Estimating Locations of Perennial Streams in 

Idaho Using a Generalized Least-Squares 

Regression Model of 7-Day, 2-Year Low Flows

Scientific Investigations Report 2009–5015

Prepared in cooperation with the Idaho Department of Environmental Quality and the 

Bureau of Reclamation

U.S. Department of the Interior

U.S. Geological Survey
Cover: Middle fork of the Payette River near Boiling Springs, Idaho, looking upstream. 

(Photograph taken by Molly S. Wood, U.S. Geological Survey, July 2007.)
Estimating Locations of Perennial Streams in 

Idaho Using a Generalized Least-Squares 

Regression Model of 7-Day, 2-Year Low Flows

By Molly S. Wood, Alan Rea, Kenneth D. Skinner, and Jon E. Hortness 

Prepared in cooperation with the Idaho Department of Environmental Quality and the 

Bureau of Reclamation

Scientific Investigations Report 2009–5015

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2009

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Suggested citation:

Wood, M.S., Rea, Alan, Skinner, K.D., and Hortness, J.E., 2009, Estimating locations of perennial streams in Idaho 

using a generalized least-squares regression model of 7-day, 2-year low flows: U.S. Geological Survey Scientific 

Investigations Report 2009-5015, 26 p. 
iii

Contents

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

Introduction.....................................................................................................................................................2

Purpose and Scope ..............................................................................................................................5

Description of Study Area ...................................................................................................................5

Idaho Definition of Perennial Streams .............................................................................................5

Related Studies .....................................................................................................................................5

Approach.........................................................................................................................................................6

Development of 7Q2 Regression Models .........................................................................................6

Development of DEMs and Continuous Parameter Grids..............................................................7

Computation of Continuous 7Q2 Estimates .......................................................................................7

Model Revisions Based on 

Spatial Patterns ................................................................................................................................8

Final Perennial Streams Model .................................................................................................................16

Evaluation of Perennial Streams Model ..................................................................................................18

Limitations and Areas for Further Study ..................................................................................................22

Summary........................................................................................................................................................23

Acknowledgments.......................................................................................................................................24

References Cited..........................................................................................................................................24

Figures

Figure 1. Map showing location of study area, eight regions, and streamflow-gaging

stations in Idaho and surrounding areas used to estimate low-flow frequency

statistics for unregulated streams......................................................... 3

Figure 2. Screen capture of spatial distribution of perennial streams, Hydrologic Unit

Code boundaries, and 1:24,000-scale quadrangles from National Hydrography

Dataset High-Resolution in northern Idaho ............................................. 4

Figure 3. Scatter plots showing improvement of 7Q2 flow estimates in extreme

extrapolation for region 8 from the Hortness (2006) regression equation to the

revised regression equation for Idaho ................................................... 11

Figure 4. Screen captures from U.S. Geological Survey perennial streams model

showing spatial pattern of stream network in a selected area in region 8

derived from Hortness (2006) 7Q2 regression equation and revised 7Q2

regression equation for Idaho ............................................................ 12

Figure 5. Screen captures from U.S. Geological Survey perennial streams model

showing spatial pattern of stream network for Hydrologic Unit Code 16010201

(in region 8) derived from Hortness (2006) 7Q2 equation and revised 7Q2

regression equation for Idaho ............................................................ 14

Figure 6. Screen capture of spatial distribution of modeled streams and Hydrologic

Unit Code boundaries from U.S. Geological Survey perennial streams model

in northern Idaho ........................................................................... 17

Figure 7. Map showing locations of comparison points from datasets used to evaluate

the U.S. Geological Survey perennial streams model for Idaho ..................... 19
iv

Tables

Table 1. Regression equations for the low-flow statistic, 7Q2 , for unregulated streams

in regions 1–8, Idaho ........................................................................ 10

Table 2. Range of values of basin characteristics used to estimate the low-flow

statistic, 7Q2 , for unregulated streams in regions 1–8, Idaho ........................ 10

Table 3. Description of datasets used for evaluation of the U.S. Geological Survey

perennial streams model for Idaho ...................................................... 18

Table 4. Agreement rules for comparing independent datasets with the U.S.

Geological Survey perennial streams model for Idaho ................................. 20

Table 5. Classification table of accuracy of the U.S. Geological Survey perennial

streams model relative to comparison datasets for Idaho ........................... 20

Table 6. Agreements between the U.S. Geological Survey perennial streams model

and comparison datasets by hydrologic region, Idaho and surrounding areas...... 21

Conversion Factors, Datums, and Abbreviations and 

Acronyms

Conversion Factors

Multiply By To obtain

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

meter (m) 3.281 foot (ft) 

mile (mi) 1.609 kilometer (km)

square mile (mi2) 2.590 square kilometer (km2) 

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).

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

Abbreviations and Acronyms

Abbreviations and 

Acronyms Definition

7Q2 7-day, 2-year low flow

BURP Beneficial Use Reconnaissance Program

DEM Digital Elevation Model

EMAP Environmental Monitoring and Assessment Program

ESRI Environmental Systems Research Institute

GIS Geographic Information System

GLS generalized least-squares

HUC Hydrologic Unit Code

IDEQ Idaho Department of Environmental Quality

NED National Elevation Dataset

NHD-Hi_Res National Hydrography Dataset High-Resolution

PDSI Palmer Drought Severity Index

RF3 River Reach File 3

SNF Suislaw National Forest

USEPA U.S. Environmental Protection Agency

USGS U.S. Geological Survey

Conversion Factors, Datums, and Abbreviations and 

Acronyms—Continued
vi

This page intentionally left blank.
Abstract 

Many State and Federal agencies use information 

regarding the locations of streams having intermittent or 

perennial flow when making management and regulatory 

decisions. For example, the application of some Idaho water 

quality standards depends on whether streams are intermittent. 

Idaho Administrative Code defines an intermittent stream as 

one having a 7-day, 2-year low flow (7Q2) less than 0.1 ft3/s. 

However, there is a general recognition that the cartographic 

representation of perennial/intermittent status of streams on 

U.S. Geological Survey (USGS) topographic maps is not as 

accurate or consistent as desirable from one map to another, 

which makes broad management and regulatory assessments 

difficult and inconsistent. To help resolve this problem, 

the USGS has developed a methodology for predicting the 

locations of perennial streams based on regional generalized 

least-squares (GLS) regression equations for Idaho streams for 

the 7Q2 low-flow statistic. Using these regression equations, 

the 7Q2 streamflow may be estimated for naturally flowing 

streams in most areas in Idaho. The use of these equations 

in conjunction with a geographic information system (GIS) 

technique known as weighted flow accumulation allows for an 

automated and continuous estimation of 7Q2 streamflow at all 

points along stream reaches. The USGS has developed a GISbased map of the locations of streams in Idaho with perennial 

flow based on a 7Q2 of 0.1 ft3/s and a transition zone of plus or 

minus 1 standard error. Idaho State cooperators plan to use this 

information to make regulatory and water-quality management 

decisions.

Originally, 7Q2 equations were developed for eight 

regions of similar hydrologic characteristics in the study area, 

using long-term data from 234 streamflow-gaging stations. 

Equations in five of the regions were revised based on spatial 

patterns observed in the initial perennial streams map and 

unrealistic behavior of the equations in extrapolation. The 

standard errors of prediction for the final equations ranged 

from a minimum of +75.0 to -42.9 percent in the central part 

of the study area to a maximum of +277 to -73.5 percent in the 

southern part of the study area. The equations are applicable 

only to unregulated, naturally-flowing streams and may 

produce unreliable results outside the range of explanatory 

variables used for equation development. Extrapolation 

outside the range of available data was necessary, however, 

to predict perennial flow initiation points and transition zones 

along stream reaches.

The map of perennial streams was evaluated by 

comparing predicted stream classifications with four 

independent datasets, including field observations by other 

government agencies. Overall, 81 percent of the comparison 

data points agreed with the USGS perennial streams model. 

Regions with the highest number of disagreements had 

a high percentage of mountainous and forested area with 

potential mountain front recharge zones, and regions with the 

highest agreements had a high percentage of low gradient, 

low elevation area. As a whole, the USGS model predicted 

a higher number of perennial streams than predictions made 

with the independent datasets. Some disagreements were due 

to poor site location coordinates, timing of the comparison 

site visits during unusually wet or dry years, discrepancies in 

classification criteria, and variable ground water contributions 

to flow in some areas.

The Idaho Department of Environmental Quality 

Beneficial Use Reconnaissance Program (BURP) dataset is 

considered the most representative dataset for comparison 

because it covered a range of climate conditions and the 

number of sites visited were consistent from year to year 

during the study period. Eighty-five percent of BURP 

comparison data points agreed with the USGS perennial 

streams model. Although site-specific flow data may be 

needed to correctly classify streams in some areas, this 

information rarely is available and is not always practical to 

obtain. The USGS perennial streams map was determined to 

be a spatially-consistent and accurate estimate of the locations 

of perennial streams on a broad scale.

Estimating Locations of Perennial Streams in Idaho 

Using a Generalized Least-Squares Regression 

Model of 7-Day, 2-Year Low Flows

By Molly S. Wood, Alan Rea, Kenneth D. Skinner, and Jon E. Hortness
2 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

Introduction

The perennial or intermittent status of a stream has 

bearing on many regulatory requirements. For example, the 

classification of flow as perennial or intermittent in a stream 

reach is considered in the application of Total Maximum 

Daily Load requirements for Idaho. Additionally, permanence 

of flow has bearing on monitoring and methods of assessing 

water quality, application of water quality standards, and 

determination of appropriate use designations. U.S. Geological 

Survey (USGS) topographic maps commonly are used to 

determine the perennial or intermittent status of stream. 

However, there is a general recognition that the cartographic 

representations of perennial and intermittent streams on USGS 

topographic maps are not as accurate or consistent as desirable 

from one map sheet to another. As a result, the USGS, in 

cooperation with the Idaho Department of Environmental 

Quality (IDEQ) and Bureau of Reclamation, is attempting to 

better define the perennial and intermittent status of streams in 

Idaho.

Idaho Administrative Code defines an intermittent stream 

as one having a hydrologically-based, unregulated 7-day, 

2-year low flow (7Q2) of less than 0.1 ft3/s (State of Idaho, 

2006). The 7Q2 is the annual minimum mean streamflow over 

7 consecutive days that has a 50 percent probability of not 

being exceeded in any one year. The USGS has developed 

regional regression equations for Idaho streams for several 

low-flow statistics, including the 7Q2 statistic (Hortness, 

2006), using long-term streamflow-gaging station data. 

Using these regression equations, the 7Q2 streamflow may 

be estimated for naturally flowing streams in most areas 

of Idaho, based on estimates of certain basin and climatic 

characteristics. The study area and hydrologic regions for 

which equations were developed are shown in figure 1. The 

boundary of region 6 was extended in the Hortness (2006) 

study to include streamflow-gaging station data in Montana; 

however, for this study, the equations were applied only 

within the Idaho State boundary in region 6. The undefined 

region shown in figure 1 represents the eastern Snake 

River Plain, which includes several dams, major irrigation 

diversions, springs, and drainages and channel bottoms with 

high infiltration rates. Due to these conditions, flows in this 

area could not be characterized using a regional regression 

approach and are not included in this analysis.

The best sources of information available regarding the 

perennial or intermittent status of streams often are the USGS 

1:24,000-scale topographic maps for the area in question: 

perennial streams are shown on these maps as solid blue 

lines, and intermittent streams are shown as dot-dashed lines. 

Streams from these maps have been digitally captured into 

the National Hydrography Dataset High-Resolution (NHD 

Hi-Res). According to the draft standards for the NHD Hi-Res, 

an intermittent stream “contains water for only part of the 

year, but more than just after rainstorms and at snowmelt”, and 

a perennial stream “contains water throughout the year, except 

for infrequent periods of severe drought” (U.S. Environmental 

Protection Agency and U.S. Geological Survey, 1999). Similar 

definitions were applied in developing the NHD MediumResolution, which generally was based on 1:100,000-scale 

USGS topographic maps.

Although the information represented on USGS 

topographic maps generally was field verified at the time of 

map compilation, it was not always possible to verify the 

perennial or intermittent status of every stream. Additionally, 

the various topographic maps were compiled over a period of 

many decades, using varying technologies, cartographers, and 

standards. Therefore, adjacent topographic maps might have 

been developed at different times, using different techniques, 

resulting in mapped streams that change perennial or 

intermittent status or density where they cross map quadrangle 

boundaries. Differing techniques and standards also were used 

and mistakes sometimes were made in the process of digitally 

capturing the topographic map information and incorporating 

it into the NHD, which was compiled under 8-digit Hydrologic 

Unit Codes (HUCs). As a result, streams in the NHD often 

show changes in patterns at HUC boundaries. The spatial 

distribution of streams identified as perennial according to 

the NHD in an area of northern Idaho is shown in figure 2. 

Several non-realistic density differences are visible following 

1:24,000-scale quadrangle and HUC boundaries.
Introduction 3

ID_TAC08_0253_PerennialStreams_Fig01

Yellowstone River

Snake

River

Big Lost River

Henrys Fork

Owyhee

River River Snake

River

Clark

Priest

River

For

S

k

aint Joe River

Snake River Lochsa River

Selway

River

Salmon River

Weiser River

Boise

Lemhi River

Big Wood River

Raft River

Portneuf R

River

Bear

River

Malheur

River

River

Bruneau

Payette

Bear

Lake

American

Falls

Reservoir

Blackfoot River Palisades

Reservoir

Jackson

Lake

Coeur

d’Alene

Lake

Pend

Oreille

Lake

Spokane

River

Kootenai

River

Bitterroot

River

Dworshak

Reservoir

Grand Ronde River

Clearwater

 River

Twin 

Falls

Boise

Sandpoint

Lewiston

Coeur 

d’Alene

Borah

Peak

Pocatello

Idaho

Falls

Salmon

9

8 7

6

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1

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7

8

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

119° 118° 117° 116° 115° 114° 113° 112° 111° 110° 109°

47°

46°

43°

42°

41°

49°

48°

45°

44°

EXPLANATION

39

Region and identification number for which

specific regression equations have been

developed (see table 1)

Undefined area

Gaging station and number (see 

Hortness, 2006)

2

Study

area

IDAHO

WASHINGTON

OREGON

MONTANA

WYOMING

NEVADA UTAH

0 4020 60 100 MILES 80

0 4020 60 100 KILOMETERS 80

Figure 1. Location of study area, eight regions, and streamflow-gaging stations in Idaho and surrounding areas used to 

estimate low-flow frequency statistics for unregulated streams (adapted from Hortness, 2006).
4 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

ID_TAC08_0253_PerennialStreams_Fig02

17010214

17010301

17010302

17010304

17010303

17010306

17060108 17060308

17010213

17010204

17010101

17010305

17010308

IDAHO

17060306 Hydrologic 

Unit Code No.

EXPLANATION

17060306

Figure 2. Screen capture of spatial distribution of perennial streams (blue), Hydrologic Unit Code boundaries

(black), and 1:24,000-scale quadrangles (red) from National Hydrography Dataset High-Resolution in northern 

Idaho.
Introduction 5

Purpose and Scope

The purpose of this report is to describe the procedures 

used to create a geospatial model of perennial streams in 

Idaho and to assess the validity of the model. A by-product 

of the effort to model perennial streams is an improved suite 

of geospatial datasets derived from 10-m resolution Digital 

Elevation Models (DEMs). A full description of the geospatial 

datasets generated and links to Federal Geographic Data 

Committee-compliant metadata are provided in Rea and 

Skinner (2009). 

This report describes some shortcomings of previous 

datasets of perennial streams in Idaho and shows qualitative 

improvements in the spatial patterns of modeled perennial 

streams. Quantitative analysis of these data improvements by 

comparison to field data also is presented.

Description of Study Area

The study area comprises the entire state of Idaho and 

parts of Washington, Oregon, Nevada, Utah, Wyoming, and 

Montana where hydrologic basins cross state boundaries 

(fig. 1). The area is divided into eight hydrologic regions and 

one undefined region, based on geographic features and a 

cluster analysis of streamflow data, as described in Hortness 

and Berenbrock (2001) and Hortness (2006). Terrain is highly 

varied across the study area, with rugged, mountainous areas 

in the central and northern areas and gently sloping plains, 

hills, and canyons in the south and western panhandle of 

Idaho. Elevations range from 738 ft in Lewiston (western 

panhandle) to 12,655 ft at Borah Peak (central mountains). 

Geologic features generally consist of igneous, metamorphic, 

and sedimentary rocks ranging in age from Precambrian to 

Holocene (Bond, 1978). The southern and western parts of the 

study area are dominated by basalts, and the granitic Idaho 

batholith is the major geologic feature in the central and far 

northern areas (Ross and Savage, 1967). Glacial erosion and 

deposition have molded the landscape in mountainous areas 

and in the northern tip of Idaho’s panhandle (Link and Welhan, 

2002).

Annual precipitation varies widely with topography, 

ranging from less than 10 in. in south-central Idaho to 60 to 

70 in. in the central mountains (Molnau, 1995). Generally, 

the source of moisture for precipitation is the Pacific Ocean, 

although many summer thunderstorms in eastern Idaho 

are generated by moisture-laden air moving north from the 

Gulf of Mexico and the Caribbean (National Oceanic and 

Atmospheric Administration, 1985). About 60 percent of 

annual precipitation falls during winter and early spring 

(October through March) as a result of orographic effects 

(Molnau, 1995); however, summer thunderstorms can 

contribute significantly to total annual precipitation in the 

southeastern part of the study area. Highest streamflows 

generally are observed in April, May, June, and July as a 

result of snowmelt and rain-on-snow storm events. Baseflow 

in most unregulated streams dominates flow during August 

through March, and annual minimum streamflows typically 

occur in October through January (Hortness, 2006).

Idaho Definition of Perennial Streams 

The State of Idaho defines intermittent and ephemeral 

streams, but not perennial streams, in its water quality rules. 

Intermittent waters are defined as “a stream, reach, or water 

body which naturally has a period of zero flow for at least 1 

week during most years” (State of Idaho, 2006). Ephemeral 

waters are on the drier end of the spectrum of flow from 

intermittent waters, and perennial waters are, by default, 

all streams with flow greater than meets the definition of 

intermittent waters. Where flow records are available, a stream 

with a hydrologically-based, unregulated 7Q2 flow of less 

than 0.1 ft3/s is considered intermittent. Streams with natural 

perennial pools containing significant aquatic life uses are not 

intermittent (State of Idaho, 2006). Because the presence of 

natural perennial pools is a site-specific determination, this 

project focuses only on the unregulated 7Q2 flow less than the 

0.1 ft3/s criterion for perennial stream classification.

Related Studies

A number of investigations have been conducted to 

classify or map intermittent and perennial streams, or both, 

often based on state-specific definitions and in response to 

observed deficiencies in existing maps. Many approaches rely 

on site-specific field determinations to classify streams, which 

may be time consuming and costly but accurate if proper and 

consistent techniques are applied. Recent approaches have 

relied on statistical techniques and GIS or remotely-sensed data 

to predict the locations of intermittent and perennial streams.

A comprehensive study involving field techniques was 

completed by the State of North Carolina. The North Carolina 

technique requires trained field technicians to score and 

classify a stream site based on hydrologic, geomorphologic, 

and biologic metrics (North Carolina Division of Water 

Quality, 2005). The technique is designed to classify a site 

based on long-term indicators of perennial or intermittent 

flow, not simply on the presence of flow at the time of visit. 

The U.S. Environmental Protection Agency (USEPA) has 

developed a similar field operations manual for assessing 

hydrologic permanence in headwater streams (Fritz and 

others, 2006). The U.S. Army Corps of Engineers and USEPA 

currently are combining elements of these methods into a 

guidance document for classifying streams in Oregon (Brian 

Topping, U.S. Environmental Protection Agency, oral and 

written commun., 2007). A similar technique has been adopted 

by the State of Virginia, Fairfax County (Fairfax County, 

Virginia, Stormwater Planning Division, 2004), although their 

technique has been adapted to account for seasonal variations 

and to include anecdotal or historical information in the final 

scoring of the site.
6 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

Jaeger and others (2007) conducted a study in southwest 

Washington State to field map channel heads and perennial 

flow initiation points in streams in three test watersheds. They 

designated areas with continuous and discontinuous flows 

along stream reaches over a range of hydrologic conditions 

from February to September 2003. The perennial flow 

initiation point was identified as the farthest upslope location 

with flow during baseflow conditions (that is, summer). 

They determined that the relation between drainage area and 

perennial flow initiation varied by lithology. For example, the 

initiation point migrated seasonally to a much greater extent 

when underlying lithology was sandstone rather than basalt; 

as a result, the relation between drainage area and perennial 

flow for all lithologic types was not well-defined. From a 

practical standpoint, Jaeger and others (2007) recommended 

establishing minimum drainage areas for each lithology (for 

example, 0.004 mi2 for sandstone and 0.0008 mi2 for basalt) 

as a conservative management strategy for identifying and 

mapping perennial flow initiation points on a broader scale.

Clarke and others (2008) combined regional GIS 

data and field observations to delineate a high-resolution, 

synthetic stream network and hydrogeomorphic attributes in 

coastal Oregon. The resulting map and dataset have served 

various uses—from management of riparian forests to habitat 

evaluation for salmonids. The probability of perennial flow 

in a stream was one of many stream attributes modeled. The 

probability was based on drainage area, developed using a 

dataset from the Siuslaw National Forest (SNF) where field 

technicians determined the upper limit of perennial flow in 

selected streams during baseflow conditions over a 2-year 

period. Clarke and others (2008) assumed that, in drainage 

areas between 0.004 and 0.14 mi2, probability of perennial 

flow in a stream reach will follow a cumulative distribution 

function developed using the SNF field dataset. For example, 

a 70 percent probability of perennial flow is assigned to stream 

reaches with a drainage area of 0.015 mi2 because 70 percent 

of the stream reaches in the field dataset at that drainage area 

had perennial flow. These probabilities were used to generate 

a map of synthetic perennial streams.

Bent and Steeves (2006) used a statistical and GIS-based 

approach to predict the locations of perennial streams in 

Massachusetts. A logistic regression equation was developed 

by relating field observations of the presence or absence 

of flow at 351 unregulated stream sites with selected basin 

characteristics such as drainage area, areal percentage of 

sand and gravel deposits, areal percentage of forest cover, 

and whether the site was in the eastern or western region 

of the state. Sites with drainage areas greater than 2.00 mi2

were assumed to flow perennially and were not used in the 

logistic regression equation. Bent and Steeves (2006) then 

used a GIS automated mapping procedure to calculate the 

explanatory variables in the logistic regression along a stream 

reach and determine where the transition from intermittent to 

perennial flow occurs, based on a probability threshold. They 

determined that the logistic regression equation correctly 

classified intermittent/perennial flow at 80.3 percent of 

streams visited for verification with drainage areas from 0.00 

to 10.99 mi2, but that USGS topographic maps portrayed the 

correct stream classifications at only 69.2 percent of the same 

verification sites. Olson and Brouillette (2006) developed a 

similar logistic regression equation to predict the locations of 

intermittent streams in Vermont. The equation was developed 

by relating field observations from 682 unregulated stream 

sites to basin characteristics such as drainage area, elevation, 

ratio of basin relief to basin perimeter, and areal percentage 

of well- and moderately well-drained soils. Their procedure 

correctly classified intermittent/perennial flow at 85 percent of 

streams visited for verification in Vermont.

Many of these efforts to predict the locations of 

intermittent and perennial streams have demonstrated 

the usefulness of larger-scale, statistical and GIS-based 

techniques combined with field verification data over a range 

of hydrologic conditions. Studies based solely on field visits 

often are hampered by time limitations. As a result, a range of 

hydrologic conditions is not always captured in the study, and 

therefore, final stream classifications may be biased.

Approach

The USGS has developed a GIS-based map of the 

locations of streams in Idaho with perennial flow based on 

generalized least-squares (GLS) regression models of 7Q2

flows and continuous parameter estimation of 7Q2 at ungaged 

locations. A transition zone of plus or minus 1 standard error 

was modeled around the 7Q2 cutpoint of 0.1 ft3/s to account 

for statistical, climatic, and hydrologic variability. Flow 

downstream of the transition zone is considered perennial, and 

flow upstream of the transition zone is considered intermittent. 

Development of 7Q2 Regression Models 

The USGS operates a network of streamflow-gaging 

stations in Idaho that provides data for various purposes, and 

low-flow statistics can be calculated from the streamflow 

data collected at these locations. Because streamflow-gaging 

stations cannot be located at all sites where streamflow 

information is needed, other methods are used to estimate 

streamflow statistics for these ungaged sites. One of the most 

common methods is to develop regression equations that relate 

streamflow statistics to selected basin characteristics. With 

certain limitations, this allows for the estimation of streamflow 

statistics at ungaged stream locations throughout the State.

During the equation development process, the study 

area was divided into eight separate geographic regions of 

similar characteristics. Data from a total of 234 streamflowgaging stations were included in the analysis. This included 

all streamflow-gaging stations in Idaho and those in adjacent 

States within an approximate 80-mi buffer surrounding Idaho 

with 10 or more years of record through water year 2003, 

which exhibited little or no sign of trends, and were unaffected 
Approach 7

by regulations, diversions, or both. More than 50 basin 

characteristics were obtained for each of the 234 streamflowgaging stations included in the study. The basin characteristics 

were obtained using GIS techniques from digital datasets 

such as DEMs, precipitation grids, and land-use grids. 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 

characteristic 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.

Relevant low-flow frequency statistics (including 7Q2) 

were computed for the 234 streamflow-gaging stations. Lowflow 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 selected. The series of annual minimum 

N-day values are then fit to a log-Pearson Type III distribution 

to determine the recurrence intervals. 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 years.

Multiple linear regression techniques then were used to 

develop equations for each region that related each low-flow 

frequency statistic to one or more basin characteristics. A 

GLS technique that weights the station data to compensate for 

spatial correlation and differences in record length was used to 

obtain the equations. The analyses resulted in the development 

of equations to estimate low-flow frequency statistics for 

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

These equations are published and described in more detail in 

Hortness (2006).

Development of DEMs and Continuous 

Parameter Grids

The datasets used in this project primarily are derived 

from the 10-m resolution DEMs produced by the USGS and 

the 1:24,000-scale NHD. The source DEM was obtained from 

the 1/3-arc-second resolution National Elevation Dataset 

(NED) and was projected into the Idaho Transverse Mercator 

projection based on the North American Datum of 1983 for 

each 8-digit HUC in Idaho. The NHD vector streams were 

integrated into the raster NED data, using a process often 

referred to as stream burning (Saunders, 2000). This process 

uses the AGREE computer program developed by Hellweger 

and Maidment (1998). The AGREE program corrects for DEM 

flow path displacement errors when delineating catchments. 

The AGREE process and additional manipulation of NED 

DEM and NHD datasets are presented in more detail in Rea 

and Skinner (2009).

A continuous parameter grid of 10 by 10 m cells was 

established for the perennial streams map. In a continuous 

parameter grid, each cell contains the value of some parameter 

measured for the entire drainage area upstream of that 

cell. The flow-accumulation grid described by Jenson and 

Domingue (1988) is the most basic continuous parameter grid. 

Each cell in a flow-accumulation grid contains the number of 

cells upstream of that cell. The upstream drainage area may be 

determined by multiplying the number of cells by the area of 

a cell. This area should be adjusted by adding the area of the 

cell of interest because the flow accumulation grid does not 

include this cell.

Values of most basin characteristics, such as mean 

elevation, were assigned to every cell to create a “weight” 

grid. A flow accumulation function in ARC/INFO 

(Environmental Systems Research Institute, 1999) sums 

values from the weight grid for each cell and accumulates cell 

values as it moves downgradient. In contrast, if no weight 

grid is assigned, the flow accumulation function simply totals 

the number of upstream cells, a process called “unweighted 

flow accumulation.” The weighted flow accumulation value, 

divided by the unweighted flow accumulation value, gives 

the mean value of the basin characteristic in the weight grid 

upstream of any grid cell.

This concept may be used with continuous-value 

parameters, such as elevation or precipitation, and with 

categorical-value parameters. For example, using a grid 

containing 1 for every cell categorized as forested in a landcover dataset, and 0 for every other cell, the fraction of the 

watershed area draining to a particular forested grid cell can be 

computed. The development of the continuous parameter grid 

is described in more detail in Rea and Skinner (2009).

Computation of Continuous 7Q2 Estimates

Most basin characteristics can be calculated on a 

continuous basis for every grid cell using the method 

described in the previous section and in Rea and Skinner 

(2009). If all parameters of a regression equation can be 

computed in this manner, then the result of the regression 

equation also may be computed continuously for every grid 

cell; therefore, the equations developed by Hortness (2006) 

were used to compute preliminary estimates of the 7Q2

statistic for every grid cell in the study area. A map of streams 

with perennial flow then was developed by comparing these 

estimates to the state standard of intermittent flow as less than 

0.1 ft3/s. A transition zone also was modeled corresponding 

to flow estimates of 0.1 ft3/s plus and minus one standard 

error. It should be noted that although standard error is valid 

only for the range of predictor variables, it was used to model 

the transition zone in the range of extrapolation because no 

other statistical measure was available. The transition zone 
8 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

represents the part of the stream that, given annual climate 

and hydrologic fluctuations as well as inherent statistical 

uncertainty, is assumed to contain the point at which a stream 

changes from perennial to intermittent. In other words, 

flow in reaches upstream of the top of the transition zone is 

considered intermittent, and flow in reaches downstream of the 

bottom of the transition zone is considered perennial. Within 

the transition zone, flow could be perennial or intermittent. 

The preliminary map generated some anomalous stream 

patterns that necessitated some revisions to the 7Q2 equations 

developed by Hortness (2006).

Model Revisions Based on 

Spatial Patterns

Statistical regression models are developed using 

measured data. Estimates of prediction error can be developed 

for data that fall inside the range of values used to develop 

the regression model. However, outside the range of the 

values used to develop the regression model, the bounds of 

statistical confidence are unknown. Regression analyses often 

yield equations that provide valid results in the range of input 

values, but may produce invalid or unrealistic estimates when 

extrapolating beyond the range of input values. Therefore, 

common statistical principles dictate that regression equations 

should not be used in extrapolation, but rather should be used 

only for interpolation (that is, within the range of measured 

values of the explanatory variables used in the regression 

analysis).

The purpose of the project was to distinguish between 

perennial and intermittent streams in Idaho; however, 

most streamflow measurements used to develop regression 

equations come from streamflow-gaging stations that are 

rarely placed on small, intermittent streams. As a result, the 

sample data typically do not represent the size of streams 

of interest in this application, and the regression equations 

must be applied in extrapolation. This was referred to as 

extreme extrapolation because the equations for 7Q2 were 

applied to small watersheds (as small as a single 10 m by 

10 m grid cell). Standard statistical measures are not always 

useful for assessing the validity of the model in extrapolation. 

Regression equations must be evaluated as to whether they 

are well behaved in extreme extrapolation for small streams. 

The spatial behavior of an equation can be evaluated based 

on the pattern of perennial streams simulated by the model. 

Regression models that simulated unrealistic stream network 

patterns were determined to be badly behaved or ineffective 

for this application.

If a regression equation includes only one explanatory 

variable (such as drainage area), regression estimates for 

a large number of values in the range of interest can be 

generated to determine how well the regression equation 

functions. A Monte-Carlo analysis often is used to generate 

simulated parameter values when multiple variables are 

involved. This analysis involves estimating the statistical 

distribution of the observed variables and randomly generating 

parameter values using this distribution for the range of 

interest. The combination of large numbers of randomly 

generated multi-parameter values then can be used to examine 

the behavior of the regression equation in extrapolation; 

however, randomly generated parameter values were not 

needed for this analysis. The complete set of parameter values 

for every grid cell in the domain of interest can be computed; 

therefore, the regression equation results can be evaluated 

for every combination of parameter values that exists in the 

modeled area, which produces a map of the spatial behavior of 

the equation.

As a test of regression equation behavior in extrapolation, 

continuous parameter grids were evaluated for the 7Q2

equation for region 8 published by Hortness (2006), and given 

here as:

7Q2 = 3.86 A0.930 BS-0.648, (1)

where:

7Q2 is the 7-day, 2-year low flow, in ft3/s

A is drainage area, in mi2, and

BS is average basin slope, in percent.

This equation was determined to be not well behaved in 

extreme extrapolation. The minimum drainage area in region 

8 used to develop this regression equation was 6.6 mi2, and 

the minimum basin slope was 6.15 percent. In the continuous 

parameter grid, the minimum drainage area is one 10 by 10 m 

grid cell, or 3.86 × 10-5 mi2. Model-generated values for 

basin slope for very small basins can be zero, which causes a 

numerically invalid result; therefore, slope is a poor predictor 

variable for estimating flow characteristics of very small 

basins, unless it is censored to remove zero values.

Alternative regression models were evaluated due to the 

poor spatial behavior of some of the previously developed 

equations. Regression models that produced stream network 

patterns that clearly were not reasonable in comparison with 

topographic maps were rejected in favor of models that 

produced more reasonable patterns. Methods described in 

Hortness (2006) were followed when developing revised 

regression equations.
Model Revisions Based on Spatial Patterns 9

Certain types of categorical variables such as forested 

area tended to produce unrealistic patterns. In small drainage 

areas, categorical variables tended to have extreme values of 

either zero or 100 percent. These extremes are rarely if ever 

present in the large basins upstream of streamflow-gaging 

stations and usually would be outside the range of data values 

used in the regression analysis. For this reason, categorical 

variables such as forested area were avoided where possible.

The final regression equations developed for modeling 

perennial streams in Idaho are shown in table 1. The ranges 

of basin characteristics used to develop the final regression 

equations are shown in table 2. Revised regression models 

were selected for five of the eight regions; the original 

equations by Hortness (2006) were retained for regions 2, 

4, and 6. These regression equations were applied to create 

revised continuous grids of 7Q2 estimates for the eight regions 

in the study area.

The scatterplot in figure 3 shows 7Q2 values plotted 

against drainage area for the (A) original and (B) revised 

regression models in small drainages in region 8. Note 

that basin slope and mean annual precipitation, although 

parameters in the original and revised equations, respectively, 

are not shown on the plot. The minimum drainage area used 

to develop the regression equations, 6.6 mi2, is shown in figure 

3 as a vertical line. Although some spatial patterns can be 

attributed to variability in additional explanatory variables, 

it is evident that the original model does not produce stable 

linear results in extreme extrapolation for small drainage 

areas. The revised model simulates linear results in extreme 

extrapolation for small drainage areas better than the original 

model.

Screen captures of the stream network derived using the 

(A) original (Hortness, 2006) and (B) revised perennial streams 

models for a small area in region 8 are shown in figure 4. 

The grid cells with 7Q2 estimates greater than or equal to 0.1 

ft3/s are shown in pink transparency over a USGS 1:24,000-

scale topographic base map. On the original map (fig. 4A), 

unreasonably dense and discontinuous drainage patterns 

appear that do not correspond to locations that appear to be 

stream channels based on topographic maps and knowledge 

of the area. This illustrates that regression equations that are 

not well behaved (in extreme extrapolation) may be detected 

by looking for unrealistic spatial patterns in the drainage 

network derived from application of the regression equation 

in a continuous manner. The spatial pattern for the revised 

model (fig. 4B) is much more reasonable than the original 

model (Hortness, 2006). However, the original model would 

still be preferred for predicting streamflow statistics in streams 

where extrapolation is not required because the standard error 

of prediction is better for the original model than the revised 

model.

The results of the revised regression models for region 8 

in a broader spatial context are shown in figure 5. Figure 5A

shows the results of the original model by Hortness (2006) for 

one 8-digit HUC (16010201). Figure 5B shows the results of 

the revised model for the same area.

The standard error of prediction for each regional 

regression equation is shown in table 1. The standard error 

of prediction is a measure of the overall model error as well 

as the sample error and is a good indicator of the overall 

predictive ability of the model within the range of input 

variables (Pope and others, 2001); however, it is not a suitable 

measure of the model error in the range of extrapolation 

because it is calculated based on measured values. The values 

presented in log10 format represent the errors in the logtransformed equations, and the percentage values represent 

the range of errors for the untransformed equations, as 

presented in table 1. The values were determined using error 

transformation equations presented in Riggs (1968). For 

example, the percent range for standard error of prediction 

for region 1 is +86.7 to -46.4 percent. In this region, the 

error range for a 7Q2 value of 1.0 ft3/s would be 0.54 to 1.87 

ft3/s. The highest standard errors of prediction are observed 

in regions 3 and 7. These regions encompass the Columbia 

Plateau, Snake River Plain, and Owyhee Uplift physiographic 

regions (not labeled in fig. 1), and are characterized by lower 

elevations, smaller terrain relief, and less rainfall compared 

to the remaining regions. Large standard errors of prediction 

also were observed for the original Hortness (2006) regression 

equations for regions 3 and 7. Hortness (2006) speculated that 

the large errors in region 3 likely were due to few streamflowgaging stations available for developing the regression model. 

Region 7 covers a large part of the study area, and Hortness 

and Berenbrock (2001) noted a high degree of natural 

variability in streamflow in region 7 that could contribute to 

a high error of prediction. Revising the regression model did 

not improve the standard error of prediction but substantially 

improved spatial patterns observed in extrapolation.
10 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

Region

7Q2

 regression equation Standard error of prediction

Original (Hortness, 2006) Revised log10 Percent

1 7Q2 = 0.731A0.613(W+1)0.907 7Q2 = 0.300A0.879 0.271 +86.7 to -46.4

12 7Q2 = 0.000153A1.04P1.92 No change 0.253 +78.9 to -44.1

3 7Q2 = 0.00953A0.392(R/1,000)3.36 7Q2 = 0.0214A0.971 0.277 +236 to -70.2

14 7Q2 = 0.0000215A1.04P2.41 No change 0.341 +119 to -54.4

5 7Q2 = 0.000453A1.04(V+1)1.51 7Q2 = 0.334A0.963 0.249 +77.3 to -43.6

16 7Q2 = 0.000133A1.05P2.10 No change 0.243 +75.0 to -42.9

7 7Q2 = 0.0329A0.678(S50+1)0.796 7Q2 = 0.0000115A0.837(E/1000)4.658 0.577 +277 to -73.5

8 7Q2 = 3.86A0.930BS-0.648 7Q2 = 0.00181A0.981P1.515 0.331 +116 to -53.4

1 Denotes region with original Hortness (2006) equation.

Table 1. Regression equations for the low-flow statistic, 7Q2 , for unregulated streams in regions 1–8, Idaho.

[Locations of regions are shown in figure 1. Standard error of prediction: Values determined using error transformation equations in Riggs (1968). 

Abbreviations: 7Q2, 7-day 2-year low flow, in cubic feet per second; A, drainage area, in square miles; BS, basin slope, in percent; E, mean elevation, in feet; 

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]

Equation variables

A E P

Region 1

Maximum 1,011.0 NA NA 

Minimum 12.5 NA NA 

Region 2

Maximum 2,442.5 NA 69.4 

Minimum 3.0 NA 24.8 

Region 3

Maximum 674.9 NA NA 

Minimum 17.6 NA NA 

Region 4

Maximum 5,507.9 NA 65.6 

Minimum 4.0 NA 15.9 

Region 5

Maximum 12,228.0 NA NA 

Minimum 19.3 NA NA 

Region 6

Maximum 6,236.7 NA 42.3 

Minimum 6.4 NA 15.3 

Region 7

Maximum 535.3 8,463.4 NA 

Minimum 7.4 2,984.4 NA 

Region 8

Maximum 874.8 NA 56.0 

Minimum 6.6 NA 14.2 

Table 2. Range of values of basin characteristics used to estimate the low-flow statistic, 7Q2 , for unregulated streams in regions 1–8, 

Idaho.

[Locations of regions are shown in figure 1. Equation variables: A, drainage area, in square miles; E, mean elevation, in feet; P, mean annual precipitation, in 

inches. Abbreviations: 7Q2, 7-day 2-year low flow, in cubic feet per second; NA, not applicable—variable not used in regression equation]
Model Revisions Based on Spatial Patterns 11

0.00001

0.0001

0.001

0.01

0.1

1

10

100

0.0001 0.001 0.01 0.1 1 10 100

DRAINAGE AREA, IN SQUARE MILES

7-DAY, 2-YEAR LOW FLOW, IN CUBIC FEET PER SECOND

Minimum drainage 

area used to develop 

regression model in 

Region 8: 6.6 square 

miles

Streams modeled

Line of extrapolation

B. Revised regression equation

ID_TAC08_0253_PerennialStreams_Fig03a

Minimum drainage 

area used to develop 

regression model in 

Region 8: 6.6 square 

miles

0.00001

0.0001

0.001

0.01

0.1

1

10

100

0.0001 0.001 0.01 0.1 1 10 100

DRAINAGE AREA, IN SQUARE MILES

7-DAY, 2-YEAR LOW FLOW, IN CUBIC FEET PER SECOND

Streams modeled

Line of extrapolation

A. From Hortness (2006) regression equation

Figure 3. Improvement of 7Q2 flow estimates in extreme extrapolation for region 8 from (A) the 

Hortness (2006) regression equation to (B) the revised regression equation for Idaho.
12 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

ID_TAC08_0253_PerennialStreams_Fig04a

IDAHO

A. Hortness (2006) 7Q2 regression equation

Figure 4. Screen captures from U.S. Geological Survey perennial streams model showing spatial pattern of stream 

network (pink pixels) in a selected area in region 8 derived from (A) Hortness (2006) 7Q2 regression equation and (B)

revised 7Q2

 regression equation for Idaho.
Model Revisions Based on Spatial Patterns 13

ID_TAC08_0253_PerennialStreams_Fig04b

B IDAHO . Revised 7Q2 regression equation

Figure 4. Continued.
14 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

Figure 5. Screen captures from U.S. Geological Survey perennial streams model 

showing spatial pattern of stream network for Hydrologic Unit Code 16010201 

(in region 8) derived from (A) Hortness (2006) 7Q2

 equation and (B) revised 7Q2

regression equation for Idaho.

ID_TAC08_0253_PerennialStreams_Fig05a

IDAHO

A. Hortness (2006) 7Q2 regression equation
Model Revisions Based on Spatial Patterns 15

Figure 5. Continued.

ID_TAC08_0253_PerennialStreams_Fig05b

IDAHO

B. Revised 7Q2 regression equation
16 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

Final Perennial Streams Model

A suite of geospatial datasets has been compiled for 

estimating streamflow statistics in Idaho, to support statistical 

modeling of perennial streams. The supporting datasets and 

metadata are described in detail in Rea and Skinner (2009).

The final map of estimated perennial streams 

consists of “synthetic” lines or vector representations 

of streams from the gridded model and is provided in 

Environmental Systems Research Institute (ESRI) shapefile 

format. The map and associated files and metadata are 

available for download at: http://water.usgs.gov/lookup/

getspatial?ds412_syntheticperennialstreams.

Although the synthetic streams derived from the 

regression models provides a consistent, connected 

representation of the stream network, many users need the 

results referenced to a commonly recognized hydrography 

framework, such as the NHD. Therefore, the modeled stream 

lines were merged with the 1:100,000-scale NHD dataset. 

Details of this process are beyond the scope of this report but 

are described in detail in Rea and Skinner (2009).

Although the full map of perennial streams in Idaho is 

too dense to display in this report, figure 6 shows a screen 

capture of the perennial streams map in the same area shown 

in figure 2. Most of the area shown is in region 2, and the 

original regression equation by Hortness (2006) was applied. 

The pattern of perennial streams shown is more reasonable 

than that derived from the NHD Hi-Res and shown in figure 2. 

However, HUC 17010305, in the northwest area of figures 2

and 6, is known as the Rathdrum Prairie and is an area of 

very porous soils with very few surface-water streams. Based 

on the authors’ knowledge of the area, the streams shown 

in figure 2 for HUC 17010305 are a better representation 

of the perennial streams than what is shown in figure 6. 

This is a good example of an area where the surface-water 

hydrography is dominated by local hydrogeologic effects and 

does not follow the general trend represented by the regression 

equations.
Final Perennial Streams Model 17

ID_TAC08_0253_PerennialStreams_Fig06a

17010214

17010301

17010302

17010304

17010303

17010306

17060108 17060308

17010213

17010204

17010101

17010305

17010308

IDAHO

17060306

17060306

Hydrologic 

 Unit Code

EXPLANATION

Figure 6. Screen capture of spatial distribution of modeled streams (blue) and Hydrologic Unit Code 

boundaries (black) from U.S. Geological Survey perennial streams model in northern Idaho.
18 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

Evaluation of Perennial Streams Model

The perennial streams model was evaluated by comparing 

classifications at various stream points on the map with four 

independent datasets from government agencies. A brief 

overview of these datasets is provided in table 3. Some stream 

classifications in the comparison datasets were based on 

single site visits and may not be representative of conditions 

throughout the year or over several years. Additionally, 

classification methods differed slightly among datasets. The 

locations of comparison points for each of the datasets are 

shown in figure 7.

The Beneficial Use Reconnaissance Program (BURP) 

dataset was provided by the IDEQ. The purpose of BURP is 

to help Idaho regulators meet the requirements of the Clean 

Water Act by collecting data for determining the existing 

uses and beneficial use support states of Idaho’s water bodies 

(Idaho Department of Environmental Quality, 2008). Field 

visits were conducted in summer and autumn each year 

to collect aquatic community samples and aquatic habitat 

information. Field crews measured flow at a site if it was not 

dry. Sites were coded intermittent if dry or measured flow was 

less than 0.1 ft3/s; otherwise, the site was coded as perennial.

The Environmental Monitoring and Assessment Program 

(EMAP) datasets were provided by the USEPA. EMAP 

was developed to monitor and assess the status and trends 

of national ecological resources with a focus on forecasting 

future risks to those resources (U.S. Environmental Protection 

Agency, 2008). EMAP datasets used in this comparison 

are “EMAP Office” and “EMAP Field”. USEPA personnel 

initially evaluated candidate stream sites using River Reach 

Dataset

Dates of field visits Classification 

method

Number 

of sites No. Source Name

1 Idaho Department 

of Environmental 

Quality 

IDEQ BURP Summer/autumn

1993–2006

Streams were coded perennial if measured flow during 

field visits was greater than or equal to 0.1 ft3/s; 

otherwise, streams were coded intermittent. 

1,804

2 U.S. Environmental 

Protection Agency

EMAP office No dates; determinations 

made in 1999

Made using several office-based approaches, including 

examining maps and GIS coverages and talking to 

regional biologists and State employees with knowledge 

of the area. No field visits.

114

3 U.S. Environmental 

Protection Agency

EMAP field Summer/autumn 

2000–2003

Streams were coded perennial if enough water was present 

to sample during field visits; otherwise, streams were 

coded intermittent. 

123

4 U.S. Geological 

Survey

USGS

 low flow

Throughout year 

1945–2001

Field visits made throughout the year, but mostly in 

summer/autumn. Sites were used for model comparison 

only if site was dry, water was pooled, or measured flow 

was <0.1 ft3/s (to be comparable with BURP sites). Sites 

selected were considered intermittent.

207

Table 3. Description of datasets used for evaluation of the U.S. Geological Survey perennial streams model for Idaho.

[Abbreviations: IDEQ BURP, Idaho Department of Environmental Quality Beneficial Use Reconnaissance Program; EMAP, Environmental Monitoring and 

Assessment Program; USGS, U.S. Geological Survey; ft3/s, cubic foot per second; GIS, geographic information system; <, less than]

File 3 (RF3) (U.S. Environmental Protection Agency, 1994) 

and NHD maps and stream classifications. The EMAP Office 

dataset included stream sites that were coded as nonperennial 

on RF3/NHD maps and stream sites that were coded perennial 

but were not considered candidates for field visits because 

of limited access or other reasons. Streams in this dataset 

were then coded as perennial or intermittent using several 

office-based approaches, including examining maps and GIS 

coverages and talking to regional and state scientists with 

knowledge of the area. The EMAP Field dataset included sites 

that were coded as perennial on RF3/NHD maps and were 

deemed candidates for further field verification. After field 

visits, sites were coded perennial if there was enough water 

present to sample, even if flow was not continuous at the time 

of the visit. Otherwise, the site was coded intermittent. Field 

visits were made during the summer/autumn baseflow period, 

which was expected to be the minimum flow period for any 

given year.

The USGS Low Flow dataset includes stream sites that 

are measured periodically as part of the USGS Idaho Water 

Science Center partial record network used to supplement 

long-term streamflow-gaging records when generating peak 

and low flow statistics. Of the master partial record network 

database, sites were included in the comparison with the 

USGS perennial streams map if the site was dry, water 

was pooled, or measured flow was less than 0.1 ft3/s (to be 

comparable with IDEQ BURP sites). All sites in this dataset 

are considered intermittent because they were observed to go 

dry or nearly dry annually. No attempt was made by the field 

hydrographer making the streamflow measurement to classify 

the stream as intermittent or perennial.
Evaluation of Perennial Streams Model 19

ID_TAC08_0253_PerennialStreams_Fig01

Yellowstone River

Snake

River

Big Lost

Fork

Owyhee

River River Snake

Clark

Priest

River

For

S

k

aint Joe River

Snake River Lochsa River

Selway

River

Salmon River

Weiser River Boise

Lemhi River

Big Wood River

Raft River

Portneuf R

River

Bear

River

Malheur

River

River

Bruneau

Payette

Bear

Lake

Blackfoot River Palisades

Reservoir

Jackson

Lake

Coeur

d’Alene

Lake

Pend

Oreille

Lake

Spokane

River

Kootenai

River

Bitterroot

River

Dworshak

Reservoir

Grand Ronde River

Clearwater

 River

River

Henrys

River

American

Falls

Reservoir

Twin 

Falls

Boise

Sandpoint

Lewiston

Coeur 

d’Alene

Idaho

Falls

Borah

Peak

Pocatello

Salmon

MONTANA

UTAH

NEVADA

OREGON

WYOMING

WASHINGTON

IDAHO

1

2

3

4

5

6

7

8

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

119° 118° 117° 116° 115° 114° 113° 112° 111° 110° 109°

47°

46°

43°

42°

41°

49°

48°

45°

44°

EXPLANATION

IDEQ BURP

EMAP Office

EMAP Field

USGS Low Flow

Undefined area

Dataset name (see table 3)

Region and identification number for 

which specific regression equations 

have been developed (see table 1)

0 4020 60 100 MILES 80

0 4020 60 100 KILOMETERS 80

2

Figure 7. Locations of comparison points from datasets used to evaluate the U.S. Geological Survey perennial streams 

model for Idaho.
20 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

The comparison datasets were overlaid on the USGS 

perennial streams model. Comparison sites were forced to 

snap to the nearest USGS modeled stream (perennial or 

transitional), and coding of the comparison site was compared 

with the coding of the nearest USGS modeled stream. Sites 

were considered “agreements” or “disagreements” with the 

model based on the rules presented in table 4. All sites that 

were initially coded “disagreements” were checked to verify 

whether the comparison point snapped to the correct stream. 

In many cases, the comparison point was on a NHD stream 

not modeled by the USGS (for example, a true intermittent 

stream) but snapped to the closest USGS-modeled perennial 

stream. Once the correct location of the comparison point was 

verified, these cases were considered agreements with the 

model, because the USGS model was intended to include only 

perennial and transitional stream reaches. Comparison data 

points were removed from the analysis if their coordinates 

appeared grossly incorrect and no accompanying description 

was available to determine the correct location of the site. 

In addition, about 20 percent of the sites that were coded as 

agreements were checked to ensure that the point snapped to 

the correct USGS-modeled stream. Codings were revised if 

necessary.

A classification table (table 5) shows a comparison 

between the USGS model and comparison datasets. Overall, 

81 percent of the comparison data points agreed with the 

USGS model according to the agreement rules shown in 

table 4. In table 5, the classification categories that are 

considered “disagreements” are: Observed intermittent 

stream―Predicted perennial stream (417 sites) and Observed 

perennial stream―Not mapped (4 sites). A comparison of each 

dataset with the USGS perennial streams model is presented 

by region in table 6. The total number of sites available for 

comparison and the percentage of total sites that agreed with 

the USGS model are shown for each dataset.

As a whole, the USGS model compared well with 

comparison datasets. In most of the disagreements, the 

USGS model overestimated the amount of perennial streams, 

meaning that many streams were predicted perennial when 

comparison datasets classified them as intermittent. Some 

disagreements were expected due to varying quality of site 

location coordinates (latitude/longitude), timing of site visits 

during unusually wet or dry years, discrepancy between 

1-day site visits and a 7-day low flow criterion, and localized 

contributions of ground water to flow in some areas.

Stream classification 

Coding

USGS model Comparison dataset

Perennial Perennial Agree

Transitional Intermittent Agree

Transitional Perennial Agree

Not mapped Intermittent Agree

Not mapped Perennial Disagree

Perennial Intermittent Disagree

Table 4. Agreement rules for comparing independent datasets 

with the U.S. Geological Survey perennial streams model for 

Idaho.

[Stream classification, USGS model: Perennial, stream reach with 7Q2

flow greater than or equal to 0.1 ft3/s; Transitional, stream reach where 7Q2

is 0.1 ft3/s ± 1 standard error; Not mapped, stream reach not on USGS model 

and assumed intermittent. Stream classification, Comparison dataset: See 

table 3. Abbreviations: USGS, U.S. Geological Survey; 7Q2, 7-day 2-year 

low flow, ft3/s, cubic foot per second]

Observations 

(all comparison 

datasets)

Predictions from USGS model

(number of sites)

Total number 

Predicted of sites

perennial 

stream

Predicted 

transitional 

stream

Not mapped 

(assumed 

intermittent 

stream)

Observed 

intermittent 

stream

417 399 171 987

Observed 

perennial 

stream

843 414 4 1,261

Total 1,260 813 175 2,248

Table 5. Classification table of accuracy of the U.S. Geological 

Survey perennial streams model relative to comparison datasets 

for Idaho.

[Shading denotes disagreements between the comparison dataset and the 

USGS model. Abbreviation: USGS, U.S. Geological Survey]
Evaluation of Perennial Streams Model 21

Region

Comparison datasets

BURP EMAP office EMAP field USGS low flow

Percentage 

agreement

Number of 

sites compared

Percentage 

agreement

Number of 

sites compared

Percentage 

agreement

Number of 

sites compared

Percentage 

agreement

Number of 

sites compared

1 80 76 80 5 33 6 8 13

2 87 115 100 12 100 2 32 19

3 89 92 100 3 86 22 40 15

4 83 178 88 16 100 10 75 40

5 81 233 81 16 60 5 8 12

6 84 316 90 10 67 12 50 24

7 87 561 93 41 84 55 63 64

8 82 233 73 11 55 11 45 20

Overall 

agreement 

85 1,804 89 114 78 123 51 207

Table 6. Agreements between the U.S. Geological Survey perennial streams model and comparison datasets by hydrologic region, 

Idaho and surrounding areas.

[See table 4 for agreement rules followed when determining “Percentage Agreement.” Abbreviations: USGS, U.S. Geological Survey; BURP, Idaho 

Department of Environmental Quality Beneficial Use Reconnaissance Program; EMAP, Environmental Monitoring and Assessment Program]

The USGS perennial streams model was generated 

based on long-term streamflow-gaging records and, with 

the inclusion of a transition zone upstream of the perennial 

stream endpoint, was expected to represent a range of climatic 

conditions. However, if a comparison dataset was generated 

solely during an unusually wet or dry period, a high number 

of disagreements with the model are expected. To evaluate 

climatic representativeness, the average Palmer Drought 

Severity Index (PDSI) for Idaho was examined for each year 

in the comparison dataset. PDSI generally ranges from -6 

(extreme drought) and +6 (extreme wet), centering on 0 as a 

“normal” condition (Palmer, 1965).

The EMAP Office dataset compared better with the 

USGS model than the EMAP Field dataset (table 6). This was 

expected because the EMAP Field dataset was based on a 

single site visit, and the EMAP Office dataset was generated 

from professional opinion based on overall long-term 

knowledge of the area and map resources. Additionally, the 

EMAP Field dataset site visits were conducted during 2000–

2003, when the statewide PDSI ranged from -1 to -4 (Cook 

and Krusic, 2008), an unusually dry period, and a higher 

number of disagreements were expected.

The highest number of disagreements with the USGS 

model was observed in the USGS Low Flow Network dataset. 

Most disagreements probably are due to poor latitude/

longitude coordinates during some periods in the dataset and 

the timing of site visits. Because the dataset spans about 6 

decades, global positioning system (GPS) receivers were not 

available to measure site latitude and longitude for the earlier 

measurements. Many coordinates were pulled from maps, 

which may not have been as accurate as GPS, and many of 

these comparison points did not include a stream name or 

description. In addition, the accuracy of GPS coordinates 

from March 1990 to May 2000 was hampered by selective 

availability, an intentional GPS signal degradation feature 

implemented by the U.S. Department of Defense for national 

defense purposes (National Executive Committee for SpaceBased Positioning, Navigation, and Timing, 2008). Selective 

availability introduced slowly changing random errors of as 

much as 100 m in publicly-available GPS navigation signals 

(U.S Department of Commerce Technology Administration, 

2000). Eight comparison points were measured during this 

period, and if site coordinates were poor, the location as 

plotted may be wrong and may indeed be located on a nonmodeled (intermittent) part of a stream or entirely on another 

stream.

Like other comparison datasets, stream classification in 

the USGS Low Flow Network dataset was made based on a 

single assessment, not a 7-day duration of flow, and no attempt 

was made by hydrographer to classify the stream when in the 

field. Stream classification in this dataset was made solely for 

comparison with the USGS perennial streams model. Also, 

most disagreements occurred during years when the statewide 

PDSI was negative, indicating dry and, in some years, drought 

conditions. Of the sites that were considered disagreements, 80 

percent were visited during years when the PDSI was negative 

according to Cook and Krusic (2008). About 25 percent of 

all site visits in this dataset were made in 1977, when the 

statewide PDSI ranged from -6 to -2 (Cook and Krusic, 2008). 
22 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

These measurements were made during abnormally dry years 

and resulted in an intermittent classification when, during 

years of normal precipitation, the stream may flow year-round. 

Mean drainage area for the sites considered disagreements was 

relatively high (38.5 mi2) in comparison with sites considered 

agreements (7.4 mi2). Several opportunistic measurements 

were made at sites with drainage areas as large as 517 mi2

during years of drought, resulting in disagreements with the 

model. Under normal hydrologic conditions, most of these 

sites were expected to agree with the model.

The BURP dataset represented a range of climate 

conditions and included the highest number of comparison 

sites. Statewide average PDSI ranged from -3.5 to 4.5 during 

the study period, 1993–2006 (Cook and Krusic, 2008). Eight 

years during the study period were considered “wet” years 

(positive PDSI) and six years were considered “dry” years 

(negative PDSI). The number of sites visited each year was 

fairly constant during the study period; therefore, the BURP 

dataset is considered the most representative dataset for 

comparison, and it agrees well with the model (85 percent 

agreement overall).

Overall, regions with the highest number of 

disagreements were 1, 5, 6, and 8, which have a high 

percentage of mountainous and forested area. These regions 

also include many areas of rapid transition from mountains 

to expansive valleys. In these areas, the USGS model overpredicted the number of perennial streams in comparison with 

the NHD and independent datasets. Highly variable ground 

water and surface water interactions, including streamflow 

losses, are documented in these regions in Donato (1998), 

Kahle and Bartolino (2007), and Skinner and others (2007). 

Streamflow losses to ground water along mountain fronts, 

where an interface can form in the surficial geology between 

residuum and more-permeable colluvium and alluvium, are 

well documented (Niswonger and others, 2005; Covino and 

McGlynn, 2007; Foster, 2008). Streams can change from 

perennial to intermittent at this interface, often called a 

mountain front recharge zone (Covino and McGlynn, 2007). 

The USGS model does not account for these site-specific 

hydrologic conditions and may not adequately represent true 

conditions in stream reaches where ground water gains and 

losses are highly variable.

Regions with the highest agreements were 2, 3, 4, and 7; 

all these regions except region 2 have a high percentage of low 

gradient, low elevation area and fewer mountain front recharge 

zones. However, most of the comparison sites in region 2 were 

in the lower gradient areas around Lake Coeur d’Alene and 

Lake Pend Oreille. These areas were expected to have more 

consistent ground water contributions to streamflow and less 

variable surficial geology, resulting in more consistent low 

flow patterns and a higher percentage of perennial streams. 

Surprisingly, the highest standard errors of prediction were 

for regions 3 and 7 in their respective regression equations; an 

explanation for these high standard errors is provided in the 

section titled “Model Revisions Based on Spatial Patterns”.

Limitations and Areas for Further Study

The GLS regression equations were generated using 

streamflow-gaging station data and are applicable for stream 

sites in the study area with drainage areas ranging from 

3.0 to 12,228 mi2; however, this range varies by region. 

Ranges for other explanatory variables used to develop the 

regression equations are presented in table 2. The regression 

equations were applied outside the range of values in table 2

to predict endpoints of perennial flow along stream reaches. 

Such extrapolation cannot be avoided because of a lack of 

streamflow data for small streams. As a result, considerable 

uncertainty exists in the perennial streams model presented in 

this report, though agreement with independent datasets was 

good. The regression models provide overall estimates based 

on the general trends within each region. 

Local factors such as a large spring or a losing reach are 

not included in these regression models, and these factors may 

greatly affect flows at any given point. Site-specific flow data, 

assuming a sufficient period of record, generally would be 

considered to better represent flow conditions at a given site 

than flow estimates based on regionalized regression models. 

However, this information rarely is available and is not always 

practical to obtain. The map is considered a first-cut, broad scale 

estimate of the locations of perennial streams that could be used 

for state-wide planning, assessment, and reporting purposes. 

The regression equations and perennial streams model presented 

are applicable only to unregulated, naturally-flowing streams.

Most studies to predict low-flow statistics at ungaged 

sites have relied on regression equations with basin 

characteristics such as drainage area, slope, elevation, and 

land cover. Permanence of flow in small streams is expected 

to depend on these characteristics as well as on ground 

water, or baseflow, contributions to the stream throughout 

the year. Baseflow recession information would be helpful 

in quantifying low-flow characteristics on a regional basis. 

Many studies have shown that the use of a baseflow recession 

constant or streamflow variability predictor greatly reduces 

the error of estimation of low-flow statistics (Vogel and Kroll, 

1992; Yu and others, 2002; Kroll and others, 2004; Eng and 

Milly, 2007). However, baseflow information typically is 

gathered from long-term, continuous streamflow-gaging 

stations. Quantifying and predicting the baseflow recession 

constant (tau) at ungaged headwater sites, through procedures 

outlined in Eng and Milly (2007), may be an important 

element in improving accuracy in low flow statistics and 

stream classification.

In June 2006, the United States Supreme Court issued 

a ruling in the consolidated cases Rapanos vs. United States 

and Carabell vs. United States that changed the interpretation 

of stream classifications under the jurisdiction of the 

Clean Water Act. The ruling, called the Rapanos Decision, 

may eventually supersede many State and Federal stream 

management and regulatory guidelines that once were applied 

based on intermittent and perennial classifications. The 

new classification considers waters jurisdictional if they are 
Summary 23

“relatively permanent”, and possibly jurisdictional if “nonrelatively permanent” when there is a “significant nexus” to an 

otherwise jurisdictional water (U.S. Environmental Protection 

Agency and U.S. Army Corps of Engineers, 2007). Streams 

are considered relatively permanent if flow is continuous on 

a seasonal basis (for example, 90 days or more). This report 

describes an example where streamflow information from the 

USGS streamflow-gaging network has been used to develop 

regression equations that predict streamflow characteristics at 

ungaged sites. However, under the Rapanos Decision, water 

quality standards may be applied to streams despite long 

durations of zero flow, and few to no long-term streamflowgaging stations are located on such streams. Therefore, the 

existing USGS streamflow-gaging network cannot be used 

alone to extrapolate statistics to the level necessary to classify 

and map streams under the Rapanos guidance. A new flowdetection monitoring network and prediction methodology 

are needed to develop a map of relatively permanent streams 

to assist regulators and water-resource managers in making 

jurisdictional determinations. The map of perennial streams 

described in this report would be useful as a reference when 

selecting locations of flow-detection monitoring sites.

Summary

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

with the Idaho Department of Environmental Quality (IDEQ) 

and Bureau of Reclamation, developed a map of streams 

with perennial flow in eight hydrologic regions in Idaho 

using generalized least-squares (GLS) regression models 

for estimating the 7-day, 2-year low flow (7Q2) statistic 

and applying a 0.1 ft3/s cutoff criterion. The regression 

equations and perennial streams model are applicable only to 

unregulated, naturally-flowing streams. A transition zone was 

modeled as plus or minus 1 standard error around the 0.1 ft3/s 

criterion to account for changes in the perennial flow initiation 

point due to climatic, hydrologic, and statistical variability. In 

many cases, it was necessary to apply the regression equations 

well below the range of values used to develop the regression 

models. This extreme extrapolation produced unrealistic flow 

estimates and spatial patterns in the modeled stream network 

in the headwaters of some regions. As a result, alternative 

regression models for 7Q2 were generated for five of eight 

regions to produce realistic results in the range of extreme 

extrapolation. Standard errors of prediction were calculated 

for the regression equations to provide a measure of overall 

error and predictive power of the model within the range of 

input variables. Standard errors of prediction for the regression 

equations were lowest for region 6 (+75.0 to -42.9 percent) 

and highest for region 7 (+277 to -73.5 percent). Although the 

equations published by Hortness (2006) remain the preferred 

equations to use for generating streamflow statistics within the 

range of the original input variables, the selected alternative 

equations are preferred for extrapolating estimates of the 

7Q2 in small drainage areas for the purpose of determining 

perennial flow initiation points.

The resulting 7Q2 equations were used in conjunction 

with a continuous parameter grid of basin characteristics 

to generate a geographic information system-based map of 

streams in Idaho with perennial flow according to the state 

definition of intermittent flow as less than 0.1 ft3/s. The 

final map of perennial streams consists of synthetic lines or 

vector representations of streams from the gridded model 

and is provided in Environmental Systems Research Institute 

shapefile format.

The perennial streams model was evaluated by 

comparing classifications at various stream points on the map 

with four independent datasets from government agencies: 

IDEQ Beneficial Use Reconnaissance Program (BURP), 

Environmental Monitoring and Assessment Program (EMAP) 

Office, EMAP Field, and USGS Low Flow Network datasets. 

Overall, 81 percent of the comparison data points agreed with 

the USGS model. As a whole, the USGS model appeared to 

overestimate the amount of perennial streams in comparison 

with the independent datasets, meaning that many streams 

were predicted perennial when comparison datasets classified 

them as intermittent. Some disagreements between the model 

and comparison datasets were due to poor site location 

coordinates, timing of the comparison site visits during 

unusually wet or dry years, discrepancy between 1-day site 

visits and a 7-day low flow criterion, localized groundwater 

contributions to flow in some areas, and uncertainty due to 

model extrapolation. The IDEQ BURP dataset represented a 

range of climate conditions, including about equal numbers 

of wet and dry years, and included the highest number of 

comparison sites. Therefore, the BURP dataset is considered 

the most representative dataset for comparison, and it agrees 

well with the USGS model (85 percent agreement overall). 

Overall, regions with the highest number of disagreements 

have a high percentage of mountainous and forested area. 

The regions also include many mountain front recharge zones 

where streamflow losses to groundwater typically occur, 

possibly resulting in a change from perennial to intermittent 

flow. In these areas, the USGS model over-predicted the 

number of perennial streams in comparison with the National 

Hydrography Dataset and independent datasets. The USGS 

model does not account for these site-specific hydrologic 

conditions and may not adequately represent true conditions 

in stream reaches where groundwater gains and losses are 

highly variable. Regions with the highest agreements have 

a high percentage of low gradient, low elevation area and 

fewer mountain front recharge zones, resulting in more 

consistent low flow patterns that were well represented 

by the GLS regression equations. Site-specific flow data, 

assuming a sufficient period of record, generally would be 

considered to better represent flow conditions at a given site 

than flow estimates based on regionalized regression models; 

however, flow data on small headwater streams rarely are 

available and not always practical to obtain. The developed 

map is considered to be a first-cut, broad scale estimate of the 

locations of streams with perennial flow.
24 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

Acknowledgments

The authors wish to thank Don Essig with IDEQ for his 

ongoing interest, patience, and input in this project and for 

supplying the BURP comparison dataset. Special thanks also 

go to Barbara Rosenbaum and David Peck with USEPA for 

supplying the EMAP comparison dataset and to Tom Brennan 

and Jon Hortness with USGS for generating the USGS partial 

record network database. In addition, the authors wish to 

thank Steve Garcia with USGS for his assistance with model 

evaluation.

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26 Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model

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http://id.water.usgs.gov
Wood and others— Estimating Perennial Streams in Idaho Using a Generalized Least-Squares Regression Model—Scientific Investigations Report 2009–5015