthly flow data collected through the 2005 water year, defined as the and QAH. The geographic information system (GIS) derived period from October 1 of a given year to September 30 of the characteristics were selected to represent the varying geologic, following year designated by the calendar year in which it climatic, physical, and statistical properties of the watersheds ends. Previous reports for low-flow statistics in Arkansas for the 113 streamflow gages. Methods of Analysis for Data from U.S. Geological Survey Continuous-Record Streamflow Gages 3
95° 94° 93° 92° 91° 90°
23 ##24 37°
13# #30 12# #44 20 #31 #25 #26 ###19 46##45 21 MISSOURI # 8 # 11# 48 47 9 # ARKANSAS 32 49### 10 # #28 #53 29 #27 54# #7 # #51 6 18 34 36 52# #50 5## # # # # 36° # 16 #22 35 33 4 #14 ## #55 17 # #56 #15 40 #61 #64 65# 37# #66 74 38## 1 62# # 39 # #63 #73 # #76 75 71#72# # #81 41 69 70 # TENNESSEE 60 59 ### # # 68 #2 67# # 77 78 #80 #42 35° # #3 #58 79 # 83 #57 #84 85 #82 # # 86 103 # 93# #94 #104 #43 #89 # 95 105# 96 # # 87 97 106 # 88 #91 # # # #98 #99
34° OKLAHOMA 90 #100 108# #102 # 107 #109
MISSISSIPPI TEXAS # 101# 92 110# 113 #112 # 33° # 111 LOUISIANA
Base from the U.S. Geological Survey digital data, 2011, 1:100,000 0 20 40 60 80 100 MILES USA Contiguous Albers Equal Area Conic USGS version North American Datum 1983 0 20 40 60 80 100 KILOMETERS EXPLANATION
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 # 92 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)
Figure 1. U.S. Geological Survey streamflow gages used for dry season mean monthly flow and harmonic mean flow regressions. 4 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas
Regression Techniques A base-10 logarithmic transformation of the MLR has the form of Ordinary-least-squares (OLS) regressions were used to develop initial multiple-linear-regression (MLR) equa- logYi = b0 + b1logX1+ b2logX2 + ··· + bnlogXn + ei (2) tions that were used for the initial analysis of streamflow data. Final equations for regional regressions were developed where using weighted-least-squares (WLS) regressions. Logarithmic log is the base-10 logarithmic transformation of transformations (base 10) were used on all response variables the variable. (mean monthly flow and QAH) and tested for select explana- tory variables (table 1) for the final regression equations. The algebraic equivalence of equation 2 after transformation Logarithmic transformations were applied based on graphical back to its original units is comparisons of response variables and explanatory variables. = b0 b 1 b 2 … bn ei Only drainage area was log transformed for the final regres- YXXXi 1 0 1 2 n 10 (3) sion equations. Other transformations were used for select explanatory variables (percent Ordovician and Mississippian) Tasker (1980) reported that OLS regression assumes that as necessary to increase linearity between the response vari- the time-sampling variance in the response-variable estimates able and explanatory variables. The response variable was is the same for each streamflow gage used in the analysis. As assumed to be a linear function of the explanatory variables. a result, this would imply that all observations of the response MLR equations followed the general form variable are equally reliable. This assumption is not always satisfied in hydrologic regressions because of the reliability of
Yi = b0 + b1X1 + b2X2 + ··· + bnXn + ei (1) the record available for computation of the response variable based on the length of the observed streamflow record (Tasker, where 1980; Eash and Barnes, 2012). The WLS regression adjusts for
Yi is the response variable for site i, the variation in the reliability of the response-variable esti-
X1 to Xn are the n explanatory variables for site i, mates by using a weight for each streamflow gage to account
b0 to bn are the n + 1 regression model coefficients, for differences in the period of record available for computa- and tion of the response variable (Eng and others, 2009; Eash and
ei is the residual error for site i. 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 First Third First Third Minimum Median Mean Maximum Minimum Median Mean Maximum quartile quartile quartile quartile 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 First Third First Third First Third Mini- Me- Maxi- Mini- Me- Maxi- Mini- Me- Maxi- quar- Mean quar- quar- Mean quar- quar- Mean quar- mum dian mum mum dian mum mum dian mum tile tile tile tile tile tile 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 First Third First Third First Third Mini- Me- Maxi- Mini- Me- Maxi- Mini- Me- Maxi- quar- Mean quar- quar- Mean quar- quar- Mean quar- mum dian mum mum dian mum mum dian mum tile tile tile tile tile tile 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 test- For QAH calculations (app. 3), the study area is com- ing all possible combinations of the 42 explanatory variables posed of the Springfield-Salem Plateaus (Arkansas and (app. 2) using the allReg() function contained within the Missouri), Boston Mountains, Arkansas Valley, Ouachita “USGSwsStats” package (Lorenz, 2013b) for R, an integrated Mountains (Arkansas and Oklahoma), and West Gulf Coastal suite of software facilities for data manipulation, calculation, Plain (Arkansas) physiographic sections (fig. 2). A QAH value and graphical display (R Core Team, 2014). The best candi- was calculated for all streamflow gages used in the regression date regression equations were selected based on the lowest equations using the USGS "DVstats" package (Lorenz, 2013a) values of Mallow’s Cp and analysis of multicollinearity using in R software (R Core Team, 2014), which is based on the the variance inflation factor (Helsel and Hirsch, 2002). The EPA’s computer program for estimating design flows for use WLS regressions were repeatedly performed in R (R Core in water-quality studies (DFLOW) (Rossman, 1990b). The Team, 2014) to reduce the number of explanatory variables to QAH statistic generally is smaller than the arithmetic mean those significant at the 95-percent confidence interval. Regres- statistic, gives more weight to lower flows, and is corrected sion diagnostics, including residual standard error, coefficient for daily flow values of zero (Rossman, 1990a). The QAH is of determination (R2), multicollinearity, Cook’s D, leverage, calculated as and graphical relations (Helsel and Hirsch, 2002), were used to evaluate the performance of WLS regressions. NN = nz nz (4) QAH N N Dry Season Mean Monthly Flow Data t nz 1 ∑ i=1 Qi Daily-mean streamflow data for 91 USGS stream- where flow gages were used to compute monthly-mean flows. A Qi is the daily mean streamflow, in cubic feet per mean monthly flow is computed as the arithmetic mean of second, all monthly-mean flows for a given month of the year for a Nnz is the number of nonzero days, and selected period of record for a streamflow gage. A monthly- N is the total number of Q values. mean flow is computed as the arithmetic mean of the daily- t i mean flows for a given month of the year. Regression analysis If Nnz equals Nt, QAH is equal to the reciprocal of the mean of was performed with ensembles for five critical, dry season the reciprocals of all Qi. months, July through November. Five regression equations were developed for the calcula- Regionalization of Harmonic Mean Flow Data tion of dry season mean monthly flows during the months of July through November. All five equations contain at least one Regionalization is a statistical framework used to esti- significant explanatory variable (table 1) derived from a previ- mate statistics at ungaged stream locations from statistics ous runoff study in Arkansas (Pugh and Westerman, 2014). calculated at USGS streamflow gages (Ries, 2007). Regional- The median number of years of record used for calculation ization techniques are used because streamflow statistics can of dry season mean monthly flow at the 91 streamflow gages vary substantially between regions because of differences in was 43 (app. 1). Equations for estimation of dry season mean geology, climate, and physical characteristics. Regionalization monthly flow are applicable only at ungaged, unaltered stream of low-flow statistics in Arkansas was first attempted by Hines locations in Arkansas. (1965). Subsequently, Ludwig and Tasker (1993) divided the western two-thirds of Arkansas into three low-flow regions of Harmonic Mean Flow Data well sustained and poorly sustained low flow. Minor changes were made to the existing low-flow statistical regions by Equations for two regions were found to be statistically Funkhouser and others (2008) attributable to enhanced GIS significant for developing regression equations for estimating capabilities for spatial data processing. No regional methods harmonic mean flow at selected ungaged basins in Arkansas. for mean flow estimation have been developed for Arkansas Of the 93 streamflow gages used for QAH (fig. 1; app. 1), 33 prior to this study. and 60 streamflow gages were used for the first and second Streamflow gages used for QAH were located on streams regions, respectively. The median number of years of data in Arkansas, Oklahoma, or Missouri. An initial OLS regres- used for QAH calculations in the WLS regression analysis was sion was performed on all gages selected for inclusion in a 34 for region 1 and 43 for region 2 (app. 1). The WLS regres- statewide regression analysis. Residuals from the statewide sion equations used to estimate QAH are applicable only to OLS regression were spatially analyzed and indicated the need ungaged, unaltered streams in region 1 and region 2. for equations in two regions. 6 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas
95° 94° 93° 92° 91° 90°
37°
MISSOURI ARKANSAS
36°
TENNESSEE
35°
34° OKLAHOMA
MISSISSIPPI TEXAS
33° LOUISIANA
Base from the U.S. Geological Survey digital data, 2011, 1:100,000 0 20 40 60 80 100 MILES USA Contiguous Albers Equal Area Conic USGS version North American Datum 1983 0 20 40 60 80 100 KILOMETERS
EXPLANATION
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
Figure 2. Physiographic sections of Arkansas. Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations 7
Region 1 includes a small part of Arkansas that is located 3). Normalized root mean square error (NRMSE) and percent exclusively in the northern part of the State (fig. 1), mostly bias (PBIAS) were additional metrics computed for all of the in the Springfield-Salem Plateaus (figs. 1 and 2). The region regression equations. Values for normalized root mean square is underlain by a series of limestone and dolomite units and error ranged from 33.6 to 38.4 percent for dry season mean therefore exhibits numerous karst features that affect regional monthly flow (table 2) and from 29.2 to 45.8 percent for QAH hydrology and groundwater/surface-water interaction (Ludwig (table 3). The NRMSE is computed as and Tasker, 1993). Streams in region 1 often are sustained by numerous springs. The well-sustained flows from numer- 1 N 2 ( predicted− observed ) ous springs are indicative of a regional source of water that is N ∑ i=1 i i NRMSE = 100 (5) supplemented during extended periods of precipitation by a sd() observed local component of groundwater recharge (Ludwig and Tasker, i 1993). where Region 2 includes the rest of the State excluding the Mis- sd is standard deviation, sissippi Alluvial Plain. The northern part of region 2 (fig. 1) N is the total number of comparisons, and includes the Boston Mountains, Arkansas Valley, Ouachita i is the individual value. Mountains, and parts of the Springfield Plateau physiographic and PBIAS as sections (fig. 2; Fenneman, 1946). Region 2 is underlain or mantled by consolidated rocks consisting primarily of sand- N ( predicted− observed ) stones and shales. The primary porosity and permeability of = ∑ i=1 i i PBIAS 100 N (6) these sandstones and shales have been greatly reduced by observed ∑ i=1 i compaction and deep burial; therefore, only limited amounts of groundwater are available from secondary openings includ- Of the 47 basin characteristics (app. 2), 5 were found ing joints and fractures. The fractures, however, do not supply to be significant explanatory variables for dry season mean the base flows of streams to the extent that numerous springs monthly flow and QAH regressions for regions 1 and 2: do in region 1 (Ludwig and Tasker, 1993). (1) drainage area; (2) base-flow index; (3) slope 1085; the The southern part of region 2 is located in the West Gulf stream slope computed as the change in elevation in feet Coastal Plain physiographic section, which is underlain by between points at 10 and 85 percent of the length in miles unconsolidated deposits composed of sand, silt, and clay. The of the longest flow path from the outlet, divided by length streams in the southern part of region 2 generally do not have between the points; (4) mean dry season total runoff; and sustained base flow because (1) the stream channels are not (5) percent Mississippian and Ordovician surficial geology incised deeply enough to intercept the water table, and (2) the (app. 3). An example regression equation for QAH for region surficial deposits typically have low permeability and porosity 2 is: (Ludwig and Tasker, 1993). logQAH = A + blogDA + cOM + dBFI (7) Dry Season Mean Monthly Flow and where log is the base-10 logarithmic transformation of Harmonic Mean Flow Regression the variable, Equations QAH is the harmonic mean flow, A is the intercept, DA is the drainage area, in square miles, Observed values of dry season mean monthly flows and OM is the percent Ordovician and Mississippian QAH (app. 3) computed from daily-mean flow data were surficial geology divided by 100 + 1, used with basin characteristics (app. 2) to identify significant BFI is the base-flow index, and explanatory variables (table 1) for multiple-linear-regression b, c, and d are the coefficients of regression for the equations (tables 2 and 3) to estimate predicted values of dry basin characteristics used as explanatory season mean monthly flows and QAH. Predicted values were variables, compared to observed values to evaluate the performance of the WLS regression equations. The widely used residual stan- Or, in the algebraic equivalence of equation 7, the regression dard error (RSE) and adjusted correlation coefficient (Helsel equation can be transformed back to the original units and Hirsch, 2002) diagnostics of the regression analysis are provided for their respective regression equations (tables 2 and 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 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]
Number of streamflow Adjusted NRMSE PBIAS Regression equation gages used RSE R2 (percent) (percent) to develop equation 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
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]
Number of streamflow NRMSE PBIAS Regression equation RSE Adjusted R2 gages used to (percent) (percent) develop equation 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 Limitations 9 Limitations the 90-percent prediction intervals; critical values may be obtained in many statistics The final regression equations are applicable only to textbooks (Iman and Conover, 1983), streams in Arkansas that are unaltered. The range of values n – p is the degree of freedom with n streamflow for explanatory variables used to develop the final regression gages included in the regression analysis equations for this report is listed in table 1. A measure of the and p parameters in the equation (the uncertainty associated with the regression of dry season mean number of explanatory variables plus one), monthly flows and QAH is the prediction interval. A predic- and S is the standard error of prediction for site i tion interval is the probability that the actual value of the esti- i mated statistic will be within a specific margin of error (Helsel and is computed as and Hirsch, 2002). For a 90-percent prediction interval, the S = [MEV + X UX' ]0.5 (11) true streamflow statistic has a 90-percent probability of being i i i within the margin of error. The following equation described by Eash and Barnes (2012), which is modified from Tasker where and Driver (1988), can be used to compute the 90-percent MEV is the mean squared error from WLS prediction interval for the true value of a streamflow statistic regression equations developed for this for an ungaged site: study using a user-defined weighting matrix;
Q Xi is the row vector for the streamflow gage Table 4. Values needed to determine the 90-percent prediction intervals for estimates obtained from regression equations using covariance matrices in A rkansas. [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) 0.04535396 -0.00365853 -0.00820081 logDA -0.00365853 0.00151157 -0.00001740 DryTotRun -0.00820081 -0.00001740 0.00188411 August mean monthly streamflow 1.6063 0.0700 (Intercept) logDA DryTotRun (Intercept) 0.07906513 -0.00637789 -0.01429639 logDA -0.00637789 0.00263511 -0.00003034 DryTotRun -0.01429639 -0.00003034 0.00328455 September mean monthly streamflow 1.7944 0.0457 (Intercept) logDA DryTotRun (Intercept) 0.04486505 -0.00361909 -0.00811240 logDA -0.00361909 0.00149528 -0.00001722 DryTotRun -0.00811240 -0.00001722 0.00186380 October mean monthly streamflow 1.9042 0.0474 (Intercept) logDA DryTotRun (Intercept) 0.04288050 -0.00345901 -0.00775356 logDA -0.00345901 0.00142914 -0.00001645 DryTotRun -0.00775356 -0.00001645 0.00178136 November mean monthly streamflow 2.2257 0.0381 (Intercept) logDA DryTotRun (Intercept) 0.03741506 -0.00301813 -0.00676531 logDA -0.00301813 0.00124698 -0.00001436 DryTotRun -0.00676531 -0.00001436 0.00155431 Harmonic mean flow region 1 1.6937 0.0641 (Intercept) logDA BFI Slope 1085 (Intercept) 0.14021140 -0.01779832 -0.16399111 -0.00097720 logDA -0.01779832 0.00820252 -0.01328758 0.00021931 BFI -0.16399111 -0.01328758 0.39735529 0.00047734 Slope1085 -0.00097720 0.00021931 0.00047734 0.00001313 Harmonic mean flow region 2 0.6311 0.0966 (Intercept) logDA OM BFI (Intercept) 0.08792426 -0.02244803 -0.01608324 -0.04605076 logDA -0.02244803 0.01227426 -0.00007389 -0.03009622 OM -0.01608324 -0.00007389 0.01884845 -0.02850505 BFI -0.04605076 -0.03009622 -0.02850505 0.62346886 Selected References 11 Summary Residual standard error, adjusted correlation coefficient, normalized root mean square error, and percent bias were used The U.S. Geological Survey (USGS), in cooperation with to evaluate the performance of the regression equations devel- the Arkansas Department of Environmental Quality (ADEQ), oped for this study. Values for normalized root mean square Southwestern Energy, the Arkansas Natural Resources Commis- error ranged from 33.6 to 38.4 percent for dry season mean sion, and the Arkansas Game and Fish Commission, developed monthly flow and from 29.2 to 45.8 percent for QAH. Equa- regression equations for estimation of dry season mean monthly tions developed during this study also are intended for delivery flows and harmonic mean flows (QAH) that are representative in the USGS StreamStats program. StreamStats will provide of natural streamflow conditions at selected ungaged basins in users the ability to estimate dry season mean monthly flow, Arkansas. Observed values of dry season mean monthly flow QAH, and 90 percent prediction intervals for ungaged streams and QAH computed from daily-mean flow data were used with in Arkansas. 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 Selected References streamflow statistics are routinely needed for ungaged streams for water-quality regulation, stream-related structural design, Acreman, W.C., and Wiltshire, S.E., 1987, Identification of wastewater management, and stream-hazard identification. Dry regions for regional flood frequency analysis [abs.]: EOS, season mean monthly flow and QAH are useful for setting cri- v. 68, no. 44, p. 1–262. teria for wastewater-treatment plant effluent and allowable pol- lutant loads to meet water-quality standards for human health Eash, D.A., and Barnes, K.K., 2012, Methods for estimating criteria, irrigation, recreation, and wildlife conservation. selected low-flow frequency statistics and harmonic mean Five dry season mean monthly flow regression equations flows for streams in Iowa: U.S. Geological Survey Scientific and two QAH regression equations were developed using dry Investigations Report 2012–5171, 99 p. (Also available at season mean monthly flow and QAH established for 91 and http://pubs.usgs.gov/sir/2012/5171/.) 93 USGS continuous-record streamflow gaging stations, respec- Eng, Ken, Chen, Yin-Yu, and Kiang, J.E., 2009, User’s guide tively. The dry season in Arkansas is defined as the months of to the weighted-multiple-linear-regression program (WREG July through November. For QAH calculations and regression version 1.0): U.S. Geological Survey Techniques and Meth- equations, the study area is composed of the Springfield-Salem ods, book 4, chap. A8, 21 p. (Also available at http://pubs. Plateaus (Arkansas and Missouri), Boston Mountains, Arkansas usgs.gov/tm/tm4a8/.) Valley, Ouachita Mountains (Arkansas and Oklahoma), and West Gulf Coastal Plain (Arkansas) physiographic sections. All Falcone, J.A., Carlisle, D.M., Wolock, D.M., and Meador, M.R., streamflow-gaging stations used to compute dry season mean 2010, GAGES: A stream gage database for evaluating natural monthly flows were located within Arkansas. Continuous- and altered flow conditions in the conterminous United record streamflow-gaging stations used for this study had a States: Ecology, v. 91, no. 2, p. 621, a data paper in Ecologi- minimum of 12 water years of daily-mean flow data. Basin cal Archives E091–045–D1. characteristics that included geologic, climatic, physical, and Fenneman, N.M., 1946, Physical divisions of the United States: statistical variables were computed for each basin. U.S. Geological Survey map, scale 1:7,000,000, 1 sheet. The median number of years used for dry season mean monthly flow calculation was 43. Regression equations for Funkhouser, J.E., Eng, Ken, and Moix, M.W., 2008, Low-flow mean monthly flow were applicable only to stream sites located characteristics and regionalization of low-flow characteristics throughout Arkansas. The regression equations for dry season for selected streams in Arkansas: U.S. Geological Survey mean monthly flow and QAH are applicable only to unaltered Scientific Investigations Report 2008–5065, 161 p. (Also streams where flows were not significantly affected by regula- available at http://pubs.usgs.gov/sir/2008/5065/.) tion, diversion, or urbanization. Haley, B.R., Glick, E.E., Bush, W.V., Clardy, B.F., Stone, C.G., Equations for two regions were found to be statistically Woodward, M.B., and Zachry, D.L., 1993 Geologic map of significant for developing regression equations for estimating Arkansas: U.S. Geological Survey, 1 sheet, scale 1:500,000. QAH at ungaged basins in Arkansas. Of the 93 continuous- record streamflow-gaging stations used for QAH, 33 and 60 Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in streamflow-gaging stations were used for the first and second water resources: U.S. Geological Survey Techniques of regions, respectively. The median number of years of data used Water-Resources Investigations, book 4, chap. A3, 510 p. for QAH calculations in the weighted-least-squares regression (Also available at http://pubs.usgs.gov/twri/twri4a3/html/ analysis was 34 for region 1 and 43 for region 2. The weighted- pdf_new.html.) least-squares regression equations used to estimate QAH were Hines, M.S., 1965, Water-supply characteristics of selected applicable only to streams in their respective regions, region 1 Arkansas streams: Arkansas Geological Commission Water and region 2. Resources Circular 9, 43 p. 12 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas Iman, R.L., and Conover, W.J., 1983, A modern approach to Rossman, L.A., 1990b, DFLOW user’s manual: Cincinnati, statistics: New York, John Wiley and Sons, Inc., 497 p. Ohio, U.S. Environmental Protection Agency, Risk Reduc- tion Engineering Laboratory, 26 p., accessed May 21, Jin, S., Yang, L., Danielson, P., Homer, C., Fry, J., and Xian, 2014, at http://nepis.epa.gov/Exe/ZyNET.exe/30001JEH. G. 2013, A comprehensive change detection method for TXT?ZyActionD=ZyDocument&Client=EPA&Index=1 updating the National Land Cover Database to circa 2011: 986+Thru+1990&Docs=&Query=600890051%20or%20 Remote Sensing of Environment, v. 132, p. 159–175. (Also dflow%20or%20user’s%20or%20manual%20or%20 available at http://www.mrlc.gov/nlcd2011.php.) rossman&Time=&EndTime=&SearchMethod=1&TocRestr ict=n&Toc=&TocEntry=&QField=pubnumber%5E%22600 Lorenz, D.L., 2013a, DVstats—An R package for manag- 890051%22&QFieldYear=&QFieldMonth=&QFieldDay=& ing daily-values data, version 0.1: U.S. Geological Survey, UseQField=pubnumber&IntQFieldOp=1&ExtQFieldOp=1 accessed March 1, 2014, at https://github.com/USGS-R/ &XmlQuery=&File=D%3A%5Czyfiles%5CIndex%20Data DVstats. %5C86thru90%5CTxt%5C00000005%5C30001JEH.txt&U Lorenz, D.L., 2013b, USGSwsStats—An R package for the ser=ANONYMOUS&Password=anonymous&SortMethod= analysis of hydrologic data, version 0.6: U.S. Geological h%7C&MaximumDocuments=10&FuzzyDegree=0&Image Survey, accessed March 1, 2014, at https://github.com/ Quality=r75g8/r75g8/x150y150g16/i425&Display=p%7Cf USGS-R/USGSwsStats. &DefSeekPage=x&SearchBack=ZyActionL&Back=ZyActi onS&BackDesc=Results%20page&MaximumPages=1&Zy Ludwig, A.H., and Tasker, G.D., 1993, Regionalization of Entry=1&SeekPage=x&ZyPURL. low-flow characteristics of Arkansas streams: U.S. Geologi- cal Survey Water-Resources Investigations Report 93–4013, Schwarz, G.E., and Alexander, R.B., 1995, STATe Soil 26 p. GeOgraphic (STATSGO) database for the conterminous United States: U.S. Geological Survey Open-File Report PRISM Climate Group, 2012, PRISM climate data: Oregon 95–449, 95 p. State University, accessed on May 30, 2014, at http://www. prism.oregonstate.edu/. Tasker, G.D., 1980, Hydrologic regression with weighted least squares: Water Resources Research, v. 16, no. 6, p. 1107– Pugh, A.L., and Westerman, D.A., 2014, Mean annual, sea- 1113. sonal, and monthly precipitation and runoff in Arkansas, Tasker, G.D., and Driver, N.E., 1988, Nationwide regression 1951–2011: U.S. Geological Survey Scientific Investiga- models for predicting urban runoff water quality at unmoni- tions Report 2014–5006, 40 p. (Also available at http:// tored sites: Water Resources Bulletin, v. 24, no. 5, p. 1091– dx.doi.org/10.3133/sir20145006.) 1101, accessed December 12, 2014, at http://onlinelibrary. R Core Team, 2014, The R project for statistical computing: wiley.com/doi/10.1111/j.1752-1688.1988.tb03026.x/pdf. Vienna, Austria, The R Foundation for Statistical Comput- U.S. Department of Agriculture, 2001, STATe Soil ing, accessed March 1, 2014, at http://www.R-project.org/. GeOgraphic (STATSGO) database—Data use information Reed, J.C., and Bush, C.A., 2005, Generalized geologic (revised July 1994): Natural Resources Conservation Ser- map of the United States, Puerto Rico, and the U.S. Vir- vice, National Soil Survey Center, Miscellaneous Publica- gin Islands: U.S. Geological Survey National Atlas of the tion No. 1492, 110 p. United States. (Also available at http://pubs.usgs.gov/atlas/ U.S. Geological Survey, 2001,USGS Water data for the geologic/.) Nation: National Water Information System: Web Interface, Ries, K.G., III, 2007, The National Streamflow Statistics accessed March 21, 2014, at http://waterdata.usgs.gov/ Program—A computer program for estimating streamflow nwis/. statistics for ungaged sites: U.S. Geological Survey Tech- U.S. Geological Survey, 2011, National elevation dataset: U.S. niques and Methods, book 4, chap. A6, 37 p. (Also available Geological Survey, accessed March 21, 2014, at http://ned. at http://pubs.usgs.gov/tm/2006/tm4a6/pdf/tm4a6.pdf.) usgs.gov/. Ries, K.G., and Friesz, P.J., 2000, Methods for estimating U.S. Geological Survey, 2012a, Welcome to StreamStats—The low-flow statistics for Massachusetts streams: U.S. Geo- StreamStats Program: U.S. Geological Survey, accessed logical Survey Water-Resources Investigations Report May 30, 2013, at http://water.usgs.gov/osw/streamstats/ 2000–4135, 81 p. (Also available at http://pubs.usgs.gov/ index.html. wri/wri004135/.) U.S. Geological Survey, 2012b, Welcome to StreamStats— Rossman, L.A., 1990a, Design stream flows based on har- Basin characteristic definitions: U.S. Geological Survey, monic means: Journal of Hydraulic Engineering, v. 116, accessed May 30, 2013, at http://water.usgs.gov/osw/ no. 7, p. 946–950 streamstats/bcdefinitions1.html. Appendixes 1–3 Appendix 1 Appendix 1 15 25 33 64 38 50 69 23 15 49 47 20 91 92 33 61 74 33 16 12 20 16 19 77 26 20 18 74 14 42 69 record (years) Period of End date 09/30/1974 09/30/2013 09/30/2013 09/30/1983 09/30/2013 09/30/2013 09/30/1944 09/30/2013 09/30/1958 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2012 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/1976 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/1970 09/30/2013 date .—Continued . Begin 10/01/1949 10/01/1970 10/01/1949 10/01/1945 10/01/1963 10/01/1944 10/01/1921 10/01/1998 10/01/1909 10/01/1966 10/01/1993 10/01/1922 10/01/1921 10/01/1980 10/01/1952 10/01/1939 10/01/1980 10/01/1996 10/01/2001 10/01/1993 10/01/1997 10/01/1994 10/01/1936 10/01/1950 10/01/1993 10/01/1995 10/01/1939 01/22/1999 10/01/1928 10/01/1944 degrees) (decimal Longitude -90.380101 -90.878056 -90.885556 -94.172622 -94.081111 -92.306056 -92.288856 -94.007500 -93.765472 -92.213889 -91.443083 -91.358167 -90.847623 -90.575393 -93.855000 -93.620833 -90.970278 -93.315833 -91.482778 -93.356111 -93.206806 -92.907278 -91.171667 -91.492084 -93.405000 -92.928889 -92.747222 -92.713333 -92.554607 -92.248139 Latitude degrees) (decimal 35.505082 35.144722 34.972778 35.982906 36.073056 36.627222 36.587611 36.104167 36.472293 35.991667 37.148167 37.154083 36.622003 36.631724 36.200000 36.427222 36.254167 36.389444 36.313611 36.454444 36.717750 36.779639 36.205556 36.784780 35.938889 35.797222 35.983056 35.940000 36.117294 36.623028 USGS station name Tyronza River near Tyronza, Ark. Tyronza, River near Tyronza L’Anguille River near Colt, Ark. River near Colt, L’Anguille L’Anguille River at Palestine, Ark. River at Palestine, L’Anguille West Fork White River at Greenland, Ark. White River at Greenland, Fork West White River near Fayetteville, Ark. White River near Fayetteville, Bryant Creek near Tecumseh, Mo. Tecumseh, Bryant Creek near North Fork River at Tecumseh, Mo. Tecumseh, North Fork River at Richland Creek at Goshen, Ark. Richland Creek at Goshen, White River at Beaver, Ark. White River at Beaver, North Sylamore Creek near Fifty Six, Ark. North Sylamore Creek near Fifty Six, Jacks Fork at Alley Spring, Mo. Jacks Fork at Jacks Fork at Eminence, Mo. Current River at Doniphan, Mo. Little Black River below Fairdealing, Mo. War Eagle Creek near Hindsville, Ark. Eagle Creek near Hindsville, War Kings River near Berryville, Ark. Kings River near Berryville, Black River at Pocahontas, Ark. Black River at Pocahontas, Long Creek at Denver, Ark. Long Creek at Denver, Spring River at Town Branch Bridge at Hardy, Ark. Branch Bridge at Hardy, Town Spring River at Yocum Creek near Oak Grove, Ark. Creek near Oak Grove, Yocum Bull Creek near Walnut Shade, Mo. Walnut Bull Creek near Beaver Creek at Bradleyville, Mo. Spring River at Imboden, Ark. Spring River at Imboden, Eleven Point River near Thomasville, Mo. Eleven Point River near Buffalo River near Boxley, Ark. River near Boxley, Buffalo Richland Creek near Witts Spring, Ark. Spring, Witts Richland Creek near Buffalo River near St. Joe, Ark. River near St. Joe, Buffalo Bear Creek near Silver Hill, Ark. Bear Creek near Silver Hill, Buffalo River near Rush, Ark. River near Rush, Buffalo North Fork River near Tecumseh, Mo. Tecumseh, North Fork River near site USGS number 07047600 07047942 07047950 07048000 07048600 07058000 07058500 07048800 07050000 07060710 07065495 07066000 07068000 07068510 07049000 07050500 07069000 07053207 07069305 07053250 07053810 07054080 07069500 07070500 07055646 07055875 07056000 07056515 07057000 07057500 /s) 3 ------ü ü ü ü ü ü ü ü ü ü ü ü ü flow (ft mean region 2 Harmonic /s) 3 ------ü ü ü ü ü ü ü ü ü ü ü ü ü ü flow (ft mean region 1 Harmonic /s) 3 ------ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü (ft mean monthly U.S. Geological Survey streamflow gages used for regression analysis dry season mean monthly flow and harmonic Dry season U.S. Geological Survey streamflow gages used for regression analysis dry season mean monthly flow and harmonic streamflow 1 2 3 4 5 6 8 7 9 11 21 22 23 24 25 26 27 10 28 29 12 13 14 30 15 16 17 18 19 20 Map /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 that station] Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in column Ark., /s, cubic feet per second; USGS, U.S. Geological Survey; /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 that station] Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in column Ark., /s, cubic feet per second; USGS, U.S. Geological Survey; identi - 3 number 3 fication Table 1–1. Table [ft Appendix 1 1–1. Table [ft 16 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas 92 84 84 34 40 51 83 34 45 22 49 83 26 23 74 16 16 18 51 12 52 34 74 12 52 55 16 74 75 55 24 20 record (years) Period of End date 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/1979 09/30/2012 09/30/2013 09/30/2013 09/30/1984 09/30/1961 09/30/2013 09/30/2010 09/30/2013 09/30/1993 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/1987 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/1970 date .—Continued Begin 10/01/1921 10/01/1929 10/01/1929 10/01/1979 10/01/1939 10/01/1961 10/01/1930 10/01/1979 10/01/1939 10/01/1939 10/01/1964 10/01/1927 10/01/1987 10/01/1970 10/01/1939 10/01/1997 10/01/1997 10/01/1995 10/01/1936 10/01/2001 10/01/1961 10/01/1979 10/01/1939 10/01/2001 10/01/1961 10/01/1958 10/01/1997 10/01/1939 10/01/1938 10/01/1958 10/01/1989 10/01/1950 degrees) (decimal Longitude -91.200833 -91.114167 -91.097778 -94.344444 -91.608474 -92.451389 -94.464167 -94.494722 -91.610974 -92.383490 -90.933056 -91.236389 -91.322500 -90.845669 -94.586889 -94.618000 -94.683611 -94.533333 -91.449444 -94.551330 -94.433611 -94.605278 -92.292778 -94.587720 -94.641389 -94.486389 -94.856340 -94.299444 -95.155799 -94.406944 -94.653002 -94.407992 Latitude degrees) (decimal 36.648694 36.346389 36.102500 36.103056 36.098959 35.586944 35.517222 36.144722 36.080626 35.566744 35.857500 35.269722 35.035556 34.555656 36.631461 36.547297 36.548889 36.108611 36.111111 36.364523 36.256111 36.216111 35.656667 36.342024 36.334722 35.880000 35.785091 34.918889 34.912599 35.162500 35.165653 35.722306 USGS station name Ark. Eleven Point River near Bardley, Mo. Eleven Point River near Bardley, Eleven Point River near Ravenden Springs, Ark. Eleven Point River near Ravenden Springs, Black River at Black Rock, Ark. Black River at Rock, Illinois River at Savoy, Ark. Illinois River at Savoy, Strawberry River near Evening Shade, Ark. Strawberry River near Evening Shade, South Fork of Little Red River at Clinton, Ark. South Fork of Little Red River at Clinton, Lee Creek near Short, Okla. Illinois River at Highway 16 near Siloam Springs Piney Fork at Evening Shade, Ark. Piney Fork at Evening Shade, South Fork Little Red River near Clinton, Ark. South Fork Little Red River near Clinton, Cache River at Egypt, Ark. Cache River at Egypt, Cache River at Patterson, Ark. Cache River at Patterson, Cache River near Cotton Plant, Ark. Cache River near Cotton Plant, Big Creek at Poplar Grove, Ark. Big Creek at Poplar Grove, Elk River near Tiff City, Mo. City, Tiff Elk River near Cave Springs Branch near South West City, Mo. City, West Cave Springs Branch near South Honey Creek near South West City, Mo. City, West Honey Creek near South Illinois River South of Siloam Springs, Ark. Illinois River South of Siloam Springs, Strawberry River near Poughkeepsie, Ark. Strawberry River near Poughkeepsie, Spavinaw Creek near Maysville, Ark. Spavinaw Creek near Maysville, Flint Creek at Springtown, Ark. Flint Creek at Springtown, Flint Creek near West Siloam Springs, Okla. West Flint Creek near Middle Fork of Little Red River at Shirley, Ark. Middle Fork of Little Red River at Shirley, Spavinaw Creek near Cherokee City, Ark. Spavinaw Creek near Cherokee City, Spavinaw Creek near Sycamore, Okla. Baron Fork at Dutch Mills, Ark. Baron Fork at Dutch Mills, Caney Creek near Barber, Okla. Caney Creek near Barber, Poteau River at Cauthron, Ark. Poteau River at Cauthron, Fourche Maline near Red Oak, Okla. James Fork near Hackett, Ark. James Fork near Hackett, Poteau River near Pama, Okla. Cove Creek near Lee Creek, Ark. Cove Creek near Lee Creek, site USGS number 07071500 07072000 07072500 07194800 07073000 07075300 07249985 07195400 07073500 07075500 07077380 07077500 07077555 07077950 07189000 07189540 07189542 07195430 07074000 07191160 07195800 07195855 07075000 07191179 07191220 07196900 07197360 07247000 07247500 07249400 07249413 07249500 /s) 3 ------ü ü ü ü ü ü ü ü ü flow (ft mean region 2 Harmonic /s) 3 ------ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü flow (ft mean region 1 Harmonic /s) 3 ------ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü (ft mean monthly U.S. Geological Survey streamflow gages used for regression analysis dry season mean monthly flow and harmonic Dry season streamflow 31 32 33 34 38 51 35 39 52 36 40 41 42 43 44 45 46 47 53 37 48 54 55 49 50 56 57 58 59 60 61 62 Map /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 that station] Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in column Ark., /s, cubic feet per second; USGS, U.S. Geological Survey; identi - 3 number fication Table 1–1. Table [ft Appendix 1 17 62 13 15 15 15 25 15 74 21 75 15 15 18 44 42 46 21 24 59 66 52 74 63 47 46 68 63 46 42 97 72 59 record (years) Period of End date 09/30/1992 09/30/2013 09/30/1969 09/30/1969 09/30/1961 09/30/1969 09/30/2013 09/30/1970 09/30/2013 09/30/1970 09/30/1969 09/30/1969 09/30/1970 09/30/1980 09/30/1992 09/30/1987 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2011 09/30/1986 09/30/2013 09/30/2013 09/30/2011 09/30/2013 09/30/1980 09/30/2013 09/30/2013 09/30/2013 date .—Continued Begin 10/01/1930 10/01/2000 10/01/1954 10/01/1954 10/01/1936 10/01/1954 10/01/1939 10/01/1949 10/01/1938 10/01/1955 10/01/1954 10/01/1954 10/01/1952 10/01/1936 10/01/1950 10/01/1941 10/01/1992 10/01/1989 10/01/1954 10/01/1947 10/01/1961 10/01/1939 10/01/1948 10/01/1939 10/01/1967 10/01/1945 10/01/1948 10/01/1967 10/01/1938 10/01/1916 10/01/1941 10/01/1954 degrees) (decimal Longitude -94.449659 -94.103056 -93.854366 -93.934392 -94.149094 -93.863058 -93.657222 -93.636026 -94.015278 -93.878247 -93.939091 -93.974647 -93.463056 -93.154623 -93.158508 -93.056111 -93.181389 -92.774444 -91.915833 -93.041111 -94.902167 -93.923611 -94.412778 -93.631582 -94.236389 -93.613056 -94.212500 -94.085000 -93.522399 -93.395556 -93.697500 -92.403889 Latitude degrees) (decimal 35.494533 35.735833 35.301478 35.350572 35.660361 35.346889 34.872500 34.560375 35.576944 35.208989 35.220925 35.248703 35.468333 34.950646 35.549525 34.911944 35.505833 34.876111 34.736667 35.466389 34.097607 35.106944 34.047500 35.104813 34.380000 34.986944 34.045000 34.096111 33.366791 35.058611 34.610000 35.298611 USGS station name Ark. Lee Creek near Van Buren, Ark. Buren, Van Lee Creek near Jones Creek at Winfrey, Ark. Winfrey, Jones Creek at Sixmile Creek at Caulksville, Ark. Sixmile Creek at Caulksville, Hurricane Creek near Branch, Ark. Hurricane Creek near Branch, Frog Bayou near Mountainburg, Ark. Frog Bayou near Mountainburg, Hurricane Creek near Caulksville, Ark. Hurricane Creek near Caulksville, Fourche LaFave River near Gravelly, Ark. Fourche LaFave River near Gravelly, Ark. South Fork Ouachita River at Mount Ida, Mulberry River near Mulberry, Ark. Mulberry River near Mulberry, Sixmile Creek subwatershed 6 near Chismville, Sixmile Creek at Chismville, Ark. Sixmile Creek at Chismville, Sixmile Creek near Branch, Ark. Sixmile Creek near Branch, Spadra Creek at Clarksville, Ark. Spadra Creek at Clarksville, Fourche LaFave River near Nimrod, Ark. Fourche LaFave River near Nimrod, Big Piney Creek near Dover, Ark. Big Piney Creek near Dover, South Fourche LaFave River near Hollis, Ark. South Fourche LaFave River near Hollis, Big Piney Creek at Highway 164 near Dover, Ark. Big Piney Creek at Highway 164 near Dover, Maumelle River at Williams Junction, Ark. Junction, Williams Maumelle River at Bayou Meto near Lonoke, Ark. Bayou Meto near Lonoke, Illinois Bayou near Scottsville, Ark. Illinois Bayou near Scottsville, Glover River near Glover, Okla. Glover River near Glover, Petit Jean River near Booneville, Ark. Petit Jean River near Booneville, Rolling Fork near DeQueen, Ark. Rolling Fork near DeQueen, Petit Jean River near Waveland, Ark. Waveland, Petit Jean River near Cossatot River near Vandervoort, Ark. Vandervoort, Cossatot River near Dutch Creek at Waltreak, Ark. Waltreak, Dutch Creek at Cossatot River near DeQueen, Ark. Cossatot River near DeQueen, Saline River near Dierks, Ark. Saline River near Dierks, Bodcau Creek at Stamps, Ark. Bodcau Creek at Stamps, Petit Jean River at Danville, Ark. Petit Jean River at Danville, Ouachita River near Mount Ida, Ark. Ouachita River near Mount Ida, Cadron Creek near Guy, Ark. Cadron Creek near Guy, site USGS number 07250000 07250935 07255000 07255500 07251000 07256000 07261500 07356500 07252000 07252500 07253000 07253500 07256500 07262500 07257000 07263000 07257006 07263295 07264000 07257500 07337900 07258500 07339500 07259500 07340300 07260000 07340500 07341000 07349430 07260500 07356000 07261000 /s) 3 ------ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü flow (ft mean region 2 Harmonic /s) 3 ------flow (ft mean region 1 Harmonic /s) 3 -- -- ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü (ft mean monthly U.S. Geological Survey streamflow gages used for regression analysis dry season mean monthly flow and harmonic Dry season streamflow 63 64 65 70 71 72 66 73 83 67 68 69 74 84 75 85 76 86 87 77 88 78 89 79 90 80 91 92 93 81 94 82 Map /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 that station] Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in column Ark., /s, cubic feet per second; USGS, U.S. Geological Survey; identi - 3 number fication Table 1–1. Table [ft 18 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas 32 15 19 49 62 59 24 40 63 52 34 12 76 26 75 15 31 15 25 record (years) Period of End date 09/30/1970 09/30/2013 09/30/1959 09/30/1977 09/30/2013 09/30/2013 09/30/2013 09/30/1977 09/30/2013 09/30/2013 09/30/1995 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/2013 09/30/1987 09/30/1971 09/30/2013 date .—Continued Begin 10/01/1938 10/01/1998 10/01/1940 10/01/1928 10/01/1951 10/01/1954 10/01/1989 10/01/1937 10/01/1950 10/01/1961 10/01/1961 10/01/2001 10/01/1937 10/01/1987 10/01/1938 10/01/1998 10/01/1956 10/01/1956 10/01/1988 degrees) (decimal Longitude -93.362681 -93.899722 -93.752128 -93.720183 -92.333333 -93.418056 -92.933889 -93.304616 -92.610278 -92.776667 -92.344597 -92.372500 -92.025833 -91.656111 -91.445833 -91.535556 -92.940556 -92.884050 -91.254444 Latitude degrees) (decimal 34.266763 34.311667 34.083443 34.048721 33.792222 34.038889 34.797500 33.878163 34.567778 33.375278 34.319541 34.228611 33.700833 33.866389 33.627778 33.235556 33.038056 33.067082 33.100278 USGS station name Caddo River Ark. Alpine, near Little Missouri River near Langley, Ark. Little Missouri River near Langley, Muddy Fork Creek near Murfreesboro, Ark. Muddy Fork Creek near Murfreesboro, Little Missouri River near Murfreesboro, Ark. Little Missouri River near Murfreesboro, Moro Creek near Fordyce, Ark. Moro Creek near Fordyce, Antoine River Ark. Antoine, at Alum Fork Saline River near Reform, Ark. Alum Fork Saline River near Reform, Little Missouri River near Boughton, Ark. Little Missouri River near Boughton, Saline River at Benton, Ark. Saline River at Benton, Smackover Creek near Smackover, Ark. Smackover Creek near Smackover, Hurricane Creek near Sheridan, Ark. Hurricane Creek near Sheridan, Hurricane Creek below Sheridan, Ark. Hurricane Creek below Sheridan, Saline River near Rye, Ark. Saline River near Rye, Bayou Bartholomew at Garrett Bridge, Ark. Bayou Bartholomew at Garrett Bridge, Bayou Bartholomew near McGehee, Ark. Bayou Bartholomew near McGehee, Bayou Bartholomew near Portland, Ark. Bayou Bartholomew near Portland, Cornie Bayou near Three Creeks, Ark. Three Creeks, Cornie Bayou near Three Creeks near Three Creeks, Ark. Three Creeks, Three Creeks near Ark. Bayou Macon at Eudora, site USGS number 07359800 07360200 07360800 07361000 07362500 07361500 07362587 07361600 07363000 07362100 07363300 07363400 07363500 07364133 07364150 07364185 07365800 07365900 07369680 /s) 3 ------ü ü ü ü ü ü ü ü ü ü ü ü ü ü flow (ft mean region 2 Harmonic /s) 3 ------flow (ft mean region 1 Harmonic /s) 3 ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü ü (ft mean monthly U.S. Geological Survey streamflow gages used for regression analysis dry season mean monthly flow and harmonic Dry season streamflow 95 96 97 98 99 111 110 112 113 102 103 100 104 101 105 106 107 108 109 Map /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 that station] Arkansas; Mo., Missouri; Okla., Oklahoma; --, gage was not used for the regression in column Ark., /s, cubic feet per second; USGS, U.S. Geological Survey; identi - 3 number fication Table 1–1. Table [ft Appendix 2 Appendix 2 19 Appendix 2. Definitions of Basin Characteristics Evaluated as Response Variables for Inclusion in the Regression Analysis Annual precipitation, in inches, is the average annual pre- Mean annual total runoff, in inches, is the total runoff at the cipitation for the drainage basin as computed from PRISM outlet that travels over the land surface and from seepage of (Prism Climate Group, 2012) data for 1951–2011. water from the ground into the stream channel as computed August average precipitation, in inches, is the basin aver- from GIS grid data from Pugh and Westerman (2014). age for the month of August averaged from PRISM (Prism Mean dry season groundwater runoff, in inches, is the Climate Group, 2012) data for 1981–2010. portion of the total runoff at the outlet from seepage of water Average basin elevation, in feet, is the average elevation of from the ground into a stream channel for the months of June the basin as determined from the National Elevation Dataset through November as computed from GIS grid data from Pugh (U.S. Geological Survey, 2011) 10 meter grid. and Westerman (2014). Base flow Index (BFI), dimensionless, is the mean ratio of Mean dry season precipitation, in inches, is the average base flow to annual streamflow from the USGS kriged BFI precipitation for the months of July through November aver- grid (Falcone and others, 2010) as an averaged value for the aged over the drainage basin as computed from PRISM (Prism basin. Climate Group, 2012) data for 1951–2011. Basin perimeter distance, in miles, is the distance around the Mean dry season surface runoff, in inches, is the portion of boundary of the basin. the total runoff at the outlet that travels over the land sur- Basin shape factor, dimensionless, is the ratio of the total face into the stream channel for the months of June through drainage area to the basin length. November as computed from GIS grid data from Pugh and Westerman (2014). Drainage area, in square miles, is the area measured in a hori- zontal plane that is enclosed by a drainage divide. Mean dry season total runoff, in inches, is the total runoff at Forest, in percent, calculated from the National Land Cover the outlet that travels over the land surface and from seep- Database as the percentage of the basin that is mixed forested age of water from the ground into the stream channel for the (Jin and others, 2013). months of June through November as computed from GIS grid data from Pugh and Westerman (2014). July average precipitation, in inches, as a basin average for the month of July averaged from PRISM (Prism Climate Mean wet season groundwater runoff, in inches, is the por- Group, 2012) data for 1981–2010. tion of the total runoff at the outlet from seepage of water from the ground into a stream channel for the months of December Longest flow path length, in miles, is the maximum flow through May as computed from GIS grid data from Pugh and distance within a basin from the start of overland flow to the Westerman (2014). outlet. Mean wet season precipitation, in inches, is the average Maximum basin elevation, in feet, is the maximum elevation precipitation for the months of December through June aver- of the basin computed from the National Elevation Dataset aged over the drainage basin as computed from PRISM (Prism (U.S. Geological Survey, 2011) 10 meter grid. Climate Group, 2012) data 1951–2011. Mean annual groundwater runoff, in inches, is the portion of the total runoff at the outlet from seepage of water from the Mean wet season surface runoff, in inches, is the portion ground into a stream channel as computed from geographic of the total runoff at the outlet that travels over the land information system (GIS) grid from Pugh and Westerman surface into the stream channel for the months of December (2014). through May as computed from GIS grid data from Pugh and Westerman (2014). Mean annual precipitation 1951–2011, in inches, at the basin outlet is the average annual precipitation as deter- Mean wet season total runoff, in inches, is the total runoff at mined from PRISM (Prism Climate Group, 2012) data for the outlet that travels over the land surface and from seep- 1951–2011. age of water from the ground into the stream channel for the months of December through May as computed from GIS grid Mean annual precipitation 1971–2000, in inches, at the data from Pugh and Westerman (2014). basin centroid and averaged for the basin is the average annual precipitation as determined from PRISM (Prism Climate Minimum basin elevation, in feet, is the maximum elevation Group, 2012) data for 1971–2000. of the basin computed from the National Elevation Dataset (U.S. Geological Survey, 2011) 10 meter grid. Mean annual surface runoff, in inches, is the portion of the total runoff at the outlet that travels over the land surface into November average precipitation, in inches, as a basin aver- the stream channel as computed from GIS grid data from Pugh age for the month of November averaged from PRISM (Prism and Westerman (2014). 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 aver- Percent Upper Paleozoic (uPz), is the percentage of the basin age for the month of October averaged from PRISM (Prism in which Upper Paleozoic sedimentary rocks dominate the Climate Group, 2012) data for 1981–2010. surface of the basin as computed from GIS grid data created Outlet elevation, in feet, is the elevation at the gage location by Reed and Bush (2005). computed from the National Elevation Dataset (U.S. Geologi- Percent Middle Proterozoic (Yv), is the percentage of the cal Survey, 2011) 10 meter grid. basin in which Middle Proterozoic volcanic rocks dominate Percent Cretaceous (K), is the percentage of the basin in the surface of the basin as computed from GIS grid data cre- which Cretaceous sedimentary rocks dominate the surface of ated by Reed and Bush (2005). the basin as computed from GIS grid data created by Reed and Relief, in feet, is the maximum basin elevation minus the Bush (2005). minimum basin elevation computed from the National Eleva- Percent Paleozoic (lPz), is the percentage of the basin in tion Dataset (U.S. Geological Survey, 2011) 10 meter grids. which lower Paleozoic sedimentary rocks dominate the sur- September average precipitation, in inches, as a basin aver- face of the basin as computed from GIS grid data created by age for the month of September averaged from PRISM (Prism Reed and Bush (2005). Climate Group, 2012) data for 1981–2010. Percent Mississippian, is the percentage of the basin in Slope, in feet per mile, of the longest flow path through the which Mississippian-age rocks dominate the surface of the basin. basin as computed from GIS grid data from Haley and others (1993). Slope 1085, in feet per mile, is the stream slope computed as the change in elevation between points at 10 and 85 percent of Percent Middle Paleozoic (mPz), is the percentage of the length along the longest flow path from the outlet, determined basin in which Middle Paleozoic sedimentary rocks dominate by GIS, divided by length between the points. the surface of the basin as computed from GIS grid data cre- ated by Reed and Bush (2005). Soil Permeability, in inches per hour, is the rate at which water flows through soil as computed from STATe Soil Percent Ordovician, is the percentage of the basin in which GeOgraphic (STATSGO) grid data (Schwarz and Alexander, Ordovician-age rocks dominate the surface of the basin as 1995; U.S. Department of Agriculture, 2001). computed from GIS grid data from Haley and others (1993). Percent Ordovician and Mississippian, is the percentage of Soil hydrologic group, dimensionless, percentage of drainage the basin in which Mississippian and Ordovician-age rocks basin in hydrologic soil group as computed from STATe Soil dominate the surface of the basin as computed from GIS grid GeOgraphic (STATSGO) grid data (Schwarz and Alexander, data from Haley and others (1993). 1995; U.S. Department of Agriculture, 2001). Percent Paleogene (pgT), is the percentage of the basin in Streamflow-variability Index, dimensionless, is a measure which Paleogene sedimentary rocks dominate the surface of of the steepness of the slope of a streamflow duration curve as the basin as computed from GIS grid data created by Reed and computed at the outlet. Bush (2005). Sum of stream lengths for basin, in miles, is the total length Percent Quaternary (Q), is the percentage of the basin in of all streams in the basin combined. which Quaternary deposits dominate the surface of the basin Urban, percent, calculated from the National Land Cover as computed from GIS grid data created by Reed and Bush Database as the percentage of the basin that is urban (Jin and (2005). others, 2013). Appendix 3 Appendix 3 21 ------4.7 4 4.3 4.8 3.9 4.3 4.8 4.1 4.2 4.3 4.3 4.2 4.3 4.3 4.3 4.3 4.3 4.3 (in.) season Mean dry total runoff 0.5 9.2 0.7 4.6 0.7 9.8 8.6 2.3 8.3 6.8 3.9 6.2 7.6 8.2 7.6 9.9 40.9 26.5 40 13.5 16.6 36.1 16.5 22.5 95.8 17.2 10.1 (ft/mi) Slope1085 0 7 0 0 1 0 0 0 0 0 0 0 10 21 50 66 28 47 36 58 48 70 79 100 100 100 100 and pian , square mile; ft/mi, foot per , square mile; ft/mi, foot per 2 (percent) 2 Mississip - Ordovician ) 2 8.4 outlet; mi 58.8 83.0 67.3 78.5 52.6 outlet; mi 332 404 534 399 788 828 194 140 265 529 562 103 569 196 304 298 (mi area 2,050 4,860 1,020 1,250 1,160 Drainage 0.25 0.26 0.30 0.30 0.29 0.55 0.31 0.31 0.34 0.51 0.51 0.34 0.34 0.33 0.35 0.43 0.34 0.58 0.38 0.53 0.36 0.50 0.33 0.38 0.47 0.38 0.50 flow index Base- /s) 3 ------1.28 1.44 1.18 4.22 6.52 8.82 flow 11.5 11.1 11.9 75.4 25.0 39.1 14.4 69.9 (ft mean 118 179 143 484 255 752 101 232 Harmonic 1,920 3,180 /s) 3 ------93 99 73 74 45 47 (ft 368 100 625 120 579 671 960 199 729 976 534 Mean stream - flow for monthly 3,700 November /s) 3 38 37 42 55 38 95 24 21 ------148 332 255 374 340 130 354 649 209 (ft Mean stream - 2,580 flow for monthly October /s) 3 22 31 44 42 70 30 31 16 26 ------ber 165 440 148 587 226 243 408 154 (ft Mean Arkansas; Mo., Missouri; Okla., Oklahoma] stream - 2,470 flow for monthly Arkansas; Mo., Missouri; Okla., Oklahoma] Septem - Ark., Ark., /s) 3 26 12 52 20 18 68 14 21 10 10 ------116 174 284 442 164 230 508 (ft Mean August stream - 2,620 flow for monthly /s) 3 11 28 25 69 26 37 29 14 ------114 244 265 412 238 129 405 660 213 July (ft Mean stream - 3,410 flow for monthly , harmonic mean flow, and explanatory variable values for final regression equations.—Continued , harmonic mean flow, , harmonic mean flow, and explanatory variable values for final regression equations. , harmonic mean flow, /s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent the longest flow path from /s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent the longest flow path from 3 3 USGS station name Dry season mean monthly flow Tyronza River near Tyronza, Ark. Tyronza, River near Tyronza Current River at Doniphan, Mo. Dry season mean monthly flow West Fork White River at Greenland, Ark. White River at Greenland, Fork West L’Anguille River near Colt, Ark. River near Colt, L’Anguille Richland Creek near Witts Spring, Ark. Spring, Witts Richland Creek near Little Black River below Fairdealing, Mo. White River near Fayetteville, Ark. White River near Fayetteville, L’Anguille River at Palestine, Ark. River at Palestine, L’Anguille Buffalo River near St. Joe, Ark. River near St. Joe, Buffalo Black River at Pocahontas, Ark. Black River at Pocahontas, Richland Creek at Goshen, Ark. Richland Creek at Goshen, Bear Creek near Silver Hill, Ark. Bear Creek near Silver Hill, War Eagle Creek near Hindsville, Ark. Eagle Creek near Hindsville, War Buffalo River near Rush, Ark. River near Rush, Buffalo White River at Beaver, Ark. White River at Beaver, North Fork River near Tecumseh, Mo. Tecumseh, North Fork River near Kings River near Berryville, Ark. Kings River near Berryville, Bryant Creek near Tecumseh, Mo. Tecumseh, Bryant Creek near Long Creek at Denver, Ark. Long Creek at Denver, North Fork River at Tecumseh, Mo. Tecumseh, North Fork River at Yocum Creek near Oak Grove, Ark. Creek near Oak Grove, Yocum North Sylamore Creek near Fifty Six, Ark. North Sylamore Creek near Fifty Six, Bull Creek near Walnut Shade, Mo. Walnut Bull Creek near Jacks Fork at Alley Spring, Mo. Jacks Fork at Beaver Creek at Bradleyville, Mo. Jacks Fork at Eminence, Mo. Buffalo River near Boxley, Ark. River near Boxley, Buffalo number USGS site 07047600 07068000 07047942 07055875 07068510 07048600 07047950 07056000 07069000 07048800 07048000 07056515 07049000 07057000 07050000 07057500 07050500 07058000 07053207 07058500 07053250 07060710 07053810 07065495 07054080 07066000 07055646 Table 3–1. Table [USGS, U.S. Geological Survey; ft in., inches; --, gage was not used for the regression in column heading that station; Appendix 3 3–1. Table [USGS, U.S. Geological Survey; ft in., inches; --, gage was not used for the regression in column heading that station; 22 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas ------4.7 4.3 4.6 4.3 4.4 4.6 4.3 4.5 4.6 4.6 4.9 3.8 4.6 4.2 4.6 4.2 4 4.1 4.2 4 4.6 4.3 4.3 3.8 4.3 (in.) season Mean dry total runoff 7.5 7.8 6.1 7.2 9.7 7.3 0.8 2 0.7 5.6 0.7 7.2 5.7 6.8 1 36.4 12.9 20.5 38.4 13.3 27.6 18.6 14.7 23.8 18.7 16.4 14.2 13 (ft/mi) Slope1085 1 1 0 0 0 0 2 89 90 76 99 58 15 74 100 100 100 100 100 100 100 100 100 100 100 100 100 100 and pian , square mile; ft/mi, foot per 2 (percent) Mississip - Ordovician ) 2 8.0 outlet; mi 14.9 56.8 99.8 41.1 48.7 88.8 845 509 568 784 358 215 374 472 853 302 148 317 691 103 132 167 (mi area 1,160 1,120 1,030 7,350 1,160 Drainage 0.49 0.43 0.50 0.43 0.52 0.65 0.29 0.48 0.47 0.30 0.51 0.47 0.32 0.48 0.37 0.31 0.42 0.46 0.28 0.46 0.28 0.27 0.46 0.32 0.46 0.46 0.48 0.41 flow index Base- /s) 3 ------6.01 7.55 2.26 5.21 3.12 3.05 2.92 flow 19.3 32 14.6 16.0 29.3 35.4 33.1 30.5 (ft mean 575 258 718 282 734 491 138 199 Harmonic 4,990 /s) 3 ------17 74 54 38 911 (ft 814 409 507 875 181 491 407 423 242 467 800 164 164 Mean stream - flow for monthly 1,170 6,730 1,100 November /s) 3 11 58 27 28 43 79 79 ------754 307 481 686 368 625 655 186 193 201 102 213 422 (ft Mean stream - 4,130 flow for monthly October 8.5 /s) 3 61 29 21 60 90 33 77 77 ------ber 578 493 618 350 634 633 198 168 103 490 386 (ft Mean Arkansas; Mo., Missouri; Okla., Oklahoma] stream - 3,940 flow for monthly Septem - Ark., 7.5 7.9 /s) 3 43 19 83 19 36 33 33 ------500 448 579 271 685 776 203 123 153 457 268 (ft Mean August stream - 4,080 flow for monthly 9.7 /s) 3 82 29 17 64 28 53 77 77 ------112 598 766 460 834 670 150 186 472 528 377 July (ft Mean stream - 5,150 flow for monthly , harmonic mean flow, and explanatory variable values for final regression equations.—Continued , harmonic mean flow, /s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent the longest flow path from 3 USGS station name Ark. Ark. Mo. Springs Ark. Dry season mean monthly flow Spring River at Town Branch Bridge at Hardy, Branch Bridge at Hardy, Town Spring River at Eleven Point River near Bardley, Mo. Eleven Point River near Bardley, Spring River at Imboden, Ark. Spring River at Imboden, Illinois River South of Siloam Springs, Ark. Illinois River South of Siloam Springs, Eleven Point River near Ravenden Springs, Eleven Point River near Thomasville, Mo. Eleven Point River near Flint Creek at Springtown, Ark. Flint Creek at Springtown, Black River at Black Rock, Ark. Black River at Rock, Cache River near Cotton Plant, Ark. Cache River near Cotton Plant, Flint Creek near West Siloam Springs, Okla. West Flint Creek near Strawberry River near Evening Shade, Ark. Strawberry River near Evening Shade, Big Creek at Poplar Grove, Mo. Piney Fork at Evening Shade, Ark. Piney Fork at Evening Shade, Elk River near Tiff City, Mo. City, Tiff Elk River near Baron Fork at Dutch Mills, Ark. Baron Fork at Dutch Mills, Strawberry River near Poughkeepsie, Ark. Strawberry River near Poughkeepsie, Cave Springs Branch near South West City, City, West Cave Springs Branch near South Middle Fork of Little Red River at Shirley, Ark. Middle Fork of Little Red River at Shirley, South Fork of Little Red River at Clinton, Ark. South Fork of Little Red River at Clinton, Honey Creek near South West City, Mo. City, West Honey Creek near South South Fork Little Red River near Clinton, Ark. South Fork Little Red River near Clinton, Cache River at Egypt, Ark. Cache River at Egypt, Spaviw Creek near Maysville, Ark. Spaviw Creek near Maysville, Cache River at Patterson, Ark. Cache River at Patterson, Spaviw Creek near Cherokee City, Ark. Spaviw Creek near Cherokee City, Spaviw Creek near Sycamore, Okla. Illinois River at Savoy, Ark. Illinois River at Savoy, Illinois River at Highway 16 near Siloam number USGS site 07069305 07071500 07069500 07195430 07072000 07070500 07195800 07072500 07077555 07195855 07073000 07077950 07073500 07189000 07196900 07074000 07189540 07075000 07075300 07189542 07075500 07077380 07191160 07077500 07191179 07191220 07194800 07195400 Table 3–1. Table [USGS, U.S. Geological Survey; ft in., inches; --, gage was not used for the regression in column heading that station; Appendix 3 23 4.4 3.8 4.2 4.1 4.2 3.8 4.6 4.1 3.9 4.3 4.5 3.9 4.1 4.3 4.3 3.9 4.2 3.8 4.5 3.9 3.8 4.1 3.8 4.2 4.1 4.1 4.1 4 4 3.8 (in.) season Mean dry total runoff 2.9 8.8 6.7 2.6 6 8.9 4 11.7 18 17.5 16.1 20.9 37.8 10.4 20.9 32.3 14.6 48.8 10.6 16.3 15.6 17.8 15.6 15.1 25.1 91.3 41.5 15.4 34.2 24.1 (ft/mi) Slope1085 0 0 0 0 0 0 0 0 0 2 0 0 1 0 5 3 0 1 3 6 0 0 0 0 0 0 0 0 11 100 and pian , square mile; ft/mi, foot per 2 (percent) Mississip - Ordovician ) 2 4.1 outlet; mi 81.8 36.3 90.2 17.7 53.0 34.8 61.3 20.5 75.0 23.8 115 147 762 103 204 172 410 120 684 210 273 434 297 438 242 241 516 374 (mi area 1,780 Drainage 0.20 0.20 0.20 0.38 0.27 0.19 0.18 0.27 0.21 0.20 0.22 0.20 0.25 0.14 0.19 0.25 0.19 0.27 0.24 0.21 0.25 0.24 0.26 0.18 0.23 0.22 0.23 0.25 0.21 0.20 flow index Base- /s) 3 ------0.62 2.55 3.27 1.96 1.71 0.97 0.85 1.17 3.45 2.51 3.97 3.16 0.70 2.28 3.09 2.71 1.21 0.74 5.78 4.68 flow 23.8 18.9 70.5 10.4 10.9 (ft mean Harmonic /s) 3.7 3 ------22 64 15 44 24 48 63 54 81 14 (ft 149 495 269 257 467 468 219 393 422 495 258 194 251 501 Mean stream - flow for monthly November 7.9 7.1 0.51 3.7 /s) 3 74 27 89 24 13 27 35 80 82 16 28 ------112 110 113 190 210 148 134 166 250 190 (ft Mean stream - flow for monthly October 5.3 2.1 6.9 8.1 0.82 3.1 /s) 3 11 31 15 53 66 21 60 51 27 89 57 33 ------ber 119 208 130 184 139 122 102 (ft Mean Arkansas; Mo., Missouri; Okla., Oklahoma] stream - flow for monthly Septem - Ark., 3.9 9.1 4.4 0.7 3.3 5.6 /s) 3 11 14 25 40 49 10 12 37 40 57 55 63 30 15 12 73 ------211 170 206 (ft Mean August stream - flow for monthly 7.7 6.2 1.6 /s) 3 49 40 61 36 22 22 21 45 69 94 62 27 26 10 15 ------345 120 394 101 127 323 125 July (ft Mean stream - flow for monthly , harmonic mean flow, and explanatory variable values for final regression equations.—Continued , harmonic mean flow, /s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent the longest flow path from 3 USGS station name Ark. Ark. Dry season mean monthly flow Caney Creek near Barber, Okla. Caney Creek near Barber, James Fork near Hackett, Ark. James Fork near Hackett, Petit Jean River at Danville, Ark. Petit Jean River at Danville, Sixmile Creek at Caulksville, Ark. Sixmile Creek at Caulksville, Poteau River near Pama, Okla. Poteau River at Cauthron, Ark. Poteau River at Cauthron, Cadron Creek near Guy, Ark. Cadron Creek near Guy, Hurricane Creek near Branch, Ark. Hurricane Creek near Branch, Fourche Maline near Red Oak, Okla. Fourche LaFave River near Gravelly, Ark. Fourche LaFave River near Gravelly, Hurricane Creek near Caulksville, Ark. Hurricane Creek near Caulksville, Cove Creek near Lee Creek, Ark. Cove Creek near Lee Creek, Fourche LaFave River near Nimrod, Ark. Fourche LaFave River near Nimrod, Spadra Creek at Clarksville, Ark. Spadra Creek at Clarksville, Lee Creek near Short, Okla. South Fourche LaFave River near Hollis, Ark. South Fourche LaFave River near Hollis, Big Piney Creek near Dover, Ark. Big Piney Creek near Dover, Maumelle River at Williams Junction, Ark. Junction, Williams Maumelle River at Big Piney Creek at Highway 164 near Dover, Big Piney Creek at Highway 164 near Dover, Lee Creek near Van Buren, Ark. Buren, Van Lee Creek near Illinois Bayou near Scottsville, Ark. Illinois Bayou near Scottsville, Jones Creek at Winfrey, Ark. Winfrey, Jones Creek at Petit Jean River near Booneville, Ark. Petit Jean River near Booneville, Petit Jean River near Waveland, Ark. Waveland, Petit Jean River near Frog Bayou near Mountainburg, Ark. Frog Bayou near Mountainburg, Dutch Creek at Waltreak, Ark. Waltreak, Dutch Creek at Mulberry River near Mulberry, Ark. Mulberry River near Mulberry, Sixmile Creek subwatershed 6 near Chismville, Sixmile Creek at Chismville, Ark. Sixmile Creek at Chismville, Sixmile Creek near Branch, Ark. Sixmile Creek near Branch, number USGS site 07197360 07260500 07255000 07249413 07247000 07261000 07255500 07247500 07261500 07256000 07249500 07262500 07256500 07249985 07249400 07263000 07257000 07263295 07257006 07250000 07257500 07250935 07258500 07259500 07251000 07260000 07252000 07252500 07253000 07253500 Table 3–1. Table [USGS, U.S. Geological Survey; ft in., inches; --, gage was not used for the regression in column heading that station; 24 Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas 4.2 5.2 4 5.4 4.6 3.7 5.6 4.4 3.7 3.7 5.6 5.6 3.6 3.7 4.5 4.2 3.9 4.9 4.1 4.9 3.9 5.1 3.9 5.4 3.6 5.6 3.8 5.6 (in.) season Mean dry total runoff 4.8 7.5 0.4 7.8 0.4 2.5 2.8 2.7 4.4 2.5 0.8 8.2 5.7 5 4.7 2.7 0.5 26.1 15.2 13.5 20.6 17.4 42.1 10.4 14.7 36 15.9 16.2 (ft/mi) Slope1085 1 0 0 0 0 0 7 0 0 0 44 80 41 90 90 88 69 23 76 83 33 99 25 77 35 50 57 100 and pian , square mile; ft/mi, foot per 2 (percent) Mississip - Ordovician ) 2 outlet; mi 89.1 50.4 26.6 61.1 35.2 67.9 207 179 608 361 320 539 180 120 183 241 236 528 414 549 204 262 120 401 382 (mi area 1,070 1,140 2,090 Drainage 0.28 0.22 0.23 0.23 0.32 0.21 0.18 0.25 0.24 0.21 0.18 0.23 0.21 0.29 0.18 0.35 0.25 0.23 0.22 0.25 0.24 0.27 0.22 0.31 0.19 0.35 0.21 0.42 flow index Base- /s) 3 ------2.26 3.69 9.33 2.74 4.71 1.14 1.32 0.61 7.57 5.58 4.80 1.88 flow 34.8 84.7 38.5 81.9 52.1 34.0 36.6 (ft mean 165 Harmonic /s) 3 -- 23 69 49 70 (ft 253 266 206 682 493 229 131 162 256 104 141 721 677 142 401 217 133 133 296 460 369 Mean stream - flow for monthly 1,180 1,290 November 6.9 /s) 3 76 44 54 97 50 26 28 43 89 60 -- 118 114 311 123 489 644 200 200 149 374 281 146 270 643 197 213 (ft Mean stream - flow for monthly October /s) 3 11 81 72 85 40 56 55 31 25 29 34 88 72 54 -- ber 110 628 424 214 108 127 243 307 127 500 136 425 174 (ft Mean Arkansas; Mo., Missouri; Okla., Oklahoma] stream - flow for monthly Septem - Ark., 7.7 4.1 /s) 3 50 28 42 15 22 56 22 19 14 24 92 58 38 12 37 -- 487 281 125 136 100 130 308 159 453 169 (ft Mean August stream - flow for monthly 3.4 /s) 3 55 80 46 53 87 48 25 78 38 46 58 54 50 90 -- 117 652 495 174 235 235 150 159 590 264 486 225 July (ft Mean stream - flow for monthly , harmonic mean flow, and explanatory variable values for final regression equations.—Continued , harmonic mean flow, /s, cubic feet per second; Slope1085, slope of channel between points at 10 and 85 percent the longest flow path from 3 USGS station name Dry season mean monthly flow Bayou Meto near Lonoke, Ark. Bayou Meto near Lonoke, Cossatot River near Vandervoort, Ark. Vandervoort, Cossatot River near Glover River near Glover, Okla. Glover River near Glover, Little Missouri River near Boughton, Ark. Little Missouri River near Boughton, Bayou Bartholomew near Portland, Ark. Bayou Bartholomew near Portland, Cossatot River near DeQueen, Ark. Cossatot River near DeQueen, Smackover Creek near Smackover, Ark. Smackover Creek near Smackover, Cornie Bayou near Three Creeks, Ark. Three Creeks, Cornie Bayou near Saline River near Dierks, Ark. Saline River near Dierks, Rolling Fork near DeQueen, Ark. Rolling Fork near DeQueen, Moro Creek near Fordyce, Ark. Moro Creek near Fordyce, Three Creeks near Three Creeks, Ark. Three Creeks, Three Creeks near Bodcau Creek at Stamps, Ark. Bodcau Creek at Stamps, Alum Fork Saline River near Reform, Ark. Alum Fork Saline River near Reform, Bayou Macon at Eudora, Ark. Bayou Macon at Eudora, Ouachita River near Mount Ida, Ark. Ouachita River near Mount Ida, Saline River at Benton, Ark. Saline River at Benton, South Fork Ouachita River at Mount Ida, Ark. South Fork Ouachita River at Mount Ida, Hurricane Creek near Sheridan, Ark. Hurricane Creek near Sheridan, Caddo River Ark. Alpine, near Hurricane Creek below Sheridan, Ark. Hurricane Creek below Sheridan, Little Missouri River near Langley, Ark. Little Missouri River near Langley, Saline River near Rye, Ark. Saline River near Rye, Muddy Fork Creek near Murfreesboro, Ark. Muddy Fork Creek near Murfreesboro, Bayou Bartholomew at Garrett Bridge, Ark. Bayou Bartholomew at Garrett Bridge, Little Missouri River near Murfreesboro, Ark. Little Missouri River near Murfreesboro, Bayou Bartholomew near McGehee, Ark. Bayou Bartholomew near McGehee, Antoine River Ark. Antoine, at number USGS site 07264000 07337900 07361600 07364185 07340500 07362100 07365800 07341000 07339500 07362500 07365900 07349430 07340300 07362587 07369680 07356000 07363000 07356500 07363300 07359800 07363400 07360200 07363500 07360800 07364133 07361000 07364150 07361500 Table 3–1. Table [USGS, U.S. Geological Survey; ft in., inches; --, gage was not used for the regression in column heading that station; Publishing support provided by Lafayette Publishing Service Center Breaker—Dry Season Mean Monthly Flow and Harmonic Mean Flow Regression Equations for Selected Ungaged Basins in Arkansas—SIR 2015–5031, ver. 1.1 ISSN 2328-0328 (online) http://dx.doi.org/10.3133/sir20155031