U.S. Department of the Interior 

U.S. Geological Survey 

Prepared in cooperation with 


Idaho Department of Environmental Quality


A Statistical Model for Estimating Stream 

Temperatures in the Salmon and Clearwater 

River Basins, Central Idaho 

Water-Resources Investigations Report 02–4195 
A Statistical Model for Estimating Stream 

Temperatures in the Salmon and Clearwater 

River Basins, Central Idaho 

By Mary M. Donato 

Water-Resources Investigations Report 02–4195 

Prepared in cooperation with 


Idaho Department of Environmental Quality


Boise, Idaho


2002

U.S. DEPARTMENT OF THE INTERIOR 

GALE A. NORTON, Secretary 

U.S. GEOLOGICAL SURVEY 

Charles G. Groat, Director 

Any use of firm, trade, and brand names in this report is for 

identification purposes only and does not constitute 

endorsement by the U.S. Government. 

Additional information can be 


obtained from:


District Chief


U.S. Geological Survey


230 Collins Road


Boise, ID 83702-4520


http://idaho.usgs.gov 

Copies of this report can be 


purchased from:


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Copies of this report also are 

available in PDF format, which can 

be viewed using Adobe Acrobat 

Reader, at URL: 

http://idaho.usgs.gov/public/reports.html 
CONTENTS 

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

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

Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 

Purpose and scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 

Modeling approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

Description of study area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

Definition of terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

Site selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 

Collection of site characteristic data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

Collection of subbasin characteristic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

Data collection and processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 

Quality control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

Characterization of stream temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

Temperature metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

Graphical display of temperature data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

Idaho stream-temperature standards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

Statistical analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

Geographic variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

Vegetation variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

Climate variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 

Stream-temperature model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 

General approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 

Grand average temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 

Seasonal component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 

Air-temperature adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 

Model evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 

Estimation errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 

General versus specific models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 

Seasonal component. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 

Air-temperature adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 

Complete model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 

Independent tests of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

Limitations of the model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 

References cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 

FIGURES 

1. Locations of the Salmon and Clearwater River Basins, central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . 4 

2.	 Monitored sites that provided stream-temperature data used to develop and test the statistical 

model, Salmon and Clearwater River Basins, central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

3.	 Daily average temperature for representative streams in the Salmon and Clearwater River 

Basins, central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

4.	 Hourly temperature for streams with contrasting diurnal temperature fluctuation in the 

Salmon and Clearwater River Basins, central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

Contents iii 
5.	 Quantile diagram for selected streams in the Salmon and Clearwater River Basins, 

central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

6.	 Exceedance curves for representative streams in the Salmon and Clearwater River Basins, 

central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

7.	 Sites where stream temperatures met or exceeded current Idaho stream-temperature 

standards for cold-water biota during the 2000 monitoring period, Salmon and Clearwater 

River Basins, central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 

8.	 Deviation from grand average temperature for representative streams in the Salmon and 

Clearwater River Basins, central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 

9.	 Locations of weather stations that provided air-temperature data used to derive the airtemperature adjustment component of the statistical model, Salmon and Clearwater River 

Basins, central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 

10.–20. Graphs showing: 

10.	 Mean daily stream-temperature error and 95-percent confidence interval for all sites 

used to develop the statistical model, Salmon and Clearwater River Basins, central 

Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 

11.	 Mean daily stream-temperature error for all sites used to develop the statistical model, 

calculated by stream-order group, Salmon and Clearwater River Basins, central Idaho. . . . . . . 27 

12.	 Periodic functions of deviation from grand average temperature for the general model 

and for three specific models based on stream-order groups, Salmon and Clearwater 

River Basins, central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 

13.	 Errors in seasonal component of the general model and three specific models based on 

stream-order groups, Salmon and Clearwater River Basins, central Idaho . . . . . . . . . . . . . . . . . 29 

14.	 Daily average air-temperature adjustments calculated by the general model and three 

specific models based on stream-order groups, Salmon and Clearwater River Basins, 

central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

15.	 Mean estimation errors for the general model and for three specific models, Salmon 

and Clearwater River Basins, central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 

16.	 Estimated and observed temperatures of the Salmon River above Redfish Lake Creek, 

1980 and 1982, Salmon River Basin, central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 

17.	 Estimated and observed temperatures of the Red River below South Fork near Red 

River 

Ranger Station, 1984 and 1986, Clearwater River Basin, central Idaho . . . . . . . . . . . . . . . . . . . 34 

18.	 Estimated and observed temperatures of Big Deer Creek, 1999 and 2000, Salmon 

River Basin, central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 

19.	 Estimated and observed temperatures of the Lochsa River above Wilderness Gateway 

Campground, 1998, Clearwater River Basin, central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 

20.	 Estimated and observed temperatures of Wilson Creek, 2001, Salmon River Basin, 

central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 

TABLES 

1.	 Definitions of subbasin and site characteristics and stream-temperature metrics used in the 

statistical model and methods used in their derivation or calculation, Salmon and Clearwater 

River Basins, central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 

2.	 Statistical summary of selected subbasin and site characteristics for monitored sites used in 

the statistical model, Salmon and Clearwater River Basins, central Idaho. . . . . . . . . . . . . . . . . . . . . . 9 

3.	 Selected stream-temperature metrics for monitored sites used in the statistical model, 

Salmon and Clearwater River Basins, central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 

iv A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
4.	 Statistical summary, grouped by stream order, of selected stream-temperature metrics for 

monitored sites used in the statistical model, Salmon and Clearwater River Basins, 

central Idaho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

5. Current Idaho stream-temperature standards for aquatic life designations. . . . . . . . . . . . . . . . . . . . . . 17 

6.	 Spearman correlation coefficients describing correlation of subbasin or site characteristics 

with stream-temperature metrics for 183 monitored sites used in the statistical model, 

Salmon and Clearwater River Basins, central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 

7.	 Results of multiple linear regression to estimate grand average temperature for 183 monitored 

sites used in the statistical model, Salmon and Clearwater River Basins, central Idaho . . . . . . . . . . . 22 

8.	 Results of simple linear regression for the air-temperature adjustment component of the 

statistical model, Salmon and Clearwater River Basins, central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . 24 

9.	 Ratio of mean August discharge to long-term average August discharge at selected streamgaging stations for the year 2000 and for years for which the model was tested, Salmon and 

Clearwater River Basins, central Idaho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 

CONVERSION FACTORS AND VERTICAL DATUM 

Multiply By To obtain 

meter (m) 3.281 foot 

kilometer (km) 0.6214 mile 

square kilometer (km2) 0.3861 square mile 

Temperature in degrees Celsius (°C) can be converted to degrees Fahrenheit (°F) as follows: 

°F=(1.8) (°C) +32 

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929—a geodetic datum 

derived from a general adjustment of the first-order level nets of the United States and Canada, formerly called Sea 

Level Datum of 1929. 

Contents v 
A Statistical Model for Estimating Stream 

Temperatures in the Salmon and Clearwater 

River Basins, Central Idaho 

By Mary M. Donato 

Abstract 

A water-quality standard for temperature is 

critical for the protection of threatened and endangered salmonids, which need cold, clean water to 

sustain life. The Idaho Department of Environmental Quality has established temperature standards to protect salmonids, yet little is known 

about the normal range of temperatures of most 

Idaho streams. A single temperature standard for 

all streams does not take into account the natural 

temperature variation of streams or the existence 

of naturally warm waters. To address these issues 

and to help the Idaho Department of Environmental Quality revise the existing State temperature 

standards for aquatic life, temperature data from 

more than 200 streams and rivers in the Salmon 

and Clearwater River Basins were collected. From 

these data, a statistical model was developed for 

estimating stream temperatures on the basis of 

subbasin and site characteristics and climatic 

factors. 

Stream temperatures were monitored hourly 

for approximately 58 days during July, August, 

and September 2000 at relatively undisturbed sites 

in subbasins in the Salmon and Clearwater River 

Basins in central Idaho. The monitored subbasins 

vary widely in size, elevation, drainage area, vegetation cover, and other characteristics. The resulting data were analyzed for statistical correlations 

with subbasin and site characteristics to establish 

the most important factors affecting stream temperature. Maximum daily average stream temperatures were strongly correlated with elevation and 

total upstream drainage area; weaker correlations 

were noted with stream depth and width and average subbasin slope. Stream temperatures also were 

correlated with certain types of vegetation cover, 

but these variables were not significant in the final 

model. 

The model takes into account seasonal temperature fluctuations, site elevation, total drainage 

area, average subbasin slope, and the deviation of 

daily average air temperature from a 30-year normal daily average air temperature. The goodnessof-fit of the model varies with day of the year. 

Overall, temperatures can be estimated with 95-

percent confidence to within approximately plus or 

minus 4 degrees Celsius. The model performed 

well when tested on independent stream-temperature data previously collected by the U.S. Geological Survey and other agencies. 

Although the model provides insight into the 

natural temperature potential of a wide variety of 

streams and rivers in the Salmon and Clearwater 

River Basins, it has limitations. It is based on data 

collected in only one summer, during which temperatures were higher and streamflows were lower 

than normal. The effects of changes in streamflow 

on the effectiveness of the model are not known. 

Because the model is based on data from minimally disturbed or undisturbed streams, it should 

not be applied to streams known to be significantly 

affected by human activities such as disturbance of 

the streambed, diversion and return of water by 

irrigation ditches, and removal of riparian vegetation. Finally, because the model is based on data 

from streams in the Salmon and Clearwater River 

Basins and reflects climatological and landscape 

characteristics of those basins, it should not be 

applied to streams outside this region. 

Abstract 1 
INTRODUCTION 

Background 

Stream temperature is a critical element of water 

quality because it directly and indirectly influences the 

biological communities, particularly fish and benthic 

invertebrates, that inhabit the stream. Salmonids 

(salmon, trout, and charr) are particularly sensitive to 

stream temperature, which affects their metabolism, 

growth rates, food requirements, and the timing of lifehistory events such as migration and smoltification. 

Temperature also plays an important role in the occurrence of diseases and parasites. Dissolved oxygen content, biochemical oxygen demand rates, algae production, and contaminant toxicity are all strongly related to 

temperature. 

Stream temperatures vary temporally (with the 

seasons and over the course of 24 hours) and spatially 

(over the length of a stream). Although stream temperatures have never been optimal in all places and at all 

times in the Pacific Northwest, salmonids have developed physiological and behavioral adaptations that 

have allowed them to thrive in this region. In many 

streams, natural cold-water refugia (protected areas) 

have played a critical role in the evolution of many 

salmonids. Fish have survived less-than-optimal temperatures by resting and cooling off in refugia during 

migration. However, human activities have played a 

role in changing the thermal regime of streams, thus 

contributing, directly and indirectly, to the decline in 

native salmonid populations. 

Water temperature is the most common waterquality violation in the Pacific Northwest. According to 

the Clean Water Act, the numerous violations must be 

addressed by Total Maximum Daily Load plans. As 

part of the overall plan for Idaho, the Idaho Department 

of Environmental Quality (DEQ) has developed 

stream-temperature standards to protect cold-water 

fauna, including the bull trout. It is recognized, however, that a single temperature standard for all streams 

may not accommodate the natural temperature variation within and among streams or the existence of naturally warm waters. For example, recent data suggest 

that streams unaffected or minimally affected by human 

impact may naturally exceed current temperature standards. Some streams known to exceed current temperature standards for bull trout appear to support populations of these cold-water fauna (Essig, 1998). To establish realistic and enforceable temperature standards, we 

must understand the natural temperature potential and 

limitations of streams. Because it is unfeasible to simulate natural stream temperatures in every drainage 

basin in Idaho, agencies would benefit from a practical 

method to estimate natural stream temperatures on the 

basis of basin characteristics and other readily available data. A statistical model was developed to help fill 

this need. 

Purpose and Scope 

This report describes the results of an investigation for which the objectives were to 1) characterize 

stream temperatures over a large region in a variety of 

settings in the Salmon and Clearwater River Basins in 

central Idaho and 2) develop a statistical model to estimate stream temperatures in subbasins where temperatures are not known or previously have not been monitored. The U.S. Geological Survey (USGS), with assistance from DEQ, used digital temperature loggers to 

collect hourly stream-temperature data at sites in more 

than 200 subbasins in the Salmon and Clearwater River 

Basins over an approximately 2-month period during 

the summer of 2000. Site characteristics such as vegetation cover, channel width, and channel orientation 

also were collected. Various stream-temperature metrics, or measures (for example, maximum weekly average temperature), were calculated, and statistical correlations between the metrics and site and subbasin characteristics and climatological data were identified. On 

the basis of these correlations, an expression was 

developed for estimating daily average stream temperatures for the interval July 24 to September 10. Because 

this study is restricted to the Salmon and Clearwater 

River Basins of Idaho, the model results are applicable 

only to streams in this region of central Idaho. 

An important aspect of establishing stream temperature standards to protect aquatic life is characterizing the biological communities and understanding their 

relationship to stream temperature and to habitat variables such as vegetation and channel characteristics. To 

address these issues and to provide DEQ with biological information, the USGS in 2001 began a detailed 

biological study of carefully selected reference sites in 

the Salmon River Basin. 

2 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
Modeling Approach 

Stream temperature as a general topic has been 

widely studied, and the physics of heat transfer is one 

of the better understood processes in natural watershed 

systems (Sullivan and others, 1990). Heat-transfer processes involved in controlling stream temperatures 

include solar radiation, long-wave radiative exchange 

with sky and vegetation, convection with air, evaporation, conduction to and from the soil and air, and 

advection from incoming water sources, including 

ground water. 

There are two basic approaches to stream-temperature modeling, both of which use the same principles 

of heat transfer. The first approach, used by many 

researchers, is an energy-balance method based on the 

physical processes of heat transfer (Bartholow, 1989). 

Mechanistic models based on this approach are essentially sophisticated energy accounting systems that 

keep track of heat input and outflow to describe and 

predict changes in stream temperature. The models first 

are calibrated to existing conditions for a stream reach 

using measured data. Natural stream temperatures then 

are simulated after adjusting the shade and hydraulic 

parameters in the model. Unfortunately, this approach 

is costly and time consuming. Another approach, 

which is less costly but still requires measured temperature data, is to use observed statistical relationships 

between stream temperature and landscape, climate, 

vegetation, and stream-channel characteristics to 

develop statistical models to predict stream temperatures (Wehrly and others, 1997). The method used in 

this study is more closely related to the second 

approach. 

Temperature data were collected from streams in 

the Salmon and Clearwater River Basins of central 

Idaho to examine the natural spatial and temporal variability of water temperatures and to create a data base 

for developing a statistical model. Subbasins in the 

Salmon and Clearwater River Basins previously were 

delineated as part of a study by Lipscomb (1998). A 

data base of characteristics, including physiographic, 

hydrologic, climatologic, geologic, and land-cover data 

for each subbasin, also was developed in that study. 

These 1,031 subbasins and their associated characteristics provided the framework of this investigation. 

Stream temperatures were monitored at fixed 1-

hour intervals from approximately July 15 through 

September 30, 2000, at more than 200 carefully 

selected sites in a variety of environments. The temperature data then were statistically analyzed to determine 

the most important environmental factors related to 

stream temperatures. The strongest statistical correlations were used to develop a model that estimates daily 

average stream temperatures for July 24 to September 

10 in subbasins where there is no a priori knowledge of 

temperature. 

Description of Study Area 

The Salmon and Clearwater River Basins encompass approximately 60,770 km2 in central Idaho (fig. 

1). The region includes extensive areas of minimal 

human impact and a variety of stream sizes in an 

assortment of hydrologic and geographic settings. It 

includes parts of seven national forests, five designated 

wild and scenic rivers, and four wilderness areas, the 

latter composing about 25 percent of the study area 

(Lipscomb, 1998). 

The headwaters of the Salmon River are in the 

Sawtooth Range of central Idaho. Principal tributaries 

are the Pahsimeroi, Lemhi, and East Fork, North Fork, 

South Fork, and Middle Fork Salmon, and Little 

Salmon Rivers. The headwaters of the Clearwater 

River are in the Bitterroot Mountains near the IdahoMontana State line. Principal tributaries are the North 

Fork, South Fork, and Middle Fork Clearwater Rivers 

and the Lochsa and Selway Rivers. 

The study area includes the highest and lowest 

points in Idaho. Borah Peak, near the headwaters of the 

Pahsimeroi River, is at an elevation of 3,859 m above 

sea level, whereas Lewiston, at the confluence of the 

Clearwater and Snake Rivers, is at an elevation of 

225 m. Total relief in the study area is more than 3 km 

(Lipscomb, 1998). 

METHODS 

Definition of Terms 

Subbasin and site characteristics and temperature 

metrics were given abbreviated names to simplify referencing in the report. Definitions of these abbreviations and methods of derivation or calculation are given 

in table 1. 

Methods 3 
Dworshak

Reservoir

Middle Fork

Clearwater R.

Clearwater River

North

Fork River

Clearwater

River

Lochsa

Selway

River

South

River Fork Clearwater

Salmon

River

Salmon

River

Salmon River

Little

South Fork

Salmon

River

East Fork

South Fork

Salmon River

Salmon

River

Middle

Fork

Salmon

River

North Fork

Lemhi

River

Pahsimeroi

River

East

Fork

Salmon

River

Salmon

River

Potlatch

River

Little North Fork

Clearwater River

River

Red

Redfish 

Lake Creek 

Pole 

Creek 

Wilson 

Creek 

SALMON RIVER MOUNTA INS

BITTERROOT 

MOUNTAINS 

CLEARWATER 

MO

UNTAINS 

BEAVERHEAD 

MOUNTAINS 

LEMHI 

RANGE

LOST 

RANGE 

RIVER

SAWTOOTH 

RANGE 

SHOSHONE

LATAH

NEZ

PERCE

LEWIS

CLEARWATER

IDAHO

ADAMS

VALLEY

LEMHI

CUSTER

BLAINE

Borah

Peak

Lewiston

Orofino

Salmon

Challis

IDAHO 

Study

area

EXPLANATION 

Boundary between Salmon

and Clearwater River

Basins

0 10 20 30 MILES 

Base from U.S. Geological Survey 

digital data, 1:100,000, 1980 

Albers Equal-Area projection 

Standard parallels 43° 30', 47° 30' 

116°

115°

47° 47°

117°

117°

114°

114°

115°

116°

46° 46°

45° 45°

44° 44°

and -114° 00', 41° 45'


No false easting or false northing 0 10 20 30 KILOMETERS


Figure 1. Locations of the Salmon and Clearwater River Basins, central Idaho. 
Table 1. Definitions of subbasin and site characteristics and stream-temperature metrics used in the statistical model and methods used in 

their derivation or calculation, Salmon and Clearwater River Basins, central Idaho 

[All stream-temperature metrics are in °C, degrees Celsius; km2, square kilometers; GIS98, derived by Lipscomb (1998) from a digital elevation model using 

a geographic information system; m, meters; GIS/NLCD, derived from a National Land Cover Data coverage using a geographic information system; PT, 

percentage of total subbasin area; ft, feet] 

Characteristic or metric Definition Method of derivation or calculation 

Subbasin characteristics 

DRAINAREA 

Sum of all upstream subbasin 

areas, in km2 GIS98 

MSLOPE Average subbasin slope, in percent GIS98 

SOUTH Subbasin area facing south, as PT GIS98 

SWEST 

Subbasin area facing southwest, as 

PT GIS98 

SUMSSW 

Sum of subbasin areas facing south 

and southwest, as PT GIS98 

Site characteristics 

SITEELEV Site elevation, in m above sea level Measured in field or determined from map 

MEANELEV 

Average subbasin elevation, in m 

above sea level GIS98 

AREASQKM Subbasin area, in km2 GIS98 

AZIMUTH 

Downstream-facing direction, in 

degrees Measured in field 

SEGAZIMUTH 

Stream segment azimuth, in 

degrees 

Derived using geographic information system and method of Bartholow (1989) 

FOREST Forest of all types, as PT GIS/NLCD 

DECIDFOR Deciduous forest, as PT GIS/NLCD 

EVERGRFOR Evergreen forest, as PT GIS/NLCD 

WETLAND Wetland, as PT GIS/NLCD 

EMERGWET Emergent wetland, as PT GIS/NLCD 

BARREN Barren land, as PT GIS/NLCD 

GRASS Grassland, as PT GIS/NLCD 

OPENCAN Open canopy angle, in degrees Measured in field using clinometer 

RCC Riparian canopy cover, in percent Measured in field using densiometer 

AUGTEMPC Mean August air temperature, in °C 

Derived using geographic information system from coverage based on 

PRISM climate model and downloaded April 16, 2001, at 

http://www.climatesource.com/ 

WIDTHFT Mean stream width, in ft Measured in field 

MDEPTHFT Mean stream depth, in ft Measured in field 

Stream-temperature metrics 

MDMT 

Maximum daily maximum temperature Highest of all measured temperatures. Equivalent to instantaneous 

maximum temperature or grand maximum temperature 

MDAT 

Maximum daily average temperature Highest of all daily mean temperatures 

MDNT 

Maximum daily minimum temperature Highest of all daily minimum temperatures 

MWMT 

Maximum weekly maximum temperature 

Starting with the 7th day of monitoring, the mean of the daily maximum temperatures for days 1 though 7 was computed. This procedure was repeated for days 2 though 8, 3 through 9, etc. The MWMT 

is the highest mean value obtained for the monitoring period 

MWAT 

Maximum weekly average temperature 

Starting with the 7th day of monitoring, the mean of the daily average 

temperatures for days 1 though 7 was computed. This procedure was 

repeated for days 2 though 8, 3 through 9, etc. The MWAT is the 

highest mean value obtained for the monitoring period 

Methods 5 
Table 1. Definitions of subbasin and site characteristics and stream-temperature metrics used in the statistical model and methods used in 

their derivation or calculation, Salmon and Clearwater River Basins, central Idaho—Continued 

Characteristic or metric Definition Method of derivation or calculation 

Stream-temperature metrics —Continued 

MAX∆T Maximum diurnal variation Daily maximum temperature minus daily minimum temperature 

BIG∆T 

Total temperature variation during 

entire monitoring period Highest recorded temperature minus lowest recorded temperature 

GAT Grand average temperature Average of all temperature measurements 

Percent >13°C 

Percent of monitoring period temperatures exceeded 13°C 100 x Number of hourly readings over 13°C divided by 1,392 

Percent >22°C 

Percent of monitoring period temperatures exceeded 22°C 100 x Number of hourly readings over 22°C divided by 1,392 

CONSEC13 

Maximum number of consecutive 

hours temperature exceeded 

13°C 

CONSEC22 

Maximum number of consecutive 

hours temperature exceeded 

22°C 

Site Selection 

Goals of site selection were to choose 1) sites in a 

large number of subbasins that represent a variety of 

total drainage area, elevation, vegetation cover, geology, and topography; 2) sites without significant 

human disturbance such as placer mining, heavy vegetation removal, and dams so that the most natural temperature conditions in and around the streams could be 

recorded; and 3) sites that were well distributed 

throughout the region. Lipscomb (1998) delineated 

1,031 hydrologic subbasins in the Salmon and Clearwater River Basins, and these subbasins comprised the 

candidates for site selection for this study. First, subbasins were grouped according to stream orders assigned 

by Lipscomb (1998). Next, commercial statistical software was used to cluster the subbasins in each group on 

the basis of similarities in total drainage area, average 

elevation, and percent forest cover. Finally, subbasins 

were selected randomly from each of the resulting 

clusters, and monitoring sites were located in these 

subbasins. 

Statistical software offers several different methods of cluster analysis and allows the user to decide on 

the final number of clusters. Divisive, hierarchical clustering into a total of eight clusters was used because 

this method discriminated well between the Salmon 

and Clearwater River Basins (facilitating geographic 

distribution of subbasins) and differentiated between 

subbasins containing higher order and lower order 

streams. A total of 868 subbasins containing first-, second-, and third-order streams were grouped in 6 clusters; a total of 163 subbasins containing fourth- and 

fifth-order streams were grouped in 2 clusters. The 

Strahler stream-order convention, based on 1:100,000 

hydrography, later was adopted for this study because 

it is used by DEQ. In most cases, the effect of reassigning stream order on the basis of this convention was to 

raise the stream order by one unit (for example, firstorder streams became second-order streams). This 

affected the way the subbasins were grouped but did 

not affect the interpretation of the results. The 8 clusters ranged in size from 19 to 268 subbasins. 

Subbasins were selected randomly from each of 

the eight clusters. The initial goal was to select 200 

subbasins and then locate one site in each. The number 

of subbasins selected from each cluster was based on 

the proportion of cluster members to the total number 

of subbasins. Several extra subbasins in each cluster 

were selected as backups to be used if no suitable site 

within a subbasin was found in the field. Because many 

of these extra subbasins also contained suitable sites, 

the number of sites included in the study was increased 

to 228. Subbasins were selected randomly by consecutively numbering the subbasins within each cluster, 

shuffling each list of subbasins using a built-in random 

selection routine in a spreadsheet, and selecting from 

the shuffled list in order from top to bottom. Because of 

6 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
budget and time constraints, each subbasin was evaluated using topographic maps to assure that it was 

accessible by road. If a subbasin was determined to be 

inaccessible by road or likely to be markedly disturbed 

by human activities, it was deleted and the next subbasin on the list was considered. This procedure continued until the required number of subbasins in each 

cluster was selected. Finally, one site within the lower 

one-third of each subbasin was targeted on a topographic map. Field crews deployed temperature loggers 

as close as possible to the target site. A total of 236 

temperature loggers were deployed at 228 sites. 

Because many large areas in central Idaho are not 

accessible by road, some subbasins, including parts of 

the Middle Fork of the Salmon River and its tributaries, 

were impossible to monitor during this phase of the 

project. However, adequate and well distributed coverage of most of the study area was achieved (fig. 2). 

Additional sites monitored in 2001 as part of the biological component of the project could provide temperature data for the omitted subbasins, but those data 

were not available for this study. 

Collection of Site Characteristic Data 

A variety of site-specific data were recorded on a 

standardized data sheet by field crews at the time the 

temperature loggers were deployed. Ten equally spaced 

measurements of temperature, depth, and specific conductance were made across the stream to assure that 

the water at the site was well mixed. General stream 

habitat (riffle, pool, or run) and stream azimuth (downstream-facing direction) were noted. Air-temperature 

and elevation data were recorded; some measurements 

were repeated at the time the loggers were retrieved. 

Photographs were taken at most sites. Vegetation cover 

was described in two ways: open canopy angle (OPENCAN) and riparian canopy cover (RCC). OPENCAN 

was measured at midstream using a clinometer (Fitzpatrick and others, 1998). RCC (in percent) was determined from the banks using a spherical densiometer 

(Fitzpatrick and others, 1998). Because of time and 

budgetary constraints, only one measurement of each 

of these parameters was made at each site. Several 

measurements along a reach might have given a better 

representation of the vegetation cover. The latitude and 

longitude of the site were determined using a global 

positioning system receiver. 

Collection of Subbasin Characteristic Data 

Many subbasin characteristics, including geographic information system (GIS)-derived parameters, 

previously had been compiled by Lipscomb (1998). 

These included total drainage area, average subbasin 

slope, aspect (slope facing directions), average subbasin elevation, subbasin area, and percent forest cover. 

Several other subbasin characteristics were derived 

or obtained as GIS coverages to test correlations with 

stream temperature. These included land cover, mean 

August air temperature, and stream segment azimuth. 

Stream segment azimuth is discussed further in the 

section “Geographic Variables.” Descriptive statistics 

for selected subbasin characteristics are presented in 

table 2. 

Land cover was analyzed in two ways: 1) as the 

percent of the entire subbasin area and 2) as a percent 

of the area within a buffer drawn 100 m from each side 

of the stream. The source of the land cover data used in 

the first method was the National Land Cover Data 

(NLCD) for Idaho, version 2000–03. Stream lines were 

previously derived from digital elevation models and 

stored in USGS data archives. 

Data Collection and Processing 

Temperature data were collected using StowAway 

TidbiT temperature loggers programmed to record date, 

time, and temperature in degrees Celsius every hour. 

Accuracy of the temperature loggers was checked in 

the laboratory before and after deployment in the field 

(see section “Quality Control”). Field crews deployed 

temperature loggers as close to the outlet of a subbasin 

as possible. If it was not possible to deploy loggers in 

approximately the lower one-third of the subbasin, an 

alternate subbasin was used. In wadeable streams, the 

loggers were wired to a 1-m piece of rebar pounded 

into the streambed at approximately midstream. Loggers were covered with foil to inhibit heating by direct 

sunlight. In large, unwadeable streams, loggers were 

deployed near the center of the stream from cables suspended from a bridge or anchored to rocks from the 

riverbank. 

Data were downloaded from the loggers at the 

end of the deployment period and entered in computer 

spreadsheets. Each temperature record was inspected; 

incomplete or flawed data sets were eliminated. Timeseries plots also were made to screen the records for 

Methods 7 
EXPLANATION 

Monitored site


Site used to test model—Number
 116° 

Dworshak 

Reservoir 

Clearwater River 

River 

Lochsa 

Selway 

Sal

River

mon River 

Salmon 

River 

Salmon River 

Little 

Salmon 

River 

Lemhi 

River 

Pahsimeroi River 

Salmon 

River 

Potlatch 

River 

River

Red 

Lewiston 

Orofino 

Salmon 

Challis 

19 

17 

16 

20 

18 

refers to figure number in this 

report 

Salmon River above Redfish Lake 

Creek 

Red River below South Fork 

Big Deer Creek 

Lochsa River above Wilderness 

Gateway Campground 

Wilson Creek 

16 

17 

18 

19 

20 

0 10 20 30 MILES 

115° 

47° 47°

117° 

117° 

114° 

114° 

115° 

116° 

46° 46° 

45° 45° 

44° 44° 

0 10 20 30 KILOMETERS 

Figure 2. Monitored sites that provided stream-temperature data used to develop and test the statistical model, Salmon and 

Clearwater River Basins, central Idaho. 

8 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
Table 2. Statistical summary of selected subbasin and site characteristics for monitored sites used in the statistical model, Salmon and 

Clearwater River Basins, central Idaho 

[km2, square kilometers; m, meters; °C, degrees Celsius; ft, feet; for measurements given in feet, multiply by 0.3048 to obtain meters] 

Characteristic Description 

No. of 

cases Minimum Maximum Median Mean 

Standard 

deviation 

DRAINAREA Sum of all upstream subbasin areas, in km2 183 28.5 34,851.0 137.3 1,738.0 5,940.2 

MSLOPE Average slope of subbasin, in percent 183 1.9 54.6 25.5 24.1 10.2 

SOUTH Percentage of subbasin area facing south 182 0 35 11.8 11.5 6.4 

SITEELEV Site elevation, in m above sea level 182 260 2,267 1,381 1,352.1 5,201 

MEANELEV Average elevation of subbasin, in m above sea level 183 501 2,744 1,965.0 1,849.0 518 

AREASQKM Area of subbasin, in km2 183 0.5 233.5 59.4 69.7 49.5 

FOREST 

Percentage of subbasin area covered by forest (all types 

combined) 182 0 99 73 64.7 27.2 

WETLAND Percentage of subbasin area covered by wetland 183 0 9 0.13 0.5 1.2 

BARREN Percentage of subbasin area covered by barren land 182 0 24 0.25 1.9 3.7 

GRASS Percentage of subbasin area covered by grassland 182 0 37 3.9 6.2 6.7 

OPENCAN Open canopy angle measured in field 152 0 100 49 51.5 26.2 

RCC Riparian canopy coverage measured in field 177 0 100 44 45.5 32.3 

AUGTEMPC Mean August temperature, in °C 183 18.7 32 25.3 25.5 2.8 

WIDTHFT Stream width measured in field, in ft 183 1.2 440.0 22.0 50.1 76.3 

MDEPTHFT Average stream depth measured in field, in ft 169 0.2 14.0 0.9 1.4 1.6 

SEGAZIMUTH 

Downstream azimuth of 600-m-long stream segment 

ending at site. Transformed using method of Bartholow (1989). See text for discussion. 176 -89 90 1 2.0 46.8 

anomalous results such as evidence of emergence from 

the water or instrument malfunction. All files were 

edited to include only data from July 15 through September 10, for a total of 1,392 hourly measurements 

(58 days), because this was the time interval that was 

recorded by all temperature loggers. 

Of the 236 deployed temperature loggers, 19 were 

missing at the end of the deployment period. Data from 

12 sites were unusable, either because the logger did 

not stay submerged in water or because of instrument 

malfunction. Data from 17 additional sites were eliminated from the analysis when it was determined that 

the sites were unsuitable for inclusion in model development (see discussion in section “Model Evaluation”). The final statistical model was developed from 

data from 183 sites (24 second-order streams, 75 thirdorder streams, 45 fourth-order streams, 28 fifth-order 

streams, 5 sixth-order streams, and 6 seventh-order 

streams). 

Quality Control 

The data loggers used in the study are stated by 

the manufacturer to be accurate to 0.40°F (0.22°C); 

their resolution is less than 0.32°F (0.18°C). All data 

loggers were tested before deployment by recording 

temperatures under controlled conditions. The loggers 

were placed in ice water for 2 hours; all loggers 

recorded temperatures within 0.2° of 0°C. The loggers 

also were placed in room-temperature distilled water 

Methods 9 
Table 3. Selected stream-temperature metrics for monitored sites used in the statistical model, Salmon and Clearwater River Basins, central 

Idaho 

[Stream name: R, River; Cr, Creek; N, North; S, South; W, West; E, East; Fk, Fork; C, Clearwater; S, Salmon. Units for stream-temperature metrics in degrees 

Celsius unless otherwise noted. Abbreviations: MDMT, maximum daily maximum temperature; MDAT, maximum daily average temperature; MWAT, 

maximum weekly average temperature; GAT, grand average temperature; MAX∆T, maximum diurnal variation; BIG∆T, total temperature variation during 

entire monitoring period; Percent >13°C, percent of monitoring period temperatures exceeded 13°C; Percent >22°C, percent of monitoring period 

temperatures exceeded 22°C; °C, degrees Celsius] 

Stream name 

River 

basin 

Strahler 

stream 

order MDMT MDAT MWAT GAT MAX∆T BIG∆T 

Percent 

>13°C 

Percent 

>22° C 

American R C 4 26.0 21.6 20.4 16.3 9.6 17.6 77 7 

Arnett Cr C 2 16.4 13.0 12.7 10.4 7.6 12.3 18 0 

Basin Cr C 3 20.2 15.7 14.7 12.1 10.4 16.6 40 0 

Bayhorse Cr C 3 22.2 17.9 16.6 14.1 10.3 15.7 60 0 

Bear Valley Cr C 5 21.4 17.9 17.0 14.3 8.2 14.8 66 0 

Bedrock Cr C 3 25.5 20.4 20.0 18.5 11.8 13.2 100 14 

Big Bear Cr C 4 27.7 22.8 22.0 18.4 11.6 18.7 89 21 

Big Canyon Cr C 4 25.2 21.7 21.0 18.5 8.3 12.4 100 14 

Big Cr C 2 26.8 23.2 21.9 17.8 7.3 18.4 87 13 

Big Cr N Fk C 2 15.5 11.9 11.1 9.6 7.1 10.9 8 0 

Big Cr S Fk C 2 16.1 13.0 12.2 10.4 7.3 11.5 15 0 

Big Eightmile Cr C 3 19.4 16.0 15.3 12.6 7.8 13.8 46 0 

Big Timber Cr C 4 20.4 17.1 15.7 13.2 8.5 15.2 51 0 

Big Timber Cr C 3 20.9 17.5 16.4 13.5 7.9 15.2 56 0 

Blackmare Cr C 3 15.8 14.0 13.4 10.8 4.8 10.4 17 0 

Bohannon Cr C 2 20.1 16.6 15.9 13.6 8.6 12.8 57 0 

Boulder Cr C 4 19.2 15.4 14.4 11.4 8.4 14.9 32 0 

Boulder Cr C 2 18.7 16.6 15.9 13.0 4.1 11.3 49 0 

Boulder Cr C 3 21.7 20.3 18.3 15.3 5.8 12.4 79 0 

Buckhorn Cr C 4 18.6 15.9 15.3 12.6 6.0 11.7 45 0 

Buckhorn Cr W Fk C 4 17.9 15.8 15.3 12.4 5.1 11.5 43 0 

Cape Horn Cr C 3 19.0 13.1 12.2 10.3 11.3 15.7 24 0 

Challis Cr C 4 21.8 17.6 16.4 14.4 10.0 15.3 64 0 

Clear Cr C 4 27.4 23.2 22.5 18.6 10.1 17.1 91 23 

Clearwater R C 6 26.7 25.2 24.7 20.9 4.8 13.6 100 41 

Clearwater R C 6 26.1 25.5 25.0 21.3 2.2 12.0 100 43 

Clearwater R C 5 27.7 25.7 24.9 21.0 7.2 15.3 100 43 

Clearwater R M Fk C 6 27.1 24.8 24.3 20.5 5.1 15.2 100 32 

Clearwater R N Fk C 5 24.0 20.8 20.0 16.7 6.8 14.2 86 4 

Clearwater R N Fk C 5 22.7 21.6 21.0 17.6 3.9 11.3 92 1 

Clearwater R S Fk C 5 24.7 21.8 20.7 16.4 6.6 15.9 80 4 

Clearwater R S Fk C 5 25.7 23.2 22.6 18.7 5.9 15.1 91 18 

Clearwater R S Fk C 5 28.0 24.8 24.1 20.1 8.1 16.9 96 34 

Corral Cr C 3 26.9 22.9 22.4 18.7 10.0 18.4 90 24 

Cottonwood Cr C 3 24.8 21.7 20.8 17.4 6.7 14.2 89 7 

Cottonwood Cr C 4 25.8 22.9 22.2 19.5 8.2 13.2 100 23 

Crooked Cr C 2 20.4 16.6 15.6 12.1 8.6 15.7 40 0 

Crooked R C 3 23.4 20.4 19.4 15.9 7.3 14.3 80 1 

Curtis Cr C 3 19.0 15.3 14.4 11.4 7.3 14.4 31 0 

Dahlonega Cr C 3 15.6 12.6 12.3 10.8 5.7 9.2 13 0 

Fitsum Cr C 3 18.6 15.7 15.2 12.3 6.3 12.3 40 0 

10 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
Table 3. Selected stream-temperature metrics for monitored sites used in the statistical model, Salmon and Clearwater River Basins, central 

Idaho —Continued 

Stream name 

River 

basin 

Strahler 

stream 

order MDMT MDAT MWAT GAT MAX∆T BIG∆T 

Percent 

>13°C 

Percent 

>22° C 

Fourmile Cr C 3 16.5 15.1 14.4 11.5 3.9 10.4 28 0 

Fourth of July Cr C 3 24.8 16.0 14.7 11.1 17.9 23.4 33 2 

French Cr C 3 19.7 16.2 15.2 12.1 7.5 13.5 39 0 

French Cr C 3 21.5 19.7 19.1 15.7 4.0 12.7 82 0 

Gedney Cr C 4 22.3 19.6 18.6 15.4 6.9 12.9 76 0 

Germania Cr C 3 15.8 12.0 11.1 9.6 7.3 11.5 9 0 

Goldburg Cr C 3 20.8 15.7 14.6 12.7 11.8 15.0 43 0 

Grasshopper Cr C 3 29.5 24.2 23.4 18.2 18.4 23.6 76 27 

Hard Cr C 3 21.8 18.6 17.9 14.4 6.4 15.0 71 0 

Hat Cr C 3 22.2 17.8 16.8 14.5 9.9 15.0 65 0 

Hayden Cr C 5 19.4 15.7 14.9 13.3 8.1 11.5 53 0 

Haynes Cr C 2 19.8 16.1 15.7 13.2 8.1 13.3 52 0 

Herd Cr S 4 20.3 15.4 14.4 13.0 11.1 14.2 47 0 

Huckleberry Cr C 2 18.6 11.9 10.8 8.9 11.9 15.2 14 0 

Iron Cr C 3 20.7 17.3 16.3 14.2 7.4 12.6 66 0 

Isabella Cr C 3 18.0 16.1 15.4 13.2 4.1 8.4 52 0 

Jim Ford Cr S 4 27.3 21.8 20.8 16.6 12.1 18.5 77 15 

John Day Cr C 3 17.4 15.4 14.8 12.7 4.7 9.0 43 0 

Johnson Cr S 4 19.3 15.2 14.6 11.8 8.3 14.3 35 0 

Johnson Cr C 4 17.9 15.7 15.4 12.8 6.1 11.6 47 0 

Johnson Cr S 3 19.7 17.2 16.5 13.2 6.2 14.0 58 0 

Johnson Cr C 3 22.0 17.8 17.1 14.0 9.2 16.1 61 0 

Kelly Cr C 5 23.6 20.1 19.1 15.7 8.2 15.1 76 2 

Kinnikinic Cr C 2 15.4 12.6 11.9 10.3 5.9 9.8 11 0 

Lake Cr S 3 15.4 12.4 11.7 9.5 6.5 10.7 9 0 

Lawyer Cr S 4 25.1 21.3 20.2 16.0 10.6 17.9 71 11 

Lawyer Cr S 4 31.5 24.9 23.8 19.4 14.9 21.8 88 31 

Lemhi R C 5 17.8 12.3 11.5 10.1 11.1 12.8 22 0 

Lemhi R S 4 21.6 15.8 15.0 13.4 12.0 15.4 51 0 

Lemhi R S 5 20.2 16.8 15.9 14.1 8.4 12.4 66 0 

Little N Fk Clearwater R S 5 19.5 17.8 17.3 14.6 3.6 10.1 73 0 

Little Salmon R S 5 21.1 18.6 17.9 15.4 5.9 11.6 82 0 

Little Slate Cr S 4 19.5 17.3 16.5 12.8 5.0 13.5 50 0 

Lochsa R S 5 23.2 22.2 21.6 18.1 3.8 11.4 95 4 

Lochsa R S 5 25.6 23.5 22.8 19.2 5.3 13.5 98 19 

Lochsa R Crooked Fk S 4 22.0 17.5 16.4 13.4 9.3 15.4 51 0 

Lochsa R Crooked Fk S 5 21.2 18.2 17.2 14.1 7.7 13.5 63 0 

Logan Cr S 3 13.8 11.8 11.4 9.2 4.6 9.3 2 0 

Lolo Cr S 4 26.0 24.2 23.2 19.2 6.0 14.4 97 25 

Long Hollow Cr S 3 20.1 17.3 16.2 13.2 7.6 13.3 50 0 

McGowan Cr S 2 16.6 12.8 11.9 10.6 8.7 11.2 20 0 

McKim Cr S 3 17.3 15.3 14.6 12.6 5.3 10.1 46 0 

Meadow Cr S 4 21.4 20.1 19.1 15.7 3.5 11.7 84 0 

Meadow Cr S 3 22.8 20.1 19.3 15.8 6.4 14.4 76 1 

Mission Cr S 3 23.6 21.9 19.3 16.2 8.0 14.2 82 3 

Moose Cr S 3 20.3 15.4 14.7 12.1 9.6 14.3 35 0 

Methods 11

Table 3. Selected stream-temperature metrics for monitored sites used in the statistical model, Salmon and Clearwater River Basins, central 

Idaho —Continued 

Stream name 

River 

basin 

Strahler 

stream 

order MDMT MDAT MWAT GAT MAX∆T BIG∆T 

Percent 

>13°C 

Percent 

>22° C 

Morgan Cr S 3 15.6 13.2 12.5 10.9 5.4 9.6 17 0 

Morgan Cr S 3 21.7 18.8 17.7 15.2 7.1 14.1 78 0 

Morse Cr S 3 13.8 11.7 11.1 9.8 4.4 7.9 2 0 

Moyer Cr S 3 17.8 14.8 14.0 11.5 8.4 13.4 31 0 

Musgrove Cr S 2 18.0 14.3 13.6 11.3 7.6 12.8 25 0 

Napias Cr S 2 20.8 15.0 14.5 12.1 11.7 16.3 38 0 

Newsome Cr S 4 23.8 19.9 18.9 15.1 9.0 15.7 70 2 

N F White Bird Cr S 3 22.5 20.4 19.8 16.7 5.9 11.9 87 1 

O'Hara Cr S 4 22.5 18.9 18.1 14.8 7.8 13.9 71 1 

Orogrande Cr S 3 19.5 16.0 15.1 12.1 8.1 13.6 37 0 

Owl Cr S 3 20.0 17.7 17.0 13.9 4.9 11.6 67 0 

Pahsimeroi R S 5 17.8 14.5 13.5 12.3 8.0 10.3 38 0 

Panther Cr S 5 22.8 16.9 15.9 12.9 12.2 18.1 45 0 

Panther Cr S 4 21.7 17.7 16.6 13.5 10.2 15.9 54 0 

Panther Cr S 3 22.6 19.1 18.5 15.3 6.8 13.7 79 0 

Papoose Cr S 3 18.3 15.4 14.7 12.4 5.6 10.5 39 0 

Patterson Cr S 3 19.7 14.4 13.4 11.8 11.1 14.9 36 0 

Peasley Cr S 2 20.3 17.8 17.0 13.8 5.9 13.1 62 0 

Perreau Cr S 2 16.0 14.2 13.7 11.8 4.0 9.2 28 0 

Pete King Cr S 3 23.0 19.5 18.7 15.5 8.3 13.7 76 1 

Pine Cr S 2 17.1 15.5 15.0 12.3 3.9 9.6 38 0 

Pole Cr S 3 15.1 10.0 9.4 8.2 9.5 12.0 6 0 

Potlatch R S 5 30.0 26.0 25.4 21.7 9.3 17.2 100 47 

Potlatch R S 5 27.6 23.8 23.1 19.6 9.0 16.8 96 27 

Potlatch R S 5 29.6 25.0 24.4 21.0 10.5 17.5 99 40 

Potlatch R E Fk S 3 25.9 21.3 20.8 17.1 10.3 17.9 80 16 

Profile Cr S 3 14.9 11.8 11.6 9.6 5.7 10.1 6 0 

Quartz Cr S 2 26.9 21.3 20.2 16.3 11.0 19.4 75 10 

Race Cr S 3 16.7 14.8 14.4 13.2 4.1 6.4 50 0 

Red R S 4 24.0 21.7 20.7 16.3 6.8 15.3 79 3 

Red R S 4 26.7 22.6 21.2 16.9 10.3 18.8 81 12 

Red R S Fk S 3 23.0 18.5 17.4 13.5 10.4 17.9 55 1 

Reeds Cr S 3 25.0 20.8 19.8 16.0 9.3 17.3 75 7 

Rice Cr S 3 24.1 21.5 20.9 17.4 6.3 13.6 91 7 

Riordan Cr S 3 17.3 15.2 14.7 11.8 5.9 11.5 34 0 

Rock Cr S 4 23.6 19.6 19.0 16.6 8.4 12.6 93 4 

Round Valley Cr S 2 14.4 12.4 11.8 9.8 4.5 9.0 4 0 

Salmon R S 7 19.9 15.2 14.3 12.2 10.5 15.0 40 0 

Salmon R S 7 19.8 15.4 14.4 12.2 10.4 14.8 40 0 

Salmon R S 7 25.1 16.8 16.0 13.0 17.4 23.3 45 6 

Salmon R S 7 21.0 18.5 17.5 15.1 7.5 13.0 82 0 

Salmon R S 7 22.6 19.0 17.8 15.4 8.2 15.1 77 0 

Salmon R S 7 23.0 21.0 20.2 17.8 5.3 11.7 96 2 

Salmon R S 6 23.7 22.2 21.5 18.2 3.8 11.3 99 5 

Salmon R S 5 23.2 23.0 22.4 18.8 7.0 10.0 100 10 

12 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
Table 3. Selected stream-temperature metrics for monitored sites used in the statistical model, Salmon and Clearwater River Basins, central 

Idaho —Continued 

Stream name 

River 

basin 

Strahler 

stream 

order MDMT MDAT MWAT GAT MAX∆T BIG∆T 

Percent 

>13°C 

Percent 

>22° C 

Salmon R S 5 23.9 23.1 22.7 19.2 1.8 10.2 100 15 

Salmon R S 5 23.8 23.2 22.9 19.4 1.8 9.9 100 17 

Salmon R S 5 23.9 23.3 22.9 19.4 1.8 9.9 100 17 

Salmon R S 5 29.7 23.6 23.3 19.8 3.3 15.6 100 23 

Salmon R E Fk S 5 18.7 14.3 13.5 12.1 9.7 12.4 35 0 

Salmon R E Fk S 4 17.6 14.3 13.4 11.9 7.3 11.4 33 0 

Salmon R E Fk S 4 19.5 15.3 14.4 13.3 9.1 11.5 48 0 

Salmon R E Fk S 3 21.0 16.5 15.4 14.0 9.6 13.3 57 0 

Salmon R M Fk S 6 18.7 12.9 12.1 10.3 11.9 15.5 26 0 

Salmon R M Fk S 3 20.4 18.3 17.6 14.9 4.8 12.0 79 0 

Salmon R N Fk S 3 18.8 15.7 15.1 12.4 6.6 12.7 41 0 

Salmon R N Fk S 4 19.5 16.1 15.6 13.2 6.7 11.7 51 0 

Salmon R N Fk S 4 21.0 17.2 16.5 14.0 7.7 13.1 63 0 

Salmon R S Fk S 4 21.8 17.9 16.9 13.8 8.5 15.6 58 0 

Salmon R S Fk S 4 22.3 19.2 18.7 10.4 6.9 14.3 90 1 

Salmon R S Fk E Fk S 5 18.1 14.2 13.9 11.4 7.5 12.7 29 0 

Salmon R S Fk E Fk S 4 16.1 14.3 13.9 11.8 4.2 8.7 28 0 

Salmon R S Fk E Fk S 4 19.0 17.4 17.0 14.2 3.2 10.8 76 0 

Sandy Cr S 2 19.2 16.6 16.1 14.1 5.8 11.1 68 0 

S F White Bird Cr S 3 22.3 20.2 19.6 16.2 6.0 12.9 84 0 

Sheep Cr S 3 14.1 11.5 11.1 9.6 5.1 8.7 2 0 

Silver Cr S 3 20.0 17.3 16.5 13.5 6.3 11.8 55 0 

Silver Cr S 2 19.8 17.8 17.0 13.5 5.3 12.8 59 0 

Skookumchuck Cr S 3 23.6 21.1 20.7 18.0 5.9 11.3 98 6 

Slate Cr S 3 19.3 13.3 12.6 11.1 11.1 14.3 28 0 

Smiley Cr S 3 21.0 16.8 15.8 13.1 9.6 16.0 49 0 

Squaw Cr S 3 17.3 14.9 14.2 12.0 6.0 9.5 32 0 

Squaw Cr S 4 21.3 16.7 15.7 13.3 11.4 16.2 50 0 

Steamboat Cr S 2 18.9 14.4 13.9 11.3 8.9 14.2 28 0 

Sulphur Cr S 2 23.3 17.1 16.6 15.4 10.7 12.3 79 1 

Sweetwater Cr S 4 25.9 19.1 21.2 17.7 7.4 13.9 95 12 

Sweetwater Cr S 4 24.6 22.2 20.9 17.8 9.0 15.8 92 14 

Tamarack Cr S 3 17.1 12.4 12.1 10.2 8.4 12.1 20 0 

Texas Cr S 3 22.4 17.5 16.3 14.0 11.4 16.6 58 0 

Thompson Cr S 3 19.8 13.8 13.2 11.8 11.5 4.3 33 0 

Three Bear Cr S 3 18.7 16.3 15.4 12.6 5.9 11.7 44 0 

Threemile Cr S 2 24.4 21.0 20.2 16.4 10.3 16.0 79 7 

Tom Beall Cr S 4 20.1 18.2 17.4 15.3 5.5 10.1 84 0 

Tower Cr S 3 18.9 16.7 16.0 14.2 5.8 9.7 73 0 

Trail Cr S 2 23.1 15.6 15.0 12.6 10.8 15.6 43 0 

Twelvemile Cr S 3 15.5 13.2 12.6 10.9 5.0 9.4 14 0 

Valley Cr S 3 20.5 15.3 14.1 12.1 11.0 16.3 37 0 

Valley Cr S 4 24.0 18.3 17.1 14.1 18.7 20.0 62 2 

Vanity Cr S 3 13.4 10.9 10.5 8.8 5.3 9.2 0 0 

Weitas Cr S 4 23.0 18.9 17.9 14.7 9.4 15.0 66 1 

Weitas Cr S 4 23.5 20.2 19.1 15.7 7.5 14.2 77 1 

Methods 13

Table 3. Selected stream-temperature metrics for monitored sites used in the statistical model, Salmon and Clearwater River Basins, central 

Idaho —Continued 

Stream name 

River 

basin 

Strahler 

stream 

order MDMT MDAT MWAT GAT MAX∆T BIG∆T 

Percent 

>13°C 

Percent 

>22° C 

Whiskey Cr S 3 23.8 20.4 19.6 16.8 7.0 12.7 90 3 

White Bird Cr C 4 26.9 23.3 22.7 18.9 10.0 16.3 93 23 

Williams Cr C 3 17.6 15.4 14.8 12.5 4.4 10.6 44 0 

Yankee Fk S 3 16.7 12.2 11.3 9.5 9.0 13.4 13 0 

Yankee Fk S 4 19.6 14.9 13.9 11.8 10.2 15.4 35 0 

along with a calibrated thermometer for 2 hours. All Pairs of temperature loggers were deployed at 

loggers recorded temperatures within 0.7°C of the ref- eight sites in order to provide duplicate temperature 

erence thermometer. After retrieval, 15 of the loggers records for the entire deployment period: two sites on 

were tested by overnight refrigeration. Recorded tem- the Salmon River, two sites on the Clearwater River, 

peratures varied by no more than 0.32°C during the and one site each on the Middle Fork Clearwater River, 

13 hours after temperatures stabilized. They also Lemhi River, Valley Creek, and the Potlatch River. 

were tested for 30 minutes in an ice bath. All loggers Both loggers from the Potlatch River site were lost. 

recorded temperatures within 0.4° of 0°C, and individ- Paired loggers usually were deployed on opposite 

ual logger temperatures varied no more than 0.3°C dur- banks of the stream. Paired data were retrieved from 

ing the test. seven of the sites. Data showed excellent agreement 

30 

25 

20 

15 

10 

5 

0 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

JULY AUGUST SEPTEMBER 

2000 

TEMPERATURE, IN DEGREES CELSIUS 

Figure 3. Daily average temperature for representative streams in the Salmon and Clearwater River Basins, central Idaho. 

14 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
Table 4. Statistical summary, grouped by stream order, of selected 

stream-temperature metrics for monitored sites used in the 

statistical model, Salmon and Clearwater River Basins, central 

Idaho 

[Abbreviations: MDMT, maximum daily maximum temperature; MDAT, 

maximum daily average temperature; MDNT, maximum daily minimum 

temperature; MWMT, maximum weekly maximum temperature; MWAT, 

maximum weekly average temperature; MAX∆T, maximum diurnal 

variation; BIG∆T, highest recorded temperature minus lowest recorded 

temperature for measurement period; GAT, grand average temperature; all 

stream-temperature metrics are in oC; No., number] 

Stream-temperature metric 

MDMT MDAT MDNT MWMT MWAT MAX∆T BIG∆T GAT 

2nd- and 3rd-order streams 

No. of sites 99 99 99 98 99 99 99 99 

Minimum 13.4 10.0 7.2 11.9 9.4 3.9 6.4 8.2 

Maximum 29.5 24.2 20.4 28.9 23.4 18.4 23.6 19.5 

Mean 19.7 16.2 13.8 18.7 15.4 7.8 13.2 12.9 

Standard 

deviation 3.4 3.1 2.9 3.4 3.1 2.8 3.1 2.5 

4th- and 5th-order streams 

No. of sites 73 73 71 73 73 73 73 73 

Minimum 16.1 12.3 9.6 15.5 11.5 3.2 8.7 10.1 

Maximum 31.5 26.0 23.6 30.7 25.4 18.7 23.3 21.7 

Mean 22.6 19.1 16.3 21.7 18.3 8.3 14.4 15.3 

Standard 

deviation 3.3 3.2 3.1 3.4 3.2 2.8 2.7 2.6 

6th- and 7th-order streams 

No. of sites 11 11 11 11 11 11 11 11 

Minimum 20.4 18.3 16.4 19.5 17.6 1.8 9.9 14.9 

Maximum 27.7 25.7 24.6 27.1 25.0 7.2 15.6 21.3 

Mean 24.3 23.0 21.8 23.7 22.5 4.0 12.1 19.1 

Standard 

deviation 2.0 2.1 2.4 2.1 2.2 2.0 2.2 1.8 

(differences less than 1°C) at five of the seven sites. 

The record from one of the loggers at Valley Creek 

indicated intermittent emergence from the water after 

approximately August 5. The data from one of the 

Clearwater River sites agreed within approximately 

1.5°C for most of the deployment period but differed 

intermittently by as much as approximately 2.6°C later 

in the summer. There was no evidence of instrument 

malfunction or emergence, but the recorded temperature differences were not considered unreasonable 

because the river at the site is 94 m wide; end-of-summer differences in water depth or exposure to sunlight 

between the two loggers could explain the divergence. 

CHARACTERIZATION OF STREAM 

TEMPERATURES 

Temperature Metrics 

Several temperature metrics are of special interest 

to biological resource managers because they help 

characterize the thermal regime in stream temperatures. Selected temperature metrics derived from the 

data for monitored sites used in the statistical model 

are presented in table 3. Stream temperature metrics 

varied with stream order. Statistical summaries of 

selected temperature metrics, grouped by stream order, 

are presented in table 4. 

Graphical Display of Temperature Data 

Daily average stream temperatures were calculated for all sites and plotted on graphs showing temperature as a function of time. Temperatures for representative streams are shown in figure 3. Temperature 

patterns for all sites monitored in this study were 

remarkably similar. Temperatures generally increased 

slightly during the first 7 to 10 days of the deployment 

period, July 15, 2000, to September 10, 2000, and 

reached the maximum temperature for the year 

between July 31 and August 2. This maximum generally was followed by a gradual decrease in temperature 

for the rest of the period, except for notable short-term 

temperature spikes on approximately August 24 to 25 

and from August 28 to September 1. These temperature 

patterns correspond to daily average air-temperature 

patterns for central Idaho during the deployment 

period. 

Distinctive temperature patterns for several sites 

on the lower Salmon River and the Clearwater River 

reflect very low diurnal fluctuation, between approximately 1.5° and 3°C. At these sites the rivers are more 

than 60 m wide and, in most cases, are approximately 

2 m deep. Time-temperature graphs of these rivers differ greatly from those of smaller streams, which show 

greater diurnal fluctuation (example shown in fig. 4). 

The low diurnal variation is best explained by the large 

thermal mass in relation to the surface area of the larger 

rivers, which dampens short-term temperature fluctuations. 

Quantile diagrams were constructed for several 

temperature metrics. The quantile of a sample is the 

data point corresponding to a given fraction of the data; 

Characterization of Stream Temperatures 15 
30 

25 

20 

15 

10 

5 

0 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

Salmon River (7th order) 

Pole Creek (3rd order) 

JULY AUGUST SEPTEMBER 

2000 

Figure 4. Hourly temperature for streams with contrasting diurnal temperature fluctuation in the Salmon and Clearwater River TEMPERATURE, IN DEGREES CELSIUS 

Basins, central Idaho. 

therefore, quantile diagrams are useful for understanding the range and overall distribution of the entire data 

set. Quantile diagrams of maximum daily average temperature (MDAT) for all sites, grouped by stream order, 

are given in figure 5. Each data point in figure 5 represents the MDAT for the deployment period for one site. 

For most sites, the date of the MDAT was the same as 

the early-August peak temperature referred to on the 

previous page. The vertical lines represent regulatory 

threshold temperatures of 9° and 19°C for salmonid 

spawning and cold-water biota, respectively. The Yaxis values at the intersection of these lines with a data 

curve indicate the fraction of the sites that are below 

those temperatures. Temperatures of all streams, 

regardless of stream order, exceeded 9°C; those of 

approximately 80 percent of second- and third-order 

streams were below 19°C; those of approximately 45 

percent of fourth- and fifth-order streams were below 

19°C. 

Another useful diagram is a type of exceedance 

curve, which shows the percentage of the deployment 

period that the temperature of a stream exceeded a 

given threshold. Several exceedance curves are shown 

in figure 6. Each curve represents all the temperature 

measurements from one stream. In general, lower order 

streams plotted toward the left side of the diagram 

(cooler temperatures), and higher order streams plotted 

toward the right side (warmer temperatures). Vertical 

lines are drawn from a temperature to a curve; the Yvalue at the intersection of these lines with a data curve 

indicates the percentage of the deployment period that 

the temperature of the stream exceeded that temperature. Vertical lines in figure 6 represent 9°C and 19°C. 

Thus, the stream represented by the heavy dashed line 

exceeded 9°C approximately 95 percent of the time and 

exceeded 19°C less than 10 percent of the time. 

Idaho Stream-Temperature Standards 

The current (April 2002) temperature standards 

for salmonid spawning and cold-water biota for Idaho 

16 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
for salmonid spawning and cold-water biota, respectively) 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 10 20 30 

2nd and 3rd order (99) 

4th and 5th order (73) 

6th and 7th order (11) 

MAXIMUM DAILY AVERAGE TEMPERATURE, 

IN DEGREES CELSIUS 

Figure 5. Quantile diagram for selected streams in the Salmon and 

Clearwater River Basins, central Idaho. (Vertical lines at 9 and 19 degrees Celsius represent temperature standards for salmonid spawning and cold-water biota, respectively) 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

0 10 20 30 

2nd and 3rd order 

4th and 5th order 

6th and 7th order 

TEMPERATURE, IN DEGREES CELSIUS 

Figure 6. Exceedance curves for representative streams in the Salmon and Clearwater River Basins, central Idaho. (Vertical lines at 9 and 

19 degrees Celsius represent temperature standards for salmonid 

spawning and cold-water biota, respectively) PERCENT OF TIME TEMPERATURE WAS EXCEEDED FRACTION OF DATA 

streams are summarized in table 5. Temperature data 

were analyzed to determine which sites met the current 

Idaho temperature standards. The results for the coldwater biota standards are shown in figure 7. One hundred nineteen of the 183 sites used in the model met the 

maximum daily average temperature standard of 19°C; 

110 sites met the instantaneous maximum temperature 

standard of 22°C. Most of the sites that met the standards are in the Salmon River Basin. None of the sites 

met the current Idaho temperature standard for salmonid spawning (maximum daily average temperature, 

< 9°C; instantaneous maximum, <13°C). 

STATISTICAL ANALYSIS 

Statistical tests were used to identify relationships 

between stream temperature and subbasin and site 

characteristics. The factors that influence stream temperature generally are well documented and are the 

basis for several widely used models that use equations 

to describe heat exchange between streams and their 

environment (Sullivan and others, 1990). Important 

heat sources include solar, atmospheric, and topographic radiation. Heat exchange occurs by convection, 

conduction, and evaporation at the water-air interface 

and by conduction at the water-streambed interface. 

Cooling (and heating, in geothermal areas) by advection from ground-water inflow is another important 

process affecting stream temperature and is one that is 

difficult to quantify without detailed study of a particular site. Back-radiation by the water is a mechanism of 

heat loss. Overall, any subbasin and site characteristics 

that have bearing on these heat exchange processes, 

such as presence of riparian vegetation, direction of 

streamflow, and slope facing direction, are likely to 

Table 5. Current Idaho stream-temperature standards for aquatic 

life designations1 

[°C, degrees Celsius] 

Stream-temperature measurement Standard 

Cold-water aquatic life 

Instantaneous maximum temperature <22°C 

Maximum daily average temperature <19°C 

Salmonid spawning 

Instantaneous maximum temperature <13°C 

Maximum daily average temperature <9°C 

1Idaho Administrative Code, Idaho Department of Environmental 

Quality, IDAPA 58.01.02, p. 139–140, accessed on April 30, 2002: 

http://www2.state.id.us/adm/adminrules/rules/idapa58/0102.pdf 

Statistical Analysis 17 
116° 

Dworshak 

Reservoir 

Clearwater River 

River Lochsa 

Selway 

River

Salmon River 

Salmon 

River 

Salmon River 

Little 

Salmon 

River 

Lemhi 

River 

Pahsimeroi River 

Salmon 

River 

Potlatch 

River 

River

Red 

Dworshak 

Reservoir 

Clearwater River 

River Lochsa 

Selway 

River

Salmon River 

Salmon 

River 

Salmon River 

Little 

Salmon 

River 

Lemhi 

River 

Pahsimeroi River 

Salmon 

River 

Potlatch River 

River

Red 

Lewiston 

Orofino 

Salmon 

Challis 

Lewiston 

Orofino 

Salmon 

Challis 

EXPLANATION 

Monitoring site—Maximum daily average 

temperature less than 19 degrees Celsius 

Monitoring site—Maximum daily average 

temperature greater than 19 degrees Celsius 

EXPLANATION 

Monitoring site—Instantaneous maximum 

temperature less than 22 degrees Celsius 

Monitoring site—Instantaneous maximum 

temperature greater than 22 degrees Celsius 

0 

0 

10 

10 

20 

20 

30 MILES 

30 KILOMETERS 

0 

0 

10 

10 

20 

20 

30 MILES 

30 KILOMETERS 

115° 47° 47°

117° 

117° 

114° 

114° 

115° 

116° 

46° 46° 

45° 45° 

44° 44° 

116° 

115° 47° 47°

117° 

117° 

114° 

114° 

115° 

116° 

46° 46° 

45° 45° 

44° 44° 

Figure 7. Sites where stream temperatures met or exceeded current Idaho stream-temperature standards for cold-water biota 

during the 2000 monitoring period, Salmon and Clearwater River Basins, central Idaho. 

18 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
influence, directly or indirectly, the temperature of the 

stream. Although the modeling approach used for this 

study was statistical rather than mechanistic, these 

principles were a useful guide. 

Twelve temperature metrics were tested for statistical correlations with more than 20 variables describing the characteristics of the subbasins and sites. Subbasin and site characteristics generally fall into three 

categories: geographic (for example, elevation and 

aspect), land cover (vegetation), and climatic (for 

example, air temperature). Table 6 lists the Spearman 

correlation coefficients for pairwise comparisons for 

selected variables. Correlation coefficients in bold are 

significant at the 95-percent or greater confidence level. 

The results discussed in the following section reflect 

observations made for statistical tests performed on all 

sites as a single group. The data also were analyzed in 

groups based on stream order (second and third, fourth 

and fifth, sixth and seventh). Correlations were generally similar to those observed for the single-group 

method. For second- through fifth-order streams, total 

drainage area, elevation, and air temperature were the 

most important variables. For sixth- and seventh-order 

streams (n=11), elevation and air temperature showed 

the strongest correlations with monitored stream 

temperatures. 

Geographic Variables 

Elevation, including average subbasin elevation 

and site elevation, was strongly negatively correlated 

with stream temperature. Total upstream drainage area 

was strongly positively correlated with temperature, 

whereas subbasin area alone was not significantly correlated with temperature. Mean subbasin slope was 

negatively correlated with temperature. The latter may 

reflect the fact that surface water in steeper subbasins 

has shorter residence time to gain heat from its surroundings and, thus, tends to stay cooler. Width and 

mean depth of the stream at the monitoring site were 

significantly positively correlated with all temperature 

metrics except seasonal variation (BIG∆T). Subbasin 

aspect, expressed as percentage of subbasin area facing 

a compass direction (for example, percent southwestfacing), was weakly correlated only with total seasonal 

variation (table 6). No other metrics were correlated 

with this variable. 

In addition to stream azimuths measured in the 

field, stream segment azimuths also were derived 

because they were considered to be a better representation of the general direction of streamflow at a site. 

Stream segments were assigned a numerical azimuth 

using a GIS by measuring the azimuth of a vector 

drawn between a point 600 m upstream from the temperature site to the site. These values then were converted to a number between –90 and +90 degrees using 

the method of Bartholow (1989). This method precluded the common problems of analyzing azimuths 

that range between 0 and 360 degrees. Neither fieldmeasured stream azimuths nor GIS-derived streamsegment azimuths were significantly correlated with 

any stream-temperature metric. However, results of 

analysis of stream-segment azimuth expressed as a 

compass direction (for example, NE, SW) were interesting. Several temperature metrics, including grand 

average temperature (GAT) and maximum weekly 

average temperature (MWAT) were significantly higher 

(p <0.05) for northwest- and southwest-flowing stream 

segments than for southeast- and northeast-flowing segments. There was no significant difference in temperature, however, between northeast- and northwest-flowing versus southeast- and southwest-flowing segments. 

This may reflect stream warming by solar radiation 

when the sun shines from the west during the afternoon 

and early evening, when stream temperatures reach 

their daily maxima. 

Vegetation Variables 

Correlations between vegetation characteristics 

derived from GIS coverages and stream temperature 

were variable (table 6). In general, when expressed as a 

percentage of the entire subbasin area, vegetation and 

stream-temperature correlations can be explained by 

vegetation providing shade to reduce solar warming. 

For example, forested area and wetland were significantly negatively correlated with stream temperature; 

grassland and barren land were significantly positively 

correlated with stream temperature. However, these 

relationships may be a stronger indication of differences in elevation rather than vegetation, because 

grassland and barren land are at lower elevations, 

whereas forested lands are chiefly at higher elevations 

in the study area. Land-cover data were buffered by 

using a GIS to look at only a 100-m-wide zone on 

either side of the stream. Buffered land-cover data 

yielded significant positive correlations between most 

temperature metrics and percent barren land, grassland, 

Statistical Analysis 19 
20 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 

Table 6. Spearman correlation coefficients describing correlation of subbasin or site characteristics with stream-temperature metrics for 183 mon

model, Salmon and Clearwater River Basins, central Idaho 

DRAI

NAREA, sum of all upstream subbasin areas, in square kilometers (k

m2); MSLOPE, average subbasin slope, in percent; SOUTH, subbasin area facing south, 

SWEST, subbasin area facing southwest, as a percentage of total subbasin area; SUMSS

W, sum of subbasin areas facing south and southwest, as a percentage of tot

elevation, in meters above sea level; MEANELE

V, average subbasin elevation, in meters above sea level; AREASQKM, subbasin area in k

m2; SEGAZIMUTH, stre

NLCD, National Land Cover Data; FOREST (NLCD), forest of all types, as a percentage of total subbasin area; DECIDFOR (NLCD), deciduous forest, as a percenEVERGRFOR (NLCD), evergreen forest, as a percentage of total subbasin area; WETLAND (NLCD), wetland, as a percentage of total subbasin area; EMERGWE

percentage of total subbasin area; BARREN (NLCD), barren land, as a percentage of total subbasin area; GRASS (NLCD), grassland, as a percentage of total subba

angle; RCC, riparian canopy cover, as a percentage; 

AUGTEMPC, mean August temperature, in degrees Celsius (°C); WIDTHFT, mean stream width, in feet; MDE

maximum daily maximum temperature; M

D

AT, maximum daily average temperature; MDNT, maximum daily minimum temperature; MWMT, maximum weekly m

maximum weekly average temperature; MA

X∆T, maximum diurnal variation; BI

G∆T, total range in observed temperature; G

AT, average of all temperature measur

number of consecutive hours temperature exceeded 13°C; CONSEC22, maximum number of consecutive hours temperature exceeded 22 ̊C; HOURS13, number of 

HOURS22, number of hours temperature exceeded 22°C; G, geographic; 

V, vegetation; C, climate; S, site. Correlation coefficients in bold are significant at the 95-p

Stream-temperature metric 

Characteristic 

Characteristic 

type MDMT MD

AT MDNT MWMT 

M

WAT MAX∆T BIG∆T GAT 

CONSEC 

13 

DRAI

NAREA G 0.541 0.556 0.505 0.546 0.544 0.019 0.236 0.579 0.516 

MSLOPE G -0.432 -0.332 -0.259 -0.416 -0.311 -0.413 -0.489 -0.309 -0.204 

SOUTH G 0.063 0.082 0.08 0.067 0.094 -0.015 0.007 0.08 0.081 

SWEST G -0.048 -0.007 0.018 -0.04 0.011 -0.129 -0.166 0.014 0.018 

SUMSSW G -0.021 0.013 0.029 -0.011 0.026 -0.105 -0.17 0.036 0.043 SITEELEV G -0.602 -0.759 -0.809 -0.636 -0.777 0.321 0.001 -0.774 -0.814 

MEANELEV G -0.539 -0.644 -0.671 -0.565 -0.661 0.138 -0.132 -0.627 -0.656 AREASQKM G 0.032 -0.043 -0.09 0.018 -0.049 0.21 0.165 -0.058 -0.091 SEGAZIMUTH G -0.09 -0.102 -0.095 -0.091 -0.103 0.049 -0.016 -0.101 -0.108 FOREST(NLCD) V -0.202 -0.186 -0.156 -0.218 -0.174 -0.131 0.009 -0.278 -0.181 DECIDFOR (NLCD) V 0.24 0.27 0.254 0.243 0.271 -0.047 -0.017 0.315 0.289 

EVERGRFOR (NLCD) V -0.165 -0.109 -0.063 -0.162 -0.097 -0.175 -0.015 -0.208 -0.086 

WETLAND (NLCD) V -0.255 -0.368 -0.434 -0.282 -0.387 0.248 0.009 -0.326 -0.399 

EMERGWET (NLCD) V -0.275 -0.384 -0.445 -0.301 -0.403 0.238 -0.008 -0.343 -0.418 BARREN (NLCD) V 0.215 0.222 0.19 0.215 0.21 -0.003 0.013 0.22 0.192 

GRASS (NLCD) V 0.259 0.328 0.36 0.281 0.343 -0.139 0.015 0.333 0.389 

OPENCAN V 0.077 -0.035 -0.057 0.067 -0.031 0.273 0.181 -0.024 -0.078 

RCC V -0.146 0.011 0.082 -0.123 0.036 -0.372 -0.325 0.042 0.11 

AUGTEMPC C 0.587 0.705 0.733 0.61 0.719 -0.199 0.062 0.741 0.743 

WIDTHFT S 0.293 0.356 0.344 0.308 0.356 -0.146 0.066 0.348 0.341 

MDEPTHFT S 0.36 0.468 0.48 0.386 0.471 -0.242 0.047 0.454 0.475 
and deciduous forest, consistent with the subbasinwide results. Evergreen forest and emergent wetlands 

were negatively correlated with temperature. The same 

ambiguities exist regarding the interactions of elevation 

and vegetation for these results. Although correlations 

observed for certain land-cover parameters were statistically significant at the 95-percent confidence level, 

these correlations were weaker than those observed for 

air temperature, total drainage area, and elevation. 

Vegetation characteristics measured in the field 

(RCC and OPENCAN) were not significantly correlated with temperature metrics except MAX∆T and 

BIG∆T and seasonal variation (OPENCAN was positively correlated; RCC was negatively correlated). 

Because the temperature of a stream is a function of the 

cumulative effects of all the upstream factors, the riparian vegetation cover at a particular point may not be as 

important as the riparian vegetation cover throughout 

the upstream drainage area. 

Climate Variables 

Air temperature, expressed as the average August 

temperature at the measurement site (AUGTEMPC) 

was significantly positively correlated with all streamtemperature metrics except BIG∆T. It should be noted 

that air temperature, elevation, and vegetation are related variables, and it is difficult to separate the effects 

of one from the other on stream temperature. Air temperature naturally decreases with increasing elevation 

because of adiabatic cooling. At the same time, higher 

elevation subbasins in the study area generally are forested, whereas those at lower elevations contain higher 

percentages of grassland. All three factors affect stream 

temperature, but they are clearly not independent 

variables. 

STREAM-TEMPERATURE MODEL 

General Approach 

Although linear regression equations that relate 

stream temperature to subbasin and site characteristics 

are useful for resource managers in a general way, the 

element of time improves the usefulness of a statistical 

model. Dyar and Alhadeff (1997) analyzed nearly 30 

years of year-round stream-temperature monitoring 

data for Georgia streams to develop a temperature 

model based on periodic functions that replicate annual 

stream-temperature fluctuations. For this study, linear 

regression and nonlinear regression were combined to 

develop a model that takes into account not only subbasin and site characteristics but also Julian day (day of 

the year) and daily changes in air temperature that 

affect stream temperature throughout the summer 

months. 

The model allows the daily average temperature to 

be estimated for each day from July 24 to September 

10. The model has three components: 1) terms for estimating the GAT; 2) terms for estimating the temperature variation caused by seasonal fluctuation, as a daily 

adjustment for deviation from the GAT; and 3) terms to 

adjust for the effect of short-term air-temperature deviations from a 30-year average air temperature on daily 

stream temperatures. 

The data for the final model were organized as a 

single group; that is, all data were treated in the same 

way, regardless of stream order. There were two primary reasons why this approach was taken. First, 

breaking the data into groups based on stream order 

caused some of the important statistical relations to be 

weakened because of the small number of sites in some 

groups (for example, sixth- and seventh-order streams 

together comprised only 11 sites). Therefore, modeling 

was more difficult and less effective, particularly for 

the estimation of the GAT. Second, keeping the model 

as simple and as usable as possible for resource managers was a priority. The small degree of precision that 

might have been gained by tailoring the model to specific stream orders probably would have been counteracted by increased difficulty in practical application 

of the model to real situations. A more detailed discussion of this issue is presented in the section “Model 

Evaluation.” 

Grand Average Temperature 

Multiple linear regression (MLR) was used to derive an equation for the GAT as a function of selected 

site and subbasin characteristics. Statistical correlations 

described in the section “Statistical Analysis” guided 

the choice of variables to use in developing the MLR 

equation. The equation that yielded the best estimate of 

the GAT included three independent variables: total 

drainage area, site elevation, and average subbasin 

slope. A log10 transformation of the total drainage area 

was used. Although several land-cover variables were 

significantly correlated with GAT, none improved the 

Stream-Temperature Model 21 
Table 7. Results of multiple linear regression to estimate grand 

average temperature for 183 monitored sites used in the statistical 

model, Salmon and Clearwater River Basins, central Idaho 

[Multiple r2 = 0.792; <, less than; km2, square kilometers; m, meters] 

Coefficient 

Standard 

error t 

2-tail 

probability 

(α= 0.05) 

Constant 17.332 0.527 32.890 <0.001 

Log(10) total 

drainage 

area (km2) 1.648 0.156 10.548 <0.001 

Mean subbasin slope 

(percent) -0.059 0.010 -5.696 <0.001 

Site 

elevation 

(m) -0.004 0.000 -16.665 <0.001 

regression. Table 7 summarizes the statistics for the 

MLR. The equation for the GAT is: 

GAT = 1.648 [log10(total drainage area, in km2)] (1) 

– [0.059 (average subbasin slope, in percent)] 

– [0.004 (site elevation, in meters)]+ 16.651 

Seasonal Component 

The shapes of the data curves of daily average 

temperature as a function of time for representative 

streams during the deployment period are similar, differing mainly in their position on the temperature axis. 

These data curves indicate a short period of increasing 

temperature until about August 1, followed by generally decreasing temperatures through the rest of the 

summer (fig. 3). The similarity of these stream-temperature data curves suggests that the seasonal component 

of the pattern, that is, the part of the S-shaped annual 

curve represented by the 58-day deployment period, 

can be isolated and modeled. 

To compare all streams regardless of their absolute temperatures, the data at each site were normalized 

by subtracting the observed GAT for that site from the 

daily average temperature for each day of the deployment period. This value, the daily deviation from the 

GAT at each site, is referred to as δ. The data then were 

smoothed by using a 20-day moving average to minimize short-term fluctuations and to emphasize the 

underlying seasonal component of the pattern. Beginning with July 24, the 20-day moving average was calculated by averaging the value for the previous 9 days, 

the present day, and the subsequent 10 days; this was 

repeated for all days. This reduced the total time interval available for consideration and introduced errors at 

the end of the time interval (no data were available 

after September 10). The averages for September 1 

through September 10 were calculated using 19 

through 10 days’ worth of data, respectively. The errors 

introduced by this method for September were considered less critical than they would have been for July 

and August, when stream-temperature concerns are 

greatest. 

The resulting smoothed curves represent δs for 

sites from July 24 through September 10, a total of 49 

days; they describe a segment of the annual streamtemperature fluctuation displayed by all streams in 

temperate climates. 

With few exceptions, the data curves of the normalized, smoothed data for all sites were strongly similar (see fig. 8 for representative streams). Note that 

most of the daily average temperatures of monitored 

streams deviated from their own GAT by less than 

+4°C early in the summer and less than –6°C later in 

the summer. Most sites reached their average temperature for the measurement period between August 11 

and August 17. 

Finally, the average δ of all 183 sites was computed so that each day from July 24 (day 206) through 

September 10 (day 254) was represented by a single set 

of values (see section, “General Versus Specific 

Model,” for further discussion). The results were used 

as the dependent variable in a nonlinear regression routine to generate a periodic function to describe the seasonal variation (after Helsel and Hirsch, 1995, p. 341): 

Average deviation (DAY) = (2) 

α +[β x sin(0.0172 x DAY)] 

+[ γ x cos(0.0172 x DAY)]+(ω x 0.0172 x DAY), 

where 

DAY = day of the year, from 206 to 254, 

α = -460.819, 

β = 77.008, 

γ = -97.037, and 

ω = 113.835. 

22 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
4 

DEVIATION FROM GRAND

AVERAGE

TEMPERATURE, IN DEGREES CELSIUS

2 

0 

-2 

-4 

-6 

-8 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

JULY AUGUST SEPTEMBER 

2000

Figure 8. Deviation from grand average temperature for representative streams in the Salmon and Clearwater River Basins, central 

Idaho. (Patterns used only to differentiate lines) 

The mean corrected r 2 of the regression was temperature from a long-term average air temperature 

0.996, indicating a very good fit between observed and for a specific day, and accordingly add to or subtract 

estimated values. from the stream-temperature estimate. 

Long-term (30-year) daily average air-temperaAir-Temperature Adjustment ture data for July 24 through September 10 for 10 

weather stations in the study area were compiled from 

The final step in estimating the daily average tem- the National Weather Service (fig. 9). Daily average 

perature involved a daily adjustment for short-term air- air-temperature data for the same 10 weather stations 

temperature fluctuations. If this adjustment had not for the time period July 24, 2000, to September 10, 

been made, stream temperatures estimated by the 2000, also were compiled. For each weather station and 

model would have represented only the climate condi- for each day, a ratio was calculated of the daily average 

tions of 2000. Whereas subbasin characteristics do not air temperature in 2000 to the long-term daily average 

change from year to year, stream temperatures fluctuate air temperature. Therefore, if the daily average air temwith changes in air temperatures at all timescales from perature in 2000 exceeded the long-term average, the 

daily to annual and from year to year. As discussed pre- ratio would be greater than 1 for that day. A ratio of 

viously, fluctuations in stream temperature were less than 1 indicated that the daily average temperature 

observed to coincide with short-term fluctuations in was lower than the long-term average for that day. 

daily average air temperatures. Therefore, the purpose Air-temperature ratios from the 10 weather staof this adjustment was to allow the model to take into tions were broadly similar. Temperature fluctuations 

account the daily deviation (positive or negative) of air were stronger at some weather stations than at others 

Stream-Temperature Adjustment 23 
(for example, the ratios at McCall ranged from 0.3 to 

1.6, whereas the ratios at Salmon ranged only from 0.7 

to 1.2). Nevertheless, the overall similarity in data 

from the 10 stations suggests that regional air-temperature patterns were fairly uniform, regardless of the 

location of the station. 

The residual (the difference between the unadjusted estimated temperature and the observed temperature for each day) was computed for each stream site. 

The average daily residual for all sites was calculated 

and used as the dependent variable in 10 simple linear 

regressions, one for each of the 10 weather stations. 

The daily air-temperature ratio was multiplied by 10 

for convenience. The regression fit was better for some 

weather stations than for others, but the results of these 

regressions were generally similar (table 8). 

The regression from the Pierce, Idaho, weather 

station (the station with the best regression statistics 

and with complete temperature records for 2000) was 

used in the final model: 

Daily air-temperature adjustment (°C) = (3) 

0.299 x (daily air-temperature ratio x 10) – 2.349 

Results of regressions based on data from the 

other weather stations also were acceptable; approximately the same daily adjustments were made using 

data from the other stations. The maximum upward 

correction was approximately 2°C; the maximum 

downward correction was approximately 1°C. No time 

lag between air-temperature changes and stream-temperature changes was used. 

This technique of adjusting the estimated stream 

temperature was reasonably effective for days in which 

the air temperature did not deviate greatly from the 30-

year average. However, the model still underestimated 

stream temperatures for very warm days in spite of the 

adjustment. This shortcoming is discussed further in 

the following section. Nevertheless, the improvement 

in matching estimated and observed temperatures indicated that this component should be included in the 

final model. 

Combining and simplifying terms gives the 

final, simplified expression for the daily average 

temperature: 

Temperature(DAY) = (4) 

1.648 [log10 (total drainage area, in km2)] 

– [0.059 (average subbasin slope, in percent)] 

– [0.004 (site elevation, in m)] 

+ [77.008 x SIN(0.0172 x DAY)] 

– [97.037 x COS(0.0172 x DAY)] 

+ [113.835 (0.0172 x DAY)] 

+ [2.99 x air-temperature ratio(DAY)] – 446.517 

MODEL EVALUATION 

Estimation Errors 

Errors in the final model were evaluated by comparing the observed and estimated daily average temperatures for all the sites used to build the model. The 

daily errors (the difference between estimated and 

observed temperatures) were calculated for each site. A 

positive error indicated that the model estimated higher 

temperatures than were observed; a negative error indicated that the model underestimated the temperature. 

Analysis of the errors allowed temperature estimations 

to be enclosed by a 95-percent confidence interval for 

each day. The temperature interval that includes 95 percent of the errors ranged from 5° to 8°C, depending on 

Table 8. Results of simple linear regression for the air-temperature 

adjustment component of the statistical model, Salmon and 

Clearwater River Basins, central Idaho 

[No., number] 

Weather 

station Constant Coefficient 

Multiple 

r

2 F-ratio 

No. of 

pairs of 

data 

Dixie -1.734 0.236 0.550 56.145 48 

Grangeville -2.241 0.264 0.459 39.909 49 

Lewiston -2.421 0.313 0.401 31.504 49 

May -1.611 0.234 0.248 15.488 49 

McCall -1.814 0.235 0.539 54.934 49 

Middle Fork 

Lodge -3.458 0.381 0.468 41.293 49 

Pierce -2.349 0.299 0.573 63.017 49 

Powell -3.161 0.372 0.365 22.463 41 

Salmon -3.083 0.373 0.365 27.056 49 

Stanley -2.791 0.333 0.486 44.479 49 

24 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
EXPLANATION 

116° Weather station 

Dworshak 

Reservoir 

Clearwater River 

River 

Lochsa 

Selway 

Salm

River

on River 

Salmon 

River 

Salmon River 

Little 

Salmon 

River 

Lemhi 

River 

Pahsimeroi River 

Salmon 

River 

Potlatch 

River 

River

Red 

Lewiston 

Pierce 

Dixie 

Powell 

Grangeville 

McCall 

Salmon 

May 

Stanley 

Middle 

Fork 

Lodge 

0 10 20 30 MILES 

115° 

47° 47°

117° 

117° 

114° 

114° 

115° 

116° 

46° 46° 

45° 45° 

44° 44° 

0 10 20 30 KILOMETERS


Figure 9. Locations of weather stations that provided air-temperature data used to derive the air-temperature adjustment component 

of the statistical model, Salmon and Clearwater River Basins, central Idaho. 

Model Evaluation 25

the day. The errors are shown graphically in figure 10. 

The mean daily error ranged from approximately -1.2° 

to +1.1°C. The largest mean errors occurred in late 

August and on September 10. 

Large negative errors occurred during a severalday period in late August and early September. This 

coincided with a period of higher-than-normal air temperatures recorded by most of the weather stations. 

Although the model adjusted temperatures in the correct sense, the correction was insufficient in most cases 

to account fully for the stream-temperature fluctuations 

that occurred. The very low streamflows in 2000, particularly in the latter part of the summer, may have contributed to more extreme stream-temperature fluctuations and, hence, larger errors. 

The root mean squared error (RMSE), one commonly used measure of goodness-of-fit, is expressed as: 

(5) 

where 

Te = temperature estimated by the model, 

in °C; 

To = observed temperature, in °C; and 

n = number of sites. 

The RMSE was calculated for each day and ranged 

from 1.3° to 2.1°C. The worst-fit days occurred in late 

July through early August and at the end of August. 

To assess the goodness-of-fit of the model for different-sized streams, the errors were examined by 

stream-order groups. The mean errors were calculated 

for second- and third-, fourth- and fifth-, and sixth- and 

seventh-order streams; the results are shown in figure 

11. The errors for sixth- and seventh-order streams 

were notably different from those of the smaller 

streams, especially later in the season. Because sixth- Σ and seventh-order streams are represented by only 11

(Te - To) 2 

n 

ERROR, IN DEGREES CELSIUS 

5 

4 

3 

2 

1 

0 

-1 

-2 

-3 

-4 

-5 

95-percent confidence interval 

Mean daily error 

Standard deviation (+ or - 1.973) 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

JULY AUGUST SEPTEMBER 

2000 

Figure 10. Mean daily stream-temperature error and 95-percent confidence interval for all sites used to develop the statistical model, 

Salmon and Clearwater River Basins, central Idaho. 

26 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
of the 183 sites included in the model, these error dif- SEASONAL COMPONENT 

ferences were apparent only if the errors were exam­


ined by stream order. The current model appears to be a 183 sites was computed and a single periodic function
 better fit for second- through fifth-order streams than was derived. This function, however, did not take into 


As stated earlier in the report, the average δ of all 

for larger streams. 	 account the wide range of seasonal temperature variation observed in the data (fig. 8). To address this issue, 

second- and third-order, fourth- and fifth-order, and 

General Versus Specific Models	 sixth- and seventh-order streams were treated as three 

separate groups, and three sets of δ values were computed. Three separate periodic functions based on the In the section, “General Approach,” it was stated 

average values for each group were derived to test the 

that the final model was developed by treating the data accuracy of the general model. A graph of these three as a single group (a general model) rather than as sepa- and the periodic function of the general model as a 

rate groups organized by stream order (specific mod- function of time are shown in figure 12. The figure 

els). The effect of this choice on the accuracy of the shows differences in modeled δ among the three 

model was assessed by deriving specific models for stream-order groups. The periodic functions for the 

each of the three stream-order groups. Specific regres- second- and third-order and fourth- and fifth-order 

sions for the seasonal and air-temperature components streams closely follow that of the general model, but the 

were derived, but the estimates of the GAT remained periodic function for sixth- and seventh-order streams 

the same for all streams. displays a larger amplitude. The periodic function of 

2.5 

2.0 

1.5 

1.0 

0.5 

0 

-0.5 

-1.0 

-1.5 

-2.0 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

2nd and 3rd order 

4th and 5th order 

6th and 7th order 

All 

JULY AUGUST SEPTEMBER 

2000 

MEAN ERROR, IN DEGREES CELSIUS 

Figure 11. Mean daily stream-temperature error for all sites used to develop the statistical model, calculated by stream-order group, 

Salmon and Clearwater River Basins, central Idaho. 

Model Evaluation 27 
the general model underestimated peak summertime 

temperatures of sixth- and seventh-order streams by 

about 0.5°C and, near the end of the summer, overestimated temperatures for these streams by as much as 

0.67°C, compared with the periodic functions of the 

specific models. 

When the errors for the seasonal component of the 

general model were analyzed by stream-order groups, 

those for sixth- and seventh-order streams range from 

0°C on about August 13 to about 1oC on September 10 

(fig. 13). By comparison, errors for this component in 

the specific models showed less variation, did not 

exceed 0.43°C, and are generally less than 0.20°C 

(fig. 13). According to this analysis, taking stream 

order into account in the seasonal component of the 

model would result in more accurate estimates for 

sixth- and seventh-order streams. 

AIR-TEMPERATURE ADJUSTMENT 

Three separate simple linear regressions, one for 

each stream-order group, were performed using the 

same method as that used for the general model 

described in the section, “Air-Temperature Adjustment.” Three daily adjustment regressions, one for 

each stream-order group, were modeled and the daily 

adjustments were calculated. The results were compared with those of the single air-temperature adjustment used in the general model. Again, specific models 

based on stream-order groups produced results that 

were nearly identical to the results for the general 

model, except for sixth- and seventh-order streams (fig. 

14). For the hottest days, the specific models adjusted 

the temperature approximately the same amount as the 

general model, but for the coolest days, the specific 

models made a stronger downward adjustment. 

COMPLETE MODEL 

Finally, the estimation errors for the general 

model, complete with seasonal and air-temperature 

adjustments, were compared with errors for the specific 

models, also complete with both adjustments. Analyzed as a single group, errors for the specific models 

were essentially identical to those for the general 

model (fig. 15). For sixth- and seventh-order streams, 

3 

2 

1 

0 

-1 

-2 

-3 

-4 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

2nd and 3rd order 

4th and 5th order 

6th and 7th order 

All 

JULY AUGUST SEPTEMBER 

2000 

Figure 12. Periodic functions of deviation from grand average temperature for the general model and for three specific models based 

on stream-order groups, Salmon and Clearwater River Basins, central Idaho. 

28 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho DEVIATION FROM GRAND 

AVERAGE 

TEMPERATURE, IN DEGREES CELSIUS 
General model 

1.0 

MEAN ERROR, IN DEGREES CELSIUS 

0.8 

0.6 

0.4 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

-0.1 

-0.2 

-0.3 

-0.4 

2nd and 3rd order 

4th and 5th order 

6th and 7th order 

All 

Specific models 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

JULY AUGUST SEPTEMBER 

2000 

Figure 13. Errors in seasonal component of the general model and three specific models based on stream-order groups, Salmon and 

Clearwater River Basins, central Idaho. 

Model Evaluation 29 
errors for the specific models and the general model 

were similar until approximately August 13 (fig. 15); 

after that date, the general model estimates higher temperatures than the specific models. The general model 

performed better than the specific models for times 

when air temperatures were unusually low (for example, August 28); after that date, errors for the specific 

models were smaller than those of the general model. 

Therefore, the complete specific models do not consistently improve the fit of the general model for larger 

streams. 

Independent Tests of the Model 

The model was tested by applying it to 14 sites in 

the Salmon and Clearwater River Basins for which historical stream-temperature data were available. Estimated temperatures were compared with observed temperatures to test the accuracy of temperature estimates 

for years other than 2000 and for subbasins not included 

in the model development data set. Stream discharges 

in years used for independent tests of the model 

included high, low, and near average (table 9). Data 

sources included records of daily average stream temperature from USGS data archives and stream-temperature records supplied by DEQ, U.S. Forest Service, 

and Bureau of Land Management. Dates of these 

records ranged from 1970 to 2001. The location of 

each test site within its subbasin was determined so 

that subbasin characteristics necessary for the model 

calculation (total drainage area, average subbasin 

slope, and site elevation) could be obtained. Site elevations were determined using a digital elevation model 

after the site had been located in a GIS. Historical airtemperature data from the Pierce weather station were 

used when available; data from another nearby weather 

station were used if Pierce data were unavailable. 

Selected examples of model tests are described in the 

following paragraphs. 

The model was applied to a site previously monitored by the USGS gaging station 13293800, Salmon 

DAILY AVERAGE AIR-TEMPERATURE 

ADJUSTMENT, IN DEGREES CELSIUS 

2.5 

2.0 

1.5 

1.0 

0.5 

0 

-0.5 

-1.0 

-1.5 

-2.0 

2nd and 3rd order 

4th and 5th order 

6th and 7th order 

All 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

JULY AUGUST SEPTEMBER 

2000 

Figure 14. Daily average air-temperature adjustments calculated by the general model and three specific models based on streamorder groups, Salmon and Clearwater River Basins, central Idaho. 

30 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
 Mean estimation errors for the general model and for the specific models, Salmon and Clearwater River Basins, 

2nd and 3rd order 

1.5 

1.0 

0.5 

0 

-0.5 

-1.0 

-1.5 

General model 

Specific model 

4th and 5th order 

1.5 

1.0 

0.5 

0 

-0.5 

-1.0 

-1.5 

6th and 7th order 

2.5 

2.0 

1.5 

1.0 

0.5 

0 

-0.5 

-1.0 

-1.5 

-2.0 

All streams 1.5 

1.0 

0.5 

0 

-0.5 

-1.0 

-1.5 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

JULY AUGUST SEPTEMBER 

2000 

MEAN ERROR, IN DEGREES CELSIUS 

Figure 15. Mean estimation errors for the general model and for three specific models, Salmon and Clearwater River Basins, central 

Idaho. 

Model Evaluation 31 
River at Highway 93 above Redfish Lake Creek near 

Stanley, Idaho. The site is in a subbasin not monitored 

by the USGS in 2000. The total subbasin drainage area 

is 793 km2, and the average subbasin slope is 18.7 percent. Stream-temperature records for July 24 through 

September 10, 1980 and 1982, were compared with 

temperatures estimated by the model; results are shown 

in figure 16. For both years, the model estimates the 

observed daily average temperature within the 95-percent confidence interval. The largest discrepancy 

between estimated and observed temperatures was 

2.9°C for 1980 and 3.5°C for 1982. The model generally estimated temperatures accurately for both years, 

as indicated by the similarity of observed and estimated 

temperature data curves; however, the model slightly 

overestimates the early-summer temperatures and 

underestimates the late-summer temperatures for 1982. 

The amplitude of the observed temperature data curve 

for 1982 is small; temperatures varied no more than 

3.5oC during the entire period. However, the estimated 

temperature data curve indicates that the temperatures 

diminished with time. 

Observed stream temperatures in the Red River 

near the Red River Ranger Station (USGS gaging station 13337180, now discontinued) from 1984 and 1986 

were compared with stream temperatures estimated by 

the model (fig. 17). The total subbasin drainage area is 

326.8 km2, the average subbasin slope is 14.7 percent, 

and the site elevation is 1,430 m. The model generally 

estimated temperatures accurately for both years, as 

indicated by the similarity of observed and estimated 

temperature data curves. The maximum difference 

between observed and estimated temperatures was 

2.8°C. 

Observed stream temperatures in Big Deer Creek, 

also in the Salmon River Basin, for 1999 and 2000 

were compared with stream temperatures estimated by 

the model (fig. 18). The total subbasin drainage area is 

120.8 km2, the average subbasin slope is 33.6 percent, 

and the site elevation is 1,320 m. Observed and estimated daily average temperatures for 1999 and 2000 

are compared in figure 18. In 1999, estimated temperatures are up to 5.0°C higher than observed temperatures 

until mid-August, barely within the 95-percent confidence limit. This appears to be related to the generally 

flat temperature profile exhibited by the stream until 

late August, when temperatures begin to cool and the 

model estimates temperatures more closely. Earlysummer stream temperatures for 2000 were more accurately modeled but still exceeded observed temperatures by a maximum of 3.6°C. 

The Lochsa River above Wilderness Gateway 

Campground was monitored by DEQ in 1998. Complete air-temperature data were not available for the 

Pierce weather station for 1998, but temperature estimates made from partial air-temperature data from 

Pierce and complete data from Grangeville were nearly 

identical. Consequently, air-temperature data from 

Grangeville were used for the test shown in figure 19. 

The total subbasin drainage area is 2,121.1 km2, the 

Table 9. Ratio of mean August discharge to long-term average August discharge at selected stream-gaging stations for the year 2000 and for 

years for which the model was tested, Salmon and Clearwater River Basins, central Idaho 

[No., number; R., river; na, not available] 

Ratio of mean August discharge to long-term average August discharge 

Station No. Station name 

Years of 

record Basin 1980 1982 1984 1986 1998 1999 2000 2001 

13302500 

Salmon R. at 

Salmon 88 Salmon 0.96 1.64 0.99 1.08 1.03 0.87 0.68 0.52 

13310700 

South Fork 

Salmon R. near 

Krassel Ranger 

Station 33 Salmon 1.04 1.58 na 0.90 1.19 1.24 0.70 0.48 

13338500 

South Fork 

Clearwater R. 

at Stites 39 Clearwater 1.10 1.43 1.19 0.86 1.11 1.10 0.50 0.75 

13336500 

Selway R. near 

Lowell 74 Clearwater 0.98 1.47 1.19 0.76 1.09 1.25 0.68 0.78 

13340000 

Clearwater R. at 

Orofino 46 Clearwater 1.02 1.49 1.17 0.77 1.01 1.28 0.68 0.79 

32 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
1980 

25 

20 

15 

10 

5 

1982 

25 

20 

15 

10 

5 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

JULY AUGUST SEPTEMBER 

2000 

Figure 16. Estimated and observed temperatures of the Salmon River above Redfish Lake Creek (U.S. Geological Survey gaging

station 13293800), 1980 and 1982, Salmon River Basin, central Idaho. TEMPERATURE, IN DEGREES CELSIUS 

95-percent confidence 

interval 

Estimated temperature 

Observed temperature 

Model Evaluation 33 
1984 

25 

20 

15 

10 

5 

95-percent confidence 

interval 

Estimated temperature 

Observed temperature 

1986 

25 

20 

15 

10 

5 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

JULY AUGUST SEPTEMBER 

2000 

Figure 17. Estimated and observed temperatures of the Red River below South Fork near Red River Ranger Station (U.S. Geological TEMPERATURE, IN DEGREES CELSIUS 

Survey gaging station 13337180), 1984 and 1986, Clearwater River Basin, central Idaho. (Gaging station discontinued in 1988) 

34 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
average subbasin slope is 34.9 percent, and the site elevation is 657 m. In this case, the amplitude of the 

observed temperature curve also was generally small: 

temperatures did not decrease in late August and early 

September as the model estimated. Although the model 

accurately estimated the observed temperatures until 

early September, it underestimated temperatures during 

the last several days of the deployment period. This is 

essentially the same pattern as that in the preceding 

examples, except that the overall position of the estimated temperature data curve is shifted downward on 

the temperature axis and, therefore, more closely 

matches the early-summer observed data curve. Again, 

the discrepancies are related to lack of curvature of the 

observed temperature data curve as the summer 

progresses. 

Examples from both large and small streams display this pattern. Wilson Creek, a third-order stream 

(fig. 20) is representative of most results from DEQ 

monitoring sites on the Middle Fork of the Salmon 

River and its tributaries in 2001. The total subbasin 

drainage area is 99.8 km2, the average subbasin slope is 

38.2 percent, and the site elevation is 1,068 m. Complete air-temperature data from Pierce were not available and data from Lewiston were substituted successfully. The model accurately estimates the observed 

temperatures within 4°C. Again, the amplitude of the 

observed stream-temperature data curve is smaller than 

that of the estimated temperature data curve, but estimates are well within the 95-percent error envelope on 

most days. 

Some of the independent tests have a common 

characteristic: whereas the model estimates decreasing 

temperatures throughout the latter part of the summer, 

observed temperatures generally remained fairly constant (see, for example, fig. 20). The small amplitude of 

these observed temperature data curves could reflect 

constant temperatures related to significant inflow from 

ground water or springs. Alternatively, this could 

reflect the lack of noticeable cooling later in the summer due to the effects of diminishing streamflows and, 

hence, uncharacteristically high stream temperatures as 

the summer progresses. The effects of changes in 

streamflow on temperature have not been assessed, but 

this would be a natural next step in refining this temperature model. Whatever the underlying cause, the 

absence of downward curvature in some observed temperature data curves from years other than 2000 suggests that the part of the model that estimates the seasonal fluctuation in temperature may not be appropriate 

for all years. This limitation is discussed further in the 

next section. 

Limitations of the Model 

One of the major shortcomings of the model is 

that it is based on data collected during only one summer, a time of below-average streamflows and aboveaverage air temperatures. Subbasin and site characteristics do not change from year to year, but the seasonal 

component of the model depends on stream-temperature data that are specific to the year 2000. Streamflows 

in 2000 were substantially lower than average for the 

Salmon and Clearwater River Basins at most USGS 

stream-gaging stations (table 9). Streamflows likely 

have a strong effect on stream temperatures, but this 

has not yet been evaluated in a systematic way. The 

seasonal component of the model, therefore, may not 

adequately represent conditions as they could occur in 

another year. This flaw in the seasonal component 

could account for some of the disagreement of model 

estimations with observed data from past years, as 

described in the previous section. Additional temperature-monitoring experiments during years of different 

streamflows could provide insights that would allow 

the effects of this variable to be understood. 

Air temperature is a factor that is not fully 

accounted for in the model, and it is not known how 

warmer or cooler air temperatures will affect the 

model’s overall effectiveness. Mean August air temperatures at Stanley and Grangeville exceeded normal in 

2000, but temperatures at McCall, Lewiston, and 

Salmon were within 1°C of normal. Mean August air 

temperatures for the entire State of Idaho in 2000 

ranked as the seventeenth warmest in 107 years of 

record and were about 4 percent above normal. 

Because air temperature and stream temperature are 

strongly related, this is undoubtedly an important issue. 

The decision was made to develop a general 

model based on average values that represented all the 

data sites as a single group rather than to develop a specific model tailored to stream order. Although this 

offered the advantage of being simpler, the model is 

not as well fit for sixth- and seventh-order streams as 

for the lower order streams, because the sixth- and seventh-order streams represent less than 10 percent of the 

data. Independent tests of the model for larger streams 

yielded acceptable results, but users should be aware 

Model Evaluation 35 
 Estimated and observed temperatures of Big Deer Creek, 1999 and 2000, Salmon River Basin, central Idaho. 

1999 

25 

20 

15 

10 

5 

2000 

25 

20 

15 

10 

5 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

JULY AUGUST SEPTEMBER 

2000 

Figure 18. Estimated and observed temperatures of Big Deer Creek, 1999 and 2000, Salmon River Basin, central Idaho. (Observed data 

from U.S. Forest Service, written communication, 2001) ( 

36 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho TEMPERATURE, IN DEGREES CELSIUS 

95-percent confidence 

interval 

Estimated temperature 

Observed temperature 
28 

24 

20 

16 

12 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

95-percent confidence 

interval 

Estimated temperature 

Observed temperature 

JULY AUGUST SEPTEMBER 

1998 

Figure 19. Estimated and observed temperatures of the Lochsa River above Wilderness Gateway Campground, 1998, Clearwater 

River Basin, central Idaho. (Observed data from Idaho Department of Environmental Quality, written communication, 2001) TEMPERATURE, IN DEGREES CELSIUS 

that errors in stream-temperature estimates for larger 

streams were large. 

Early tests of the model suggested that it was 

effective for streams that were free flowing, minimally 

affected or unaffected by human activities, and unaffected by natural features such as geothermal springs, 

but the model did not perform well if these conditions 

were not met. Therefore, the model should not be 

applied in such areas, or in areas where activities such 

as disturbance of the streambed, diversion and return of 

water by irrigation ditches, and removal of riparian 

vegetation are known to have occurred. 

Because the statistical model is based on streamtemperature data from the Salmon and Clearwater 

River Basins, it should be applied only to streams in 

that region. However, the methods described in this 

study could be used to derive a similar model for other 

regions. 

SUMMARY 

Stream temperatures were monitored at more than 

200 sites in the Salmon and Clearwater River Basins in 

central Idaho during the summer of 2000 to provide 

data to assist DEQ in revising Idaho’s stream-temperature standards for protecting cold-water biota and to 

develop a statistical stream-temperature model. 

Temperature results were compared with the current Idaho stream-temperature standards for aquatic 

life. One-hundred nineteen of the 183 sites used to 

build the statistical model met the 24-hour maximum 

daily average temperature standard of 19oC; 110 sites 

met the instantaneous maximum temperature standard 

of 22°C. Most of the sites that met the standards are in 

the Salmon River Basin. None of the monitored sites 

met the current Idaho temperature standards for salmonid spawning (24-hour maximum daily average temperature, <9oC; instantaneous maximum, <13°C). 

Summary 37 
25 

20 

15 

10 

5 

24 26 28 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 

95-percent confidence 

interval 

Estimated temperature 

Observed temperature 

JULY AUGUST SEPTEMBER 

2001 

Figure 20. Estimated and observed temperatures of Wilson Creek, 2001, Salmon River Basin, central Idaho. (Observed data from 

Idaho Department of Environmental Quality, written communication, 2001) TEMPERATURE, IN DEGREES CELSIUS 

Temperature metrics were calculated from the 

monitoring data and statistical tests were performed to 

determine correlations between temperature and a variety of subbasin and site characteristics. Total drainage 

area, average subbasin slope, site elevation, average 

subbasin elevation, air temperature, stream width and 

mean depth, and several subbasin-scale vegetation 

characteristics were significantly correlated with stream 

temperature. Subbasin aspect and stream-segment azimuth were not significantly correlated with stream 

temperature. Riparian canopy cover and open canopy 

angle (vegetation characteristics measured in the field) 

were not significantly correlated with stream-temperature metrics except maximum diurnal variation and 

seasonal variation. 

The monitoring data were used to derive a statistical model for estimating daily average stream temperatures between July 24 and September 10. The model is 

composed of three parts: 1) an estimation of the grand 

average temperature, which takes into account total 

drainage area, average subbasin slope, and site elevation; 2) a seasonal component of the temperature, as a 

daily adjustment for deviation from the grand average 

temperature; and 3) a component based on deviation of 

daily average air temperature from a 30-year average 

air temperature, which adjusts the stream-temperature 

estimate to account for short-term air-temperature fluctuations. The model estimated stream temperatures to 

within 5° to 8°C with 95-percent confidence. Although 

the model was based on data representing predominantly second- through fifth-order streams, it also can 

be applied to sixth- and seventh-order streams, 

although errors probably will be slightly higher in 

those cases. 

Independent tests of the model were carried out by 

using it to estimate temperatures for a variety of 

streams and comparing the results with historical data 

from Federal and State archives. In general, the model 

successfully estimated temperatures within the 95-percent confidence interval. In some cases, data curves 

derived from model-estimated temperatures did not 

completely match those derived from observed temper38 A statistical model for estimating stream temperatures in the Salmon and Clearwater River Basins, central Idaho 
atures, a shortcoming that could be a result of groundwater effects or limitations of the model’s seasonal 

component. 

A limitation of the model is that it is based on 

monitoring data from only one summer, during which 

streamflows were lower than average and air temperatures were higher than average. Additional data from 

other years would improve the model’s general applicability, particularly with regard to the seasonal component. Although the model is intended for use on 

undisturbed streams in the Salmon and Clearwater 

River Basins, the methods used to build the model 

could be used to build a similar model for other 

regions. 

REFERENCES CITED 

Bartholow, John M., 1989, Stream temperature investigations — field and analytical methods: U.S. Fish 

and Wildlife Service Instream Flow Information 

Paper no. 13, 139 p. 

Dyar, T.R., and Alhadeff, S.J., 1997, Stream-temperature characteristics in Georgia: U.S. Geological 

Survey Water-Resources Investigations Report 

96–4203, 150 p. 

Essig, D.A., 1998, The dilemma of applying uniform 

temperature criteria in a diverse environment— an 

issue analysis: Idaho Department of Environmental Quality, 29 p., accessed September 15, 2001, 

at URL 

http://www2.state.id.us/deq/water/tempcritpg.htm 

Fitzpatrick, F.A., Waite, I.R., D’Arconte, P.J., Meador, 

M.R., Maupin, M.A., and Gurtz, M.E., 1998, 

Revised methods for characterizing stream habitat 

in the National Water-Quality Assessment Program: U.S. Geological Survey Water-Resources 

Investigations Report 98–4052, 67 p. 

Helsel, D.R., and Hirsch, R.M., 1995, Statistical methods in water resources: Amsterdam, Elsevier, 

Studies in Environmental Science 49, 529 p. 

Idaho Administrative Code, Idaho Department of Environmental Quality, IDAPA 58.01.02, p. 139–140, 

accessed April 30, 2002, at URL 

http://www2.state.id.us/admin/adminrules/rules/idapa58/ 

0102.pdf 

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. 

Sullivan, K.J., Tooley, J., Doughty, K., Caldwell, J.E., 

and Knudsen, P., 1990, Evaluation of prediction 

models and characterization of stream temperature regimes in Washington: Washington Department of Natural Resources Timber-Fish-Wildlife 

Report no. TFW–WQ2–90–006, 224 p. 

Wehrly, K.E., Wiley, M.J., and Seelbach, P.W., 1997, 

Landscape-based models that predict July thermal 

characteristics of lower Michigan rivers: State of 

Michigan Department of Natural Resources 

Report no. 2037, 22 p. 

References Cited 39 
U.S. Geological Survey Water-Resources Investigations Report 02 – 4195 

Donato —A Statistical Model for Estimating Stream Temperatures in the Salmon and Clearwater River Basins, Central Idaho — 

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