Estimating Low-Flow Frequency Statistics for

Unregulated Streams in Idaho 

Scientific Investigations Report 2006–5035

Prepared in cooperation with the Idaho Department of Environmental Quality

U.S. Department of the Interior

U.S. Geological Survey
Estimating Low-Flow Frequency Statistics for 

Unregulated Streams in Idaho

By Jon E. Hortness

Prepared in cooperation with the

Idhao Department of Environmental Quality

Scientific Investigations Report 2006-5035

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

P. Patrick Leahy, Acting Director

U.S. Geological Survey, Reston, Virginia: 2006

For sale by U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

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Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Hortness, J.E., 2006, Estimating low-flow frequency statistics for unregulated streams in Idaho: U.S. Geological 

Survey Scientific Investigations Report 2006-5035, 31 p. 
iii

Contents

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

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

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

Description of Study Area ........................................................................ 2

Previous Investigations ........................................................................... 2

Low-Flow Frequency Statistics at Gaging Stations ................................................... 4

Estimating Low-Flow Frequency Statistics at Ungaged Sites ....................................... 4

Drainage-Area Ratio .............................................................................. 5

Regional Regression Equations .................................................................. 5

Determination of Regions..................................................................... 5

Basin Characteristics ........................................................................ 5

Logistic Regression Analysis ............................................................... 7

Multiple Linear Regression Analysis ...................................................... 7

Final Estimating Equations .................................................................. 8

Accuracy and Limitations .................................................................. 11

Application of Regional Regression Method ............................................. 12

Example 1 .............................................................................. 13

Example 2 .............................................................................. 13

Example 3 .............................................................................. 13

Summary ................................................................................................... 14

References Cited.......................................................................................... 14
iv

Tables

Table 1. Sources for data used to obtain basin characteristics used to estimate

low-flow frequency statistics for unregulated streams in Idaho ..................... 6

Table 2. Description of basin characteristics used in the final equations for

estimating low-flow frequency statistics for unregulated streams in

Idaho........................................................................................... 6

Table 3. Logistic regression equations used to estimate the probability of zero flow

for unregulated streams in regions 4, 6, and 7 in Idaho................................. 9

Table 4. Regression equations for estimating low-flow frequency statistics for

unregulated streams in regions 1-8 in Idaho ............................................. 10

Table 5. Range of values of basin characteristics used to estimate low-flow

frequency statistics for unregulated streams in regions 1-8 in Idaho ............... 12

Table 6. Selected information for gaging stations used to estimate low-flow

frequency statistics for unregulated streams in regions 1-8 in Idaho ............... 16

Table 7. Low-flow frequency statistics for streamflow-gaging stations used in

low-flow regression analyses for unregulated streams in regions 1-8 in

Idaho .......................................................................................... 21

Table 8. Basin characteristics considered during the low-flow regressin analyses for

unregulated streams in Idaho ............................................................ 23

Table 9. Basin characteristic values used to develop the final probability and

estimating equations for low-flow frequency statistics for unregulated

streams in regions 1-8 in Idaho ............................................................ 24

Table 10. Total years with the N-day low flow equal to zero and total years of record

for streamflow-gaging stations used in logistic regression analyses for

unregulated streams in regions 1-8 in Idaho ............................................. 29

Figures

Figure 1. Map showing location of the study area, streamflow-gaging stations, and

eight regions used to estimate low-flow frequency statistics for unregulated

streams in Idaho ........................................................................... 3

Figure 2. Graph showing joint distribution of two example basin characteristics, mean

basin elevation and mean annual precipitation.......................................... 11
Conversion Factors, Datums, Definitions, and 

Abbreviations and Acronyms

Conversion Factors

Multiply By To obtain

cubic foot per second (ft3/s) 0.02832 cubic meter per second

foot (ft) 0.3048 meter

inch (in.) 2.54 centimeter

inch per year (in/yr) 25.4 millimeter per year

mile (mi) 1.609 kilometer

square mile 2.590 square kilometer

Datums

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).

Altitude, as used in this report, refers to distance above the vertical datum.

Definitions

Water year: In U.S. Geological Survey reports, a water year is the 12-month period from October 

1 through September 30. The water year is designated by the calendar year in which it ends; 

thus, the water year ending September 30, 2001, is called the “2001 water year”.

Climatic year: In U.S. Geological Survey reports, a climatic year is the 12-month period from 

April 1 through March 31. The climatic year is designated by the calendar year in which it 

begins; thus, the climatic year beginning April 1, 2001, is called the”2001 climatic year.”

Abbreviations and Acronyms

Abbreviations and Acronyms Meaning

GIS Geographic Information System

GLS Generalized Least Squares

IDEQ Idaho Department of Environmental Quality

MSE mean square error

NPDES National Pollution Discharge Elimination System

OLS Ordinary Least Squares

TMDL Total Maximum Daily Load

USGS U.S. Geological Survey
vi

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Abstract

Low-flow frequency statistics are needed by Federal, 

State, and local agencies for regulatory activities and wateruse planning and management, as well as by commercial and 

hydroelectric facilities to determine the availability of water 

for supply and power generation. Logistic and multiplelinear regression analyses were used to develop zero-flowprobability and low-flow-estimating equations for eight 

separate geographic regions of Idaho and parts of adjacent 

States, using physical and climatic characteristics as the 

explanatory variables. As part of this process, the relevant 

statistics were updated for all gaging stations in Idaho, and 

some in adjacent States, that, in general, had 10 or more years 

of record through water year 2003 and were unaffected by 

regulation and(or) diversions.

Zero-flow-probability equations were developed for three 

of the eight geographic regions. These equations can be used 

to estimate the annual probability that the 1-, 7-, or 30-day 

low flows will equal zero. Using only data from the gaging 

stations used in the development process (sample data), these 

equations produced results with percent-correct values ranging 

from 74 to 100 percent. Any variability in the zero-flow 

characteristics within each region that was not represented 

by the data used to develop the equations may affect the 

predictive accuracy of the final equations.

Estimating equations were developed that can be used for 

estimating the 1Q10, 7Q2, 7Q10, and 30Q5 low-flow frequency 

statistics at ungaged, unregulated sites on streams in Idaho. 

The standard errors of prediction for these equations exhibited 

a minimum range of +26.9 to -21.2 percent and a maximum 

range of +311 to -75.7 percent. The 7Q2 estimating equations 

generally exhibited the lowest standard errors and the 1Q10

equations generally exhibited the largest standard errors. The 

equations may not yield reliable results for sites with basincharacteristic values that are outside of the range of values 

used to develop the equations. The equations also are not 

applicable for sites on regulated streams or on streams that 

are affected by significant gains and(or) losses resulting from 

factors including spring flow, channel seepage, diversions, and 

irrigation returns.

Introduction

Frequency statistics, such as the 7-day, 10-year low flow 

[7Q10; annual minimum mean discharge for 7 consecutive 

days, which has a 0.1 (1/10; 10 percent) probability of not 

being exceeded in any one year], commonly are used by States 

when setting effluent limits and allowable pollutant loads to 

meet water-quality standards. These same low-flow frequency 

statistics also indicate the probable availability of water in 

streams during times when conflicts between water supply and 

demand are most prevalent. Because of this, low-flow statistics 

are needed by Federal, State, and local agencies for regulatory 

activities and water-use planning and management. Lowflow statistics also are used by commercial and hydroelectric 

facilities to determine the availability of water for supply and 

power generation.

In Idaho, more than 800 river reaches have been 

designated as impaired [exceeding water-quality and(or) 

biological criteria]. These reaches have or will have their 

load of pollutants analyzed and maximum loading rates set 

by Total Maximum Daily Load (TMDL) assessments. To 

determine the load of a constituent in a stream, streamflowquantity information is needed. This information is especially 

important for low-flow periods when agencies need to 

determine the maximum effluent limits for National Pollution 

Discharge Elimination System (NPDES) discharge permits.

The U.S. Geological Survey (USGS) operates a 

network of streamflow-gaging stations in Idaho that provides 

streamflow data for a variety of purposes, and low-flow 

statistics can be calculated from the streamflow data collected 

at these locations. However, it is not feasible to operate gaging 

stations at all locations where low-flow statistics are needed. 

Because of this, methods are needed that can be used to 

estimate low-flow statistics at locations where no streamflow 

information exists. This is most often accomplished using 

regionalization techniques and regression analyses that 

relate low-flow statistics to selected physical and climatic 

characteristics of drainage basins.

Estimating Low-Flow Frequency Statistics for 

Unregulated Streams in Idaho

By Jon E. Hortness
The last Statewide evaluation of low-flow characteristics 

by the USGS was published in 1996 and included flow data 

through 1990 (Kjelstrom and others, 1996). Although this 

report included low-flow statistics over a wide range of flow 

durations and recurrence intervals, it only included low-flow 

statistics at gaged sites with 10 or more years of continuous 

record. Because methods are needed to estimate low-flow 

statistics at ungaged sites throughout Idaho, the USGS, in 

cooperation with the Idaho Department of Environmental 

Quality (IDEQ), began a study to develop methods for 

estimating the 1Q10, 7Q2, 7Q10, and 30Q5 low-flow frequency 

statistics at ungaged sites. In the past, estimating low-flow 

statistics at ungaged sites has met with only limited success 

because of difficulties in adequately describing the effects 

of geology and other factors that typically affect low flows 

(Riggs, 1972). The use of GIS (Geographic Information 

System) to obtain a larger number of basin characteristics, 

especially geologic characteristics, and the improved accuracy 

of source data may significantly improve the success of this 

method.

Purpose and Scope

This report presents techniques used to develop regional 

regression equations that can be used to estimate various 

low-flow statistics for ungaged sites on unregulated streams 

in Idaho. Multiple linear regression analyses were used to 

develop equations for estimating the 1Q10, 7Q2, 7Q10, and 

30Q5 low-flow frequency statistics at ungaged, unregulated 

sites on streams in Idaho, and logistic regression analyses 

were used to develop equations for estimating the zero-flow 

probability for 1-, 7-, and 30-day low flows. The report 

also describes the associated reliability and limitations of 

the regression equations. Regression statistics, such as the 

standard error of estimate, were calculated to help assess the 

reliability and accuracy of each equation.

Relevant low-flow frequency statistics (1Q10, 7Q2, 7Q10, 

and 30Q5) were updated for the gaging stations in Idaho and 

adjacent States used in the equation development process. 

These gaging stations included all those in Idaho, and some in 

adjacent States, with generally 10 or more years of record on 

streams unaffected by regulation and(or) diversions. Relevant 

low-flow statistics updated through water year 2003 for these 

gaging stations also are presented in this report.

Description of Study Area

The study area (fig. 1) includes the entire State of Idaho 

and areas in the adjacent States of Washington, Oregon, 

Nevada, Utah, Wyoming, and Montana where particular 

drainage basins cross over State boundaries. The northern 

and central parts of the area are composed mainly of rugged, 

mountainous terrain; broad plains and mildly sloping 

valleys and hills predominate in the south. Geologic features 

across the study area consist of sedimentary, igneous, and 

metamorphic rocks ranging in age from Precambrian to 

Holocene (Bond, 1978). The granitic Idaho batholith is the 

major structural feature in the central part of the study area, 

and basalt covers much of the southern and western parts 

(Ross and Savage, 1967).

Most precipitation in the study area results from storms 

moving inland from the Pacific Ocean. The amount of 

precipitation varies widely throughout the area and is greatly 

affected by topography. Precipitation ranges from less than 

10 in/yr on the Snake River Plain in south-central Idaho to 60 

to 70 in/yr in the central mountains of Idaho (Molnau, 1995). 

The most significant amounts of precipitation are a direct 

result of orographic effects and occur primarily in the winter 

months. Spring and summer thunderstorms in the southern 

part of the study area sometimes produce large amounts 

of localized precipitation. Resulting streamflow varies 

geographically and seasonally and can be affected by land use 

and vegetation. During much of the year, typically August 

through March, streamflow in most unregulated streams in 

the study area is minimal base flow; during April, May, June, 

and July, streamflow is significantly greater, primarily as a 

result of snowmelt. Annual minimum streamflows typically 

occur during October through January. Occasionally during 

the winter months, large frontal systems carrying warmer 

air release moisture as rain on the snowpack and frozen 

ground, which results in rapid snowmelt and high runoff rates, 

particularly at altitudes less than 6,000 ft above sea level 

(National Oceanic and Atmospheric Administration, 1971).

Previous Investigations

Various low-flow statistics for selected gaging stations 

in Idaho with 10 or more years of record through 1990 were 

determined by Kjelstrom and others (1996). The statistics 

included the annual minimum mean discharges for periods 

of 1, 3, 5, 7, 14, 30, 60, 90, 120, and 183 consecutive days 

for recurrence intervals of 2, 5, 10, 20, 50, and 100 years. 

Kjelstrom and others (1995) also documented annual 

minimum discharges for selected gaging stations in Idaho with 

5 to 9 years of record through 1990.

Although no studies have been completed that document 

methods for estimating low-flow statistics at ungaged sites 

in Idaho, several studies resulted in methods for estimating 

monthly-exceedance, annual-mean, and peak-flow statistics at 

ungaged sites. Most recently, regional regression techniques 

were used to develop equations that can be used to estimate 

various streamflow statistics at ungaged sites. These 

techniques resulted in equations for estimating the following 

statistics: monthly-exceedance and annual-mean discharges 

(Hortness and Berenbrock, 2001); peak-flow discharges 

(Berenbrock, 2002); and bankfull-flow discharges (Hortness 

and Berenbrock, 2003).

 Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
ID_9IU02.fig01

Base from U.S. Geological Survey digital data, 1:2,000,000, 1999; Regions based on Hydrologic Unit Boundaries, 1:2,000,000, 1999;

Transverse Mercator projection. Factor at central meridian: 0.99960. Longitude of central meridian: -114° 00'. Latitude of origin: 42° 00'

False easting (meters): 500,000.0 False northing (meters): 100,000.0

Yellowstone River

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EXPLANATION

GAGING STATION AND NO.

 NUMBER (see table 2) 39

0 20 40 60 80 100 MILES

0 20 40 60 80 100 KILOMETERS

REGION AND IDENTIFICATION NO.

 FOR WHICH SPECIFIC REGRESSION

 EQUATIONS HAVE BEEN DEVELOPED

(see table 5)

2

UNDEFINED AREA

117° 114° 111°

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Figure 1. Location of the study area, streamflow-gaging stations, and eight regions used to estimate low-flow frequency statistics 

for unregulated streams in Idaho.

Introduction 
Quillian and Harenberg (1982) and Horn (1988) 

developed methods for estimating mean annual discharges 

in streams across Idaho. Kjelstrom (1998) developed a 

method for estimating the 20-, 50-, and 80-percent monthlyexceedance discharge values for the Salmon and Clearwater 

River Basins in central Idaho using the mean monthly 

discharge and a multiplication factor. This method pertains 

only to the approximately 1,050 subbasins identified by 

Lipscomb (1998), who estimated the mean monthly discharges 

for each subbasin by apportioning mean annual discharges 

into monthly increments on the basis of records from gaging 

stations selected as being characteristic of the subbasin. 

Lipscomb estimated the mean annual discharges by using 

the regional regression equations developed by Quillian and 

Harenberg (1982).

Thomas and others (1973), Kjelstrom and Moffatt 

(1981), and Quillian and Harenberg (1982) developed regional 

regression equations for estimating peak flows at ungaged 

sites in Idaho. Portions of Idaho also were included in regional 

peak-flow studies by Hedman and Osterkamp (1982) and 

Thomas and others (1994). Regression equations specific to 

bankfull flows were developed for the Salmon River Basin by 

Emmett (1975) and for the entire State by Harenberg (1980).

Low-Flow Frequency Statistics at 

Gaging Stations

Low-flow frequency statistics are determined using the 

annual minimum mean flows for any given number of days 

(N-day low flows) during an annual period. The mean flow for 

each N-day period throughout the annual period is computed 

and the minimum value is used for that period. The series of 

annual minimum N-day values are then fit to a log-Pearson 

Type III distribution to determine the recurrence intervals 

(Riggs, 1972). The annual period referred to as a climatic 

year (April 1 through March 31) is often used in low-flow 

analyses because the annual low-flow period in most parts 

of the country occurs during the late summer and autumn 

months. Use of the climatic year allows for inclusion of the 

entire low-flow period in the same year, whereas use of the 

traditional water year (October 1 through September 30) may 

artificially separate the low-flow period into two different 

years.

Updated relevant low-flow frequency statistics (1Q10, 

7Q2, 7Q10, and 30Q5) were computed for 234 gaging stations 

located throughout Idaho and portions of the adjacent States 

(fig. 1). This included all of those gaging stations located 

in Idaho and those in adjacent States within about an 80-mi 

buffer surrounding Idaho that, in general, had 10 or more 

years of record through water year 2003, exhibited little or 

no signs of trends, and were unaffected by regulations and/or 

diversions. A small number of gaging stations with fewer than 

10 years of record were included in the analyses after the data 

were analyzed and found to contain a broad enough range of 

streamflow conditions that they would not bias the statistical 

results. Selected information for each gaging station included 

in the final dataset are presented in table 6 (at back of report) 

and the relevant low-flow frequency statistics for each gaging 

station are presented in table 7 (at back of report).

Streamflow data were analyzed for trends using Kendall’s 

tau hypothesis test. Trends in the data could introduce an 

element of error into the frequency analyses, since a major 

assumption is that annual low flows are independent and 

stationary over time. The Kendall’s tau test measures the 

monotonic relationship between two data sets, in this case, 

streamflow and time (Helsel and Hirsch, 1992). A relatively 

stringent P-value threshold of 2 percent (α = 0.02) was used 

in this study. Data from gaging stations that exhibited trends 

based on this criteria were analyzed further and compared to 

data from nearby gaging stations to determine inclusion or 

exclusion from the dataset.

Streamflow data were screened to prevent data affected 

by regulations and/or diversions from biasing the dataset. 

Decisions to include or exclude data from a specific gaging 

station were made using hydrologic judgment based on all 

available information regarding the occurrence, timing, and 

magnitude of regulations and diversions upstream of the 

gaging stations. No specific criteria were used. In general, all 

gaging stations with data affected by upstream regulations 

were removed from the dataset, as well as those with data 

affected by upstream diversions during typical low-flow 

periods. The information available was not always complete 

and the accuracy was questionable in some cases, especially 

with regard to magnitudes of upstream diversions. Therefore, 

it is possible that data affected by regulations or diversions 

could have been included in the final datasets. However, the 

overall effects on the data are believed to be minimal.

Estimating Low-Flow Frequency 

Statistics at Ungaged Sites

Because gaging stations cannot be located at all sites 

where streamflow information is needed, other methods are 

used to estimate streamflow statistics for these sites. The two 

most commonly used methods for estimating streamflow 

statistics at ungaged sites are the drainage-area ratio method 

and regression equations (Ries and Friesz, 2000). The 

drainage-area ratio method can be used when the ungaged site 

is located near a gaging station on the same stream. Regression 

equations can be used to estimate streamflow statistics at most 

ungaged sites.

 Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Drainage-Area Ratio

A major assumption of the drainage-area ratio method 

is that the streamflow at the ungaged site is the same per unit 

area as the streamflow at a nearby gaging station located on 

the same stream (index site). The method involves determining 

the drainage areas for both the ungaged site and the index 

site. The streamflow statistics are computed for the index 

site and then are divided by the drainage area to determine 

the streamflow per unit area for each statistic. The values for 

streamflow per unit area are then multiplied by the drainage 

area for the ungaged site to estimate the statistics for that site. 

The accuracy of this method depends on the proximity of 

the two sites and the similarities in drainage area and other 

physical and climatic (basin) characteristics of their drainage 

basins. The equation that represents this method is as follows:

Q DA

DA u Q u

g

= g

æ

è

ç

ç

ç

çç

ö

ø

÷

÷

÷

÷

÷

 , (1)

where

Qu is the streamflow statistic for the ungaged site,

DAu is the drainage area for the ungaged site,

DAg is the drainage area for the gaged site, and

Qg is the streamflow statistic for the gaged site.

It is fairly common practice to use this method when the 

sites are located on the same stream and the ratio between 

the drainage areas of the index site and the ungaged site is 

between 0.5 and 1.5. On the basis of specific analyses in 

certain areas, some researchers have found that this range 

should be either reduced or expanded. Koltun and Schwartz 

(1986) recommended a range of 0.85 to 1.15 times the area 

of the index site for estimates of low-flow statistics in Ohio, 

and Ries and Friesz (2000) determined that a range of 0.3 to 

1.5 was applicable for low-flow statistics in Massachusetts. 

Parrett and Johnson (2004) recommended the standard ratio 

of 0.5 to 1.5 for flood frequency analyses in Montana, as did 

Berenbrock (2002) and Kjelstrom (1998) for flood-frequency 

analyses in Idaho.

Regional Regression Equations

The regression analyses were completed for eight 

separate geographic regions of the State, as was done in the 

recent peak-flow and monthly exceedance studies (Hortness 

and Berenbrock, 2001 and 2003; Berenbrock, 2002). Basin 

and climatic variables (basin characteristics) for the gaging 

stations used in this study were obtained from previous studies 

or determined using GIS algorithms equivalent to those used 

in previous studies. Two types of regression analyses, logistic 

and multiple linear, were used. Logistic regression analysis 

was used for regions that included gaging stations at which 

any of the relevant N-day low flows equaled zero. Data from 

those stations were used to develop an equation for use in 

determining the probability of the annual minimum N-day 

flow being zero for an ungaged site. Multiple linear regression 

analyses were used in all regions to develop equations for 

estimating low-flow frequency statistics.

Determination of Regions

The regional boundaries used in this study are the same 

ones that were defined by Hortness and Berenbrock (2001): 

eight study regions and one undefined region that was not 

included in the analysis (fig. 1). The region boundaries 

were determined on the basis of the following: (1) grouping 

of gages with similar basin characteristics revealed during 

cluster analyses (statistical method for grouping data with 

similar characteristics), (2) location of geographic features, 

such as large mountain ranges or breaks between mountains 

and plains, and (3) use of hydrologic judgment based on 

general knowledge of the area. The undefined region is made 

up almost entirely of the area commonly referred to as the 

eastern Snake River Plain. This area includes several dams, 

major irrigation diversions, springs with extremely large 

discharges, and flat-land drainages and channel bottoms with 

very high infiltration rates. This area was not included in the 

analysis because flows influenced by these conditions cannot 

be characterized by a regional regression approach. More 

detailed information on how the regional boundaries were 

determined can be found in the previous report by Hortness 

and Berenbrock (2001).

Basin Characteristics

More than 30 separate basin characteristics were obtained 

for each of the 234 gaging stations included in this study. 

The basin characteristics for gaging stations included in 

previous studies by Hortness and Berenbrock (2001; 2003) 

and Berenbrock (2002) were used in this study. For gaging 

stations not included in those studies, the basin characteristics 

were derived using current GIS techniques equivalent to 

those used in the previous studies. In general, all basin 

characteristics were obtained using either custom Arc Macro 

Language (AML) programs written for ArcGIS or current 

tools (ArcHydro Tools) available in ArcGIS version 9.0 

(Environmental Systems Research Institute, Inc., 2005). The 

sources for the values of all basin characteristics are given in 

table 1 and a list of all basin characteristics considered during 

this study are presented in table 8 (at back of report).

Several basin characteristics were removed from 

consideration after a review of the correlation plots of the data. 

Generally, if two basin characteristics correlated well with 

each other, the one that was the least difficult to obtain was 

kept and the other was removed. Other characteristics were 

removed because of missing data or difficulty in obtaining the 

data. Descriptions of the basin characteristics used in the final 

equations and the methods of determination are provided in 

table 2, and basin-characteristic values for each gaging station 

are listed in table 9 (at back of report).

Estimating Low-Flow Frequency Statistics at Ungaged Sites 
Table 1. Sources for data used to obtain basin characteristics used to estimate low-flow frequency statistics for unregulated streams in Idaho.

Dataset Source

National Elevation Dataset (NED) Several basin characteristics were calculated using 30-meter-resolution digital-elevation data derived 

from the 1-arc-second National Elevation Dataset (NED) (URL: http://ned.usgs.gov/).

Elevation Derivatives for National 

Applications (EDNA)

Hydrologic derivatives of NED data were developed using procedures similar to those of EDNA 

Stage 1 processing, using a custom projection for Idaho (URL: http://edna.usgs.gov/Edna/

methodology.asp).

National Land Cover Dataset (NLCD) Vogelmann, J.E., Sohl, T.L., Campbell, P.V., and Shaw, D.M., 1998, Regional land-cover 

characterization using Landsat Thematic Mapper data and ancillary data sources: Environmental 

Monitoring and Assessment v. 51, p. 415-428 (URL: http://landcover.usgs.gov/natllandcover.asp).

Major lithology, Pacific Northwest U.S. Geological Survey, 1995, Major lithology: Spokane, Washington, U.S. Geological Survey, 

polygon data converted to grid-cell resolution 200 meters (URL: http://www.icbemp.gov/spatial/

min).

Mean annual precipitation, Idaho

(used for areas within Idaho)

Molnau, M., 1995, Mean annual precipitation, 1961-1990, Idaho: Moscow, University of Idaho, 

Agricultural Engineering Department, State Climate Program, scale 1:1,000,000 (URL: http://

snow.ag.uidaho.edu/Climate/reports.html).

Western United States average monthly 

or annual precipitation

(PRISM; used for areas outside of 

Idaho)

Daly, C., and Taylor, G., 1998, Western United States average monthly or annual precipitation, 1961-

90, Oregon: Portland, Water and Climate Center of the Natural Resources Conservation Service, 

grid-cell resolution 4 kilometers (URL: http://www.ocs.orst.edu/prism/prism_new.html).

Table 2. Description of basin characteristics used in the final equations for estimating low-flow frequency statistics for unregulated streams in Idaho.

Basin characteristic

(identifier) Description

Drainage area (A) Drainage area of the basin that contributes surface runoff, in square miles; estimated using Arc/Info 

Grid with 30-meter-resolution digital-elevation models (DEMs).

Mean annual precipitation (P) Mean annual precipitation over the entire drainage area, in inches; estimated using Arc/Info Grid with 

a combination of 500-meter resolution (within Idaho) and 4-kilometer resolution (outside of Idaho) 

precipitation grids covering the 1961-1990 period.

Developed land (DV) Areas of residential, commercial, industrial, and transportation lands, in percentage of drainage area; 

estimated from the National Land Cover Dataset (NLCD) 1992 version. 

Agricultural land (AG) Areas of pasture, row crop, small grain, fallow, and urban/recreational grass lands, in percentage of 

drainage area; estimated from the National Land Cover Dataset (NLCD) 1992 version.

Basin slope (BS) Average slope of the basin, in percent; estimated using the SLOPE function in Arc/Info Grid with 

30-meter-resolution DEMs.

Water (W) Areas of open water or perennial ice and snow, in percentage of drainage area; estimated from the 

National Land Cover Dataset (NLCD) 1992 version.

Basin relief (R) Relief of the basin, in feet; estimated using Arc/Info Grid with 30-meter-resolution digital-elevation 

models (DEMs).

Surficial volcanic rocks (V) Areas of surficial volcanic rocks, in percentage of drainage area; estimated from the Pacific 

Northwest Major Lithology data set.

Slopes greater than 50 percent (S50) Area with slopes greater than 50 percent, in percentage of drainage area; estimated using the SLOPE 

function in Arc/Info Grid with 30-meter-resolution DEMs.

 Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Logistic Regression Analysis

Logistic regression analyses were used to develop 

equations that relate the probability of a specific N-day low 

flow equaling zero to basin characteristics. The use of logistic 

regressions for water-resources applications is discussed in 

more detail by Helsel and Hirsch (1992). Applications specific 

to low-flow analyses can be found in a paper by Tasker (1989) 

and a report by Ludwig and Tasker (1993). Hosmer and 

Lemeshow (2000) provide a complete discussion of logistic 

regression.

The output variable in a logistic regression equation is 

dichotomous (binary), meaning that there are two possible 

outcomes. In this study, the possible outcomes were flow or 

no flow. Logistic regression is conceptually similar to multiple 

linear regression because the relation between one dependent 

variable and several independent variables is evaluated. The 

differences are reflected in the form of the equation and in 

the assumptions. Four important concepts regarding logistic 

regression analyses are as follows: (1) the conditional mean of 

the regression equation must fall between zero and 1; 

(2) the distribution of the errors is binomial, not normal; 

(3) equation coefficients are estimated using the log likelihood 

function, not least squares as is done in linear regression; and 

(4) the general principles that guide the development of linear 

regression equations are also relevant for logistic regression 

(Hosmer and Lemeshow, 2000).

The final form of the logistic regression equation 

results in a probability of success of one of the two possible 

outcomes. For this study, it was the probability that the 

specific N-day low flow is equal to zero. The final form of the 

logistic regression equation can be written as follows: 

P e

e zero

a c V c V c V

a c V c V c V

n n

n n

=

+

+ + + +

+ + + +

( ... )

( ... )

1 1 2 2

1 1 1 2 2

 , (2)

where

Pzero is the probability of the N-day low flow being 

equal to zero,

a is the regession model constant,

e is a mathematical constant,

c c 1 to n are the regression model coefficients, and

V V 1 to n are the required basin characteristics.

Data from each of the gaging stations listed in table 6

were used in the logistic regression analyses. The Statit 

Custom QC (Statit Software, 2005) statistical software 

package was used to perform the logistic regression analyses. 

The data required to perform the analyses included the total 

number of years of record, total number of years that each 

of the specific N-day low flows equaled zero, and basin 

characteristics for each gaging station in the region being 

analyzed. In the analyses, the number of years that the 

specific N-day low-flow equaled zero was the dependent 

variable, the total number of years of record was the binomial 

trials variable (number of possible zero-flow years), and the 

basin characteristics were the independent variables. The 

total years of N-day zero flows and total years of record 

for each of the gaging stations are presented in table 10 (at 

back of report). Only region 2 had no gaging stations with 

at least 1 year where one of the N-day low flows equaled 

zero. Basin-characteristic data for the gaging stations were 

presented previously in table 9. 

Several statistical parameters were used to help with 

the selection of the final probability equations. The overall 

likelihood ratio tests whether the model coefficients are 

significantly different from zero. This ratio follows a 

chi-squared distribution and computed p-values indicate 

whether model coefficients are significantly different from 

zero. A p-value threshold of 0.05 was used for this analysis. 

McFadden’s R2 is a transformation of the log-likelihood ratio 

intended to be similar to the unadjusted R2 in linear regression. 

However, McFadden’s R2 tends to be smaller than R2 in linear 

regression. The percentage of correct responses is calculated 

as the number of observed zero flows that were predicted by 

the model as zero flows, plus the number of non-zero flows 

predicted by the model as non-zero flows, divided by the 

total number of gaging stations used in the analysis. The odds 

ratio is a measure of the relative influence of an independent 

variable on the model.

Multiple Linear Regression Analysis

The use of multiple linear regression equations is 

the most common method used for estimating streamflow 

statistics at ungaged sites. In multiple linear regression 

analyses, streamflow statistics from several long-term gaging 

stations are statistically related to various basin characteristics 

for each of the gaging stations. The resulting equation can 

then be used with the relevant basin characteristics to estimate 

streamflow statistics at ungaged sites where no streamflow 

data are available.

The typical form of equations generated from multiple 

linear regression analyses is 

Y b i = +0 1b X1 2 + + b X2 + + b Xn n i ... e , (3)

where

Yi is the estimate of the dependent variable for site i,

b b 0 to n are the n +1 regression model coefficients,

X X i n to are the n independent variables, and

ei is the residual error (difference between the 

observed and estimated values of the dependent 

variable) for site i .

Four assumptions are associated with the regression analyses: 

(1) the mean of ei is zero, (2) the variance of ei is constant 

and independent of the values of Xn , (3) the values for ei are 

normally distributed, and (4) the values for ei are independent 

of each other (Haan, 1977).

Estimating Low-Flow Frequency Statistics at Ungaged Sites 
Streamflow statistics and basin characteristics generally 

are log-normally distributed. As a result, a log transformation 

of the variables is necessary to satisfy assumption 1 above. 

The use of log-transformed values results in an equation of the 

following linear form:

logY b i = +0 1b X log 1 2 + + b X log 2 ... + + b X n log n ie . (4)

The coefficients for this equation are derived from the 

multiple linear regression analyses and then the equation is 

transformed back to original units. The retransformed equation 

takes on the following form:

Y X i X X b b b n

b = 10 0 1 1 2 2 ... n i 10e . (5)

In hydrologic terms, assuming that ei is zero as stated in 

the assumptions above, the equation can be written as:

Q a i V V V c c n

c = n 1 2 1 2 ... , (6)

where

Q1 is the low-flow statistic,

a is the model constant transformed back to original 

units,

V V 1 to n are the required basin characteristics, and

c c 1 to n are the regression model coefficients.

Because streamflow data are essentially correlated 

spatially and in time, assumption 4 is not strictly satisfied when 

the most commonly used form of regression analysis, Ordinary 

Least Squares (OLS) is used. As a result, Generalized Least 

Squares (GLS) regression techniques were developed for use in 

regression analysis of peak- and low-flow frequency statistics. 

GLS techniques are the most appropriate for dealing with 

hydrologic regressions because the algorithms allow for the 

weighting of station data to compensate for spatial correlation 

and differences in record length (Tasker and Stedinger, 1989). 

For this study, OLS techniques were used to narrow down the 

list of possible explanatory variables (basin characteristics) 

and then GLS techniques were used to determine the final 

estimating equations. The Statit Custom QC (Statit Software, 

2005) statistical software package was used to perform the 

initial regressions using OLS techniques and the USGS 

software package GLSNET (U.S. Geological Survey, 1998) 

was used to finalize the equations using GLS techniques.

Because the regression technique for low-flow statistics 

requires a log transformation, zero values cannot be used in the 

multiple linear regression analyses. All gaging stations listed 

in table 6 were used in the analyses except those with specific 

low-flow statistics equal to zero (see table 7). Depending on the 

values of the various low-flow statistics for a specific gaging 

station, it would be possible to include the gaging station in the 

analysis for one statistic but exclude it from the analysis for 

another. The basin characteristic values used in the analyses 

were presented previously in table 8. To ensure that zero 

values, which cannot be transformed, would not result for 

any gaging station, 1 percent was added to the values of the 

following basin characteristics prior to the log transformation: 

developed land (DV), agricultural land (AG), water (W), 

volcanic rock (V), and slopes greater than 50 percent (S50). 

In addition, basin relief (R) was divided by 1,000 prior to 

transformation to allow for more convenient coefficients in the 

final equations.

The final equations were chosen primarily, but 

not exclusively, on the basis of the following statistical 

parameters: (1) mean square error (MSE), the model error 

variance of the estimates for the stations included in the 

analysis; (2) R2adj, the percentage of the variation in the 

dependent variable explained by the independent variables, 

adjusted for the number of stations and the number of 

independent variables used in the regression analysis; and 

(3) the PRESS statistic, an estimate of the prediction error 

sum of squares. In the end, simpler equations were chosen 

over more complex equations if the statistical parameters were 

similar.

Final Estimating Equations

Logistic regression analyses were performed for each 

of the regions with at least one gaging station with N-day 

low-flow data equal to zero (all the regions except region 2). 

The analyses in three of those regions—4, 6, and 7—resulted 

in equations that were statistically significant for estimating 

the annual probability of zero flows for 1-, 7-, and 30-day 

periods. Likely reasons why statistically significant equations 

could not be developed for regions 1, 3, 5, and 8 are that there 

were a relatively small number of gaging stations with N-day 

low-flow values equal to zero or there were a small number of 

zero values per gaging station.

The logistic regression equations developed for regions 

4, 6, and 7 are presented in table 3 and should be used to 

determine the probability of the specific annual minimum 

N-day flows equaling zero for ungaged sites in those regions 

before low-flow frequency statistics are estimated. Values for 

some of the previously defined statistical parameters used to 

evaluate the quality of the equations are included in table 3. 

If the resulting probability is greater than the non-exceedance 

probability for the statistic of interest, then the expected value 

for that statistic would be zero and the low-flow frequency 

equations should not be used. If the resulting probability 

is less than the non-exceedance probability for the statistic 

of interest, then the low-flow frequency equations should 

be used to estimate the value of the statistic. For example, 

if the probability of a specific 7-day low flow equaling 

zero was 0.35 from the equation, the expected value for the 

7Q10 statistic would be zero (0.35 > 0.10 or 1/10), and the 

expected value for the 7Q2 statistic would be greater than 

zero (0.35 < 0.50 or 1/2) and should be estimated using the 

low-flow frequency equation.

 Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Although equations were not able to be developed 

for regions 1, 3, 5, and 8, the data show that it is possible, 

though not very common, to have occurrences of zero flow 

at certain locations within these regions. Thus, low-flow 

estimates approaching zero for ungaged sites (determined 

from the regression equations) may need additional analyses to 

determine if zero flows also are likely. Analyses could include 

comparisons of basin characteristics to gaging stations with 

known zero-flow occurrences in the same region (table 10) or 

field observations during expected low-flow periods.

Multiple linear regression analyses resulted in the 

development of four equations to estimate the low-flow 

frequency statistics 1Q10, 7Q2, 7Q10, and 30Q5 for 

unregulated streams in each of the eight regions in the State. 

The final equations are presented in table 4, along with the 

associated standard error of the model and the standard error 

of prediction for each equation. The standard error of the 

model measures how well the regression model fits the data 

used to develop it. The standard error of prediction includes 

the model error as well as an estimate of the sample error and 

is a better indicator of the model’s overall predictive ability 

(Pope and others, 2001). The values presented in log10 format 

represent the errors of the log-transformed equations. The 

percentage values represent the range of errors for the final 

untransformed equations. These values were determined using 

error transformation equations presented in Riggs (1968).

Table 3. Logistic regression equations used to estimate the probability of zero flow for unregulated streams in regions 4, 6, and 7 in Idaho.

[Locations of regions are shown in figure 1. Zero flow annual probability equation: Pn-day, annual probability of zero flow for n days; A, drainage area in 

square miles; P, mean annual precipitation, in inches; DV, developed land in percentage of drainage area; AG, agricultural land in percentage of drainage area; 

BS, basin slope in percent. OLR: Overall likelihood ratio. OLR-p: chi-square p-value for the overall likelihood ratio. Percentage correctly estimated: Based 

only on the sample data used to develop the equation]

Zero flow annual probability equation McFadden’s R2 OLR OLR-p Percentage correctly 

estimated

Region 4

P1-day = e (–47.5 – 0.0264A – 0.243P + 50.5(DV+1)) 0.757 148.3 <0.0001 90

1 + e (–47.5 – 0.0264A – 0.243P + 50.5(DV+1))

P7-day = e (–50.3 – 0.0323A – 0.224P + 52.5(DV+1)) .717 125.1 <.0001 95 (10-year)

1 + e (-50.3 – 0.0323A – 0.224P + 52.5(DV+1)) 100 (2-year)

P30-day = e (–57.1 – 0.0369A – 0.246P + 59.5(DV+1)) .772 127.4 <.0001 100

1 + e (–57.1 – 0.0369A – 0.246P + 59.5(DV+1))

Region 6

P1-day = e (25.5 – 0.0160A – 1.29P + 0.908(AG+1)) 0.847 353.2 <0.0001 100

1 + e (25.5 – 0.0160A – 1.29P + 0.908(AG+1))

P7-day = e (25.0 – 0.0156A – 1.27P + 0.899(AG+1)) .828 338.8 <.0001

96 (10-year)

1 + e (25.0 – 0.0156A – 1.27P + 0.899(AG+1)) 92 (2-year)

P30-day = e (26.8 – 0.0157A – 1.39P + 0.932(AG+1)) .809 285.9 <.0001 96

1 + e (26.8 - 0.0157A – 1.39P + 0.932(AG+1))

Region 7

P1-day = e (8.39 – 0.0136A – 0.442BS) 0.537 217.1 <0.0001 78

1 + e (8.39 – 0.0136A – 0.442BS) 

P7-day = e (8.09 – 0.0121A – 0.454BS)

 .547 200.3 <.0001 74 (10-year)

1 + e (8.09 – 0.0121A – 0.454BS) 96 (2-year)

P30-day = e (8.92 – 0.0141A – 0.516BS) .607 183.4 <.0001 89 

1 + e (8.92 – 0.0141A – 0.516BS)

Estimating Low-Flow Frequency Statistics at Ungaged Sites 
Table 4. Regression equations for estimating low-flow frequency statistics for unregulated streams in regions 1-8 in Idaho.

[Locations of regions are shown in figure 1. Low-flow frequency equation: A, drainage area, in square miles; BS, basin slope, in percent; P, mean annual 

precipitation, in inches; R, basin relief, in feet; S50, slopes greater than 50 percent in percentage of drainage area; V, surficial volcanic rocks, in percentage of 

drainage area; W, water, in percentage of drainage area]

Low-flow frequency equation

Standard error of model Standard error of prediction

log10 Percent log10 Percent

Region 1

1Q10 = 0.794 A0.420 (W + 1)1.32 0.078 +19.7 to –16.6 0.177 +50.3 to –33.5

7Q10 = 0.804 A0.453 (W + 1)1.22 .032 +7.55 to –7.02 .155 +43.0 to –30.1

7Q2 = 0.731 A0.613 (W + 1)0.907 .032 +7.55 to –7.02 .132 +35.4 to –26.1

30Q5 = 0.911 A0.512 (W + 1)1.05 .032 +7.55 to –7.02 .136 +36.7 to –26.8

Region 2

1Q10 = 0.0000497 A1.05 P2.03 0.333 +115 to–53.5 0.346 +122 to –54.9

7Q10 = 0.0000728 A1.06 P1.98 .317 +107 to –51.8 .329 +113 to –53.1

7Q2 = 0.000153 A1.04 P1.92 .243 +74.9 to –42.8 .253 +78.9 to –44.1

30Q5 = 0.000164 A1.04 P1.87 .270 +86.3 to –46.3 .281 +91.0 to –47.6

Region 3

1Q10 = 0.00492 A–0.0990 (R/1,000)5.15 0.467 +193 to –65.9 0.552 +257 to –72.0

7Q10 = 0.00964 A–0.0923 (R/1,000)4.76 .462 +190 to –65.5 .545 +251 to –71.5

7Q2 = 0.00953 A0.392 (R/1,000)3.36 .298 +98.6 to –49.6 .351 +125 to –55.4

30Q5 = 0.0186 A0.109 (R/1,000)3.84 .327 +112 to –52.9 .386 +143 to –58.9

Region 4

1Q10 = 0.00000187 A1.03 P2.90 0.452 +183 to –64.7 0.471 +195 to –66.2

7Q10 = 0.00000222 A1.05 P2.88 .432 +170 to –63.0 .449 +181 to –64.4

7Q2 = 0.0000215 A1.04 P2.41 .328 +113 to –53.0 .341 +119 to –54.4

30Q5 = 0.00000993 A1.04 P2.58 .360 +129 to –56.4 .375 +137 to –57.8

Region 5

1Q10 = 0.0000497 A0.968 (V+1)1.96 0.382 +141 to –58.5 0.419 +163 to –61.9

7Q10 = 0.0000654 A0.959 (V+1)1.96 .341 +120 to –54.4 .378 +139 to –58.1

7Q2 = 0.000453 A1.04 (V+1)1.51 .042 +10.3 to –9.31 .103 +26.9 to –21.2

30Q5 = 0.000190 A0.981 (V+1)1.74 .222 +66.6 to –40.0 .255 +80.0 to –44.5

Region 6

1Q10 = 0.0000324 A1.06 P2.38 0.287 +93.8 to –48.4 0.309 +104 to –50.9

7Q10 = 0.0000360 A1.06 P2.38 0.286 +98.3 to –43.3 .307 +103 to –50.7

7Q2 = 0.000133 A1.05 P2.10 0.226 +68.5 to –40.6 .243 +75.0 to –42.9

30Q5 = 0.000127 A1.04 P2.10 0.264 +83.5 to –45.5 .283 +91.9 to –47.9

Region 7

1Q10 = 0.0149 A0.613 (S50 + 1)0.949 0.544 +250 to –71.5 0.614 +311 to –75.7

7Q10 = 0.0177 A0.627 (S50 + 1)0.924 .503 +219 to –68.6 .570 +271 to –73.1

7Q2 = 0.0329 A0.678 (S50 + 1)0.796 .483 +204 to –67.1 .533 +241 to –70.7

30Q5 = 0.0272 A0.648 (S50+1)0.851 .485 +206 to –67.3 .541 +248 to –71.2

Region 8

1Q10 = 3.15 A0.866 BS –0.640 0.201 +59.0 to –37.1 0.226 +68.3 to –40.6

7Q10 = 2.27 A0.903 BS –0.545 .124 +33.0 to –24.8 .157 +43.6 to –30.4

7Q2 = 3.86 A0.930 BS –0.648 .136 +36.9 to –27.0 .157 +43.4 to –30.3

30Q5 = 6.17 A0.940 BS –0.844 .119 +31.6 to –24.0 .144 +39.2 to –28.1

10 Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Accuracy and Limitations

The percentage of correct values for the zero-flow 

probability equations ranged from 74 to 100 percent (table 3). 

The values for regions 4 and 6 were all 90 percent or higher. 

The values for region 7 ranged from 74 to 96 percent. These 

values provide an indication of the accuracy of the equations 

based only on the data used to develop the equations. It is 

assumed that the data used in each region provide a good 

representation of the zero-flow characteristics of streams 

in the region. However, any variability in the zero-flow 

characteristics within each region that was not represented in 

the development of the equations may have an effect on the 

final predictive accuracy of the equations.

The model and prediction standard errors for the final 

estimating equations range significantly across the eight 

regions (table 4). Equations for regions 1 and 8 had relatively 

low standard errors, whereas those for regions 3 and 7 were 

quite large. The large errors associated with the region 3 

equations may be the result of the low number of gaging 

stations (eight) available for the analysis. The large errors 

associated with the region 7 equations likely indicate that the 

available basin characteristics do not adequately represent the 

factors that affect low flows in this area. The natural variability 

of streamflow may also be an important factor. Prediction of 

streamflow statistics that have a high degree of variability 

will always have more uncertainty than prediction of statistics 

that are more stable. Hortness and Berenbrock (2001) noted 

that the natural variability of streamflow in regions 6 and 

7 is generally greater than the natural variability in the 

other regions. It is also important to note that even a large 

percentage error associated with low-flow values does not 

necessarily result in a large-magnitude error range around the 

value. For example, a low-flow value of 5.0 ft3/s with errors 

of +150 and -75 percent would have a resulting error range of 

1.25 to 12.5 ft3/s.

The standard errors of prediction for the equations 

across the eight regions had a minimum range of +26.9 to 

-21.2 percent for the 7Q2 statistic in region 5 and a maximum 

range of +311 to -75.7 percent for the 1Q10 statistic in 

region 7. These error values represent the general predictive 

ability of the estimating equations; however, other factors 

could limit the applicability of the equations. It is important 

to note that because of the transformation from log to back to 

arithmetic units, the standard error values will always have 

larger positive values than negative values.

Because the zero-flow probability and low-flow 

estimating equations are based on regression analyses, 

the equations might not be reliable for sites where the 

basin-characteristic values are outside of the range of 

values that were used to develop the equations (table 5). In 

addition, using basin characteristic values near their extremes 

(maximum or minimum, table 5) might result in unreliable 

estimates. Figure 2 shows a “cloud of common values” for 

two basin characteristics. In this example, if the minimum 

value for mean annual precipitation and the maximum value 

for mean basin elevation were used, the combination would 

plot outside of the “cloud of common values,” thus the 

corresponding equation might result in unreliable estimates. 

Generating basin-characteristic values by using datasets or 

processes other than those described in this study also will 

result in estimates of unknown reliability. The standard errors 

for each equation are only applicable if the datasets presented 

in table 1 are used to obtain the required basin characteristics.

The equations are not applicable for stream reaches 

affected by irrigation diversions and(or) returns, or dams that 

regulate streamflow. The Boise River downstream from Lucky 

Peak Lake, the Clearwater River downstream from Dworshak 

Reservoir, and the entire Snake River in Idaho are examples of 

stream reaches within the study area for which the estimating 

equations are not applicable. However, the equations could 

be used on regulated streams to provide an estimate of 

natural flow statistics for comparison with the regulated 

statistics, given that, as previously explained, all of the basin 

characteristics for the site fall within the ranges of those used 

to develop the equations.

Figure 2. Joint distribution of two example basin 

characteristics, mean basin elevation and mean annual 

precipitation.

MEAN BASIN ELEVATION,

IN THOUSANDS OF FEET ABOVE SEA LEVEL

MEAN ANNUAL

PRECIPITATION, IN INCHES

100

80

60

40

20

0

0 2 4 6 8 10

CLOUD OF

COMMON VALUES

EXAMPLE

COMBINATION POINT

(outside of cloud)

Estimating Low-Flow Frequency Statistics at Ungaged Sites 11
Table 5. Range of values of basin characteristics used to estimate low-flow frequency statistics for unregulated streams in regions 1-8 in Idaho.

[Location of regions are shown in figure 1. Equation variables: A, drainage area, in square miles; P, mean annual precipitation, in inches; DV, developed land, 

in percentage of drainage area; AG, agricultural land, in percentage of drainage area; BS, basin slope, in percent; W, water, in percentage of drainage area; R, 

basin relief, in feet; V, surficial volcanic rocks, in percentage of drainage area; S50, slopes greater than 50 percent, in percentage of drainage area]

Equation variables

A P DV AG BS W R V S50

Region 1

Maximum 1,011.0 54.3 3.59 23.2 46.4 6.69 5,866.9 27.9 41.4

Minimum 12.5 25.1 .000 .005 12.2 .004 2,230.6 .000 1.04

Region 2

Maximum 2,442.5 69.4 1.83 4.43 66.8 3.98 7,789.6 99.9 67.4

Minimum 3.0 24.8 .000 .000 23.8 .000 1,643.9 .000 2.62

Region 3

Maximum 674.9 30.1 18.6 91.6 35.4 0.258 5,098.9 92.7 27.5

Minimum 17.6 19.3 .031 7.46 10.0 .006 1,442.8 14.5 .018

Region 4

Maximum 5,507.9 65.6 0.126 18.4 57.2 1.04 8,364.5 100.0 63.1

Minimum 4.0 15.9 .000 .000 18.7 .000 1,821.4 18.2 1.27

Region 5

Maximum 12,228.0 44.5 2.21 2.44 46.7 4.37 10,701.3 100.0 46.1

Minimum 19.3 22.4 .000 .000 20.2 .002 2,743.5 27.1 3.47

Region 6

Maximum 6,236.7 42.3 0.385 9.27 66.2 1.19 9,419.7 93.0 77.2

Minimum 6.4 15.3 .000 .000 8.60 .000 2,395.4 .000 1.36

Region 7

Maximum 535.3 29.3 0.296 28.1 35.3 0.599 5,683.3 100.0 28.5

Minimum 7.4 12.3 .000 .000 10.1 .000 1,681.7 .000 .189

Region 8

Maximum 874.8 56.0 0.176 70.7 53.2 3.83 6,232.1 90.1 60.5

Minimum 6.6 14.2 .000 .000 6.15 .000 1,100.5 .000 .002

The estimating equations may not be applicable for 

streams that exhibit significant gains as a result of spring 

flow or significant losses as a result of channel seepage. The 

effects of headwater springs and other small springs that are 

representative of many or all streams in a particular region 

because of similar geologic conditions likely would be reflected 

in the equations for that region. The effects of larger springs 

which significantly affect streamflows likely would not be 

reflected in the equations. Similarly, the effects of small losses 

due to channel seepage which are representative of streams in 

a particular region likely would be reflected in the equations, 

while the effects of larger losses likely would not. In specific 

instances, user judgment may be required to decide if the 

particular ungaged site of interest is affected by factors similar 

to those that affected the gaging station data used to develop 

the relevant equations. For example, results for an ungaged site 

on the Lemhi River near Lemhi in region 6, which has fairly 

significant and highly variable streamflow gains and losses 

(Donato, 1998), may be suspect since no mainstem Lemhi 

River gaging stations were used to develop the equations. 

However, if a gaging station from the Lemhi River or another 

river with similar characteristics were included, the equations 

likely would produce satisfactory results.

Application of Regional Regression Method

Three examples are given for using the equations to 

estimate low-flow frequency statistics for unregulated streams 

in Idaho. Example 1 addresses the basic ungaged site with 

the entire upstream drainage area located within the same 

region and no zero-flow probabilities, example 2 addresses 

the situation where zero-flow probability equations are used 

to estimate the probability of zero flows at a site (regions 4, 

6, and 7, only) and example 3 addresses the situation where 

the drainage area of a specific site encompasses parts of two 

separate regions.

12  Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Example 1

An estimate of the 7Q2 low-flow statistic is required for 

a stream location in region 2. The following required basin 

characteristics were determined for region 2 equations: 

A, 2180.5 mi2; and P, 30.2 in. Since region 2 has no zero 

flow annual probability equations, the user would go directly 

to the low-flow frequency regression equations. Based on the 

basin-characteristic values, the estimated 7Q2 statistic can be 

computed as follows:

7 0 000153

7 0 000153 2180 5 30 2

7

2

1 04 1 92

2

1 04 1 92

Q A P

Q

Q

=

=

.

. ( . ) ( . )

. .

. .

2 = 315 ft /s 3

The predicted range of the actual values for this low-flow 

statistic, based on the range of the standard error of prediction 

given in table 4, is as follows:

7Q2 = 176 ft /s to 562 ft /s +78 9 4 to - 4 1 percent 3 3 ( . . ) .

Example 2

An estimate of the 7Q10 low-flow statistic is required for 

a stream location in region 6. The following required basin 

characteristics were determined for region 6 equations: A , 

8.2 mi2; and P , 24.7 in.; and AG , 1.35 percent. Based on 

these values, the probability of the 7-day low-flow equaling 

zero at this site is computed as follows:

P e

e

A P AG

7-day

 

=

+

( . - . - . + + . ( ))

( . -

25 0 0 0156 1 27 0 899 1

25 0 0 1 . - . . ( ))

( . - . ( . )

0156 1 27 0 899 1

25 0 0 0156 8 2

A P AG

P e

 

7-day

 

+ +

=

- . ( . ) . ( . ))

( . - . ( . ) - .

 

 

1 27 24 7 0 899 1 35 1

25 0 0 0156 8 2 1 2 1

+ +

+e 7 24 7 0 899 1 35 1

0 012

( . ) . ( . ))

. 7-day

+ +

P =

.

Because the probability is less than 0.10 (1/10 for 10 year 

recurrence), the equation estimates that the 7-day low flow for 

this site is greater than zero. The estimated 7Q10 statistic can 

then be computed as follows:

7 0 0000360

7 0 0000360 8 2 24 7

7

10

1 06 2 38

10

1 06 2 38

Q A P

Q

=

=

.

. ( . ) ( . )

. .

. .

Q10 = 0.691 ft 3s

.

The predicted range of the actual values for this low-flow 

statistic, based on the range of the standard error of prediction 

given in table 4, is as follows:

7 0 Q10 = .341 ft /s to 1 4. 0 ft (+103 to - 50.7 percent) 3 3s .

Example 3

An estimate of the 30Q5 low-flow statistic is required 

for a site in region 5 on a stream with a drainage basin 

encompassing parts of regions 5 and 6. The recommended 

method for handling sites with portions of its drainage 

basin in two regions is as follows: (1) calculate values for 

the entire drainage basin by using equations from the first 

region, (2) calculate values for the entire drainage basin by 

using equations from the second region, and (3) average the 

two values on the basis of the proportion of drainage area 

in each region (Sando, 1998). The following required basin 

characteristics were determined for region 5 and 6 equations: 

A, 5,153.0 mi2; V, 78.5 percent; and P, 39.4 in. The portion 

of the drainage area located in region 5 covers 1,622.0 mi2

and the portion in region 6 covers 3,531.0 mi2. The step to 

check for the probability of zero flow in region 6 was skipped 

because of the large portion of the drainage area in region 5. 

Because the region boundaries were almost exclusively drawn 

along hydrologic boundaries, the occurrence of zero flows at 

sites that have portions of the drainage area in two regions is 

highly unlikely, but should be verified.

Region 5 calculations:

30 0 000127

30 0 000127 5153 0 39 4

5

1 04 2 10

5

1 04 2 10

Q A P

Q

=

=

.

. ( . ) ( . )

. .

. .

30Q5 = 2, 060 ft /s 3

.

Region 6 calculations:

30 0 000127

30 0 000127 5153 0 39 4

5

1 04 2 10

5

1 04 2 10

Q A P

Q

=

=

.

. ( . ) ( . )

. .

. .

30Q5 = 2, 060 ft /s 3

.

Area-weighted average:

30 1 690 1 622 0

5 153 0

2 060 3 531 Q5 = æ

è

ç

ç

ç

ö

ø

÷

÷

÷÷ , + , .

, . , , ft /s ft /s 3 3 ., .

,

0

5 153 0

30 5 1 940

æ

è

ç

ç

ç

ö

ø

÷

÷

÷÷

Q = ft /s 3

.

Estimating Low-Flow Frequency Statistics at Ungaged Sites 13
Summary

The USGS, in cooperation with the Idaho Department 

of Environmental Quality (IDEQ), used multiple linear 

regression analyses to develop equations that can be used for 

estimating the 1Q10, 7Q2, 7Q10, and 30Q5 low-flow frequency 

statistics at ungaged, unregulated sites on streams in Idaho. 

As part of this process, the relevant statistics were updated for 

all gaging stations in Idaho and some in adjacent States that, 

in general, had 10 or more years of record through water year 

2003 and were unaffected by regulation and/or diversions. In 

regions of the State where one or more of these statistics are 

sometimes equal to zero, logistic regression analyses were 

used to develop equations for estimating the probability that 

the annual N-day low flow is equal to zero. Various physical 

and climatic characteristics of the drainage basins (basin 

characteristics) were used as the explanatory variables in each 

of the equations.

The logistic regression analyses in regions 4, 6, and 7 

resulted in equations that were statistically significant for 

estimating the annual probability of zero flows for 1-, 7-, 

and 30-day periods. The final probability equations correctly 

predicted zero-flow values for 74 to 100 percent of the gaging 

stations used to develop the equations, depending on the 

region and the N-day period. Although it is assumed that these 

gaging stations provide a good representation of zero-flow 

characteristics in each of the regions, any variability in the 

zero-flow characteristics within each region that was not 

represented may affect the predictive accuracy of the final 

equations. The zero-flow probability equations should be 

used for sites in regions 4, 6, and 7 before low-flow frequency 

statistics are estimated. If the resulting probability is greater 

than the non-exceedance probability for the statistic of 

interest, then the expected value for that statistic would be 

zero and the low-flow frequency equations should not be used. 

If the resulting probability is less than the non-exceedance 

probability for the statistic of interest, then the low-flow 

frequency equations should be used to estimate the value of 

the required statistic.

The equations for estimating low-flow frequency 

statistics had standard errors of prediction with a minimum 

range of +26.9 to -21.2 percent and a maximum range 

of +311 to -75.7 percent. In general, the 7Q2 estimating 

equations exhibited the lowest standard errors, whereas 

the 1Q10 equations exhibited the largest standard errors. 

The equations may not yield reliable results for sites with 

basin-characteristic values that are outside of the range of 

values used to develop the equations. The equations also are 

not applicable for sites on regulated streams or on streams that 

are affected by significant gains and(or) losses resulting from 

factors including spring flow, channel seepage, diversions, and 

irrigation returns. If desired, however, the equations could be 

used on regulated streams to provide an estimate of natural 

flow statistics for comparison with the regulated statistics.

References Cited

Berenbrock, Charles, 2002, Estimating the magnitude of peak 

flows at selected recurrence intervals for streams in Idaho: 

U.S. Geological Survey Water-Resources Investigations 

Report 02-4170, 59 p.

Bond, J.G., 1978, Geologic map of Idaho: Moscow, Idaho 

Bureau of Mines and Geology, 1 sheet, scale 1:500,000.

Daly, C., and Taylor, G., 1998, Western United States average 

monthly or annual precipitation, 1961-90, Oregon: Portland, 

Water and Climate Center of the Natural Resources 

Conservation Service, accessed DATE at URL: http://www.

ocs.orst.edu/prism/prism_new.html.

Donato, M.M., 1998, Surface-water/ground-water relations in 

the Lemhi River Basin, East-Central Idaho: U.S. Geological 

Survey Water-Resources Investigations Report 98-4185, 

20 p.

Emmett, W.W., 1975, The channels and waters of the 

upper Salmon River area, Idaho: U.S. Geological Survey 

Professional Paper 870-A, 115 p.

Environmental Systems Research Institute, Inc., 2005, ArcGIS 

desktop help: accessed June, 2005, at URL: http://webhelp.

esri.com/arcgisdesktop/9.1.

Haan, C.T., 1977, Statistical methods in hydrology: Ames, 

Iowa State University Press, 378 p.

Harenberg, W.A., 1980, Using channel geometry to estimate 

flood flows at ungaged sites in Idaho: U.S. Geological 

Survey Water-Resources Investigations 80-32, 39 p.

Hedman, E.R., and Osterkamp, W.R., 1982, Streamflow 

characteristics related to channel geometry of streams 

in western United States: U.S. Geological Survey 

Water-Supply Paper 2193, 17 p.

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in 

water resources: New York, Elsevier Science Publishing 

Company, Inc., 522 p.

Horn, D.R., 1988, Annual flow statistics for ungaged streams 

in Idaho: American Society of Civil Engineers, Journal of 

Irrigation and Drainage Engineering, v. 114, no. 3, 

p. 463-474.

Hortness, J.E., and Berenbrock, Charles, 2001, Estimating 

monthly and annual streamflow statistics at ungaged 

sites in Idaho: U.S. Geological Survey Water-Resources 

Investigations Report 0-4093, 36 p.

Hortness, J.E., and Berenbrock, Charles, 2003, Estimating 

the magnitude of bankfull flows for streams in Idaho: 

U.S. Geological Survey Water-Resources Investigations 

Report 03-4261, 36 p.

Hosmer, D.W., and Lemeshow, S., 2000, Applied logistic 

regression: New York, John Wiley & Sons, Inc., 373 p.

Kjelstrom, L.C., 1998, Methods for estimating selected 

flow-duration and flood-frequency characteristics at 

ungaged sites in central Idaho: U.S. Geological Survey 

Water-Resources Investigations Report 94-4120, 10 p.

14  Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Kjelstrom, L.C., and Moffatt, R.L., 1981, A method of 

estimating flood-frequency parameters for streams in Idaho: 

U.S. Geological Survey Open-File Report 81-909, 99 p.

Kjelstrom, L.C., Stone, M.A.J., and Harenberg, W.A., 1995, 

Statistical summaries of streamflow data for selected gaging 

stations in Idaho and western Wyoming through September 

1990—Volume 2: Gaging stations with 5 to 9 years of 

record or that measure discharge from springs: U.S. 

Geological Survey Water-Resources Investigations 

Report 94-4070, 94 p.

Kjelstrom, L.C., Stone, M.A.J., and Harenberg, W.A., 1996, 

Statistical summaries of streamflow data for selected gaging 

stations in Idaho and adjacent States through September 

1990—Volume 1. Gaging stations with 10 or more years 

of record: U.S. Geological Survey Water-Resources 

Investigations Report 94-4069, 533 p.

Koltun, G.F., and Schwartz, R.R., 1986, Multiple-regression 

equations for estimating low flows at ungaged stream 

sites in Ohio: U.S. Geological Survey Water-Resources 

Investigations Report 86-4354, 39 p., 6 pls.

Lipscomb, S.W., 1998, Hydrologic classification and 

estimation of basin and hydrologic characteristics of 

subbasins in central Idaho: U.S. Geological Survey 

Professional Paper 1604, 49 p.

Ludwig, A.H., and Tasker, G.D., 1993, Regionalization 

of low-flow characteristics of Arkansas streams: U.S. 

Geological Survey Water-Resources Investigations 

Report 93-4013, 19 p.

Molnau, M., 1995, Mean annual precipitation, 1961-1990, 

Idaho: Moscow, University of Idaho, Agricultural 

Engineering Department, State Climate Program, scale 

1:1,000,000. Available at URL: http://snow.ag.uidaho.edu/

Climate/reports.html.

National Oceanic and Atmospheric Administration, 1971, 

Climates of the states, climate of Idaho, in Climatography 

of the United States: Silver Spring, Md., no. 60-10, 18 p.

Parrett, Charles, and Johnson, D.R., 2004, Methods for 

estimating flood frequency in Montana based on data 

through water year 1998: U.S. Geological Survey 

Water-Resources Investigations Report 03-4308, 

101 p.,1 pl.

Pope, B.F., Tasker, G.D., and Robbins, J.C., 2001, Estimating 

the magnitude and frequency of floods in rural basins of 

North Carolina—revised: U.S. Geological Survey 

Water-Resources Investigations Report 01-4207, 44 p.

Quillian, E.W., and Harenberg, W.A., 1982, An evaluation 

of Idaho stream-gaging networks: U.S. Geological Survey 

Open-File Report 82-865, 57 p.

Ries, K.G., and Friesz, P.J., 2000, Methods for estimating 

low-flow statistics for Massachusetts streams: U.S. 

Geological Survey Water-Resources Investigations 

Report 00-4135, 81 p.

Riggs, H.C., 1968, Some statistical tools in hydrology: 

U.S. Geological Survey Techniques of Water-Resources 

Investigations, Book 4, Chap. A1, 39 p.

 Riggs, H.C., 1972, Low-flow investigations: U.S. Geological 

Survey Techniques of Water-Resources Investigations, 

Book 4, Chap. B1, 18 p.

Ross, S.H., and Savage, C.N., 1967, Idaho earth science: 

Moscow, Idaho Bureau of Mines and Geology, 285 p.

Sando, S.K., 1998, Techniques for estimating peak-flow 

magnitude and frequency relations for South Dakota 

streams: U.S. Geological Survey Water-Resources 

Investigations Report 98-4055, 48 p.

Statit Software, 2005, Statit Custom QC: accessed January 

2005, at URL: http://www.statit.com/statitcustomqc/

customqc_default.htm.

Tasker, G.D., 1989, Regionalization of low flow characteristics 

using logistic and GLS regression, in Kavvas, M.L., 

ed., New directions for surface water modeling: IAHS 

Publication No. 181, p. 323-331.

Tasker, G.D., and Stedinger, J.R., 1989, An operational GLS 

model for hydrologic regression: Journal of Hydrology, v. 3, 

p. 361-375.

Thomas, C.A., Harenberg, W.A., and Anderson, J.M., 1973, 

Magnitude and frequency of floods in small drainage 

basins in Idaho: U.S. Geological Survey Water-Resources 

Investigations Report 7-73, 61 p.

Thomas, B.E., Hjalmarson, H.W., and Waltemeyer, S.D., 1994, 

Methods for estimating magnitude and frequency of floods 

in the Southwestern United States: U.S. Geological Survey 

Open-File Report 93–419, 211 p.

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Washington: accessed July 2004, at URL: http://www.

icbemp.gov/spatial/min.

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Software, GLSNET: accessed February 2005, at URL: 

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D.M., 1998, Regional land cover characterization using 

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p. 415-428, accessed July 2004, at URL: http://edcwww.

cr.usgs.gov/programs/lccp.

References Cited 15
Map

No.

Gaging 

station 

No.

Gaging station name Periods of record 

(water years)

Region 1

1 12305500 Boulder Creek near Leonia, ID 1928–71,1973–77

2 12311000 Deep Creek at Moravia, ID 1928–71

3 12316800 Mission Creek near Copeland, ID 1958–81

4 12320500 Long Canyon Creek near Porthill, ID 1931–59

5 12321000 Smith Creek near Porthill, ID 1928–60

6 12392155 Lightning Creek at Clark Fork, ID 1989–2003

7 12392300 Pack River near Colburn, ID 1958–82

8 12393500 Priest River at Outlet of Priest Lake near Coolin, ID 1912–48

9 12396000 Calispell Creek near Dalkena, WA 1950–73

10 12408500 Mill Creek near Colville, WA 1940–72,1977–86

11 12409000 Colville River at Kettle Falls, WA 1923–2003

12 12427000 Little Spokane River at Elk, WA 1948–71

13 12431000 Little Spokane River at Dartford, WA 1929–32,1947–2003

Region 2

14 12301300 Tobacco River near Eureka, MT 1959–2003

15 12301999 Wolf Creek near Libby, MT 1967–77

16 12302000 Fisher River near Jennings, MT 1951–69

17 12302055 Fisher River near Libby, MT 1968–2003

18 12302500 Granite Creek near Libby, MT 1933–34,1936–44,1960–69

19 12303100 Flower Creek near Libby, MT 1960–92

20 12303500 Lake Creek at Troy, MT 1945–57,1983–96

21 12340000 Blackfoot River near Bonner, MT 1898–1901,1903–06,1940–2003

22 12341000 Rattlesnake Creek at Missoula, MT 1899–1900,1958–67

23 12343400 East Fork Bitterroot River near Conner, MT 1956–72,2001–03

24 12344000 Bitterroot River near Darby, MT 1937–2003

25 12346500 Skalkaho Creek near Hamilton, MT 1949–53,1957–79,2001–03

26 12347500 Blodgett Creek near Corvallis, MT 1947–69

27 12350000 Bear Creek near Victor, MT 1938–55,1957–59

28 12350500 Kootenai Creek near Stevensville, MT 1949–53,1957–63

29 12351000 Burnt Fork Bitterroot River near Stevensville, MT 1920–24,1938–62

30 12352000 Lolo Creek above Sleeman Creek near Lolo, MT 1951–60

31 12353280 Ninemile Creek near Huson, MT 1973–83

32 12354000 St. Regis River near St. Regis, MT 1910–17,1958–75,2002–03

33 12375900 South Crow Creek near Ronan, MT 1982–2003

34 12377150 Mission Creek above Res near St. Ignatius, MT 1982–2003

35 12389500 Thompson River near Thompson Falls, MT 1911,1956–2003

36 12390700 Prospect Creek at Thompson Falls, MT 1956–2003

37 12411000 North Fork Coeur d’Alene River above Shoshone Creek near Prichard, ID 1951–2003

38 12413000 North Fork Coeur d’Alene River at Enaville, ID 1911–13,1939–2003

39 12413140 Placer Creek at Wallace, ID 1967–97,1999–2000

40 12413150 South Fork Coeur d’Alene River at Silverton, ID 1968–88,1999–2000

41 12413210 South Fork Coeur d’Alene at Elizabeth Park near Kellogg, ID 1987–2003

42 12413470 South Fork Coeur d’Alene River near Pinehurst, ID 1987–2003

43 12413500 Coeur d’Alene River at Cataldo, ID 1911–12,1920–72,1987–2003

44 12414500 St. Joe River at Calder, ID 1911–12,1920–2003

45 12414900 St. Maries River near Santa, ID 1966–2003

46 12415000 St. Maries River at Lotus, ID 1912–13,1920–66

47 12416000 Hayden Creek below North Fork near Hayden Lake, ID 1948–54,1959,1966–97

48 13336500 Selway River near Lowell, ID 1911,1930–2003

Table 6. Selected information for gaging stations used to estimate low-flow frequency statistics for unregulated streams in regions 1-8 in Idaho.

[Location of gaging stations and regions are shown in figure 1. Gaging station name: ID, Idaho; WA, Washington; MT, Montana; OR, Oregon; UT, Utah; NV, 

Nevada; WY, Wyoming. Water year: The 12-month period from October 1 through September 20, designated by the calendar year in which it ends]

16  Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Map

No.

Gaging 

station 

No.

Gaging station name Periods of record 

(water years)

Region 2 (Continued)

49 13336900 Fish Creek near Lowell, ID 1958–67

50 13337000 Lochsa River near Lowell, ID 1911–12,1930–2003

51 13340500 North Fork Clearwater River at Bungalow Ranger Station, ID 1945–69

52 13340600 North Fork Clearwater River near Canyon Ranger Station, ID 1967–2003

53 13341000 North Fork Clearwater River at Ahsahka, ID 1926–68

54 13341300 Bloom Creek near Bovill, ID 1959–72

55 13341400 East Fork Potlatch River near Bovill, ID 1959–72

Region 3

56 12424000 Hangman Creek at Spokane, WA 1948–2003

57 13334700 Asotin Creek below Kearney Gulch near Asotin, WA 1960–82,1992

58 13341500 Potlatch River at Kendrick, ID 1946–60

59 13342450 Lapwai Creek near Lapwai, ID 1975–2003

60 13345000 Palouse River near Potlatch, ID 1915–19,1967–2003

61 13346100 Palouse River at Colfax, WA 1964–73,1976–79

62 13346800 Paradise Creek at University of Idaho at Moscow, ID 1979–2003

63 13348000 South Fork Palouse River at Pullman, WA 1934–42,1960–81,2001–2003

64 13348500 Missouri Flat Creek at Pullman, WA 1934–40,1960–79

Region 4

65 13196500 Bannock Creek near Idaho City, ID 1939–42,1951–72

66 13200000 Mores Creek above Robie Creek near Arrowrock Dam, ID 1951–2003

67 13200500 Robie Creek near Arrowrock Dam, ID 1951–72

68 13201000 Mores Creek near Arrowrock, ID 1916–54

69 13207000 Spring Valley Creek near Eagle, ID 1955–59,1961–72

70 13207500 Dry Creek near Eagle, ID 1954–68

71 13250600 Big Willow Creek near Emmett, ID 1962–82

72 13251300 West Branch Weiser River near Tamarack, ID 1959–77

73 13251500 Weiser River at Tamarack, ID 1937–72,1974–76

74 13253500 Weiser River at Starkey, ID 1939–49

75 13256000 Weiser River near Council, ID 1937–53

76 13257000 Middle Fork Weiser River near Mesa, ID 1911–13,1919–22,1937–49,1981–83,

1985–88

77 13258500 Weiser River near Cambridge, ID 1939–2003

78 13260000 Pine Creek near Cambridge, ID 1938–62

79 13261000 Little Weiser River near Indian Valley, ID 1920–21,1923–27,1938–71

80 13267000 Mann Creek near Weiser, ID 1911–13,1920–21,1937–62

81 13269300 North Fork Burnt River near Whitney, OR 1964–80

82 13270800 South Fork Burnt River above Barney Creek near Unity, OR 1963–81

83 13275500 Powder River near Baker, OR 1904–14,1929–68

84 13288200 Eagle Creek above Skull Creek near New Bridge, OR 1958–98

85 13289960 Wildhorse River at Brownlee Dam, ID 1979–96

86 13290190 Pine Creek near Pine, OR 1967–96

87 13291000 Imnaha River above Gunboot Creek, OR 1945–53

88 13315500 Mud Creek near Tamarack, ID 1937–38,1946–59

89 13316500 Little Salmon River at Riggins, ID 1951–55,1957–2003

90 13316800 North Fork Skookumchuck Creek near White Bird, ID 1959–71

91 13319000 Grande Ronde River at La Grande, OR 1904–15,1918–23,1926–89

92 13320000 Catherine Creek near Union, OR 1932–96

Table 6. Selected information for gaging stations used to estimate low-flow frequency statistics for unregulated streams in regions 1-8 in Idaho.—

Continued

[Location of gaging stations and regions are shown in figure 1. Gaging station name: ID, Idaho; WA, Washington; MT, Montana; OR, Oregon; UT, Utah; NV, 

Nevada; WY, Wyoming. Water year: The 12-month period from October 1 through September 20, designated by the calendar year in which it ends]

Table 6  17
Map

No.

Gaging 

station 

No.

Gaging station name Periods of record 

(water years)

Region 4 (Continued)

93 13323600 Indian Creek near Imbler, OR 1938–50

94 13325500 Wallowa River above Wallowa Lake near Joseph, OR 1924–33

95 13329500 Hurricane Creek near Joseph, OR 1915,1924–78

96 13330000 Lostine River near Lostine, OR 1912–15,1925–91,1995–2003

97 13330500 Bear Creek near Wallowa, OR 1915,1924–85,1995–2003

98 13331500 Minam River at Minam, OR 1912–14,1965–2003

99 13337500 South Fork Clearwater River near Elk City, ID 1945–74,2002–03

100 13338000 South Fork Clearwater River near Grangeville, ID 1911–16,1923–63

101 13338500 South Fork Clearwater River at Stites, ID 1912,1965–2003

102 13339000 Clearwater River at Kamiah, ID 1910–66

103 13339500 Lolo Creek near Greer, ID 1980–2003

104 13340000 Clearwater River at Orofino, ID 1931–38,1965–2003

105 14010000 South Fork Walla Walla River near Milton, OR 1903,1907–17,1931–91,2001

106 14011000 North Fork Walla Walla River near Milton, OR 1930–69

Region 5

107 13135500 Big Wood River near Ketchum, ID 1948–72

108 13136500 Warm Springs Creek at Guyer Hot Springs near Ketchum, ID 1941–58

109 13139500 Big Wood River at Hailey, ID 1889–90,1915–2003

110 13141000 Big Wood River near Bellevue, ID 1911–96

111 13185000 Boise River near Twin Springs, ID 1911–2003

112 13186000 South Fork Boise River near Featherville, ID 1945–2003

113 13186500 Lime Creek near Bennett, ID 1945–56

114 13187000 Fall Creek near Anderson Ranch Dam, ID 1945–56

115 13235000 South Fork Payette River at Lowman, ID 1941–2003

116 13240000 Lake Fork Payette River above Jumbo Creek near McCall, ID 1946–2003

117 13292500 Salmon River near Obsidian, ID 1941–53

118 13293000 Alturas Lake Creek near Obsidian, ID 1941–52

119 13295000 Valley Creek at Stanley, ID 1911–14,1921–72,1993–2003

120 13295500 Salmon River below Valley Creek at Stanley, ID 1925–61

121 13296000 Yankee Fork Salmon River near Clayton, ID 1921–49

122 13296500 Salmon River below Yankee Fork near Clayton, ID 1922–92,2000–03

123 13308500 Middle Fork Salmon River near Capehorn, ID 1929–72

124 13309000 Bear Valley Creek near Capehorn, ID 1922–60

125 13309220 Middle Fork Salmon R at Middle Fork Lodge nr Yellow Pine, ID 1973–81,1999–2003

126 13310000 Big Creek near Big Creek, ID 1945–59

127 13310199 Middle Fork Salmon R at mouth near Shoup, ID 1994–2003

128 13310500 South Fork Salmon River near Knox, ID 1929–61

129 13310700 South Fork Salmon River near Krassel Ranger Station, ID 1967–82,1985–86,1989–2003

130 13311000 East Fork South Fork Salmon River at Stibnite, ID 1928–43,1983–97

131 13311500 East Fork South Fork Salmon River near Stibnite, ID 1928–41

132 13312000 East Fork South Fork Salmon River near Yellow Pine, ID 1928–43

133 13313000 Johnson Creek at Yellow Pine, ID 1928–2003

134 13313500 Secesh River near Burgdorf, ID 1943–52

135 13314000 South Fork Salmon River near Warren, ID 1931–43

136 13314300 South Fork Salmon River at mouth nr Mackay Bar, ID 1994–2003

137 13315000 Salmon River near French Creek, ID 1945–56

Table 6. Selected information for gaging stations used to estimate low-flow frequency statistics for unregulated streams in regions 1-8 in Idaho.—

Continued

[Location of gaging stations and regions are shown in figure 1. Gaging station name: ID, Idaho; WA, Washington; MT, Montana; OR, Oregon; UT, Utah; NV, 

Nevada; WY, Wyoming. Water year: The 12-month period from October 1 through September 20, designated by the calendar year in which it ends]

18  Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Map

No.

Gaging 

station 

No.

Gaging station name Periods of record 

(water years)

Region 6

138 06013500 Big Sheep Creek below Muddy Creek near Dell, MT 1936,1946–53,1961–79

139 06015500 Grasshopper Creek near Dillon, MT 1921–33,1946–54,1955–58,1960–61

140 06019500 Ruby River above Reservoir near Alder, MT 1938–2003

141 06037500 Madison River near West Yellowstone, MT 1913–73,1983–86,1989–2001

142 13108500 Camas Creek at 18–mile Shearing Corral near Kilgore, ID 1937–54,1969–73

143 13112000 Camas Creek at Camas, ID 1925–2003

144 13113000 Beaver Creek at Spencer, ID 1941–54,1969–82,1985–93

145 13113500 Beaver Creek at Dubois, ID 1921–73,1983,1985–87

146 13117300 Sawmill Creek near Goldburg, ID 1960–73

147 13120000 North Fork Big Lost River at Wild Horse near Chilly, ID 1944–2003

148 13120500 Big Lost River at Howell Ranch near Chilly, ID 1904–14,1920–2003

149 13128900 Lower Cedar Creek above Diversions near Mackay, ID 1966–73,1980–84

150 13297330 Thompson Creek near Clayton, ID 1973–2003

151 13297350 Bruno Creek near Clayton, ID 1971–2003

152 13297355 Squaw Creek below Bruno Creek near Clayton, ID 1973–2003

153 13297450 Little Boulder Creek near Clayton, ID 1970–86

154 13298000 East Fork Salmon River near Clayton, ID 1929–39,1973–82

155 13299000 Challis Creek near Challis, ID 1944–63

156 13302500 Salmon River at Salmon, ID 1913–16,1919–2003

157 13305000 Lemhi River near Lemhi, ID 1939,1955–63,1967–2003

158 13305500 Lemhi River at Salmon, ID 1928–43

159 13306000 North Fork Salmon River at North Fork, ID 1930–40

160 13306385 Napias Creek blw Arnett Creek nr Salmon, ID 1991–2003

161 13306500 Panther Creek near Shoup, ID 1945–78

162 13307000 Salmon River near Shoup, ID 1945–81,2003

Region 7

163 10119000 Little Malad River above Elkhorn Reservoir near Malad City, ID 1911–13,1932,1941–69

164 10172940 Dove Creek near Park Valley, UT 1959–68,1971–73

165 10315500 Marys River above Hot Springs Creek near Deeth, NV 1944–80,1982–2003

166 10329500 Martin Creek near Paradise Valley, NV 1922–2003

167 10352500 McDermitt Creek near McDermitt, NV 1949–84,1985–2003

168 10353000 East Fork Quinn River near McDermitt, NV 1949–82

169 10396000 Donner Und Blitzen River near Frenchglen, OR 1911–21,1938–2003

170 10406500 Trout Creek near Denio, NV 1933–91

171 13057940 Willow Creek below Tex Creek near Ririe, ID 1977–79,1986–2003

172 13075000 Marsh Creek near McCammon, ID 1954–2003

173 13077700 George Creek near Yost, UT 1959–89

174 13079100 Cassia Creek abv Stinson Creek nr Elba, ID 1965–75

175 13092000 Rock Creek near Rock Creek, ID 1910–13,1939,1944–74

176 13154000 Clover Creek below Calf Creek near Bliss, ID 1938–43,1957–62

177 13155300 Little Canyon Creek at Stout Crossing near Glenns Ferry, ID 1966–71

178 13161500 Bruneau River at Rowland, NV 1913–18,1967–2003

179 13162500 East Fork Jarbidge River near Three Creek, ID 1929–33,1954–71

180 13169500 Big Jacks Creek near Bruneau, ID 1939–50,1965–2003

181 13170000 Little Jacks Creek near Bruneau, ID 1939–50

182 13172680 Reynolds Creek at Tollgate near Reynolds, ID 1966–93

183 13172720 Macks Creek near Reynolds, ID 1964–91

184 13172735 Salmon Creek near Reynolds, ID 1964–99

185 13172740 Reynolds Creek at Outlet near Reynolds, ID 1963–93

186 13176000 Owyhee River above China Diversion Dam near Owyhee, NV 1939–84

Table 6. Selected information for gaging stations used to estimate low-flow frequency statistics for unregulated streams in regions 1-8 in Idaho.—

Continued

[Location of gaging stations and regions are shown in figure 1. Gaging station name: ID, Idaho; WA, Washington; MT, Montana; OR, Oregon; UT, Utah; NV, 

Nevada; WY, Wyoming. Water year: The 12-month period from October 1 through September 20, designated by the calendar year in which it ends]

Table 6  19
Map

No.

Gaging 

station 

No.

Gaging station name Periods of record 

(water years)

Region 7 (Continued)

187 13177000 Jack Creek near Tuscarora, NV 1913–25

188 13178000 Jordon Creek above Lone Tree Creek near Jordan Valley, OR 1946–53,1955–72,2003

189 13226500 Bully Creek at Warmsprings near Vale, OR 1965–85

Region 8

190 09208000 LaBarge Creek near LaBarge Meadows Ranger Station, WY 1951–82

191 09224000 Hams Fork at Diamondville, WY 1918–33,1945–49

192 10010400 East Fork Bear River near Evanston, WY 1974–86

193 10015700 Sulphur Creek below La Chapelle Creek near Evanston, WY (above Res) 1958–97

194 10032000 Smiths Fork near Border, WY 1942–2003

195 10040000 Thomas Fork near Geneva, ID 1940–51

196 10040500 Salt River near Geneva, ID 1940–51

197 10041000 Thomas Fork near Wyoming–Idaho State Line 1950–92

198 10047500 Montpelier Creek at weir near Montpelier, ID 1943–79

199 10058600 Bloomington Creek at Bloomington, ID 1961–86

200 10069000 Georgetown Creek near Georgetown, ID 1940–56

201 10077000 Soda Creek near Soda Springs, ID 1913–29

202 10093000 Cub River near Preston, ID 1940–52,1956–86

203 10096000 Cub River above Maple Creek near Franklin, ID 1940–52

204 10099000 High Creek near Richmond, UT 1944–52,1971–72,1979–89

205 10102300 Summit Creek above diversions near Smithfield, UT 1962–79

206 10104700 Little Bear River below Davenport Creek near Avon, UT 1961–92

207 10104900 East Fork Little Bear River above reservoir near Avon, UT 1964–86

208 10105000 East Fork Little Bear River near Avon, UT 1938–51

209 10109000 Logan River above State Dam near Logan, UT 1954–2003

210 10113500 Blacksmith Fork above UP&L Co Dam near Hyrum, UT 1914–96,2000–03

211 13010065 Snake River above Jackson Lake at Flagg Ranch, WY 1984–2003

212 13011500 Pacific Creek at Moran, WY 1917–18,1944–75,1978–2003

213 13011900 Buffalo Fork above Lava Creek near Moran, WY 1965–2003

214 13012000 Buffalo Fork near Moran, WY 1917–18,1945–60

215 13014500 Gros Ventre River at Kelly, WY 1918,1945–58

216 13018300 Cache Creek near Jackson, WY 1962–2003

217 13019438 Little Granite Creek at mouth near Bondurant, WY 1982–93

218 13019500 Hoback River near Jackson, WY 1917–18,1945–58

219 13023000 Greys River above Reservoir near Alpine, WY 1917–18,1937–39,1954–2003

220 13024500 Cottonwood Creek near Smoot, WY 1933–57

221 13025000 Swift Creek near Afton, WY 1943–80

222 13025500 Crow Creek near Fairview, WY 1946–50,1962–67

223 13027000 Strawberry Creek near Bedford, WY 1932–43

224 13032000 Bear Creek above Reservoir near Irwin, ID 1917–18,1934–37,1953–71

225 13044500 Warm River at Warm River, ID 1912–15,1918–32

226 13045500 Robinson Creek at Warm River, ID 1912–15,1918–32

227 13046680 Boundary Creek near Bechler Ranger Station Y.N.P., WY 1984–2003

228 13046995 Falls River above Yellowstone Canal near Squirrel, ID 1994–2003

229 13047500 Falls River near Squirrel, ID 1905–09,1918–2003

230 13047600 Falls River near Ashton, ID 1994–2003

231 13049500 Falls River near Chester, ID 1962–2003

232 13052200 Teton River above South Leigh Creek near Driggs, ID 1962–2003

233 13054000 Teton River near Tetonia, ID 1930–33,1934–37,1940–57

234 13055000 Teton River near St Anthony, ID 1890–93,1903–09,1920–76,1978–2003

Table 6. Selected information for gaging stations used to estimate low-flow frequency statistics for unregulated streams in regions 1-8 in Idaho.—

Continued

[Location of gaging stations and regions are shown in figure 1. Gaging station name: ID, Idaho; WA, Washington; MT, Montana; OR, Oregon; UT, Utah; NV, 

Nevada; WY, Wyoming. Water year: The 12-month period from October 1 through September 20, designated by the calendar year in which it ends]

20 Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Gaging 

station No. 1Q10 7Q10 7Q2 30Q5

Region 1

12305500 4.42 5.07 9.18 7.56

12311000 7.83 8.65 13.0 11.44

12316800 1.81 1.94 3.54 3.13

12320500 2.82 3.40 6.25 4.92

12321000 5.15 5.65 11.0 9.46

12392155 2.20 2.50 11.4 2.47

12392300 18.6 19.5 28.3 26.3

12393500 142 145 215 176

12396000 3.86 6.10 9.28 9.68

12408500 4.96 5.54 8.47 7.64

12409000 15.5 21.1 61.9 39.6

12427000 31.0 34.8 40.3 38.6

12431000 84.0 87.2 123 104

Region 2

12301300 30.5 37.7 61.8 57.3

12301999 3.22 3.80 6.81 5.70

12302000 63.4 75.1 95.9 91.5

12302055 48.5 59.8 85.4 79.5

12302500 4.60 5.06 7.59 7.55

12303100 3.55 3.84 4.90 4.63

12303500 61.2 76.2 108 94.5

12340000 230 284 390 402

12341000 .596 .859 4.65 2.84

12343400 29.2 41.0 60.8 64.2

12344000 97.9 122 173 167

12346500 14.0 16.5 19.3 20.6

12347500 2.08 2.34 5.15 4.25

12350000 1.08 1.43 3.06 2.76

12350500 3.06 3.75 7.95 6.72

12351000 4.92 7.17 11.1 11.9

12352000 8.53 9.77 20.5 15.5

12353280 12.4 14.1 19.9 18.5

12354000 50.5 65.2 86.2 83.9

12375900 3.92 4.56 5.53 5.35

12377150 5.94 6.69 7.78 7.65

12389500 73.5 93.4 128 123

12390700 29.5 30.8 42.7 36.4

12411000 52.8 58.6 79.6 75.5

12413000 144 164 220 207

12413140 .901 1.07 3.17 2.33

12413150 26.6 31.6 42.2 41.8

12413210 40.3 48.6 60.3 56.3

12413470 61.6 70.4 90.3 82.7

12413500 215 238 317 292

12414500 185 233 333 313

12414900 28.3 32.9 45.3 42.4

12415000 24.1 28.7 45.1 39.1

12416000 2.39 2.56 3.59 3.39

13336500 255 333 496 463

13336900 22.9 23.3 29.8 28.0

13337000 199 243 358 335

13340500 328 405 587 541

13340600 330 477 629 641

13341000 525 645 1000 935

13341300 .496 .546 .729 .677

13341400 4.08 4.36 6.01 5.51

Gaging 

station No. 1Q10 7Q10 7Q2 30Q5

Region 3

12424000 2.69 2.95 9.15 5.18

13334700 23.3 26.6 32.7 32.4

13341500 5.00 5.49 7.81 7.20

13342450 1.43 1.61 3.93 2.86

13345000 .956 1.81 6.20 4.26

13346100 .200 .287 3.20 1.63

13346800 .075 .116 .186 .244

13348000 .494 .627 1.77 1.06

13348500 .000 .000 .105 .012

Region 4

13196500 0.155 0.168 0.313 0.240

13200000 9.67 10.4 25.6 17.4

13200500 .000 .045 .312 .156

13201000 12.1 12.7 26.6 19.0

13207000 .000 .000 .000 .000

13207500 .000 .000 .099 .045

13250600 1.76 2.16 2.87 2.82

13251300 .475 .572 .800 .753

13251500 1.48 3.12 4.73 4.54

13253500 10.2 10.4 14.6 12.8

13256000 28.4 33.4 44.7 47.5

13257000 .000 .000 1.054 .396

13258500 25.7 29.6 61.8 47.9

13260000 0.991 1.29 2.41 2.15

13261000 4.94 5.60 8.50 7.78

13267000 .185 .258 1.24 .874

13269300 .210 .246 .646 .494

13270800 13.0 14.6 17.6 17.6

13275500 .40 .70 4.86 2.25

13288200 44.2 53.1 69.6 67.5

13289960 9.11 9.61 18.8 13.3

13290190 18.0 18.9 33.1 25.2

13291000 21.3 31.3 48.4 47.1

13315500 1.01 1.05 1.31 1.31

13316500 97.5 111 153 135

13316800 .183 .211 .768 .547

13319000 7.58 8.95 18.2 14.6

13320000 12.6 15.9 21.4 20.7

13323600 1.50 1.58 3.06 2.37

13325500 15.3 15.6 22.6 19.7

13329500 8.37 9.34 14.4 12.5

13330000 15.1 17.5 25.9 23.2

13330500 6.03 6.54 9.83 8.54

13331500 24.9 36.8 62.7 57.0

13337500 19.3 21.9 31.7 29.9

13338000 48.6 74.8 118 112

13338500 80.3 111 152 145

13339000 481 672 1,090 992

13339500 18.9 21.1 31.8 29.0

13340000 584 768 1,120 1,040

14010000 82.2 83.5 98.7 91.1

14011000 1.18 1.47 2.45 2.16

Table 7. Low-flow frequency statistics for streamflow-gaging stations used in low-flow regression analyses for unregulated streams in regions 1-8 

in Idaho.

[1Q10, 1-day, 10-year low flow; 7Q10, 7-day, 10-year flow; 7Q2, 7-day, 2-year low flow; 30Q5, 30-day, 5-year low flow]

Table 7  21
Gaging 

station No. 1Q10 7Q10 7Q2 30Q5

Region 5

13135500 22.5 34.0 39.1 40.5

13136500 19.0 24.3 27.4 27.7

13139500 .412 .752 47.3 6.89

13141000 22.2 23.4 44.6 32.4

13185000 163 214 279 268

13186000 101 126 171 159

13186500 6.38 10.2 16.5 14.5

13187000 10.1 11.1 13.3 12.5

13235000 158 198 251 244

13240000 1.89 6.70 12.1 11.0

13292500 2.94 3.05 7.04 4.75

13293000 11.3 11.5 14.8 13.5

13295000 44.5 46.4 64.1 57.4

13295500 165 179 272 229

13296000 19.8 29.2 37.9 34.9

13296500 239 262 351 318

13308500 46.3 49.5 61.5 57.1

13309000 59.4 64.3 81.9 72.8

13309220 202 268 358 364

13310000 70.8 94.3 108 109

13310199 382 561 714 698

13310500 21.1 23.0 32.5 28.2

13310700 66.5 80.8 107 97.9

13311000 4.41 4.77 6.17 5.48

13311500 10.2 11.2 12.3 12.0

13312000 27.7 27.9 35.1 31.5

13313000 35.3 44.1 59.7 54.1

13313500 29.8 31.2 39.1 34.9

13314000 191 230 338 317

13314300 177 289 397 368

13315000 2,040 2,480 2,890 3,120

Region 6

6013500 28.8 30.7 37.6 34.4

6015500 .000 .520 8.25 5.57

6019500 54.9 60.4 84.9 78.9

6037500 283 301 361 335

13108500 4.46 4.46 14.43 7.94

13112000 .000 .000 .000 .000

13113000 .000 .000 7.72 1.87

13113500 .000 .000 .000 .000

13117300 9.14 9.94 13.7 12.5

13120000 12.3 13.7 17.4 16.3

13120500 38.8 44.0 60.7 53.9

13128900 1.63 1.72 2.83 2.96

13297330 1.66 2.04 2.94 2.61

13297350 .000 .000 .137 .093

13297355 4.14 4.72 6.88 6.14

13297450 2.79 3.37 4.39 4.04

13298000 32.1 44.0 60.8 57.0

13299000 6.60 7.09 10.4 8.82

13302500 483 553 808 711

13305000 50.0 55.4 98.3 86.0

13305500 15.0 16.4 32.6 27.3

13306000 14.4 18.3 24.8 23.7

13306385 4.74 5.41 6.74 6.52

13306500 34.5 46.9 65.3 63.7

13307000 854 938 1,250 1,180

Gaging 

station No. 1Q10 7Q10 7Q2 30Q5

Region 7

10119000 6.13 6.42 13.44 9.81

10172940 .083 .083 .140 .104

10315500 .365 .402 1.06 .701

10329500 3.64 3.80 5.23 4.64

10352500 .000 .000 1.09 .239

10353000 .484 .581 1.30 .936

10396000 14.9 20.7 30.6 28.7

10406500 .605 .695 2.44 1.49

13057940 4.86 5.30 18.1 9.57

13075000 20.3 23.9 38.3 33.1

13077700 1.17 1.27 1.65 1.54

13079100 0.251 .280 .670 .458

13092000 4.23 4.50 6.81 5.92

13154000 .000 .000 .145 .072

13155300 .016 .092 .299 .228

13161500 3.47 3.72 8.57 5.85

13162500 3.68 5.00 7.45 6.52

13169500 .000 .000 .000 .000

13170000 .000 .000 .000 .000

13172680 .000 .000 .202 .025

13172720 .000 .000 .016 .006

13172735 .000 .000 .016 .000

13172740 .079 .195 .848 .490

13176000 5.98 6.97 16.5 12.0

13177000 .958 .955 1.60 1.42

13178000 .475 .940 1.96 1.50

13226500 .145 .187 .708 .500

Region 8

9208000 2.10 2.23 3.05 2.75

9224000 .000 1.71 13.55 8.92

10010400 5.39 5.98 7.86 6.89

10015700 .000 .000 .123 .008

10032000 39.8 42.8 55.0 50.7

10040000 1.36 1.67 2.55 2.07

10040500 1.40 1.47 3.21 2.34

10041000 6.96 7.73 11.9 9.96

10047500 3.03 4.61 6.43 5.63

10058600 12.5 12.7 14.8 13.7

10069000 18.8 18.9 22.8 20.7

10077000 39.0 39.7 46.1 43.4

10093000 14.7 15.0 18.2 16.8

10096000 0.879 1.10 2.15 1.60

10099000 4.42 4.71 6.82 5.82

10102300 2.84 3.30 4.40 3.84

10104700 10.9 14.0 20.9 17.1

10104900 4.67 5.22 6.79 6.01

10105000 6.35 6.77 9.95 8.28

10109000 14.1 15.0 56.1 26.6

10113500 39.7 46.4 66.3 55.8

13010065 176 182 265 221

13011500 22.6 25.9 35.6 32.3

13011900 74.9 86.2 100.9 98.8

13012000 91.6 103 123 115

13014500 106 118 132 133

13018300 1.79 2.11 3.30 2.82

13019438 2.86 3.23 4.60 3.94

13019500 116 149 164 167

Table 7. Low-flow frequency statistics for streamflow-gaging stations used in low-flow regression analyses for unregulated streams in regions 1-8 

in Idaho.—Continued

[1Q10, 1-day, 10-year low flow; 7Q10, 7-day, 10-year flow; 7Q2, 7-day, 2-year low flow; 30Q5, 30-day, 5-year low flow]

22  Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Gaging 

station No. 1Q10 7Q10 7Q2 30Q5

Region 8 (Continued)

13023000 117 136 169 160

13024500 8.70 8.98 11.5 10.8

13025000 25.0 27.3 31.0 30.5

13025500 21.5 24.2 31.7 29.6

13027000 24.4 24.8 27.7 27.4

13032000 12.3 13.9 17.8 16.5

13044500 145 164 183 175

13045500 30.4 36.6 54.7 47.6

Gaging 

station No. 1Q10 7Q10 7Q2 30Q5

Region 8 (Continued)

13046680 51.3 53.4 63.0 58.5

13046995 278 303 381 352

13047500 192 233 335 295

13047600 233 256 400 336

13049500 25.8 38.6 139 92.8

13052200 94.2 112 165 144

13054000 97.9 128 172 168

13055000 246 278 335 318

Table 7. Low-flow frequency statistics for streamflow-gaging stations used in low-flow regression analyses for unregulated streams in regions 1-8 

in Idaho.—Continued

[1Q10, 1-day, 10-year low flow; 7Q10, 7-day, 10-year flow; 7Q2, 7-day, 2-year low flow; 30Q5, 30-day, 5-year low flow]

Table 8. Basin characteristics considered during the low-flow regressin analyses for unregulated streams in Idaho.

[Equation variables are shown in bold]

Basin characteristic Explanation

AG Pasture and hay; row crops; small grains; fallow; urban or recreational grasses

A Area of drainage basin

Aluv alluvial deposits

Barren Bare rock, sand, or clay; quarries, mines, or pits; transitional

BS Average slope of drainage basin

DV Residential, commercial, industrial, or transportation lands

E Mean drainage basin elevation

F Deciduous, evergreen, or mixed forest land

Glacial Glacial drift and ice

Granite Granitic rocks

GT6000 Percentage of drainage basin area above 6,000 ft

HS Dec Median Dec 21 hillshading 

HS June Median June 21 hillshading 

Loess Loess

Met/Sed Metamorphic or sedimentary rocks

NF30 Percentage of drainage basin area with north-facing slopes greater than 30 percent

NF50 Percentage of drainage basin area with north-facing slopes greater than 50 percent

P Combination precipitation based on Molnau (1995) and PRISM (Daly and Taylor, 1998)

P2 PRISM (Daly and Taylor, 1998) precipitation

Perim Perimeter drainage basin, in miles

R Relief of drainage basin

S30 Percentage of drainage basin area with slopes greater than 30 percent

S50 Percentage of drainage basin area with slopes greater than 50 percent

Sand Dune sand

Shdw Dec Percentage of drainage basin area in shadow on Dec 21

Shdw June Percentage of drainage basin area in shadow on June 21 

Shrub Shrubland

Slope Average slope of drainage basin, in percent

Undefined Unclassified lithology units

Upland Grasslands or herbaceous lands

V Volcanic rocks

W Open water or perennial ice and snow

W(2) Open water

Wetland Woody wetlands; emergent, herbaceous wetlands

Woody Orchards or vineyards

Table 8 23
Table 9. Basin characteristic values used to develop the final probability and estimating equations for low-flow frequency statistics for unregulated 

streams in regions 1-8 in Idaho.

[Locations of regions are shown in figure 1. Equation variables: A, drainage area, in square miles; P, mean annual precipitation, in inches; DV, developed land, 

in percentage of drainage area; AG, agricultural land, in percentage of drainage area; BS, basin slope, in percent; W, water, in percentage of drainage area; R, 

basin relief, in feet; V, surficial volcanic rocks, in percentage of drainage area; S50, slopes greater than 50 percent, in percentage of drainage area]

Gaging station No.

Equation variables

A P DV AG BS W R V S50

Region 1

12305500 55.3 48.3 0.001 0.005 37.1 0.018 4,134.8 14.1 18.0

12311000 133.1 30.4 1.13 6.47 21.2 .721 5,376.7 12.3 4.09

12316800 12.5 29.1 .088 .042 25.4 .004 3,178.5 4.65 1.89

12320500 29.9 41.3 .000 .009 46.4 .009 5,803.1 .000 41.4

12321000 71.1 46.1 .368 .269 37.0 .343 5,866.9 .000 22.9

12392155 115.1 54.3 .081 .347 43.2 .168 4,844.3 3.78 37.7

12392300 121.4 38.1 .463 .519 32.2 .366 5,441.4 .000 12.7

12393500 596.6 38.8 .328 .141 28.9 6.69 5,124.1 21.1 14.1

12396000 68.2 36.7 .017 .972 30.1 .347 3,731.6 17.6 8.12

12408500 82.5 37.7 .119 1.30 29.6 .016 3,832.5 4.45 11.1

12409000 1,011.0 27.6 .983 9.74 22.3 .777 5,308.7 15.3 6.39

12427000 84.4 28.2 2.04 6.30 13.2 .618 2,230.6 9.75 1.80

12431000 634.9 25.1 3.59 23.2 12.2 .895 4,281.5 27.9 1.04

Region 2

12301300 460.2 32.7 0.463 1.86 24.5 0.830 4,956.2 0.000 13.7

12301999 216.0 24.8 .205 .214 24.3 .041 3,996.5 .000 5.19

12302000 785.3 28.1 .122 1.15 26.7 .265 5,103.5 .000 10.0

12302055 843.7 28.0 .175 1.07 27.2 .249 5,413.7 .000 10.5

12302500 23.7 53.0 .033 .000 54.1 .847 5,917.3 24.5 56.1

12303100 11.3 52.6 .009 .000 48.3 1.60 4,788.9 4.35 43.6

12303500 125.0 43.9 .735 .426 38.5 .300 5,752.5 9.89 33.8

12340000 2,283.6 29.4 .006 4.43 25.7 .858 6,056.4 9.00 11.6

12341000 80.7 37.1 .935 .087 36.7 .623 5,406.1 .600 26.0

12343400 379.3 28.4 .079 .569 33.2 .164 5,278.4 82.2 16.2

12344000 1,049.7 31.9 .044 .553 37.7 .185 6,187.1 65.1 24.0

12346500 88.1 29.6 .037 .000 38.8 .071 4,576.0 15.5 26.0

12347500 26.1 60.9 .000 .000 57.0 .397 4,871.1 80.4 59.4

12350000 27.8 55.0 .000 .000 52.1 .269 4,957.9 83.6 53.0

12350500 29.0 55.6 .000 .000 58.8 .368 5,711.5 88.4 66.4

12351000 73.0 30.6 .102 .589 36.5 .123 4,390.9 2.39 20.3

12352000 250.3 46.7 .180 .669 35.4 .029 5,865.4 37.3 20.1

12353280 169.7 28.7 .046 2.31 31.2 .019 4,956.2 .000 14.1

12354000 43.6 44.5 .007 .000 47.2 .066 4,434.8 .000 44.8

12375900 7.6 55.1 .000 .000 59.7 3.98 5,273.5 .000 59.7

12377150 12.4 69.4 .000 .000 66.8 1.21 5,901.2 .000 67.4

12389500 641.5 29.6 .063 .362 30.0 .797 4,998.9 .000 14.5

12390700 181.5 43.7 .038 .036 43.5 .039 4,349.7 .000 37.9

12411000 334.0 48.2 .021 .006 40.8 .170 3,722.1 .000 30.7

12413000 893.7 45.4 .076 .177 41.9 .223 4,637.1 .151 32.7

12413140 15.0 41.5 .042 .000 49.6 .000 3,461.3 1.94 52.9

12413150 105.6 42.5 .779 .338 45.8 .130 4,133.8 2.83 43.8

12413210 181.8 43.3 1.22 .224 45.8 .127 4,438.3 1.64 43.9

12413470 287.1 45.1 1.83 .200 44.6 .220 4,605.6 1.04 41.2

12413500 1,207.4 45.0 .552 .199 42.3 .239 4,673.2 0.360 34.3

12414500 1,024.5 47.0 .036 .014 41.3 .057 5,487.6 2.96 30.2

12414900 272.6 37.7 .470 2.44 25.1 .140 3,792.4 8.60 3.45

12415000 434.5 35.6 .422 1.54 23.8 .154 4,214.6 13.9 3.13

12416000 21.5 38.8 .092 .104 41.8 .126 3,243.5 .000 28.7

13336500 1,913.1 40.6 .000 .000 44.2 .190 7,789.6 56.1 38.6

24  Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Gaging station No.

Equation variables

A P DV AG BS W R V S50

Region 2 (Continued)

13336900 88.3 46.3 0.007 0.000 34.7 0.027 4,633.9 99.9 21.1

13337000 1,179.4 46.6 .051 .000 38.5 .191 7,331.2 68.5 28.0

13340500 997.5 52.5 .006 .000 39.0 .058 5,663.4 31.0 26.2

13340600 1,294.2 51.4 .004 .001 40.4 .059 6,182.5 33.0 29.5

13341000 2,442.5 47.6 .016 .157 36.5 1.04 6,894.5 25.6 23.1

13341300 3.0 48.1 .000 .000 32.0 .000 1,643.9 .000 7.74

13341400 42.7 42.7 .001 .034 26.3 .000 2,146.1 .000 2.62

Region 3

12424000 674.9 20.8 2.55 64.8 10.5 0.186 3,187.9 17.8 0.431

13334700 170.5 23.0 .031 7.46 35.4 .006 5,098.9 92.7 27.5

13341500 453.7 29.5 .865 32.0 18.2 .258 3,849.7 35.7 2.76

13342450 268.9 19.3 .784 33.3 18.9 .248 4,100.8 68.7 7.82

13345000 316.0 30.1 .863 25.0 21.2 .165 2,859.7 16.1 2.49

13346100 491.7 26.9 1.11 48.3 17.7 .153 3,350.1 14.5 1.74

13346800 17.6 24.5 18.6 63.4 11.8 .030 1,801.2 34.4 .128

13348000 126.9 23.8 5.54 83.9 11.9 .041 2,637.5 34.4 .152

13348500 27.1 23.2 6.34 91.6 10.0 .008 1,442.8 33.8 .018

Region 4

13196500 4.8 22.1 0.000 0.000 32.9 0.000 2,396.4 100 10.6

13200000 397.0 24.8 .008 .005 31.3 .014 5,019.7 92.9 13.2

13200500 16.0 23.3 .000 .000 39.8 .000 3,410.5 99.4 27.4

13201000 424.4 24.5 .009 .010 31.7 .132 5,068.8 92.8 14.1

13207000 19.2 19.4 .082 4.15 24.3 .025 3,094.6 71.3 3.21

13207500 59.4 20.4 .051 5.42 25.3 .011 4,310.4 50.6 6.73

13250600 55.2 15.9 .002 .006 23.6 .000 2,987.5 97.2 3.77

13251300 4.0 39.8 .000 .423 27.3 .000 1,821.4 97.6 3.98

13251500 36.6 34.6 .061 5.55 22.3 .000 1,896.9 86.4 1.53

13253500 105.4 32.3 .025 1.93 26.5 .005 4,662.7 93.5 5.94

13256000 391.9 29.6 .069 4.24 24.2 .318 5,242.5 91.9 5.22

13257000 86.1 34.0 .013 .672 27.4 .026 5,221.5 80.0 6.87

13258500 596.4 29.2 .051 3.60 23.5 .293 5,444.7 88.2 4.86

13260000 55.3 22.4 .003 .673 26.4 .034 5,035.8 97.9 8.01

13261000 79.5 28.2 .002 .011 26.9 .008 4,618.1 89.5 6.12

13267000 56.8 22.1 .001 .007 31.6 .963 4,800.2 89.9 11.4

13269300 110.8 25.1 .024 1.21 18.7 .008 3,066.8 59.3 1.27

13270800 38.9 28.6 .003 .052 28.2 .000 3,427.4 100 7.38

13275500 205.2 24.7 .111 2.42 26.5 1.04 5,393.4 28.9 10.5

13288200 155.7 47.5 .000 .007 40.5 .144 6,684.6 56.7 32.3

13289960 177.1 27.5 .001 .810 29.4 .009 6,313.8 85.3 15.4

13290190 298.5 33.7 .032 8.34 27.4 .060 7,681.4 77.3 13.2

13291000 99.9 56.2 .000 .005 37.1 .092 5,791.9 62.6 27.1

13315500 15.1 35.4 .000 .418 27.4 .000 2,183.3 98.7 1.31

13316500 576.1 29.6 .039 3.83 33.4 .228 7,591.0 66.2 20.9

13316800 15.3 30.2 .038 .000 30.6 .014 3,191.9 100 19.3

13319000 687.4 27.6 .126 .149 20.3 .061 5,095.2 83.7 3.83

13320000 104.1 39.7 .001 .001 28.6 .007 5,586.1 97.2 12.9

Table 9. Basin characteristic values used to develop the final probability and estimating equations for low-flow frequency statistics for unregulated 

streams in regions 1-8 in Idaho.—Continued

[Locations of regions are shown in figure 1. Equation variables: A, drainage area, in square miles; P, mean annual precipitation, in inches; DV, developed land, 

in percentage of drainage area; AG, agricultural land, in percentage of drainage area; BS, basin slope, in percent; W, water, in percentage of drainage area; R, 

basin relief, in feet; V, surficial volcanic rocks, in percentage of drainage area; S50, slopes greater than 50 percent, in percentage of drainage area]

Table 9 25
Table 9. Basin characteristic values used to develop the final probability and estimating equations for low-flow frequency statistics for unregulated 

streams in regions 1-8 in Idaho.—Continued

[Locations of regions are shown in figure 1. Equation variables: A, drainage area, in square miles; P, mean annual precipitation, in inches; DV, developed land, 

in percentage of drainage area; AG, agricultural land, in percentage of drainage area; BS, basin slope, in percent; W, water, in percentage of drainage area; R, 

basin relief, in feet; V, surficial volcanic rocks, in percentage of drainage area; S50, slopes greater than 50 percent, in percentage of drainage area]

Gaging station No.

Equation variables

A P DV AG BS W R V S50

Region 4 (Continued)

13323600 24.8 43.6 0.000 0.000 21.3 0.000 3,278.0 100 3.31

13325500 43.7 65.6 .000 .000 50.9 .887 5,390.9 80.5 53.1

13329500 29.6 64.6 .000 .000 57.2 .876 5,298.0 45.4 63.1

13330000 71.5 56.7 .064 .276 49.2 .512 5,981.8 75.6 50.5

13330500 72.1 44.7 .104 .736 45.6 .085 5,859.0 95.6 43.9

13331500 239.2 46.5 .017 .169 43.5 .472 6,598.7 98.2 41.1

13337500 260.8 35.3 .018 .001 24.1 .008 3,584.2 18.2 2.05

13338000 843.4 34.9 .007 .000 29.7 .055 7,070.0 29.7 11.1

13338500 1,168.3 31.3 .120 18.4 25.7 .068 7,553.9 48.0 9.56

13339000 4,827.4 38.3 .057 7.94 36.2 .203 8,163.1 57.4 26.2

13339500 241.4 31.5 .001 5.93 22.6 .005 4,938.4 74.8 5.75

13340000 5,507.9 37.4 .055 8.65 34.4 .208 8,364.5 58.2 23.9

14010000 61.9 46.4 .000 .000 46.3 .000 3,818.7 100 52.1

14011000 42.6 42.2 .000 .006 42.1 .006 4,263.5 96.8 40.4

Region 5

13135500 137.5 31.4 0.044 0.009 40.6 0.041 4,932 37.3 33.3

13136500 92.6 35.8 .002 .015 42.6 .011 4,229 47.4 35.2

13139500 627.6 29.4 .273 .530 42.7 .048 6,616 27.5 39.2

13141000 786.2 26.5 .379 2.05 40.2 .079 7,120 27.1 36.1

13185000 831.6 32.4 .002 .001 44.3 .070 7,338 83.6 41.3

13186000 641.6 34.7 .007 .002 42.1 .035 6,089 91.9 35.2

13186500 133.6 22.4 .000 .000 29.3 .002 5,459 97.1 10.4

13187000 55.6 32.2 .000 .000 33.6 .007 5,094 96.4 16.0

13235000 449.3 34.5 .027 .001 46.7 .294 6,786 81.1 46.1

13240000 48.7 37.2 .000 .040 42.1 .087 3,861 86.6 36.4

13292500 93.9 34.7 .090 2.34 32.8 .022 3,434 43.0 25.1

13293000 35.6 44.5 .000 .000 37.6 4.37 3,579 70.5 34.0

13295000 148.9 23.9 .076 2.30 26.1 .627 4,478 39.8 13.0

13295500 510.4 29.6 .092 2.44 30.4 1.46 4,677 38.0 19.9

13296000 187.3 27.1 .003 .008 41.0 .048 4,201 95.2 32.9

13296500 811.1 28.0 .066 1.55 33.6 .977 4,965 59.3 23.0

13308500 133.8 28.4 .068 .002 26.6 .158 3,135 83.4 11.3

13309000 181.7 30.0 .000 .000 20.2 .086 2,987 71.7 3.47

13309220 1,037.9 29.0 .008 .009 38.4 .127 5,307 83.3 31.9

13310000 451.5 28.7 .001 .001 44.3 .050 5,385 69.1 42.1

13310199 2,871.6 26.9 .003 .009 45.4 .173 7,277 70.2 44.4

13310500 91.7 37.5 .000 .001 31.7 .030 3,717 92.4 13.5

13310700 329.3 33.6 .000 .002 38.0 .215 5,387 92.9 26.8

13311000 19.3 34.0 2.21 .068 35.3 .095 2,744 96.5 17.3

13311500 42.9 30.9 1.86 .033 40.8 .067 3,364 100.0 31.9

13312000 106.9 30.0 .759 .013 41.7 .072 4,183 99.4 34.2

13313000 216.4 34.3 .006 .008 28.2 .085 4,458 87.0 12.6

13313500 102.5 43.9 .002 .000 24.8 .078 3,005 84.9 6.41

13314000 1,164.0 33.2 .071 .004 37.4 .115 6,378 93.8 27.0

13314300 1,306.0 32.9 .065 .013 38.9 .126 7,117 92.4 29.9

13315000 12,228.0 24.4 .050 1.65 37.8 .238 10,701 53.3 30.3

26  Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Table 9. Basin characteristic values used to develop the final probability and estimating equations for low-flow frequency statistics for unregulated 

streams in regions 1-8 in Idaho.—Continued

[Locations of regions are shown in figure 1. Equation variables: A, drainage area, in square miles; P, mean annual precipitation, in inches; DV, developed land, 

in percentage of drainage area; AG, agricultural land, in percentage of drainage area; BS, basin slope, in percent; W, water, in percentage of drainage area; R, 

basin relief, in feet; V, surficial volcanic rocks, in percentage of drainage area; S50, slopes greater than 50 percent, in percentage of drainage area]

Gaging station No.

Equation variables

A P DV AG BS W R V S50

Region 6

6013500 277.0 18.8 0.020 0.000 24.1 0.032 4,691.8 9.77 10.0

6015500 349.0 19.2 .014 2.99 18.8 .016 5,193.8 20.5 3.70

6019500 525.5 22.9 .002 2.13 20.1 .025 5,130.4 2.32 5.36

6037500 434.9 42.3 .166 .000 11.3 .264 2,785.6 81.6 2.13

13108500 228.4 26.8 .000 9.27 12.8 .128 3,641.5 34.2 2.35

13112000 393.9 21.1 .016 9.10 8.60 .075 5,062.4 60.6 1.36

13113000 123.2 20.3 .383 3.12 19.6 .017 3,015.2 4.85 2.10

13113500 238.7 19.4 .385 2.05 16.7 .009 3,696.0 38.3 2.02

13117300 74.2 23.8 .004 .099 32.7 .008 4,280.2 35.3 16.1

13120000 114.7 29.8 .000 .000 43.1 .094 4,984.0 34.0 38.0

13120500 440.4 27.0 .005 .030 37.8 .233 5,284.1 42.3 28.6

13128900 8.4 26.6 .000 .000 66.2 .056 5,123.4 0.000 77.2

13297330 29.5 22.6 .064 .057 47.7 .035 3,963.8 61.5 46.9

13297350 6.4 21.7 .180 .090 40.8 .000 3,470.0 29.7 32.4

13297355 71.6 25.2 .018 .012 36.3 .042 4,114.3 62.0 22.4

13297450 18.3 32.0 .000 .000 41.3 1.19 5,501.5 60.5 28.0

13298000 540.2 26.0 .001 .089 38.2 .167 6,227.5 81.9 25.9

13299000 84.6 25.6 .000 .340 37.2 .175 4,996.6 93.0 25.1

13302500 3,746.1 21.6 .084 2.54 33.4 .398 8,655.9 50.9 22.7

13305000 907.1 15.6 .017 5.83 25.2 .033 6,430.2 10.3 14.4

13305500 1,258.0 15.3 .017 7.05 26.4 .028 7,370.8 12.2 14.7

13306000 210.3 22.9 .173 .440 43.6 .010 6,244.4 3.96 37.4

13306385 40.7 24.9 .001 .022 22.9 .000 2,395.4 4.28 2.58

13306500 520.7 24.0 .000 .029 38.6 .039 6,652.8 9.68 29.4

13307000 6,236.7 20.4 .070 3.23 33.3 .281 9,419.7 34.9 23.0

Region 7

10119000 107.1 13.2 0.039 21.3 17.7 0.434 3,724.2 15.1 2.39

10172940 28.7 17.0 .000 .000 17.5 .000 2,659.9 6.02 0.19

10315500 389.8 15.2 .002 3.51 17.5 .002 5,032.4 44.9 4.76

10329500 176.2 21.9 .001 .017 21.0 .048 4,930.3 90.9 4.26

10352500 225.4 17.0 .000 6.16 17.3 .023 3,931.3 88.6 2.99

10353000 137.9 22.2 .005 .022 22.2 .017 3,436.4 87.6 4.12

10396000 204.7 29.1 .001 .002 16.2 .096 5,455.7 98.8 7.28

10406500 86.7 16.9 .011 1.64 23.1 .009 3,926.9 87.3 6.50

13057940 431.4 16.6 .001 14.5 13.3 .039 2,544.2 31.5 0.68

13075000 367.4 14.3 .296 28.1 16.8 .088 4,652.6 20.5 4.70

13077700 7.8 23.6 .000 .000 32.6 .031 2,707.3 .000 16.2

13079100 7.4 21.8 .000 .014 25.2 .000 1,681.7 11.5 2.38

13092000 81.6 14.5 .001 .174 31.6 .001 3,685.2 86.1 19.9

13154000 103.3 14.0 .000 1.64 15.1 .039 3,683.5 83.6 1.82

13155300 14.2 23.5 .033 .000 25.2 .000 2,397.6 100.0 5.26

13161500 380.8 18.3 .000 1.86 25.1 .021 4,956.4 56.5 8.87

13162500 84.9 24.8 .001 .035 35.3 .023 5,683.3 86.5 28.5

13169500 243.7 13.8 .000 .016 10.1 .006 3,447.7 96.1 3.62

13170000 103.4 14.2 .000 .002 13.2 .000 3,447.5 89.9 6.08

13172680 18.7 21.2 .000 .011 23.0 .126 2,569.4 100.0 2.53

13172720 12.5 13.6 .000 3.60 21.1 .092 2,467.9 96.9 1.13

13172735 13.1 14.7 .048 .052 26.1 .008 2,329.3 100.0 4.88

13172740 91.8 14.8 .010 4.27 20.2 .107 3,719.2 91.5 1.72

13176000 452.3 21.6 .112 1.24 20.6 .599 3,672.2 60.1 3.84

Table 9  27
Table 9. Basin characteristic values used to develop the final probability and estimating equations for low-flow frequency statistics for unregulated 

streams in regions 1-8 in Idaho.—Continued

[Locations of regions are shown in figure 1. Equation variables: A, drainage area, in square miles; P, mean annual precipitation, in inches; DV, developed land, 

in percentage of drainage area; AG, agricultural land, in percentage of drainage area; BS, basin slope, in percent; W, water, in percentage of drainage area; R, 

basin relief, in feet; V, surficial volcanic rocks, in percentage of drainage area; S50, slopes greater than 50 percent, in percentage of drainage area]

Gaging station No.

Equation variables

A P DV AG BS W R V S50

Region 7 (Continued)

13177000 26.8 29.3 0.005 0.505 29.9 0.016 4,247.5 0.362 10.5

13178000 454.2 26.1 .258 .726 19.5 .221 3,905.0 79.3 3.69

13226500 535.3 12.3 .016 1.86 17.4 .026 3,958.2 73.5 1.47

Region 8

9208000 6.6 40.3 0.000 0.000 29.6 0.000 1,442.8 0.000 10.6

9224000 390.1 23.6 .057 .434 15.4 .747 3,048.4 .000 1.56

10010400 34.5 40.4 .000 .101 39.5 2.15 3,997.8 .000 31.1

10015700 58.5 21.6 .000 10.8 9.65 .000 2,997.9 .000 .002

10032000 165.2 34.1 .000 .000 31.3 .500 4,033.0 .000 13.3

10040000 45.4 23.8 .000 .000 26.5 .051 2,730.5 .000 6.05

10040500 37.8 26.8 .000 .000 28.0 .046 2,443.9 .256 5.46

10041000 113.8 25.1 .000 .000 27.4 .024 2,826.5 .085 6.25

10047500 50.6 21.5 .000 .000 32.0 .390 3,225.2 .000 15.5

10058600 24.3 35.1 .000 .000 27.4 .071 3,487.4 .806 7.64

10069000 21.9 26.1 .000 .000 41.0 .044 3,534.8 .000 31.9

10077000 50.9 18.2 .000 70.7 6.15 .157 1,100.5 77.0 .639

10093000 30.4 36.0 .000 .000 31.3 .022 3,983.1 .000 19.4

10096000 23.2 14.2 .011 17.9 19.8 .000 1,695.4 .000 1.13

10099000 16.3 40.9 .000 .000 49.4 .003 4,510.9 .000 50.2

10102300 11.6 39.3 .000 .000 53.2 .182 4,577.3 .000 60.5

10104700 62.2 38.0 .000 1.05 30.1 .040 4,381.5 .000 14.5

10104900 56.8 35.4 .000 .000 28.3 .040 3,719.8 .000 16.3

10105000 69.2 35.2 .000 .000 30.1 .368 3,932.8 .000 18.9

10109000 214.4 35.6 .010 .008 33.3 .175 5,255.6 .000 20.0

10113500 264.6 28.3 .000 .153 28.5 .097 4,206.7 .000 14.9

13010065 502.5 47.4 .036 .000 15.8 3.83 3,509.4 45.0 3.12

13011500 162.7 36.3 .076 .000 20.3 1.70 3,763.2 17.8 3.75

13011900 330.1 37.1 .055 .407 27.0 .296 4,566.8 6.88 13.4

13012000 370.2 36.6 .056 .984 26.3 .264 4,619.9 6.16 12.5

13014500 608.0 31.6 .015 .516 23.3 .436 5,015.9 .127 7.14

13018300 10.7 34.7 .000 .000 40.3 .049 3,551.7 .000 27.6

13019438 82.7 31.0 .154 .182 38.6 .030 4,943.0 .585 26.3

13019500 561.3 26.7 .032 2.55 30.3 .020 5,650.1 .086 16.3

13023000 448.8 34.9 .003 .105 35.1 .059 5,632.6 .000 22.5

13024500 25.7 39.5 .000 .000 45.1 .311 3,738.3 .000 40.0

13025000 27.7 39.3 .000 .000 49.3 .000 4,223.5 .000 52.2

13025500 113.8 29.4 .000 2.83 24.9 .261 3,647.1 .000 5.63

13027000 20.1 40.8 .000 .000 49.7 .000 3,663.7 .000 50.1

13032000 78.3 26.7 .000 .000 38.8 .135 3,806.4 .000 26.3

13044500 131.1 31.8 .000 .000 9.05 .255 2,604.8 62.8 .475

13045500 123.7 35.3 .000 2.44 10.6 .582 2,516.2 61.5 1.05

13046680 85.4 56.0 .001 .000 6.94 .232 2,270.2 90.1 .656

13046995 322.3 53.5 .001 .000 10.9 1.48 3,501.7 84.2 1.75

13047500 333.6 52.9 .000 .110 11.0 .755 3,655.8 82.8 1.71

13047600 336.9 52.2 .001 2.35 10.8 1.48 3,897.7 82.0 1.68

13049500 512.9 42.6 .020 19.5 9.89 .582 4,197.5 71.3 1.52

13052200 341.4 31.7 .176 24.8 23.6 .290 5,223.4 9.11 15.4

13054000 479.2 30.3 .138 26.7 21.5 .350 5,277.0 18.7 12.9

13055000 874.8 27.7 .080 32.8 19.0 .281 6,232.1 47.7 9.69

28  Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Table 10. Total years with the N-day low flow equal to zero and total years of record for streamflow-gaging stations used in logistic regression analyses 

for unregulated streams in regions 1-8 in Idaho.

Gaging station 

No.

1-day zero 

flow

7-day zero 

flow

30-day zero 

flow

Total years 

of record

Region 1

12305500 0 0 0 45

12311000 0 0 0 42

12316800 0 0 0 22

12320500 0 0 0 28

12321000 0 0 0 30

12392155 1 1 0 12

12392300 0 0 0 23

12393500 0 0 0 32

12396000 0 0 0 22

12408500 0 0 0 40

12409000 0 0 0 79

12427000 0 0 0 22

12431000 0 0 0 58

Region 2

12301300 0 0 0 44

12301999 0 0 0 9

12302000 0 0 0 18

12302055 0 0 0 35

12302500 0 0 0 14

12303100 0 0 0 31

12303500 0 0 0 24

12340000 0 0 0 65

12341000 0 0 0 8

12343400 0 0 0 18

12344000 0 0 0 66

12346500 0 0 0 27

12347500 0 0 0 22

12350000 0 0 0 16

12350500 0 0 0 9

12351000 0 0 0 23

12352000 0 0 0 9

12353280 0 0 0 9

12354000 0 0 0 17

12375900 0 0 0 20

12377150 0 0 0 20

12389500 0 0 0 47

12390700 0 0 0 47

12411000 0 0 0 52

12413000 0 0 0 63

12413140 0 0 0 30

12413150 0 0 0 20

12413210 0 0 0 13

12413470 0 0 0 15

12413500 0 0 0 67

12414500 0 0 0 82

12414900 0 0 0 37

12415000 0 0 0 45

12416000 0 0 0 36

13336500 0 0 0 73

13336900 0 0 0 9

13337000 0 0 0 74

13340500 0 0 0 24

13340600 0 0 0 35

Gaging station 

No.

1-day zero 

flow

7-day zero 

flow

30-day zero 

flow

Total years 

of record

Region 2 (Continued)

13341000 0 0 0 38

13341300 0 0 0 11

13341400 0 0 0 11

Region 3

12424000 0 0 0 53

13334700 0 0 0 22

13341500 0 0 0 14

13342450 0 0 0 28

13345000 0 0 0 40

13346100 0 0 0 10

13346800 0 0 0 24

13348000 0 0 0 30

13348500 5 4 3 25

Region 4

13196500 0 0 0 22

13200000 0 0 0 52

13200500 2 0 0 20

13201000 0 0 0 38

13207000 14 14 14 14

13207500 5 2 1 13

13250600 0 0 0 20

13251300 0 0 0 17

13251500 0 0 0 35

13253500 0 0 0 10

13256000 0 0 0 15

13257000 3 3 2 16

13258500 0 0 0 64

13260000 0 0 0 23

13261000 0 0 0 35

13267000 1 1 1 25

13269300 0 0 0 13

13270800 0 0 0 18

13275500 2 0 0 49

13288200 0 0 0 39

13289960 0 0 0 17

13290190 0 0 0 29

13291000 0 0 0 8

13315500 0 0 0 13

13316500 0 0 0 49

13316800 0 0 0 11

13319000 0 0 0 78

13320000 0 0 0 64

13323600 0 0 0 12

13325500 0 0 0 8

13329500 0 0 0 53

13330000 0 0 0 73

13330500 0 0 0 68

13331500 0 0 0 38

13337500 0 0 0 29

13338000 0 0 0 44

13338500 0 0 0 38

13339000 0 0 0 54

Table 10  29
Table 10. Total years with the N-day low flow equal to zero and total years of record for streamflow-gaging stations used in logistic regression analyses 

for unregulated streams in regions 1-8 in Idaho.—Continued

Gaging station 

No.

1-day zero 

flow

7-day zero 

flow

30-day zero 

flow

Total years 

of record

Region 4 (Continued)

13339500 0 0 0 23

13340000 0 0 0 45

14010000 0 0 0 68

14011000 0 0 0 39

Region 5

13135500 0 0 0 22

13136500 0 0 0 17

13139500 7 6 2 87

13141000 0 0 0 57

13185000 0 0 0 92

13186000 0 0 0 57

13186500 0 0 0 10

13187000 0 0 0 10

13235000 0 0 0 61

13240000 0 0 0 57

13292500 0 0 0 11

13293000 0 0 0 11

13295000 0 0 0 60

13295500 0 0 0 34

13296000 0 0 0 26

13296500 0 0 0 66

13308500 0 0 0 43

13309000 0 0 0 31

13309220 0 0 0 12

13310000 0 0 0 13

13310199 0 0 0 9

13310500 0 0 0 31

13310700 0 0 0 30

13311000 0 0 0 26

13311500 0 0 0 12

13312000 0 0 0 13

13313000 0 0 0 74

13313500 0 0 0 8

13314000 0 0 0 11

13314300 0 0 0 9

13315000 0 0 0 11

Region 6

6013500 0 0 0 24

6015500 2 1 0 20

6019500 0 0 0 64

6037500 0 0 0 69

13108500 0 0 0 10

13112000 55 54 48 69

13113000 4 3 2 20

13113500 32 32 28 46

13117300 0 0 0 12

13120000 0 0 0 59

13120500 0 0 0 55

13128900 0 0 0 10

13297330 0 0 0 30

13297350 6 5 1 31

13297355 0 0 0 30

Gaging station 

No.

1-day zero 

flow

7-day zero 

flow

30-day zero 

flow

Total years 

of record

Region 6 (Continued)

13297450 0 0 0 14

13298000 0 0 0 17

13299000 0 0 0 19

13302500 0 0 0 86

13305000 0 0 0 42

13305500 0 0 0 14

13306000 0 0 0 9

13306385 0 0 0 11

13306500 0 0 0 32

13307000 0 0 0 36

Region 7

10119000 0 0 0 29

10172940 0 0 0 11

10315500 0 0 0 57

10329500 0 0 0 81

10352500 12 10 4 53

10353000 0 0 0 32

10396000 0 0 0 72

10406500 0 0 0 59

13057940 0 0 0 18

13075000 0 0 0 48

13077700 0 0 0 29

13079100 0 0 0 9

13092000 0 0 0 33

13154000 3 2 0 8

13155300 0 0 0 5

13161500 0 0 0 40

13162500 0 0 0 21

13169500 43 41 35 46

13170000 10 10 10 10

13172680 7 5 4 37

13172720 9 4 1 26

13172735 15 13 9 39

13172740 1 0 0 40

13176000 0 0 0 45

13177000 0 0 0 11

13178000 0 0 0 22

13226500 1 1 0 21

Region 8

9208000 0 0 0 30

9224000 2 1 1 17

10010400 0 0 0 12

10015700 16 11 7 39

10032000 0 0 0 60

10040000 0 0 0 11

10040500 0 0 0 11

10041000 0 0 0 42

10047500 1 0 0 36

10058600 0 0 0 25

10069000 0 0 0 16

10077000 0 0 0 13

10093000 0 0 0 42

30 Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho
Table 10. Total years with the N-day low flow equal to zero and total years of record for streamflow-gaging stations used in logistic regression analyses 

for unregulated streams in regions 1-8 in Idaho.—Continued

Gaging station 

No.

1-day zero 

flow

7-day zero 

flow

30-day zero 

flow

Total years 

of record

Region 8 (Continued)

10096000 0 0 0 12

10099000 0 0 0 17

10102300 0 0 0 17

10104700 0 0 0 31

10104900 0 0 0 22

10105000 0 0 0 11

10109000 0 0 0 49

10113500 0 0 0 83

13010065 0 0 0 19

13011500 0 0 0 54

13011900 0 0 0 37

13012000 0 0 0 15

13014500 0 0 0 13

13018300 0 0 0 40

13019438 0 0 0 10

13019500 0 0 0 13

Gaging station 

No.

1-day zero 

flow

7-day zero 

flow

30-day zero 

flow

Total years 

of record

Region 8 (Continued)

13023000 0 0 0 51

13024500 0 0 0 24

13025000 0 0 0 28

13025500 0 0 0 8

13027000 0 0 0 10

13032000 0 0 0 17

13044500 0 0 0 14

13045500 0 0 0 17

13046680 0 0 0 17

13046995 0 0 0 18

13047500 0 0 0 9

13047600 0 0 0 87

13049500 0 0 0 9

13052200 0 0 0 42

13054000 0 0 0 41

13055000 0 0 0 76

Table 10  31
Manuscript approved for publication, February 3, 2006

Prepared by the Enterprise Publishing Network, 

Publishing Service Center, Tacoma, Washington

Bill Gibbs 

Sharon Wahlstrom

Judy Wayenberg

For more information concerning the research in this report, contact the 

Idaho Water Science Center Director, 

U.S. Geological Survey, 230 Collins Road

Boise, Idaho 83702-4520

http://id.water.usgs.gov
SIR 2006–5035 Hortness Estimating Low-Flow Frequency Statistics for Unregulated Streams in Idaho