Estimating Water Temperatures in Small Streams in

Western Oregon Using Neural Network Models

Prepared in cooperation with the

OREGON WATERSHED

ENHANCEMENT BOARD

U.S. GEOLOGICAL SURVEY

Water-Resources

Investigations

Report 02-4218
Estimating Water Temperatures in Small 

Streams in Western Oregon Using Neural 

Network Models

By John C. Risley, U.S. Geological Survey, Edwin A. Roehl, Jr., Advanced Data Mining, LLC, 

and Paul A. Conrads, U.S. Geological Survey

Prepared in cooperation with the

OREGON WATERSHED ENHANCEMENT BOARD

Portland, Oregon

2003

Water-Resources Investigations Report 02-4218

U.S. GEOLOGICAL SURVEY
For additional information write to:

District Chief

U.S. Geological Survey

10615 S.E. Cherry Blossom Drive

Portland, Oregon 97216-3159

Email: info-or@usgs.gov

Internet: http://oregon.usgs.gov

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does 

not imply endorsement by the U.S. Government.

Copies of this report can be purchased from:

U.S. Geological Survey

Information Services

Building 810

Box 25286, Federal Center

Denver, CO 80225-0286

U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director
Contents iii

CONTENTS

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

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

Background ................................................................................................................................................. 1

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

Study Area................................................................................................................................................... 3

Previous Investigations ............................................................................................................................... 3

Acknowledgments....................................................................................................................................... 6

Data Collection..................................................................................................................................................... 6

Water Temperature...................................................................................................................................... 6

Stream Habitat Surveys............................................................................................................................... 8

Basin Characteristics................................................................................................................................... 8

Climate ........................................................................................................................................................ 9

Model Development............................................................................................................................................. 11

Background Theory..................................................................................................................................... 11

Clustering Analysis ..................................................................................................................................... 12

Model Framework....................................................................................................................................... 15

Training....................................................................................................................................................... 19

Validation.................................................................................................................................................... 21

Model Application................................................................................................................................................ 30

Shade Adjustment ....................................................................................................................................... 30

Climate Adjustment .................................................................................................................................... 31

Future Improvements .................................................................................................................................. 34

Summary and Conclusions................................................................................................................................... 35

References Cited .................................................................................................................................................. 36

Appendix A. Site list for water temperature and habitat survey data collection ................................................. 38

Appendix B. Model input variable tables and sensitivity analyses..................................................................... 42

Appendix C. Model operation instructions ......................................................................................................... 56
iv Figures

FIGURES

Figure 1. Map showing western Oregon study region ...................................................................................... 4

Figure 2. Graphs showing mean monthly precipitation and air temperature at Astoria, 

Brookings, Crater Lake, Eugene, Medford, North Bend, and Salem, Oregon .................................. 5

Figure 3. Map showing locations of stream temperature stations, climate stations, and 

snowpack measurement stations in western Oregon ......................................................................... 7

Figure 4. Diagram showing feed-forward neural network architecture with three inputs, 

five hidden-layer nodes, and a single output ..................................................................................... 12

Figure 5. Graph showing density of water temperature records ....................................................................... 13

Figure 6. Graph showing results of clustering analysis .................................................................................... 14

Figure 7. Map showing distribution of the three groups of stream temperature stations 

within the study area .......................................................................................................................... 16

Figure 8. Graph showing mean of normalized 24-hour moving average hourly water 

temperature time series from each of the three groups...................................................................... 17

Figure 9. Diagram showing components of artificial neural network water temperature models .................... 18

Figure 10. Map showing location of model validation sites ............................................................................... 22

Figure 11. Graphs showing measured and simulated 24-hour moving average hourly water 

temperatures for selected sites in western Oregon............................................................................. 25

Figure 12. Graphs showing measured and simulated hourly water temperatures for selected 

sites in western Oregon...................................................................................................................... 27

Figure 13. Graphs showing simulated 24-hour moving average hourly water temperatures for 

varying shade conditions for selected sites in western Oregon ......................................................... 32
Tables v

TABLES

Table 1. Stream habitat and basin variables used as model inputs and their statistics .................................... 9

Table 2. Climate time series data assembled for the model simulations ......................................................... 10

Table 3. Statistical results for the training and testing of simulations for each model .................................... 20

Table 4. Location, stream habitat, and basin characteristics data for the validation stream sites.................... 23

Table 5. Comparison of static, 24-hour moving average, and hourly model errors for the 

simulation period (June 21, 1999, to September 20, 1999) for the validation stream sites............... 24

Table 6. Existing and adjusted shade and vegetation variable values for selected stream sites ...................... 31

Table 7. Mean of simulated hourly temperatures for varying shade conditions for selected stream sites ...... 31

Table 8. Departure of 1999 mean monthly water temperatures from the period of record 

at selected stations in western Oregon............................................................................................... 34
vi Conversion Factors and Vertical Datum

CONVERSION FACTORS AND VERTICAL DATUM

Conversion Factors

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

°F=1.8 °C+32

Vertical Datum

In this report, vertical coordinates are referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Multiply By To obtain

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

millimeter (mm) 0.03937 inch

meter (m) 3.281 foot (ft)

kilometer (km) 0.5400 mile (mi)

square kilometer (km2) 0.3861 square mile (mi2)

cubic meter (m3) 1.308 cubic yard (yd3)
Introduction 1

Estimating Water Temperatures in Small Streams in 

Western Oregon Using Neural Network Models

By John C. Risley1, Edwin A. Roehl, Jr.2, and Paul A. Conrads3

ABSTRACT

Artificial neural network models were developed 

to estimate water temperatures in small streams using 

data collected at 148 sites throughout western Oregon 

from June to September 1999. The sites were located 

on 1st-, 2nd-, or 3rd-order streams having undisturbed 

or minimally disturbed conditions. Data collected at 

each site for model development included continuous 

hourly water temperature and description of riparian 

habitat. Additional data pertaining to the landscape 

characteristics of the basins upstream of the sites were 

assembled using geographic information system (GIS) 

techniques. Hourly meteorological time series data 

collected at 25 locations within the study region also 

were assembled.

Clustering analysis was used to partition 142 

sites into 3 groups. Separate models were developed for 

each group. The riparian habitat, basin characteristic, 

and meteorological time series data were independent 

variables and water temperature time series were 

dependent variables to the models, respectively. 

Approximately one-third of the data vectors were used 

for model training, and the remaining two-thirds were 

used for model testing. Critical input variables included 

riparian shade, site elevation, and percentage of 

forested area of the basin. Coefficient of determination 

and root mean square error for the models ranged from 

0.88 to 0.99 and 0.05 to 0.59 oC, respectively. The 

models also were tested and validated using 

temperature time series, habitat, and basin landscape 

data from 6 sites that were separate from the 142 sites 

that were used to develop the models.

The models are capable of estimating water 

temperatures at locations along 1st-, 2nd-, and 3rdorder streams in western Oregon. The model user must 

assemble riparian habitat and basin landscape 

characteristics data for a site of interest. These data, in 

addition to meteorological data, are model inputs. 

Output from the models include simulated hourly water 

temperatures for the June to September period. 

Adjustments can be made to the shade input data to 

simulate the effects of minimum or maximum shade on 

water temperatures.

INTRODUCTION

Background

Stream water temperature has become a major 

concern in Oregon. Temperature affects dissolved 

oxygen concentrations, biochemical oxygen demand 

rates, algae production, and contaminant toxicity. 

Although warm water can occur naturally in Oregon, it 

is commonly induced by anthropogenic activities such 

as effluent point sources, removal of riparian shade, 

stream channel alterations, water diversions, and 

urbanization. Many States have adopted water 

temperature standards as a part of their compliance 

with the Federal Clean Water Act. Elevated water 

temperature is the single most common water-quality 

violation for streams in Oregon. Hundreds of stream 

reaches exceed the maximum State standard, which is 

17.8-degrees Celsius (oC) based on a 7-day moving

1U.S. Geological Survey, Portland, Oregon.

2Advanced Data Mining, LLC, Greenville, South Carolina.

3U.S. Geological Survey, Columbia, South Carolina.
2 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

average maximum daily temperature for most streams 

with cold-water fisheries during summer low-flow 

conditions. Such reaches are designated “water-qualitylimited” by the State. Once a waterway is designated 

water-quality-limited, the State must develop a Total 

Maximum Daily Load (TMDL) plan for that water 

body to meet the established water-quality standard.

Temperature has a major affect on the 

distribution, health, and survival of native salmonids 

(salmon, trout, and charr) and other aquatic species. 

Salmonid feeding, growth, resistance to disease, 

competitive ability, and predator avoidance are 

impaired when salmonids are exposed to unsuitable 

temperatures. Very high temperatures can cause direct 

mortality of salmonids. While lethal temperatures do 

occur naturally and can be locally problematic, 

temperatures in the range where sublethal effects occur 

are widespread and probably have the greatest effect on 

the overall well-being and patterns of occurrence of 

native fish populations (Poole and Berman, 2001). In 

recent years, a growing number of salmon, steelhead, 

and other species in Oregon have been listed as 

threatened and endangered under the Federal 

Endangered Species Act (ESA).

With the addition of ESA issues, the need to 

address water-quality violations associated with 

elevated temperatures has become more critical. 

However, developing water temperature TMDL plans 

can be expensive. In many TMDL plans, mechanistic 

models are used to determine current and potential 

water temperatures. For input, these models typically 

require extensive amounts of field collected water 

temperature and meteorological data. Mechanistic 

models must to be adequately calibrated and validated. 

Using preexisting water temperature statistical models, 

which use stream reach and basin characteristics as 

their only inputs, is one way to reduce costs in a TMDL 

plan. Statistical models might not be able to eliminate 

the need for using mechanistic models in the lower 

reaches of river basins, but they could eliminate the 

need for using mechanistic models in headwater 1st-, 

2nd-, and 3rd-order streams. Water temperatures 

predicted by a statistical model can serve as upper 

boundary inputs to mechanistic models reducing the 

need for collecting water temperature data at many 

locations. A water temperature statistical model also 

can be used to efficiently identify and prioritize stream 

reaches that are grossly out of compliance and in most 

need of remediation and to establish attainable 

temperature-reduction goals for reaches that have 

naturally elevated water temperatures.

Aside from assisting TMDL plans, a water 

temperature statistical model will help researchers 

better understand the relationship between physical 

landscape characteristics and water temperature, and 

monitor stream health.

In response to the need for a relatively 

inexpensive method of developing temperature TMDLs 

for Oregon streams, in 1999, the U.S. Geological 

Survey began a cooperative study with the Oregon 

Watershed Enhancement Board to develop a statistical 

model capable of predicting water temperature time 

series for 1st-, 2nd-, and 3rd-order streams in western 

Oregon.

Purpose and Scope

The study design included field-data collection 

and statistical analyses. Continuous water temperature, 

riparian habitat, and basin landscape-characteristics 

data were collected at 148 sites having relatively 

undisturbed riparian zones located throughout western 

Oregon during the summer of 1999 by the U.S. 

Geological Survey and the Oregon Department of 

Environmental Quality. Available meteorological 

hourly time series data collected at various locations 

around the study region also were assembled. 

Clustering analysis was performed on the overall data 

set to determine optimal subsets. Artificial neural 

network (ANN) models were developed based on data 

from the subsets. The models were tested and validated 

on a group of stream sites that were not included in the 

set used to create the models. The models also were 

used to simulate the effect of varying shade conditions 

on water temperatures.

This report provides (1) a description of the data 

used to develop the water temperature models, (2) 

some background theory on ANN models, (3) a 

description of the model development, (4) examples of 

model application, and (5) a user’s guide for operating 

the models.
Introduction 3

Study Area

Located in western Oregon, the boundaries of the 

study area are the Columbia River (north), the 

California border (south), the Pacific Ocean (west), and 

the Cascade Range divide (east) (fig. 1). This region 

covers approximately 80,000 square kilometers. 

Elevations range from sea level near the Columbia 

River to more than 3,000 meters in the mountains of 

the Cascade Range. Almost 3 million people, 

representing approximately 85 percent of the State’s 

population (2000 census), live in the region. The region 

supports an economy based on agriculture, 

manufacturing, timber, and recreation, and contains 

extensive fish and wildlife habitat.

Western Oregon has a temperate marine climate 

characterized by dry summers and wet winters (fig. 2). 

Over 80 percent of annual precipitation typically falls 

between October and May. Mean annual precipitation 

ranges from about 500 millimeters in Medford to 4,000 

millimeters at crests in the Coast Range. About 35 

percent of the precipitation falls as snow at the 1,200 

meter elevation, and more than 75 percent falls as snow 

at 2,100 meters. Because the region is largely 

dominated by maritime systems, the range of both 

seasonal and diurnal air temperatures is relatively 

small.

On the basis of various geologic, physiographic, 

biological, and climatic indices, the study area is 

divided into four ecoregions (U.S. Environmental 

Protection Agency, 1996). These ecoregions include 

the Coast Range, Willamette Valley, Cascades, and 

Klamath Mountains (fig. 1).

The Coast Range is characterized by highly 

productive, rain-drenched coniferous forests. Dominant 

tree species in the Oregon coastal region include Sitka 

spruce, western red cedar, western hemlock, and 

Douglas fir. The Coast Range is composed of Tertiary 

marine sandstone, shale, and mudstone interbedded 

with volcanic basalt flows and volcanic debris. Soils 

are typically loamy and well drained. 

Prior to European settlement, the Willamette 

Valley consisted of rolling prairies, deciduous/ 

coniferous forests, and extensive wetlands. Annual 

precipitation, less than the Coast Range or Cascades 

regions, is typically from 1,000 to 1,200 millimeters. 

Much of the terrain in the Willamette Valley up to an 

elevation of about 120 meters is covered by sandy to 

silty terrace deposits that settled from water ponded in 

the great glaciofluvial lake resulting from the Missoula 

Floods (Glenn, 1965; Allison, 1978). Alluvial deposits 

that border existing rivers and form alluvial fans near 

river mouths were derived from the surrounding 

mountains, and they consist of intermingled layers of 

clay, silt, sand, and gravel.

The Cascades, the most mountainous region of 

the study area, is characterized by steep ridges, highly 

productive coniferous forests, a moist temperate 

climate, dormant and active volcanos, and alpine 

glaciers at higher elevations. The region is composed of 

volcanic rocks consisting of Tertiary basaltic and 

andesitic rocks together with volcanic debris, primarily 

in the western part of the range, and Quaternary 

basaltic and andesitic lava flows, primarily in the High 

Cascades.

The Klamath Mountains region is located in the 

southern portion of the study area. The region is 

physically and biologically more diverse than the other 

three regions. The climate is mild and subhumid with 

hot dry summers. Forest vegetation is dominated by a 

mix of northern Californian and Pacific Northwest 

conifers. The topography of the region is characterized 

by highly dissected, folded mountains, foothill terraces, 

and floodplains. The region is underlain by igneous, 

sedimentary, and some metamorphic rock.

Previous Investigations

A large body of research has been generated in 

recent years in water temperature prediction. Models 

that predict water temperature are often classified as 

mechanistic or statistical. 

A heat-transport model, an example of a 

mechanistic or process-base model, predicts water 

temperature using an energy-balance equation. 

Mathematical equations are used to represent the 

physical processes of heat transfer between the stream 

and the surrounding environment. Meteorological data 

(solar radiation, air temperature, wind speed, and 

humidity) are typical inputs to mechanistic models. 

Mechanistic water temperature models also typically 

contain, or are coupled with, a hydrologic flow model. 

Mechanistic models typically are applied to a specific 

stream reach. Boundary flow and water temperature 

time series data must be collected at the site. After the 

model has been calibrated and validated with the 

measred data, it is possible to use the model to simulate 

cooler water temperatures that could exist under a 

“natural” shade scenario.
4 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

EXPLANATION

ECOREGIONS IN WESTERN

 OREGON STUDY REGION

Willamette Valley

Cascades

Coast Range

Klamath Mountains

DRAINAGE BASIN BOUNDARY

0 10 20 30 50 60 MILES 40

0 10 20 30 50 60 KILOMETERS 40

Portland

Corvallis

Eugene

Ashland

WASHINGTON

PACIFIC OCEAN

Eastern Oregon

CALIFORNIA

OREGON

124 ̊ 123 ̊ 122 ̊

46 ̊

45 ̊

44 ̊

43 ̊

42 ̊

Columbia River

C

A

SCADE RA

N

GE DIVIDE

Figure 1. Western Oregon study region.
Introduction 5

Astoria

Brookings

Crater Lake

Eugene

Medford

North Bend

Salem

-5

0

5

10

15

20

25

TEMPERATURE, IN DEGREES CELSIUS

0

100

200

300

400

PRECIPITATION, IN MILLIMETERS

JAN FEB MAR APR MAY JUNE JULY AUG SEP OCT NOV DEC

Mean-monthly precipitation (1971-2000)

Mean-monthly air temperature (1971-2000)

Figure 2. Mean monthly precipitation and air temperature at Astoria, Brookings, Crater Lake, Eugene, Medford, North 

Bend, and Salem, Oregon.
6 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

An early mechanistic model applied to small 

streams in Oregon was developed by Brown (1969). 

Examples of other mechanistic models include a 

steady-state model developed by Theurer and others 

(1984), one-dimensional dynamic flow and heattransport models developed by Jobson (1989), Jobson 

and Schoellhamer (1987), and a two-dimensional, 

laterally averaged model developed by Edinger and 

Buchak (1975) and Cole and Buchak (1995). 

To model water temperature over a broad region, 

such as western Oregon, a mechanistic modeling 

approach would not have been practical due to the 

substantial data requirements. Most statistical models 

that predict water temperatures use univariate or 

multivariate regression techniques. Some univariate 

regression models use air temperature as a predictor of 

water temperature because the two variables often have 

a high statistical correlation. Mohseni and others 

(1998) developed a four-parameter nonlinear 

regression model that uses weekly air temperature to 

predict weekly water temperatures. With multivariate 

statistical models, the temperature estimates are usually 

based on the physical characteristics of the stream site 

(elevation, stream morphology, channel aspect, riparian 

shade) and ambient climate conditions (air 

temperature, humidity, and solar radiation). Many of 

these multivariate models use a harmonic-analysis 

regression fit of annual variability (Ward, 1963; 

Collings, 1973; Tasker and Burns, 1974; and Dyar and 

Alhadeff, 1997). These models can be applied on a 

regional scale and used to predict temperatures at 

locations where no data have been collected. This 

approach is similar to using regionalized hydrologic 

statistical models which estimate flood or low-flow 

frequency streamflow statistics at ungaged sites (Riggs, 

1973).

Some detailed studies generally on small streams 

have evaluated the relation between stream site 

physical characteristics, ambient climate conditions, 

and water temperatures (Moore, 1967; Pluhowski, 

1970; Theurer and others, 1985; Lewis and others, 

2000; and Poole and Berman, 2001). Additional studies 

by Brown and Krygier (1970), Feller (1981), Beschta 

and Taylor (1988), Bartholow (2000), and Johnson and 

Jones (2000) assessed the effects of forest practices on 

water temperatures. These studies confirmed that there 

is typically an increase in thermal loading in many 

streams as a result of the removal of riparian vegetation 

and increased solar radiation.

Acknowledgments

The authors gratefully acknowledge several 

agencies and individuals for assistance during the 

study. Approximately one-half of the water 

temperature and riparian habitat data used to develop 

the ANN models were collected by the Oregon 

Department of Environmental Quality. Rick Hafele and 

Mike Mulvey were especially helpful. Ken Bierly, 

Oregon Watershed Enhancement Board, was 

instrumental in securing funding for the study.

DATA COLLECTION

 Continuous water temperature and riparian 

habitat data were collected at 148 sites located 

throughout western Oregon during the summer of 

1999. Topographic data describing the basin upstream 

of each site were computed using geographic 

information system (GIS) techniques. Available 

climate time series data collected at various locations 

around the study region were assembled.

Water Temperature

Continuous half-hourly water temperature was 

collected by the USGS and the Oregon Department of 

Environmental Quality at 148 western Oregon stream 

sites during the 1999 low-flow period (May through 

September) (fig. 3). The sites were located on 1st-, 

2nd-, or 3rd-order streams. The streams at these sites 

drained basins ranging in size from 0.31 to more than 

300 square kilometers. Site elevations ranged from 7 to 

1,446 meters above mean sea level. A list of the 148 

sites and their locations is shown in Appendix A.

Sites were selected based on accessibility and a 

minimum of upstream anthropogenic impacts. 

Locations below point sources were not used. Also, 

most locations which had been extensively denuded of 

upstream riparian vegetation were not used. However, 

an attempt was made to provide an even distribution of 

sites across the study region. Locating sites with 

minimal anthropogenic impacts was more difficult in 

populated agricultural lowlands, such as the Willamette 

Valley, as opposed to forested regions in the Cascades.
Data Collection 7

EXPLANATION

STREAM -TEMPERATURE STATION

CLIMATE STATION

SNOWPACK-MEASUREMENT STATION

0 10 20 30 50 60 MILES 40

0 10 20 30 50 60 KILOMETERS 40

DRAINAGE BASIN BOUNDARY

Portland

Corvallis

Eugene

Ashland

WASHINGTON

Eastern Oregon

CALIFORNIA

PACIFIC OCEAN

124 ̊ 123 ̊ 122 ̊ 

46 ̊

45 ̊

44 ̊

43 ̊

42 ̊

Figure 3. Locations of stream temperature stations, climate stations, and snowpack measurement stations in western Oregon.
8 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Stream Habitat Surveys

Stream habitat surveys were conducted at all the 

sites during the summer of 1999. The surveys used the 

U.S. Environmental Protection Agency (EPA) 

Environmental Monitoring and Assessment Program 

(EMAP) field methods for measuring physical habitat 

in wadeable streams (Kaufman and Robison, 1994, 

1998). The methodology used to compute metrics from 

the field data are described in Kaufmann and others 

(1999). Each survey was made along a stream reach 

just upstream of the temperature probe location. The 

length of the stream reach was 40 times the width of 

the stream at the temperature probe location, but no 

shorter than 150 meters. Habitat measurements were 

taken at 11 cross sections at equal intervals along the 

stream reach. 

The EMAP habitat parameters measured for this 

study included stream bearing, stream gradient, canopy 

cover, stream wetted widths, stream depth, and 

streambed substrate (table 1).

Stream bearing for each site was computed from 

the mean of 10 compass bearing measurements 

between the 11 cross sections along the stream reach. 

The bearings, measured in an upstream to downstream 

direction, were in degrees from 0 to 360. Stream 

bearing, like basin aspect, is important to water 

temperature because of its relation to the amount of 

solar radiation reaching the water surface. South facing 

basins (in the northern hemisphere) typically have 

warmer water temperatures than north facing basins.

Stream gradient, defined as the rise over run ratio 

percent, was computed from the mean of 10 gradient 

measurements made with a clinometer between each of 

the 11 cross sections. Stream gradient has relevance to 

water temperature as an indication of stream velocity 

and residence time within the reach.

Summer canopy cover was measured using a 

Convex Spherical Densiometer, model B (Lemmon, 

1957). At each of the 11 cross sections, 4 

measurements were taken from the center of the 

channel facing upstream, downstream, and each bank. 

The 44 values were averaged and computed as a 

percentage. A second set of densiometer measurements 

were made, at each cross section, from both 

streambanks facing the water. These 22 values were 

averaged and computed as a percentage. Canopy cover 

directly affects water temperature because it controls 

the amount of short-wave solar radiation reaching the 

water surface.

Stream wetted width and depth were measured at 

each of the 11 cross sections. The depth to width ratio 

can affect water temperature. Deep narrow streams are 

typically cooler than wide shallow streams.

Streambed substrate was sampled at five 

locations at each cross section. These locations 

included both the left and right edge of water and 

within the channel (one-quarter, one-half, and threequarters of the distance across the stream). At each 

location, the substrate material was visually evaluated 

as either bedrock (particle size greater than 4,000 

millimeters), boulder (between 250 to 4,000 

millimeters), cobble (between 64 to 250 millimeters), 

gravel (between 2 to 64 millimeters), sand (between 

0.06 to 2 millimeters), or fine silt or muck (less than 

0.06 millimeter). For the entire stream reach, the 

percentage breakdown for these 6 classes was 

computed using data from a total of 55 sampling 

locations (5 locations at each of 11 cross sections). 

Basin Characteristics

For many streams, the temperature at a particular 

location is influenced by habitat and vegetation 

conditions that exist farther upstream than the length of 

the stream reach defined for the habitat field surveys 

(40 times the downstream channel width). Using GIS, 

topographic and vegetative characteristics of the 

drainage basin upstream of the temperature probe were 

computed (table 1). The 148 basins for the sites were 

delineated using 10-meter digital elevation models 

(DEM).

The percentage of forest cover and forest cover 

density were computed for each basin using a GIS 

coverage of forest vegetation in western Oregon that 

was created from LANDSAT imagery developed by 

Cohen and others (1995, 1998, 2001, and 2002). The 

LANDSAT imagery was taken in 1995 and resampled 

to a 25-meter cell resolution. For this study, all areas 

that contained forest vegetation were classified as 

“forested” and areas absent of forest vegetation (which 

included forest clear cuts and fire burns) were 

classified as “open.” Most regions outside of forested 

areas, such as agricultural or urban areas, were usually 

classified as “open.”

Mean summer air temperature data were 

computed for each basin using a GIS coverage of mean 

monthly air temperatures (1961-1990) developed by 

Daly and others (1997). The mean for the summer 

period was based on the months of May through 

September.
Data Collection 9

Climate

Hourly climatological time series data collected 

at various stations around western Oregon also were 

assembled (table 2; fig. 3). The climate stations are 

operated by the U.S. National Weather Service, U.S. 

Bureau of Reclamation, and the U.S. Forest Service. 

The climate parameters used in the study included air 

temperature, dew-point temperature, short-wave solar 

radiation, air pressure, and precipitation. Daily 

snowpack time series data collected by the U.S. Natural 

Resource Conservation Service at nine sites also were 

assembled (table 2; fig. 3).

Table 1. Stream habitat and basin variables used as model inputs and their statistics

[Statistics are based on 142 sites. Six sites from the total set of 148 sites were held aside for later model validation]

Model label Explanation Mean Standard 

deviation Minimum Maximum

STRMRB Stream reach bearing (degrees) 206.93 98.67 0.00 360

SLOPEPCT Slope (percent) 4.57 5.75 0.10 33.65

STRMBDEN Streambank densiometer (percent) 90.20 11.87 29.95 100

MIDCHDEN Mid-channel densiometer (percent) 78.94 18.94 2.27 100

DEPTH Depth (centimeters) 33.13 19.86 3.67 126

WETTEDWD Wetted width (meters) 5.93 3.89 0.54 19.56

SBSUBSTF Streambed substrate percent Fines/others 17.60 24.07 0.00 100

SBSUBSTS Streambed substrate percent Sand 7.08 8.23 0.00 42.59

SBSUBSTG Streambed substrate percent Gravel 26.58 13.78 0.00 65.45

SBSUBSTC Streambed substrate percent Cobble 23.60 14.31 0.00 63.64

SBSUBSBO Streambed substrate percent Boulder 14.04 14.32 0.00 74.55

SBSUBSBE Streambed substrate percent Bedrock 11.10 14.00 0.00 60.00

BASBEARA Basin bearing (degrees) 204.07 103.07 4.00 359

BASBEARS Basin bearing (sine) -0.2719 0.6701 -1.0000 1.0000

BASBEARC Basin bearing (cosine) 0.0299 0.6947 -0.9998 0.9998

STRMCHBE Stream-channel bearing (degrees) 201.44 103.82 0.00 350

BASINKM2 Basin area (square kilometers) 34.06 47.77 0.32 300.65

BASMELEV Basin mean elevation (meters) 725.11 475.69 50.71 2,871.10

BASOELEV Basin outlet elevation (meters) 394.63 350.14 7.20 1,445.80

BASXELEV Basin maximum elevation (meters) 1,142.41 639.24 61.00 4,470.00

STCHMELV Stream-channel mean elevation (meters) 523.17 405.26 33.77 1,649.59

BASMSLOP Basin mean slope (percent) 34.82 15.43 1.40 123.36

STMCHSLO Stream-channel mean slope (percent) 3.51 3.17 0.07 16.30

BASFOREA Basin forest area (percent) 79.38 25.12 0.00 100

BASOPENA Basin open area (percent) 20.62 25.12 0.00 100

DENBASFA Density of basin forest area (percent) 88.85 16.04 0.00 98.94

STCHFORA Stream-channel forest area (percent) 82.16 29.43 0.00 100

STCHOPA Stream-channel open area (percent) 17.84 29.43 0.00 100

DNSTCHFA Density of stream-channel forest area (percent) 83.84 22.01 0.00 98.29

BASMSATC Basin mean summer air temperature (degrees Celsius) 14.81 1.38 10.79 17.62

STMSUATC Stream-channel mean summer air temperature (degrees Celsius) 14.93 1.38 11.04 17.67

OUTMSATC Outlet mean summer air temperature (degrees Celsius) 15.41 1.82 11.67 24.94

XCOORD Longitude (normalized decimal value) 0.4933 0.2546 0.0048 0.9426

YCOORD Latitude (normalized decimal value) 0.5115 0.2587 0.0002 0.9444
10 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Typically, ANN models are more efficient if the 

input time series data sets have been normalized to 

accentuate the variability within the data set. 

Normalizing the climate data can be done by selecting 

a centrally located climate station as a standard. Data 

measurements from the standard station are subtracted 

from corresponding data measurements collected at 

nonstandard stations. Being centrally located in the 

study area, Corvallis was selected as a standard. Hourly 

Corvallis climate data for air temperature, dewpoint 

temperature, rainfall, and solar radiation were used to 

normalize corresponding non-Corvallis station data. 

However, air pressure data were normalized with air 

pressure data from Eugene, because Corvallis air 

pressure data were unavailable.

Table 2. Climate time series data assembled for the model simulations

[Agencys: NRCS, U.S. Natural Resources Conservation Service; USBR, U.S. Bureau of Reclamation; NWS, U.S. National Weather Service; USFS, U.S. Forest 

Service; Meteorological parameters: AP, air pressure; SWE, snow water equivalent; DT, dewpoint temperature; AT, air temperature; SR, solar radiation; RN, 

rainfall]

Station name Latitude Longitude Elevation

(meters) Agency

Meteorological parameter

AP SWE DT AT SR RN

Corvallis 44 38 03 123 11 24 70.1 USBR X X X X

Aurora 45 16 55 122 45 01 42.7 USBR X X X X

Bandon 43 05 28 124 25 02 24.4 USBR X X X X

Dee Flat 45 34 25 121 38 50 384 USBR X X

Forest Grove 45 33 11 123 05 01 54.9 USBR X X X X

Medford 42 19 52 122 56 16 408 USBR X X X X

Billie Creek Divide 42 25 00 122 17 00 1,615 NRCS X

Diamond Lake 43 11 00 122 08 00 1,620 NRCS X

Holland Meadows 43 40 00 122 34 00 1,494 NRCS X

Jump Off Joe 44 23 00 122 10 00 1,067 NRCS X

Little Meadows 44 37 00 122 13 00 1,219 NRCS X

North Fork 45 33 00 122 01 00 951 NRCS X

Peavine Ridge 45 03 00 121 56 00 1,067 NRCS X

Roaring River 43 54 00 122 02 00 1,494 NRCS X

Saddle Mountain 45 32 00 123 22 00 991 NRCS X

Astoria 46 09 00 123 53 00 2.13 NWS X X

Brookings 42 02 00 124 15 00 7.32 NWS X X X

Eugene 44 07 00 123 13 00 34.7 NWS X X X

Hillsboro 45 31 00 122 59 00 18.9 NWS X X X

Medford 42 23 00 122 53 00 123 NWS X

North Bend 43 25 00 124 15 00 1.22 NWS X X X

Portland 45 36 00 122 36 00 3.66 NWS X X X

Roseburg 43 14 00 123 22 00 48.8 NWS X X X

Salem 44 55 00 123 00 00 18.6 NWS X X X

Cannible 44 21 00 123 55 00 593.1 USFS X X X

Pebble 44 14 00 121 59 00 1,085 USFS X X X

Rye Mountain 45 13 00 123 32 00 610 USFS X X X
Model Development 11

MODEL DEVELOPMENT

Background Theory

An artificial neural network (ANN) model is a 

flexible mathematical structure capable of describing 

complex nonlinear relations between input and output 

data sets. Although used in industrial applications for 

years, ANN modeling is increasingly being used in 

environmental sciences, particularly for problems 

where the characteristics of the processes are difficult 

to simulate using a mechanistic modeling approach. 

Within hydrologic studies, ANN modeling has been 

used for a variety of purposes. Kuligowski and Barros 

(1998) used ANN modeling to estimate missing 

rainfall data. Karunanithi and others (1994) and Hsu 

and others (1998) used ANN modeling for streamflow 

forecasting. River stage also has been forecasted using 

ANN modeling (Thirumalaiah and Deo, 1998). Hsu 

and others (1995) and Shamseldin (1997) describe 

applications of ANN modeling to rainfall-runoff 

processes. In a water-quality application, Conrads and 

Roehl (1999) used an ANN model to simulate salinity, 

temperature, and dissolved oxygen in a complex tidal 

estuary. Morshed and Kaluarachchi (1998) present an 

ANN model used in complex ground-water flow and 

contaminant transport simulations. Cannon and 

Whitfield (2001) modeled transient pH depressions 

using an ANN model.

The architecture of ANN models is loosely based 

on the biological nervous system (Hinton, 1992). 

ANNs contain interconnected units that are analogous 

to neurons. The function of the synapse is modeled by a 

modifiable weight which is associated with each 

connection. Probably the most commonly used ANN 

model is the feed-forward neural network shown in 

figure 4. This example contains three nodes in the input 

layer, five nodes in the hidden layer, and a single node 

in the output layer. The model output is generated by 

feeding input data through the model from left to right. 

The output from each hidden layer node hj is computed 

in the following equation:

(1)

where

Output from the ANN model is computed in the 

following:

(2)

where

Nonlinear relationships in the model are 

represented by the hyperbolic tangent function, a 

sigmoid-shaped function, in the hidden-layer nodes. 

However, the output variable, Y, is a linear function of 

the weighted hidden-layer outputs.

The root mean square error (RMSE) of the ANN 

model is defined as:

(3)

where

Training the ANN model involves minimizing 

the RMSE by continually adjusting the model weights 

and bias terms. Usually, training is accomplished using 

a nonlinear multivariate optimization algorithm. The 

back propagation algorithm (or gradient descent) is 

commonly used in many training applications.

hj Xi w

1

ij

i

∑ b

1

j = tanh +

hj is the computed output from each 

hidden-layer node,

j is the hidden-layer node index,

tanh is the hyperbolic tangent,

i is the input layer node index,

Xi is the input variable,

1wij is the hidden layer weight, and

1bj is hidden-layer bias.

Y is the output variable

2wj is the output layer weights, and

2b is the output layer bias.

E is the root mean square error,

N is the number of input and output cases,

Y is the predicted output, and

Yobs is the measured output.

Y hj

2

j

∑ wj b

2 = +

E 1

N

--- Y Yobs ( ) – 2

cases

= ∑
12 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Clustering Analysis

For many spatial modeling problems, it is 

necessary to subdivide a larger study area and create 

separate models for regions rather than create a single 

model for an entire study area. This approach is 

typically used in regional regression studies for flood 

statistic (Riggs, 1973). The western Oregon study area 

varies broadly with respect to climate, topography, and 

ecology. A preliminary assessment of the water 

temperature data revealed expected time series 

discontinuities. One large ANN model for all of 

western Oregon would not have been capable of 

simulating much of the time series discontinuities. 

However, instead of subdividing western Oregon into 

spatially contiguous regions, separate and more 

homogenous groups of temperature sites were created 

using clustering analysis. The clustering analysis, 

which is discussed in more detail below, was based on 

only continuous water temperature time series data 

collected in the summer of 1999 from 142 sites 

throughout western Oregon. (Six sites were randomly 

removed from the original set of 148 sites and set aside 

for post-model-development validation.) In addition to 

determining which specific sites fall into which groups, 

clustering analysis can be used to determine an optimal 

number of groups. A higher number of groups will 

create more distinct homogenous groups. However, 

these groups will contain a smaller number of sites, 

which may be insufficient for creating robust ANN 

models. 

Output layer

Hidden layer

Input layer

b2

Wj 2

Wij

Y

1

bj 1

Xi

1

1

Figure 4. Feed-forward neural network architecture with three inputs, five hidden-layer nodes, and a single output.
Model Development 13

Prior to the clustering analysis, it was necessary 

to determine an optimal period of record for all 142 

sites. The beginning and ending dates for the records of 

these sites varied within the period from early May to 

early October 1999. The period from June 21 to 

September 20, 1999, was selected as an optimum 

period having the highest density of records (fig. 5). 

This period also included the warmest part of the 

summer in western Oregon, which is when water 

temperature standard violations are mostly likely to 

occur. This same period also was used for the 

subsequent modeling after the clustering analysis. To 

improve file storage and simulation speed, hourly 

(instead of half-hourly) temperature values were used 

in the analysis. In analyzing water temperature records 

in the Pacific Northwest, Dunham and others (2001) 

found that accurate measures of the daily maximum 

and minimum temperatures are still retained if an 

hourly record is used rather than a half-hourly record.

Figure 5. Density of water temperature records.

0

20

MAY JUNE JULY AUGUST

1999

SEPTEMBER OCTOBER

40

60

80

100

120

140

160

NUMBER OF WATER TEMPERATURE SITES

Simulation period: June 21 to Sept. 20
14 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

The actual clustering analysis was performed 

using a proprietary methodology developed by 

Advanced Data Mining, LLC of Greenville, South 

Carolina1. All continuous hourly water temperature 

time series data, for the period from June 21 to 

September 20, 1999, from all 142 sites were converted 

into an intermediate representation of characteristics to 

which k-means clustering is applied. The k-means 

clustering implementation used was provided by the 

Data Miner Software Kit (DMSK) package (Weiss and 

Indurkhya, 1998). For k number of groups, clustering 

analysis optimizes which members of the overall group 

of 142 should be in groups 1-k based on the cumulative 

distances between each vector and the mean of that 

vector’s group.

As the number of groups is increased, the RMSE 

(which is computed by the DMSK software and 

described on pages 102-103 of Weiss and 

Indurkhya,1998) decreases as shown in figure 6. 

Sometimes the optimal number of groups can be 

selected at the inflection point between a sharp vertical 

decline and a horizontal plateau. However, this plot did 

not have a marked decline. The RMSE for three, four, 

and five group clustering was 0.104, 0.098, and 0.092, 

respectively. The three group clustering, which would 

yield three separate models, was the optimal number of 

groups. The four- or five-group clustering yielded 

lower RMSE; however, the number of sites in some of 

the groups was insufficient for model creation.

1The proprietary clustering methodology is available through: Advanced Data Mining, LLC, 3620 Pelham Road, PMB #351, 

Greenville, South Carolina, 29615-5044; email: ed.roehl, ed@advdatamining.com; http://www.advdatamining.com, telephone: 864-

676-9790.

NUMBER OF GROUPS

0.04

0.06

0.08

0.10

0.12

0.14

0.16

ROOT MEAN SQUARE ERROR

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Figure 6. Results of clustering analysis. 
Model Development 15

The distribution of the sites across western 

Oregon for each of the three groups is shown in 

figure 7. Group 1 sites are generally located in warmer 

climate regions at lower elevations and in the southern 

portion of the study area. This includes the Klamath 

Mountains ecoregion and the Willamette River Valley 

lowlands. However, group 2 sites are more 

predominant at higher elevations, particularly in the 

Cascades. Group 3 sites are not restricted to any 

geographic area in western Oregon. Figure 8 shows the 

mean of all the normalized 24-hour moving average 

temperatures of all the sites for each of the three 

groups. All 24-hour moving average temperatures for 

all 142 time series (using a common period of record 

from June 21 to September 20, 1999) were normalized 

to values between 0 and 1. Normalizing was done by 

first subtracting the minimum 24-hour moving average 

temperature in a time series (for the period of record) 

from each 24-hour moving average temperature in that 

time series. All these values were then divided by the 

difference between the maximum and minimum 24-

hour moving average temperatures (for the period of 

record) in that time series. The mean of the normalized 

values for all time series in a group was then calculated 

into a single time series for that group. These three time 

series, for the three groups, are what is shown in the 

figure.

Figure 8 shows that in June and July, 

temperatures for group 2 remained low (in relation to 

its period of record) due to the influence of an extended 

season of snowpack in 1999. Group 1, which has many 

sites at lower elevations and in the southern coast 

region, are influenced by maritime climatic changes 

and have some of their highest temperatures in June 

and July. Group 1 had its lowest temperatures in 

September, and group 2 had its highest temperatures in 

August. Group 3 followed a trend in between the two 

other groups. Because of these differences, it was 

possible to make more accurate and robust models by 

subdividing the pool of 142 sites into these 3 groups.

Model Framework

All the ANN models made in this study were 

developed using the Neural Fusion (NNModel32 

Version1.0) software package2. The models were 

developed as a linked series which, when used in a 

consecutive order, can provide a user with a time series 

of simulated hourly temperatures for a stream site of 

interest (fig. 9). The period of the simulated time series, 

June 21 to September 20, encompasses the warmest 

period of a typical year.

The group assignment model determines into 

which of the three groups, determined in the clustering 

analysis, a site would fall. This model uses static site 

data (stream habitat and basin characteristics listed in 

table 1) as input variables.

Using a decomposition approach, the hourly time 

series was broken into static, chaotic, and periodic 

components (as shown in equation 4). Separate ANN 

models were created for each component. The static 

component predicts the mean temperature for the 

modeling period (June 21 to September 20). The 

chaotic component (as shown in equation 5) predicts 

the normalized 24-hour moving average temperature. 

The periodic component (as shown in equation 6) 

predicts the normalized residual of the 24 hour period. 

The breakdown of these components is shown in the 

following:

HOURLY = MEANT + NAVG24 + NHOURLY (4)

where

HOURLY is hourly temperature,

MEANT is the mean of hourly 

temperature for the simulation 

period (static component),

NAVG24 is the normalized 24-hour 

moving average temperature 

(chaotic component), and

NHOURLY is the normalized 24-hour 

residual (periodic component).

2All property rights of Neural Fusion software are owned by: EnvaPower, Inc, 90 Windom Street, Suite 2A, Boston, MA 02134 Phone:

617-254-5300; email: info@envapower.com; http://www.envapower.com.
16 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

GROUPS OF STREAM

 TEMPERATURE STATIONS

Group 2

Group 3

Group 1

0 10 20 30 50 60 MILES 40

0 10 20 30 50 60 KILOMETERS 40

EXPLANATION

DRAINAGE BASIN BOUNDARY

Portland

Corvallis

Eugene

Ashland

WASHINGTON

PACIFIC OCEAN

Eastern Oregon

CALIFORNIA

124 ̊ 123 ̊ 122 ̊ 

46 ̊

45 ̊

44 ̊

43 ̊

42 ̊

Figure 7. Distribution of the three groups of stream temperature stations within the study area.
Model Development 17

Mean of normalized 24-hour moving average hourly water temperature time series

0

0.1

0.2

20 25 30 10 5 20 30 4 9 14 19 24 29 3 13 15 25 8

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Group 1

Group 2

Group 3

JUNE JULY

1999

AUGUST SEPTEMBER

Figure 8. Mean of normalized 24-hour moving average hourly water temperature time series from each of the three groups.
18 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Chaotic ANN models (Groups 1-3)

Simulates NAVG24, normalized moving average component

Moving average ANN models (Groups 1-3)

Simulates 24-hour moving average

temperature time series

Periodic ANN models (Groups 1-3)

Simulates NHOURLY, normalized hourly component

Hourly ANN models (Groups 1-3)

Simulates Hourly temperature time series

Hourly

temperature

time series

output

24-hour moving

average temperature

time series

output

1999 hourly

climate data from

western Oregon

locations

Site specific

data collected by

the user

Static ANN model

Simulates MEANT,

mean stream temperature

for 1999 simulation period

Groups assignment ANN model

Simulates G1, G2, or G3,

group assignment values

Figure 9. Components of artificial neural network water temperature models.
Model Development 19

The chaotic component is computed as:

NAVG24 = 24AVG - MEANT (5)

where

The periodic component is computed as:

NHOURLY = HOURLY - MEANT - NAVG24 (6)

To predict the static component, a single ANN 

model was used for all 142 sites. Like the group 

assignment model, only static site data (stream habitat 

and basin characteristics listed in table 1) were used as 

input variables.

For the chaotic and periodic components, 

separate sets of ANN models were created for each of 

the three groups. It was also necessary to subdivide 

both groups 2 and 3 into their own northern and 

southern zones. This was done because the size of the 

input files for these groups would have exceeded 

storage capacity of the ANN software. The dividing 

line separating group 2 is at latitude 44 degrees 34 

minutes 12 seconds (44.57 in decimal degree units), 

and the dividing line separating group 3 is at latitude 44 

degrees 18 minutes 0 seconds (44.30 in decimal degree 

units).

Separate sets of models were made for each zone 

in groups 2 and 3. In all, a total of five separate sets of 

models (for the chaotic and periodic components) were 

developed. 

The input variables for the chaotic models 

included static site data (stream habitat and basin 

characteristics as listed in table 1) and normalized 

hourly 24-hour moving average climate station data for 

the period of June 21 to September 20, 1999. As 

described earlier, non-Corvallis climate stations (listed 

in table 2) were normalized using Corvallis data. The 

input variables for the periodic models included static 

site data and normalized hourly climate station data.

Two final models for each group and zone were 

developed to simulate hourly and 24-hour moving 

average water temperature time series. The hourly 

model used simulated static (MEANT), chaotic 

(NAVG24), and periodic (NHOURLY) values as input 

variables. The 24-hour moving average model used 

simulated static (MEANT) and chaotic (NAVG24) 

values as input variables. The linkages between the 

models are illustrated in figure 9.

Training

For each model, a training matrix was arranged 

with a row for each data vector and a column for each 

input or output variable. The matrices for the group 

assignment and static component models had 142 rows 

(or data vectors), which contained stream habitat and 

basin characteristics as input variables for each site. 

These matrices also contained 142 output variables for 

either group assignment or mean seasonal temperature. 

However, the matrices for the chaotic and periodic 

models, which used hourly meteorological time series 

data as input, contained thousands of rows (or data 

vectors). For example, the matrix for the northern zone 

of group 3, which has 41 sites, has 86,216 rows. 

Although each site contained a varying number of rows 

of data depending on the length of its data collection 

period from June to September, many sites contained 

approximately 2,000 rows of hourly time series data. 

The time series data sets for each site were stacked on 

top of each other in the matrix for that model. The 

chaotic and periodic model matrices also contained 

some columns of static variable data. These columns 

had the same value for all the rows (approximately 

2,000) that pertained to the same site. 

Analogous to statistical software used to create 

multiple regression models, the ANN modeling 

software creates a model based on input and output 

variable data sets and provides a coefficient of 

determination (R-square) and RMSE terms in the 

results. The software also allows the user to randomly 

divide the data points into separate training and testing 

sets. Approximately one-third of the data vectors were 

used for model training and the remaining two-thirds 

were used for model testing. During the training 

process, the ANN model is developed from just the 

training data set. The software then tests (or validates) 

the model using the testing data set. Often an indication 

of “overtraining” occurs if both the coefficient of 

determination and RMSE terms for the testing data set 

are significantly lower and higher, respectively, than 

these terms for training data set.

24AVG is the 24-hour moving average hourly 

temperature data.
20 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

During each training session, continual 

adjustments are automatically made to the model 

weights and bias terms to maximize the coefficient of 

determination and minimize the RMSE. The simulation 

is completed when the coefficient of determination and 

RMSE terms have stabilized. At the beginning of the 

training process, all available input variables were 

used. For each subsequent training simulation, those 

input variables having an insignificant relation to the 

output variable, based on a sensitivity analysis, were 

removed. However, a model with too few input 

variables can produce a model that has a higher error 

and a lower coefficient of determination. The statistical 

results for all the models are shown in table 3. 

Coefficients of determination and the RMSE for the 

models ranged from 0.88 to 0.99 and 0.05 to 0.59 oC, 

respectively. Tables containing the model input 

variables used in the group assignment, static 

component, chaotic component, and periodic 

component models are in Appendix B. These tables 

also include the sensitivity analysis results for each 

model and lists the input variables in their order of 

importance. Critical input variables for most of the 

models typically included riparian shade, site elevation, 

and percent forested area of the basin. Model operation 

instructions are shown in Appendix C.

Table 3. Statistical results for the training and testing of simulations for each model

[Abbreviations: RSQ, coefficient of determination; N, number of data points; Tobs, measured hourly water temperature; Tsim, simulated hourly water 

temperature. A smaller root mean square error (RMSE) is an indication of more accurate model performance; –, number of data points was too small for testing. 

RMSE, root mean square error = 

Model

Training Testing

RSQ RMSE N RSQ RMSE N

Group assignment–Group 1 0.98 0.05 142 – – –

Group assignment–Group 2 0.93 0.13 142 – – –

Group assignment–Group 3 0.95 0.11 142 – – –

Static 0.96 0.59 142 – – –

Chaotic–Group 1 0.94 0.41 5,383 0.93 0.44 21,946

Periodic–Group 1 0.92 0.40 4,190 0.87 0.52 17,148

Moving average–Group 1 0.98 0.59 5,543 0.98 0.59 21,786

Hourly–Group 1 0.99 0.57 4,190 0.98 0.66 17,148

Chaotic Group 2 North 0.98 0.21 9,889 0.98 0.23 39,860

Periodic Group 2 North 0.88 0.26 8,436 0.86 0.29 33,466

Moving average–Group 2 North 0.99 0.23 9,997 0.99 0.23 39,752

Hourly–Group 2 North 0.99 0.29 8,436 0.98 0.32 33,466

Chaotic Group 2 South 0.98 0.24 8,254 0.98 0.26 33,267

Periodic Group 2 South 0.94 0.23 6,610 0.88 0.33 26,635

Moving average–Group 2 South 0.99 0.26 8,245 0.99 0.26 33,276

Hourly–Group 2 South 0.99 0.33 6,575 0.99 0.33 26,670

Chaotic Group 3 North 0.96 0.30 10,194 0.96 0.32 41,285

Periodic Group 3 North 0.89 0.34 8,156 0.85 0.39 32,323

Moving average–Group 3 North 0.98 0.32 10,440 0.98 0.32 41,039

Hourly–Group 3 North 0.98 0.36 8,156 0.98 0.40 32,323

Chaotic Group 3 South 0.98 0.22 9,382 0.97 0.25 38,459

Periodic Group 3 South 0.93 0.27 7,225 0.90 0.32 28,629

Moving average–Group 3 South 0.99 0.26 9,694 0.99 0.26 38,147

Hourly–Group 3 South 0.99 0.27 7,225 0.98 0.32 28,629

1

N

--- ( ) Tobs Tsim – 2

n = 1

N

∑
Model Development 21

Validation

 Prior to model development, 6 stream sites were 

randomly removed from the original data set of 148 

sites and not used in the ANN model training process. 

The location of these sites is shown in figure 10, and 

their stream habitat and basin characteristics data are 

listed in table 4.

To determine the group assignment for each of 

the six sites, stream habitat and basin characteristics 

data from each site were entered into the group 

assignment model. The sites were all assigned to 

groups 2 and 3. Based on the latitude of each site, the 

sites were further assigned to either the northern or 

southern zone. None of the six sites happened to fall 

into group 1.

Stream habitat and basin characteristics data 

from each site also were entered into the static model to 

simulate the mean water temperatures for the 

simulation period from June 21, 1999 to September 20, 

1999. A comparison of the difference between 

measured and simulated mean temperatures for the six 

sites is shown in table 5. With the exception of Palmer 

and Fisher Creeks, the differences were less than 1 oC.

The static model simulated mean temperature for 

Fisher Creek was approximately 3 oC warmer than the 

measured mean temperature. Out of the entire set of 

148 sites that were used in the study, the elevation of 

the Fisher Creek site was one of the highest. Because of 

a limited representation of high elevation sites in the 

model, the static model may not have performed as 

well at this elevation. The Fisher Creek Basin also may 

have been an aberration compared to other basins in the 

same region. The influence of the heavy spring 

snowpack in 1999 could have been more persistent in 

the Fisher Creek Basin and made water temperatures 

cooler than expected. Cooler than expected water 

temperatures also could be the result of ground water 

inflows from possible springs and cold-water pockets 

just upstream of the site. As a result, the site specific 

data collected at Fisher Creek, and used for the model 

input variables, may not have adequately represented 

these cooling ground-water influences.

 The static model simulated mean temperature 

for Palmer Creek was approximately 2 oC Celsius 

warmer than the measured mean temperature. The 

Palmer Creek site is a low elevation agricultural basin 

in the Willamette Valley. The streambank 

(STRMBDEN) and mid channel (MIDCHDEN) shade 

densiometer measurements for this site were high, 

because of the presence of thick riparian vegetation. 

However, the percentage of basin forest area 

(BASFOREA) and percentage of stream channel forest 

area (STCHFORA) estimations for this site were very 

low. It is possible that this discrepancy caused some 

problems for the static model in estimating a mean 

seasonal value. Higher BASFOREA and STCHFORA 

values would have yielded a lower mean seasonal 

value.

Using the chaotic and periodic models, 24-hour 

moving average and hourly water temperature time 

series were simulated for the six sites. A comparison of 

measured and simulated 24-hour moving average water 

temperatures for the sites are shown in figure 11. These 

figures show how well the combination of just the 

static and chaotic models (without the periodic model) 

performed. Figure 12 shows a comparison of measured 

and simulated hourly water temperatures. The RMSE 

between measured and simulated 24-hour moving 

average water temperatures for the sites are shown in 

table 5. These errors are a measure of the combined 

performance of the static and chaotic models. Table 5

also shows the RMSE between measured and simulated 

hourly water temperatures for the sites. These errors 

are a measure of the combined performance of static, 

chaotic, and periodic models. A measure of how well 

just the periodic models performed can be inferred by 

the difference between these two types of errors.

For Palmer Creek, the static model, which uses 

only site data (field measurements and GIS derived 

basin characteristics) as input, simulated a seasonal 

error greater than 2 oC. However, the effect of the 

chaotic and periodic models appears to have 

compensated and reduced the error. The RMSE for the 

hourly temperature values (table 5) was approximately 

1 oC. 

For Boardtree Creek, the RMSE for hourly 

temperatures was 0.6 oC greater than the RMSE for 24-

hour moving average hourly temperatures. This 

difference was an indication of error from the periodic 

model as shown in figure 12D. Boardtree Creek is a 

well shaded low elevation site. Some of the low 

elevation sites included in the modeling data set of 142 

sites were not as well shaded as Boardtree Creek. This 

would provide some explanation as to why the 

simulated daily variation was greater than the measured 

daily variation.
22 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

EXPLANATION

VALIDATION SITE AND NUMBER—See table 8

Maroney Creek near Fairdale

0 10 20 30 50 60 MILES 40

0 10 20 30 50 60 KILOMETERS 40

Mack Creek near McKenzie Bridge

Boardtree Creek near Gillespie Corners

Fisher Creek near McCredie Springs

Beaver Creek near Drew

2 Palmer Creek at Dayton

3

4

5

6

1

DRAINAGE BASIN BOUNDARY

Ashland

1

2

3

4 5

6

Portland

Corvallis

Eugene

WASHINGTON

PACIFIC OCEAN

Eastern Oregon

CALIFORNIA

124 ̊ 123 ̊ 122 ̊ 

46 ̊

45 ̊

44 ̊

43 ̊

42 ̊

Figure 10. Location of model validation sites.
Model Development 23

Table 4. Location, stream habitat, and basin characteristics data for the validation stream sites

Model label

Stream sites

Maroney

Creek

Palmer

Creek

Mack

Creek

Boardtree 

Creek

Fisher

Creek

Beaver

Creek

Latitude (degree, minute, second) 45 21 48 45 13 09 44 13 10 43 56 31 43 51 56 42 56 34

Longitude (degree, minute, second) 123 23 10 123 04 15 122 10 02 123 10 41 122 08 11 122 49 05

STRMRB 8.5 315.95 333.67 301.11 250.87 359.81

SLOPEPCT 7.05 0.23 8.46 0.74 2.02 1.48

STRMBDEN 97.86 94.12 90.64 93.58 98.4 95.88

MIDCHDEN 92.11 79.28 80.08 87.57 97.59 82.62

DEPTH 21.82 107.73 18.51 51.45 34.2 12.64

WETTEDWD 2.73 5.83 4.52 3.03 6.05 6.31

SBSUBSTF 0 90.91 1.8 63.64 12.73 3.64

SBSUBSTS 14.55 0 0 10.91 5.45 9.09

SBSUBSTG 29.09 0 14.6 23.64 20 18.18

SBSUBSTC 38.18 9.09 41.8 0 50.91 41.82

SBSUBSBO 18.18 0 38.2 1.82 10.91 20

SBSUBSBE 0 0 3.6 0 0 7.27

BASBEARA 76 17 297 348 320 298

BASBEARS 0.9703 0.2924 -0.8910 -0.2079 -0.6428 -0.8829

BASBEARC 0.2419 0.9563 0.4540 0.9781 0.7660 0.4695

STRMCHBE 43 17 320 350 320 300

BASINKM2 3.38 82.35 5.27 4.6 28.16 89.03

BASMELEV 557.85 76.77 1221.49 302.71 1315.73 973.61

BASOELEV 216.4 23 779.9 197.2 815.1 410.9

BASXELEV 786 355 1625.8 423.6 1735.5 1563.4

STCHMELV 417.56 34.49 993.77 225.9 932.61 592.98

BASMSLOP 38.71 6.08 46.89 20.93 38.25 29.28

STMCHSLO 7.05 0.07 10.4 1.78 1.92 2.23

BASFOREA 85.93 0.85 100 89.44 99 89.4

BASOPENA 14.07 99.15 0 10.56 1 10.6

DENBASFA 97.18 98.04 91.32 94.86 90 85.28

STCHFORA 78.33 0 100 94.57 100 100

STCHOPA 21.67 100 0 5.43 0 0

DNSTCHFA 93.02 0 92.95 89.1 95.39 86.52

BASMSATC 13.76 16.74 14.26 16.34 13.67 15.69

STMSUATC 13.82 16.82 14.23 16.33 13.79 15.72

OUTMSATC 14.28 16.72 14.28 16.33 14.22 16.44

XCOORD 0.3809 0.4914 0.8636 0.4522 0.8267 0.5826

YCOORD 0.8060 0.7707 0.5590 0.4602 0.4425 0.2174
24 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

For Mack Creek, the static model, which uses 

only site data (field measurements and GIS basin 

characteristics) as input, was able to simulate the mean 

temperature of the simulation period to within almost 

0.3 oC of measured mean temperature (table 5). The 

periodic component also appeared accurate (fig. 12C). 

However, the chaotic model component generally 

under simulated. The chaotic component is dependent 

on various climatic time series inputs. Most of the 

climate data were collected at larger towns, which are 

at lower elevations. These climate stations may not 

have been adequate to represent the climate near Mack 

Creek, which is at a higher elevation than most basins 

and located closer to the eastern edge of the study 

region.

Interestingly, the chaotic and periodic simulated 

components for Fisher Creek did not appear to 

contribute significant error to the simulated 24-hour 

moving average and hourly temperatures (figs. 11E and 

12E). However, the simulated mean temperature, for 

possible reasons explained above, was greater than the 

measured mean temperature. With the exception of 

being shifted upwards, the simulated hourly 

temperatures appear to be almost identical to the 

measured hourly temperatures.

If a model user were to make several 

instantaneous temperature measurements at a site 

during the simulation period (from June to September), 

it might be possible to combine this measured 

information with the simulated results. If the measured 

measurements are consistently above or below the 

simulated hourly time series by the same magnitude, it 

would seem reasonable for the model user to shift the 

simulated time series accordingly. During the 1999 

field surveys to the 148 sites used in the study, a 

manual instantaneous temperature measurement was 

made at each site with a lab calibrated thermometer. 

(These measurements were made for verification of the 

temperature data loggers.) The Fisher Creek site field 

survey was made on August 24, 1999. The 

instantaneous water temperature measurement, made at 

1430, was 10.8 oC. The model simulated a water 

temperature of 13.2 oC for the same date and time. 

With a difference of 2.4 oC, a downward shift was then 

applied to the simulated time series as shown in figures 

11E and 12E. This resulted in a much closer match 

with the measured time series.

Although the models performed less adequately 

for some sites at higher elevations, the model error in 

this study were comparable to model error in other 

water temperature regionalization studies in Georgia 

and Washington (Dyar and Alhadeff, 1997; Collings, 

1973). Those two studies used a harmonic (sinusoidal) 

function to predict daily mean water temperatures. 

Differences between the measured and predicted 

harmonic curves were sometimes greater than 5 oC for 

some sites.

Table 5. Comparison of static, 24-hour moving average, and hourly model errors for the simulation period (June 21, 1999, to September 20, 1999) for the 

validation stream sites

[Abbreviations: oC, degrees Celsius; N, number of data points; Tobs, measured hourly water temperature; Tsim, simulated hourly water temperature; Model 

error: Static model error, measured mean temperature of the simulation period – simulated mean temperature of the simulation period; RMSE, root mean 

square error = 

Stream sites

Maroney

Creek

Palmer

Creek

Mack

Creek

Boardtree 

Creek

Fisher

Creek

Beaver

Creek

Static model error (oC) -0.72 -2.21 0.32 0.31 -3.18 0.19

24-hour moving average model 

error (RMSE) (oC)

0.70 0.95 2.77 0.97 2.41 0.49

Hourly model error (RMSE) (oC) 0.84 1.05 3.04 1.63 2.32 0.64

1

N

--- ( ) Tobs Tsim – 2

n = 1

N

∑
Model Development 25

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20 9

10

11

12

13

14

15

16

WATER TEMPERATURES

Measured

Simulated

JUNE JULY AUGUST SEPTEMBER

1999

6

7

8

9

10

11

12

13

14

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

A. Maroney Creek near Fairdale, Oregon

B. Palmer Creek at Dayton, Oregon

C. Mack Creek near McKenzie Bridge, Oregon

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

15

16

17

18

19

20

21

22

23

WATER TEMPERATURE, IN DEGREES CELSIUS

Figure 11. Measured and simulated 24-hour moving average hourly water temperatures for selected sites in western 

Oregon.
26 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

10

11

12

13

14

15

16

17

18

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

WATER TEMPERATURE, IN DEGREES CELSIUS

5

6

7

8

9

10

11

12

13

14

WATER TEMPERATURES

Measured

Simulated

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

Shifted Simulated

12

13

14

15

16

17

18

19

20

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

JUNE JULY AUGUST SEPTEMBER

1999

D. Boardtree Creek near Gillespie Corners, Oregon

E. Fisher Creek near McCredie Springs, Oregon

F. Beaver Creek near Drew, Oregon

Figure 11.—Continued.
Model Development 27

8

9

10

11

12

13

14

15

16

17

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

WATER TEMPERATURES

Measured

Simulated

23

12

13

14

15

16

17

18

19

20

21

22

WATER TEMPERATURE, IN DEGREES CELSIUS

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

JUNE JULY AUGUST SEPTEMBER

1999

A. Maroney Creek near Fairdale, Oregon

B. Palmer Creek at Dayton, Oregon

Figure 12. Measured and simulated hourly water temperatures for selected sites in western Oregon.
28 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20 5

6

7

8

9

10

11

12

13

14

15

WATER TEMPERATURES

Measured

Simulated

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

JUNE JULY AUGUST SEPTEMBER

1999

9

10

11

12

13

14

15

16

17

18

19

20

WATER TEMPERATURE, IN DEGREES CELSIUS

C. Mack Creek near McKenzie Bridge, Oregon

D. Boardtree Creek near Gillespie Corners, Oregon

Figure 12.—Continued.
Model Development 29

WATER TEMPERATURES

Measured

Simulated

Shifted Simulated

5

6

7

8

9

10

11

12

13

14

15

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

E. Fisher Creek near McCredie Springs, Oregon

F . Beaver Creek near Drew, Oregon

21

22

10

11

12

13

14

15

16

17

18

19

20

WATER TEMPERATURE, IN DEGREES CELSIUS

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

JUNE JULY AUGUST SEPTEMBER

1999

Figure 12.—Continued.
30 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

MODEL APPLICATION

Shade Adjustment

A major objective of the study was creating a 

model that could be used to simulate water 

temperatures representing “natural” (undisturbed) 

conditions at stream sites in western Oregon that 

currently are in a disturbed state. Water-quality 

professionals in regulatory agencies need this 

information to be able to (1) set reach-specific 

temperature standards that have a scientific basis, (2) 

identify and prioritize stream reaches that are grossly 

out of compliance and in most need of remediation, and 

(3) establish attainable temperature-reduction goals for 

reaches that have elevated water temperatures.

A model user must still measure and collect 

existing riparian field data at a site of interest. 

However, in addition to simulating water temperatures 

for existing conditions, it is possible to simulate water 

temperatures for minimum and maximum shade 

scenarios by adjusting the measured values used for the 

shade and vegetation variables. These variables include 

streambank and mid channel densiometer shade 

measurements in addition to estimated percent of the 

basin that is forested or open. Table 6 shows existing 

and adjusted shade and vegetation variable values for 

the validation sites.

Two of the six validation stream sites, Mack 

Creek and Fisher Creek, were in pristine settings. 

Measured values for the shade and vegetation variables 

for these two sites already represented near maximum 

shade conditions. However, the other four sites, Palmer 

Creek, Maroney Creek, Boardtree Creek, and Beaver 

Creek, had measured values that were between the 

maximum and minimum values for the shade and 

vegetation variables. Using the variable values shown 

in table 6, minimum and maximum shade scenarios 

were simulated for Maroney Creek, Boardtree Creek, 

and Beaver Creek. Because the existing shade for 

Palmer Creek was already minimal, only the maximum 

shade scenario was simulated for that site. Results for 

the adjusted shade simulations are shown in table 7. 

The simulated 24-hour moving average temperature 

time series for the minimum and maximum shade in 

addition to the existing conditions are shown in 

figure 13. Maximizing shade at Palmer Creek resulted 

in the greatest decrease in water temperature, 

approximately 4 oC on average. However, maximizing 

shade at Maroney Creek, which was already reasonably 

well shaded, decreased water temperature only by 

approximately 0.5 oC on average.

Like any statistical models, ANN models have 

their limitations as tools for extrapolation. These 

models become more unstable when they are asked to 

make predictions based on inputs that may be outside 

the boundaries of the input data set used to create the 

models. An indication of this instability can be seen in 

figure 13A. Simulated water temperatures under 

minimum shade conditions at Maroney Creek are 

unrealistically low for a few days in early July. 
Model Application 31

Table 6. Existing and adjusted shade and vegetation variable values for selected stream sites

Model label Explanation

Existing conditions Simulated conditions

Maroney

Creek

Palmer

Creek

Boardtree

Creek

Beaver

Creek

Minimum

shade

Maximum

shade

STRMBDEN Stream bank densiometer 

(percent)

97.86 94.12 93.58 95.88 33 100

MIDCHDEN Midchannel densiometer 

(percent)

92.11 79.28 87.57 82.62 5 100

BASFOREA Basin forest area 

(percent)

85.93 0.85 89.44 89.4 5 100

BASOPENA Basin open area 

(percent)

14.07 99.15 10.56 10.6 95 0

STCHFORA Stream channel forest area 

(percent)

78.33 0 94.57 100 5 100

STCHOPA Stream channel open area 

(percent)

21.67 100 5.43 0 95 0

Table 7. Mean of simulated hourly temperatures for varying shade conditions for selected stream sites

[Mean temperature: Mean of simulated hourly water temperatures for the simulation period from June 22, 1999, to September 20, 1999; Abbreviations: (

oC), 

degrees Celsius; –, no data]

Shade 

condition

Maroney Creek Palmer Creek Boardtree Creek Beaver Creek

Mean 

temperature 

(

oC)

Difference 

from existing 

shade (

oC)

Mean 

temperature 

(

oC)

Difference 

from existing 

shade (

oC)

Mean 

temperature 

(

oC)

Difference 

from existing 

shade (

oC)

Mean 

temperature 

(

oC)

Difference 

from existing 

shade (

oC)

Minimum 15.44 +3.09 – – 17.38 +3.07 17.64 +1.75

Existing 12.36 – 18.83 – 14.32 – 15.89 –

Maximum 11.83 -0.53 14.68 -4.15 12.72 -1.59 13.62 -2.27

Climate Adjustment

Time series output from the ANN models 

simulated hourly water temperatures representing 

climatic conditions from June 21 to September 20, 

1999. However, the summer of 1999 in western Oregon 

was cooler and wetter than normal. Table 8 shows the 

departure of 1999 mean monthly water temperatures 

from the period of record of long-term USGS water 

temperature monitoring stations in western Oregon. 

These stations are located on relatively unregulated 

streams ranging from large rivers to creeks. They are 

generally in the northern and southern regions of the 

study area. Unregulated long-term stations in the 

central region of the study area were less common.
32 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

WATER TEMPERATURES

Minimum shade

Existing shade

Maximum shade

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

10

9

8

11

12

13

14

15

16

17

18

WATER TEMPERATURE, IN DEGREES CELSIUS

15

14

13

16

17

18

19

20

21

22

23

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

JUNE JULY AUGUST SEPTEMBER

1999

A. Maroney Creek near Fairdale, Oregon

B. Palmer Creek at Dayton, Oregon

Figure 13. Simulated 24-hour moving average hourly water temperatures for varying shade conditions for selected 

sites in western Oregon.
Model Application 33

Figure 13.—Continued.

WATER TEMPERATURES

Minimum shade

Existing shade

Maximum shade

9

20

10

11

12

13

14

15

16

17

18

19

WATER TEMPERATURE, IN DEGREES CELSIUS

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20

C. Boardtree Creek near Gillespie Corners, Oregon

D. Beaver Creek near Drew, Oregon

21

20

10

11

12

13

14

15

16

17

18

19

JUNE JULY AUGUST SEPTEMBER

1999

25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 20
34 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Table 8. Departure of 1999 mean monthly water temperatures from the period of record at selected stations in western Oregon

[Abbreviations: USGS, U.S. Geological Survey; (oC), temperature in degrees Celsius; (km2), square kilometers; Sept., September; –, data not available]

USGS 

station 

No.

Station name Drainage 

area (km2)

Period of 

record

Temperature difference (

oC)

June July August Sept.

11492200 Crater Lake near Crater Lake, Oregon 67.9 1979-00 -2.3 -2.3 -1.1 -0.2

14138850 Bull Run River near Multnomah Falls, Oregon 124 1978-01 -1.9 -1.1 -0.1 -0.9

14138870 Fir Creek near Brightwood, Oregon 14.1 1978-00 -1.5 -0.9 -0.2 -0.4

14138900 North Fork Bull Run River near Multnomah Falls, Oregon 21.5 1979-00 -0.8 -0.5 -0.1 -0.6

14139800 South Fork Bull Run River near Bull Run, Oregon 39.9 1979-01 -1.4 -1.2 -0.2 -0.7

14200400 Little Abiqua Creek near Scotts Mills, Oregon 25.4 1993-00 -0.2 -0.5 0.39 0.0

14201300 Zollner Creek near Mount Angel, Oregon 38.8 1993-01 -0.6 -1.2 0.16 -1.0

14207200 Tualatin River at Oswego Dam near West Linn, Oregon 1,829 1991-01 -0.5 – -0.1 -0.1

14246900 Columbia River at Beaver Army Terminal, Oregon 665,371 1993-00 -0.7 -1.1 -0.2 -0.2

14330000 Rogue River below Prospect, Oregon 982 1977-00 -2.0 -1.0 -0.3 -0.5

14337500 Big Butte Creek near McLeod, Oregon 635 1979-00 -1.0 -0.8 -0.2 -0.2

14337870 West Branch Elk Creek near Trail, Oregon 36.8 1978-00 -1.0 -1.1 -0.6 -1.6

14338000 Elk Creek near Trail, Oregon 334 1979-00 -2.5 -1.0 1.3 0.4

14369500 Applegate River near Applegate, Oregon 1,808 1979-01 -2.0 -1.1 -1.1 -1.1

Some possible options for the model user in 

dealing with year to year climate variations include:

(1) Simulate hourly water temperature time 

series for a non-1999 year (or years) of interest for a 

stream site of interest. To do this, the user would need 

to acquire hourly climatological time series data for the 

simulation period (June 21 to September 20) for the 

non-1999 year that were collected at the same 25 

climate stations in western Oregon used in the model 

development. If data from a certain station were 

unavailable, interpolation techniques would have to be 

used to recreate the time series. The the non-1999 year 

climatological time-series data would also have to be 

normalized to Corvallis and Eugene climatological 

time-series data before it is used as input to the models.

(2) Adjust computed 1999 mean monthly water 

temperature values. The user would simulate a water 

temperature time series for 1999 for a stream site of 

interest, and then compute the mean monthly values. 

These values would be then adjusted to the long-term 

climate trend using the mean-monthly departures for an 

appropriate station that is listed in table 8. As an 

example, table 8 shows that the mean water 

temperature for June 1999 at the Elk Creek station was 

2.5 oC less than the period of record mean water 

temperature for the month of June. A model user who 

is using the Elk Creek station as a guide would add 2.5 

oC to the June mean water temperature.

(3) Simulate a water temperature time series for 

1999 for a stream site of interest, and make no 

adjustments at all. The model user could state that their 

water temperatures time series output were simulated 

using 1999 climatological time-series as input, and that 

1999 was cooler and wetter than average for most 

locations in western Oregon. They could also include 

data from table 8 to show how much 1999 water 

temperatures departed from long-term water 

temperatures.

Future Improvements

Simulation results using data from the six 

validation sites suggest that water temperatures may be 

affected by upstream ground-water processes at some 

stream sites to a greater extent than originally thought. 

The specific physical habitat variables measured in the 

field surveys, and then subsequently used as model 

input, may not be adequate in capturing these 

anomalies. Future water temperature ANN modeling 

studies should investigate other possible physical 
Summary and Conclusions 35

habitat variables to include in the field surveys. When 

more information about a site and its upstream 

environment can be collected, a more reliable a 

temperature estimate can be made. A series of 

temperature measurements collected along the reach, 

even upstream of the defined reach used in the habitat 

survey, might locate significant springs and cold water 

pockets that are affecting water temperature at the site. 

Also, additional temperature measurements collected at 

the site at different dates during the summer period 

could be used to shift the simulated temperature time 

series if needed. 

SUMMARY AND CONCLUSIONS

Stream water temperature is a major concern in 

Oregon. Temperature affects dissolved oxygen 

concentrations, biochemical oxygen demand rates, 

algae production, and contaminant toxicity. 

Temperature also has a major effect on the distribution, 

health, and survival of native salmonids (salmon, trout, 

and charr) and other aquatic species. Although warm 

water temperatures occur naturally, they are also 

induced by anthropogenic activities such as effluent 

point sources, removal of riparian shade, stream 

channel alterations, water diversions, and urbanization. 

To reduce the effects of elevated water temperatures, 

the State of Oregon is developing Total Maximum 

Daily Load (TMDL) plans for stream reaches that 

exceed State standards. A reliable method of estimating 

water temperatures that reflect natural or undisturbed 

conditions for these currently disturbed reaches was 

needed. In response to this need, ANN models were 

developed to estimate “natural” water temperatures in 

small streams using data from at 148 sites throughout 

western Oregon from June to September 1999. The 

sites were located on 1st-, 2nd-, or 3rd-order streams 

having undisturbed or minimally disturbed conditions. 

Data collected at each site included continuous hourly 

water temperature and riparian habitat. Additional data 

pertaining to the landscape characteristics of the basins 

upstream of the sites were assembled using geographic 

information system techniques. Hourly meteorological 

time series data collected at 25 locations within the 

study region were also assembled.

Clustering analysis were used to partition 142 

sites into 3 groups. Separate models were developed for 

each group. The riparian habitat, basin characteristic, 

and meteorological time series data were independent 

variables and water temperature time series were 

dependent variables to the models, respectively. 

Approximately one-third of the data vectors were used 

for model training and the remaining two-thirds were 

used for model testing. Critical input variables included 

riparian shade, site elevation, and percent forested area 

of the basin. Coefficient of determination and the 

RMSE for the models ranged from 0.88 to 0.98 and 

0.05 to 0.59 oC, respectively. Final output from the 

models included simulated hourly and 24-hour moving 

average temperature time series from June to 

September.

The models also were tested using temperature 

time series, habitat, and basin landscape data from 6 

validation sites, located throughout the study area, that 

were not among the 142 sites that were used to develop 

the models. The error between measured and simulated 

hourly water temperatures for the simulation period for 

these sites ranged from 0.84 to 3.04 oC. This range of 

error is comparable to error in other water temperature 

regionalization studies. It is possible that error at some 

of the validation sites could be the result of the effect of 

ground-water processes (such springs and cold-water 

pockets) on water temperatures upstream of the site. 

These processes may not have been adequately 

identified and quantified during the site field surveys, 

and subsequently not used in the model formulation. 

The capabilities of the models might be improved with 

further research into the interactions between groundwater processes and water temperature.

The validation sites were also used to simulate 

water temperatures for minimum and maximum shade 

scenarios by adjusting the measured values used for the 

shade and vegetation variables. Maximizing shade at 

one site resulted in a decrease in water temperature of 

about 4 oC on average. However, maximizing shade at 

another site that was already heavily forested decreased 

water temperature by only about 0.5 oC.

The water temperature models developed in the 

study can estimate approximate natural water 

temperatures in small unregulated streams in western 

Oregon having either disturbed or undisturbed riparian 

conditions. This methodology should useful to 
36 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

agencies engaged in monitoring stream health. Using 

the models may save the expense of installing water 

temperature data loggers at a site. Estimates of water 

temperature under natural shade conditions, which can 

be scientifically defended, are needed for future TMDL 

activities. These models would not substitute the use of 

mechanistic water temperature modeling in the lower 

reaches of rivers in a TMDL study. However, output 

from the ANN models could be used as the upstream 

boundary input to the mechanistic models.

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38 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Appendix A. Site list for water temperature and habitat survey data collection—Continued

Site model 

label name

Latitude Longitude

Agency/Project Stream name

(degrees, minutes, and seconds)

abbott15 42 54 58 122 31 37 USGS/OWEB North Fork Abbott Creek near Union Creek, Oregon

anvil52 42 44 25 124 23 46 USGS/OWEB Anvil Creek near Port Orford, Oregon

bauns3 45 41 23 123 00 58 USGS/OWEB Unnamed tributary to Baunswick Canyon, Mountaindale, Oregon

bear29 44 58 54 123 52 57 USGS/OWEB Bear Creek near Rose Lodge, Oregon

bear39 43 32 58 122 12 40 USGS/OWEB Unnamed tributary to Bear Creek near Cascade Summit, Oregon

bear69 44 45 38 122 49 25 USGS/OWEB Bear Branch near Sublimity, Oregon

beaver21 42 56 34 122 49 05 USGS/OWEB Beaver Creek near Drew, Oregon

beaver25 44 51 01 122 49 29 USGS/OWEB Beaver Creek near Sublimity, Oregon

bickmo46 44 19 32 122 50 24 USGS/OWEB Bickmore Creek near Crawfordsville, Oregon

bigbnd56 43 25 20 122 36 01 USGS/OWEB Big Bend Creek near Steamboat, Oregon

boardt41 43 56 31 123 10 41 USGS/OWEB Boardtree Creek near Gillespie Corners, Oregon

canyon35 44 20 37 122 21 56 USGS/OWEB Canyon Creek near Upper Soda, Oregon

cast60 45 22 39 121 51 01 USGS/OWEB Cast Creek near Rhododendron, Oregon

champ67 45 15 10 122 52 58 USGS/OWEB Champoeg Creek near Butteville, Oregon

cheat64 44 42 07 121 55 20 USGS/OWEB Cheat Creek near Marion Forks, Oregon

coal36 44 58 21 122 30 23 USGS/OWEB Coal Creek near Wilhoit, Oregon

coast6 45 09 26 123 31 23 USGS/OWEB Coast Creek near Willamina, Oregon

cummin12 44 16 02 124 06 02 USGS/OWEB Cummins Creek near Yachats, Oregon

dickey62 44 55 54 122 03 05 USGS/OWEB Dickey Creek near Breitenbush Hotsprings, Oregon

dickey66 45 06 46 122 30 20 USGS/OWEB Dickey Creek near Molalla, Oregon

drift14 44 26 58 123 56 56 USGS/OWEB Drift Creek near Tidewater, Oregon

evans19 42 36 01 122 58 37 USGS/OWEB Evans Creek near Sams Valley, Oregon

fisher38 43 51 56 122 08 11 USGS/OWEB Fisher Creek near McCredie Springs, Oregon

fourbt18 42 30 15 122 26 08 USGS/OWEB Fourbit Creek near Butte Falls, Oregon

fourth28 44 48 05 123 42 55 USGS/OWEB Fourth of July Creek near Valsetz, Oregon

gales4 45 38 35 123 21 40 USGS/OWEB Gales Creek near Glenwood, Oregon

gribbl72 45 13 51 122 41 57 USGS/OWEB Gribble Creek near Barlow, Oregon

hamilt33 44 30 41 122 43 13 USGS/OWEB Hamilton Creek near Waterloo, Oregon

image63 44 58 15 122 19 50 USGS/OWEB Image Creek near Elkhorn, Oregon

indigo50 42 34 47 123 47 19 USGS/OWEB East Fork Indigo Creek near Galice, Oregon

junipr45 43 36 53 122 19 16 USGS/OWEB Juniper Creek near McCredie Springs, Oregon

kelsey10 43 46 38 122 15 23 USGS/OWEB Kelsey Creek near McCredie Springs, Oregon

kentuck30 43 26 47 124 06 21 USGS/OWEB Kentuck Creek near Allegany, Oregon

knob61 44 52 48 122 02 12 USGS/OWEB Knobrock Creek near Breitenbush Hotsprings, Oregon

little42 44 18 59 123 04 31 USGS/OWEB Little Muddy Creek near Halsey, Oregon

lobstr53 42 36 18 124 11 12 USGS/OWEB South Fork Lobster Creek near Illahe, Oregon

lonewo20 43 00 35 122 31 14 USGS/OWEB Lonewoman Creek near Union Creek, Oregon

marony40 45 21 48 123 23 10 USGS/OWEB Maroney Creek near Fairdale, Oregon

mcfee1 45 24 05 122 56 22 USGS/OWEB Mcfee Creek at Scholls, Oregon

moose34 44 25 32 122 23 16 USGS/OWEB Moose Creek near Cascadia, Oregon

Appendix A. Site list for water temperature and habitat survey data collection

[Agency/Project abbreviations: USGS, U.S. Geological Survey; OWEB, Oregon Watershed Enhancement Board; ODEQ/COAST, Oregon Department of 

Environmental Quality coastal study sites; ODEQ/REMAP, Oregon Department of Environmental Quality REMAP study sites; USFS, U.S. Forest Service]
Appendix A 39

muddy43 44 22 39 123 17 48 USGS/OWEB Muddy Creek near Bellfountain, Oregon

nell54 42 05 54 124 10 39 USGS/OWEB Nell Creek near Harbor, Oregon

nfpedee7 44 46 50 123 27 09 USGS/OWEB North Fork Pedee Creek near Pedee, Oregon

olalla22 43 06 49 123 30 22 USGS/OWEB Olalla Creek near Tenmile, Oregon

opal27 44 50 43 122 12 23 USGS/OWEB Opal Creek near Elkhorn, Oregon

palmer71 45 13 09 123 04 15 USGS/OWEB Palmer Creek at Dayton, Oregon

panther5 45 15 14 123 12 08 USGS/OWEB Panther Creek near Carlton, Oregon

poodle44 44 05 48 123 29 16 USGS/OWEB Poodle Creek near Noti, Oregon

powell55 42 15 51 123 18 00 USGS/OWEB Powell Creek near Williams, Oregon

rain57 43 08 56 122 25 20 USGS/OWEB Rainbow Creek near Clearwater, Oregon

redbl16 42 47 58 122 16 10 USGS/OWEB Red Blanket Creek near Crater Lake, Oregon

rock13 44 11 14 124 06 24 USGS/OWEB Rock Creek at Roosevelt Beach, Oregon

rock24 45 08 42 122 43 15 USGS/OWEB Rock Creek near Yoder, Oregon

rock26 44 42 33 122 25 16 USGS/OWEB Rock Creek near Gates, Oregon

sfm9 43 57 10 122 00 57 USGS/OWEB South Fork McKenzie River near Foley Springs, Oregon

south23 43 06 04 123 57 27 USGS/OWEB South Fork Elk Creek near Dora, Oregon

stilsn11 44 31 28 123 28 53 USGS/OWEB Stilson Creek near Wren, Oregon

tanner59 45 35 47 121 56 37 USGS/OWEB Tanner Creek near Bonneville, Oregon

tobe32 44 20 14 123 34 39 USGS/OWEB Tobe Creek near Alsea, Oregon

trail37 44 00 23 122 10 18 USGS/OWEB Trail Creek near Foley Springs, Oregon

trib68 45 16 58 122 49 21 USGS/OWEB Unnamed tributary to Willamette River near Butteville, Oregon

trout65 44 23 58 122 20 48 USGS/OWEB Trout Creek near Upper Soda, Oregon

tryon70 45 25 27 122 39 36 USGS/OWEB Tryon Creek at Lake Oswego, Oregon

warble2 45 34 11 122 57 19 USGS/OWEB Unnamed tributary to McKay Creek near North Plains, Oregon

wfa48 42 09 03 122 42 53 USGS/OWEB West Fork Ashland Creek near Ashland, Oregon

wfmill31 43 29 11 124 00 45 USGS/OWEB West Fork Millicoma River near Allegany, Oregon

wfmull51 42 43 38 123 52 31 USGS/OWEB West Fork Mule Creek near Marial, Oregon

wikiup17 42 36 35 122 17 22 USGS/OWEB Wickiup Creek near Rocky Point, Oregon

wolf58 43 13 53 122 56 52 USGS/OWEB Wolf Creek near Peel, Oregon

woods47 44 32 44 123 29 39 USGS/OWEB Woods Creek near Wren, Oregon

c3riv 45 10 42 123 45 57 ODEQ/COAST Three Rivers at River mile 10.1

cands 45 45 43 123 54 15 ODEQ/COAST Anderson Creek at River mile 2.73

cbensm 45 35 09 123 30 57 ODEQ/COAST Ben Smith Creek at River mile 0.44

cbig1 44 10 15 124 06 21 ODEQ/COAST Big Creek at River mile 0.79

cbrock 43 08 30 122 33 11 ODEQ/COAST Black Rock Fork at River mile 4.8

cbvr6 42 05 47 122 59 02 ODEQ/COAST Beaver Creek at River mile 6.44

cbvrm 45 17 05 123 49 21 ODEQ/COAST Beaver Creek at River mile 0.79

ccant 43 29 25 122 43 24 ODEQ/COAST Canton Creek at River mile 15.66

ccarp 45 30 29 123 07 30 ODEQ/COAST Carpenter Creek at River mile 1.7

cchrm 42 02 43 123 58 47 ODEQ/COAST Chrome Creek at River mile 0.22

Appendix A. Site list for water temperature and habitat survey data collection—Continued

Site model 

label name

Latitude Longitude

Agency/Project Stream name (degrees, minutes, and seconds)
40 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

cco 45 35 42 123 44 32 ODEQ/COAST Company Creek at River mile 0.76

ccoal 43 27 56 122 27 43 ODEQ/COAST Coal Creek tributary at River mile 2.0

ccum 44 15 58 124 05 24 ODEQ/COAST Cummins Creek at River mile 1.02

cdoneg 42 54 44 122 38 21 ODEQ/COAST Donnegan Creek at River mile 2.62

cdumnt 43 05 28 122 48 56 ODEQ/COAST Dumont Creek at River mile 4.95

cefwin 42 03 03 124 05 22 ODEQ/COAST East Fork Winchuck River at River mile 1.18

celkh 44 29 59 123 58 47 ODEQ/COAST Elkhorn Creek at River mile 1.56

cemile 43 14 44 122 47 40 ODEQ/COAST Emile Creek tributary at River mile 0.76

cfhwk 45 55 56 123 30 25 ODEQ/COAST Fishhawk Creek at River mile 1.07

cflyn 44 32 19 123 51 04 ODEQ/COAST Flynn Creek at River mile 1.71

cglen 44 56 52 123 06 04 ODEQ/COAST Glenn Creek at River mile 5.45

cgrav 45 44 55 123 50 15 ODEQ/COAST Gravel Creek at River mile 0.34

chalf 43 44 57 123 34 59 ODEQ/COAST Halfway Creek tributary at River mile 0.29

chall 42 46 07 124 01 45 ODEQ/COAST Hall Creek at River mile 1.48

chicks 42 39 17 124 00 57 ODEQ/COAST Hicks Creek off Highway 1160

cjjoe 42 31 25 123 29 00 ODEQ/COAST Jumpoff Joe Creek at River mile 1.17

cjord 45 33 10 123 29 24 ODEQ/COAST Jordan Creek at River mile 7.52

cking 43 44 26 122 53 22 ODEQ/COAST King Creek at River mile 0.24

clnest 45 05 39 123 47 05 ODEQ/COAST Little Nestucca at River mile 11.6

clnfw 45 29 08 123 44 08 ODEQ/COAST Little North Fork at River mile 1.5

cmhwk 44 15 32 122 44 12 ODEQ/COAST Mohawk River at River mile 22.13

cmidd 43 15 22 123 52 41 ODEQ/COAST Middle Creek at River mile 23.2

cmina 45 13 44 123 37 19 ODEQ/COAST Mina Creek at River mile 1.43

cmonty 44 34 50 123 55 43 ODEQ/COAST Montgomery Creek at River mile 0.91

cneha 45 44 33 123 17 05 ODEQ/COAST Nehalem River near River mile 109

cnest 45 16 41 123 33 02 ODEQ/COAST Nestucca River at River mile 38.6

cnfwlf 45 47 41 123 23 01 ODEQ/COAST North Fork Wolf Creek at River mile 0.45

cnmyrt 43 07 17 123 07 29 ODEQ/COAST North Myrtle Creek at River mile 14.3

cnorth 44 54 33 123 54 26 ODEQ/COAST North Creek at River mile 0.54

cobri 42 06 07 123 14 20 ODEQ/COAST Obrien Creek at River mile 0.9

cpeak 44 21 06 123 28 55 ODEQ/COAST Peak Creek at River mile 3.5

cpnthr 42 22 52 123 48 46 ODEQ/COAST Panther Creek at River mile 0.17

crck 44 11 12 124 06 21 ODEQ/COAST Rock Creek at River mile 1.5

credi 43 01 41 124 22 13 ODEQ/COAST Redibaugh Creek at River mile 1.33

croarr 44 37 49 122 44 16 ODEQ/COAST Roaring River at River mile 0.10

cschol 43 03 18 123 10 39 ODEQ/COAST School Hollow Creek at River mile 1.64

csfsmt 43 46 27 123 27 50 ODEQ/COAST South Fork Smith at River mile 0.83

cshas 42 34 23 124 02 03 ODEQ/COAST Shasta Costa Creek at River mile 1.11

csixes 42 48 15 124 18 19 ODEQ/COAST Sixes River at River mile 19.2

ctill 45 21 07 123 49 51 ODEQ/COAST Tillamook River at River mile 14.9

ctiog 43 11 43 123 45 21 ODEQ/COAST Tioga Creek at River mile 17.74

ctsfcm 42 47 55 124 01 43 ODEQ/COAST South Fork Coquil at River mile 0.13

cwfash 42 08 56 122 42 52 ODEQ/COAST West Fork Ashland at River mile 0.16

Appendix A. Site list for water temperature and habitat survey data collection—Continued

Site model 

label name

Latitude Longitude

Agency/Project Stream name (degrees, minutes, and seconds)
Appendix A 41

rbeav089 45 02 14 122 36 46 ODEQ/REMAP Beaver Creek

rbigh135 45 15 46 121 55 11 ODEQ/REMAP Big Horn

rbric095 43 37 21 122 35 09 ODEQ/REMAP Brice Creek

rcany049 44 22 26 122 23 20 ODEQ/REMAP Canyon Creek

rcnty115 44 16 19 122 06 22 ODEQ/REMAP County Creek

rcrab053 44 34 40 122 34 20 ODEQ/REMAP Crabtree

rdona022 44 31 08 122 11 26 ODEQ/REMAP Donaca Creek

reigt025 43 50 06 122 23 37 ODEQ/REMAP Eight Creek

rfish057 45 05 51 122 10 02 ODEQ/REMAP Fish Creek Low Creek

rfish087 45 03 52 122 09 39 ODEQ/REMAP Fish Creek Up

rlook009 44 13 32 122 14 01 ODEQ/REMAP Lookout Creek

rmart099 44 06 46 122 30 34 ODEQ/REMAP Marten Creek

rmart021 43 32 31 122 43 05 ODEQ/REMAP Martin Creek

rnfea037 45 18 50 122 15 06 ODEQ/REMAP North Fork Eagle Creek

rnfwi045 43 54 04 122 36 31 ODEQ/REMAP North Fork Winberry

rpeat119 44 58 03 122 02 18 ODEQ/REMAP Peat Creek

rrone023 44 06 28 122 01 07 ODEQ/REMAP Roney Creek

rsalt015 43 44 35 122 38 10 ODEQ/REMAP Saltpeter

rshor019 43 44 27 122 29 09 ODEQ/REMAP Shortridge Creek

rtabl029 44 58 53 122 22 59 ODEQ/REMAP Table Rock Fork

rtumb085 43 26 15 122 15 01 ODEQ/REMAP Tumblebug Creek

rwfho033 45 27 52 121 46 52 ODEQ/REMAP West Fork Hood River

rwile109 44 19 18 122 31 52 ODEQ/REMAP Wiley Creek

rzigz097 45 20 20 121 55 18 ODEQ/REMAP Zigzag River

mack 44 13 10 122 10 02 USFS Mack Creek near Blue River, Oregon

Appendix A. Site list for water temperature and habitat survey data collection—Continued

Site model 

label name

Latitude Longitude

Agency/Project Stream name (degrees, minutes, and seconds)
42 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Appendix B. Model input variable tables and sensitivity analyses

Tables included in the appendix:

Explanation of climate station model input variable labels

Group assignment model input variables

Static model input variables

Chaotic model input variables--Group 1

Chaotic model input variables--Group 2, northern zone

Chaotic model input variables--Group 2, southern zone

Chaotic model input variables--Group 3, northern zone

Chaotic model input variables--Group 3, southern zone

Periodic model input variables--Group 1

Periodic model input variables--Group 2, northern zone

Periodic model input variables--Group 2, southern zone

Periodic model input variables--Group 3, northern zone

Periodic model input variables--Group 3, southern zone
Appendix B. Model input variable tables and sensitivity analyses 43

Explanation of climate station model input variable labels

Model label 

for hourly 

values

Model label 

for 24-hour 

moving 

average 

values

Meteorological parameter and units Station name Latitude Longitude Elevation 

(feet)

BILLIEZNWS na Snow water equivalent (inches) Billie Creek Divide 42 25 00 122 17 00 5,300

DIAMONDZ na Snow water equivalent (inches) Diamond Lake 43 11 00 122 08 00 5,315

HOLLANDZ na Snow water equivalent (inches) Holland Meadows 43 40 00 122 34 00 4,900

JUMPZ na Snow water equivalent (inches) Jump Off Joe 44 23 00 122 10 00 3,500

LITTLEZ na Snow water equivalent (inches) Little Meadows 44 37 00 122 13 00 4,000

NORTHZ na Snow water equivalent (inches) North Fork 45 33 00 122 01 00 3,120

PEAVINEZ na Snow water equivalent (inches) Peavine Ridge 45 03 00 121 56 00 3,500

ROARZ na Snow water equivalent (inches) Roaring River 43 54 00 122 02 00 4,900

SADDLEZ na Snow water equivalent (inches) Saddle Mountain 45 32 00 123 22 00 3,250

2DSTD* 1DSTD* Dewpoint temperature (degrees Celsius) Corvallis 44 38 03 123 11 24 230

2AURXRAD 1AURXRAD Dewpoint temperature (degrees Celsius) Aurora 45 16 55 122 45 01 140

2BANXOND 1BANXOND Dewpoint temperature (degrees Celsius) Bandon 43 05 28 124 25 02 80

2EEFXATD 1EEFXATD Dewpoint temperature (degrees Celsius) Dee Flat 45 34 25 121 38 50 1,260

2OREXTGD 1OREXTGD Dewpoint temperature (degrees Celsius) Forest Grove 45 33 11 123 05 01 180

2EDFXRDD 1EDFXRDD Dewpoint temperature (degrees Celsius) Medford 42 19 52 122 56 16 1,340

2ROOXIND 1ROOXIND Dewpoint temperature (degrees Celsius) Brookings 42 02 00 124 15 00 24

2EUGXNED 1EUGXNED Dewpoint temperature (degrees Celsius) Eugene 44 07 00 123 13 00 114

2ILLXBOD 1ILLXBOD Dewpoint temperature (degrees Celsius) Hillsboro 45 31 00 122 59 00 62

2ORTXBED 1ORTXBED Dewpoint temperature (degrees Celsius) North Bend 43 25 00 124 15 00 4

2ORTXAND 1ORTXAND Dewpoint temperature (degrees Celsius) Portland 45 36 00 122 36 00 12

2OSEXURD 1OSEXURD Dewpoint temperature (degrees Celsius) Roseburg 43 14 00 123 22 00 160

2SALXEMD 1SALXEMD Dewpoint temperature (degrees Celsius) Salem 44 55 00 123 00 00 61

2ANNXBLD 1ANNXBLD Dewpoint temperature (degrees Celsius) Cannible 44 21 00 123 55 00 1,946

2PEBXLED 1PEBXLED Dewpoint temperature (degrees Celsius) Pebble 44 14 00 121 59 00 3,560

2RYEXTND 1RYEXTND Dewpoint temperature (degrees Celsius) Rye Mountain 45 13 00 123 32 00 2,000

2PSTD* 1PSTD* Air Pressure (millibar) Eugene 44 07 00 123 13 00 114

2STOXIAP 1STOXIAP Air Pressure (millibar) Astoria 46 09 00 123 53 00 7

2ROOXINP 1ROOXINP Air Pressure (millibar) Brookings 42 02 00 124 15 00 24

2ILLXBOP 1ILLXBOP Air Pressure (millibar) Hillsboro 45 31 00 122 59 00 62

2EDFXRDP 1EDFXRDP Air Pressure (millibar) Medford 42 23 00 122 53 00 405

2ORTXBEP 1ORTXBEP Air Pressure (millibar) North Bend 43 25 00 124 15 00 4

2ORTXANP 1ORTXANP Air Pressure (millibar) Portland 45 36 00 122 36 00 12

2OSEXURP 1OSEXURP Air Pressure (millibar) Roseburg 43 14 00 123 22 00 160

2SALXEMP 1SALXEMP Air Pressure (millibar) Salem 44 55 00 123 00 00 61

2PEBXLEP 1PEBXLEP Air Pressure (millibar) Pebble 44 14 00 121 59 00 3,560

2AURORAR 1AURORAR Rainfall (inches) Aurora 45 16 55 122 45 01 140

2BANDONR 1BANDONR Rainfall (inches) Bandon 43 05 28 124 25 02 80

2ORVALLR 1ORVALLR Rainfall (inches) Corvallis 44 38 03 123 11 24 230

2ORESTGR 1ORESTGR Rainfall (inches) Forest Grove 45 33 11 123 05 01 180

2EDFORDR 1EDFORDR Rainfall (inches) Medford 42 19 52 122 56 16 1,340
44 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

2ANNIBLR 1ANNIBLR Rainfall (inches) Cannible 44 21 00 123 55 00 1,946

2RYEMTNR 1RYEMTNR Rainfall (inches) Rye Mountain 45 13 00 123 32 00 2,000

2SSTD* 1SSTD* Solar Radiation (langleys) Corvallis 44 38 03 123 11 24 230

2AURXRAS 1AURXRAS Solar Radiation (langleys) Aurora 45 16 55 122 45 01 140

2BANXONS 1BANXONS Solar Radiation (langleys) Bandon 43 05 28 124 25 02 80

2OREXTGS 1OREXTGS Solar Radiation (langleys) Forest Grove 45 33 11 123 05 01 180

2EDFXRDS 1EDFXRDS Solar Radiation (langleys) Medford 42 19 52 122 56 16 1,340

2TSTD* 1TSTD* Air Temperature (degrees Celsius) Corvallis 44 38 03 123 11 24 230

2AURXRAT 1AURXRAT Air Temperature (degrees Celsius) Aurora 45 16 55 122 45 01 140

2BANXONT 1BANXONT Air Temperature (degrees Celsius) Bandon 43 05 28 124 25 02 80

2EEFXATT 1EEFXATT Air Temperature (degrees Celsius) Dee Flat 45 34 25 121 38 50 1,260

2OREXTGT 1OREXTGT Air Temperature (degrees Celsius) Forest Grove 45 33 11 123 05 01 180

2EDFXRDT 1EDFXRDT Air Temperature (degrees Celsius) Medford 42 19 52 122 56 16 1,340

2STOXIAT 1STOXIAT Air Temperature (degrees Celsius) Astoria 46 09 00 123 53 00 7

2ROOXINT 1ROOXINT Air Temperature (degrees Celsius) Brookings 42 02 00 124 15 00 24

2EUGXNET 1EUGXNET Air Temperature (degrees Celsius) Eugene 44 07 00 123 13 00 114

2ILLXBOT 1ILLXBOT Air Temperature (degrees Celsius) Hillsboro 45 31 00 122 59 00 62

2ORTXBET 1ORTXBET Air Temperature (degrees Celsius) North Bend 43 25 00 124 15 00 4

2ORTXANT 1ORTXANT Air Temperature (degrees Celsius) Portland 45 36 00 122 36 00 12

2OSEXURT 1OSEXURT Air Temperature (degrees Celsius) Roseburg 43 14 00 123 22 00 160

2SALXEMT 1SALXEMT Air Temperature (degrees Celsius) Salem 44 55 00 123 00 00 61

2ANNXBLT 1ANNXBLT Air Temperature (degrees Celsius) Cannible 44 21 00 123 55 00 1,946

2PEBXLET 1PEBXLET Air Temperature (degrees Celsius) Pebble 44 14 00 121 59 00 3,560

2RYEXTNT 1RYEXTNT Air Temperature (degrees Celsius) Rye Mountain 45 13 00 123 32 00 2,000

Explanation of climate station model input variable labels

Model label 

for hourly 

values

Model label 

for 24-hour 

moving 

average 

values

Meteorological parameter and units Station name Latitude Longitude Elevation 

(feet)
Appendix B. Model input variable tables and sensitivity analyses 45

Group assignment model input variables

Notes:

Output variables are G1, G2, and G3. Input 

variable labels are defined in table 1. Input variables 

are listed below in the order of their importance for 

each group. Weight, was determined through model 

sensitivity analysis. The sum of the weight values for 

each group equals 1.

Group 1 Group 2 Group 3

Input

Variable Weight Input

Variable Weight Input

Variable Weight

BASFOREA 0.09339 BASFOREA 0.12899 BASFOREA 0.12637

BASXELEV 0.08896 DENBASFA 0.08123 DENBASFA 0.08317

XCOORD 0.07912 XCOORD 0.06593 XCOORD 0.06871

DENBASFA 0.07556 STCHFORA 0.06223 STRMRB 0.06389

STRMRB 0.07016 STRMRB 0.06037 STCHFORA 0.06025

MIDCHDEN 0.05439 BASMSATC 0.05682 BASMSATC 0.05560

YCOORD 0.05335 STRMBDEN 0.04952 YCOORD 0.04865

STRMBDEN 0.05017 MIDCHDEN 0.04907 BASXELEV 0.04841

STMSUATC 0.04391 YCOORD 0.04670 MIDCHDEN 0.04572

STCHFORA 0.04274 BASXELEV 0.04441 STRMBDEN 0.04403

STRMCHBE 0.03647 STRMCHBE 0.04034 STRMCHBE 0.04014

SBSUBSTC 0.03330 SBSUBSTC 0.03969 SBSUBSTC 0.03874

BASMSATC 0.03298 DNSTCHFA 0.03476 OUTMSATC 0.03327

DEPTH 0.03013 OUTMSATC 0.03207 WETTEDWD 0.03295

OUTMSATC 0.02733 WETTEDWD 0.03200 STMSUATC 0.03290

BASINKM2 0.02656 BASMSLOP 0.03169 BASMSLOP 0.03196

DNSTCHFA 0.02609 STMSUATC 0.02901 DNSTCHFA 0.03091

BASMSLOP 0.02506 BASINKM2 0.02336 BASOELEV 0.02391

STCHMELV 0.02455 DEPTH 0.02275 BASINKM2 0.02388

BASOELEV 0.02424 BASOELEV 0.02253 DEPTH 0.02088

BASBEARS 0.02163 BASBEARS 0.01676 STCHMELV 0.01933

WETTEDWD 0.02135 STCHMELV 0.01673 BASBEARS 0.01594

BASBEARC 0.01857 BASBEARC 0.01305 BASBEARC 0.01039
46 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Static model input variables

Notes:

Output variable is MEANT, which is defined in 

equation 4 as the mean hourly temperature for the 

simulation period. Input variable labels are defined in 

table 1. Input variables are listed below in the order of 

their importance. Weight, was determined through 

model sensitivity analysis. The sum of the weight 

values equals 1.

Chaotic model input variables—Group 1

Notes:

Output variable is NAVG24, which is defined in 

equation 5 as the normalized 24-hour hourly moving 

average residual. Input variable labels are defined in 

table 1 and appendix b. Input variables are listed below 

in the order of their importance. Weight, was 

determined through model sensitivity analysis. The 

sum of the weight values equals 1.

Input 

Variable Weight

XCOORD 0.11630

BASOELEV 0.10562

STMSUATC 0.10342

BASMSATC 0.10037

MIDCHDEN 0.08401

STCHMELV 0.08228

STCHFORA 0.07860

BASFOREA 0.06855

DNSTCHFA 0.06302

YCOORD 0.06300

BASXELEV 0.05761

SBSUBSTG 0.03330

BASINKM2 0.02941

SBSUBSBO 0.01450 

Input 

Variable Weight

1TSTD 0.09840

DENBASFA 0.07685

1PEBXLEP 0.05520

MEANTP 0.04683

1EDFXRDS 0.04528

OUTMSATC 0.04378

1ROOXINT 0.04196

BASOPENA 0.04187

1SSTD 0.04003

1ORTXANP 0.03869

SBSUBSTC 0.03822

BASMSATC 0.03372

1ILLXBOP 0.03099

BASXELEV 0.03093

STRMBDEN 0.03044

STCHOPA 0.03022

1OSEXURT 0.02995

1ROOXINP 0.02901

LITTLEZ 0.02604

MIDCHDEN 0.02526

1STOXIAP 0.02445

1BANXONT 0.02262

BASBEARA 0.02190

1PSTD 0.01905

1EDFXRDT 0.01840

X 0.01810

1EEFXATT 0.01598

DNSTCHFA 0.01394

DEPTH 0.01197
Appendix B. Model input variable tables and sensitivity analyses 47

Chaotic model input variables—Group 2, northern 

zone

Notes:

Output variable is NAVG24, which is defined in 

equation 5 as the normalized 24-hour hourly moving 

average residual. Input variable labels are defined in 

table 1 and appendix b. Input variables are listed below 

in the order of their importance. Weight, was 

determined through model sensitivity analysis. The 

sum of the weight values equals 1.

Input 

Variable Weight

1TSTD 0.07206

LITTLEZ 0.07111

STCHFORA 0.04389

1ILLXBOP 0.04205

1SSTD 0.03487

1EEFXATT 0.03239

1DSTD 0.02916

XCOORD 0.02784

1BANXONT 0.02706

BASFOREA 0.02539

1SALXEMT 0.02266

1ILLXBOT 0.02211

1ANNXBLD 0.02081

1ORTXANT 0.02004

BASOELEV 0.01962

BASBEARA 0.01927

1EDFXRDS 0.01825

1BANXONS 0.01795

1PEBXLEP 0.01795

1EDFXRDP 0.01754

1STOXIAP 0.01746

1SALXEMP 0.01734

1ILLXBOD 0.01677

1EDFXRDT 0.01622

DEPTH 0.01602

YCOORD 0.01577

1ORTXANP 0.01567

SBSUBSTG 0.01545

1OREXTGS 0.01505

1ORTXBET 0.01498

DENBASFA 0.01489

MIDCHDEN 0.01478

1PEBXLET 0.01420

OUTMSATC 0.01371

ROARZ 0.01352

STRMCHBE 0.01322

BASMSLOP 0.01303

1ORTXBEP 0.01256

1EUGXNET 0.01204

SBSUBSBO 0.01152

SBSUBSTC 0.01145

1OREXTGD 0.01134

SBSUBSTC 0.01132

SBSUBSTF 0.01092

1EDFXRDR 0.01089

1AURXRAS 0.01053

SBSUBSBE 0.01022

1BANXOND 0.01020

SLOPEPCT 0.00935

DNSTCHFA 0.00811

Input 

Variable Weight
48 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Chaotic model input variables—Group 2, southern 

zone

Notes:

Output variable is NAVG24, which is defined in 

equation 5 as the normalized 24-hour hourly moving 

average residual. Input variable labels are defined in 

table 1 and appendix b. Input variables are listed below 

in the order of their importance. Weight, was 

determined through model sensitivity analysis. The 

sum of the weight values equals 1.

Input Variable Weight

LITTLEZ 0.05829

1TSTD 0.05542

DNSTCHFA 0.04284

DENBASFA 0.04173

MEANTP 0.03663

STCHFORA 0.03551

MIDCHDEN 0.03524

1DSTD 0.03158

BASOELEV 0.03144

1ROOXINP 0.02640

1ILLXBOP 0.02601

STRMBDEN 0.02494

BASBEARA 0.02449

BASMSLOP 0.02403

1ROOXINT 0.02374

1SSTD 0.02308

1SALXEMP 0.02257

1PEBXLEP 0.02176

ROARZ 0.02135

1EDFXRDT 0.02038

1STOXIAP 0.02000

STRMRB 0.01993

1ORTXANP 0.01896

1EDFXRDD 0.01755

1EDFXRDP 0.01718

1EDFXRDR 0.01647

XCOORD 0.01618

1EEFXATT 0.01581

YCOORD 0.01543

1OSEXURT 0.01527

BASFOREA 0.01506

1AURXRAS 0.01487

1ILLXBOD 0.01430

SBSUBSBO 0.01375

1PSTD 0.01234

BASBEARS 0.01230

1BANXONS 0.01225

1SALXEMT 0.01224

SLOPEPCT 0.01164

1ORTXANT 0.01137

STRMCHBE 0.01048

1ORTXBEP 0.01024

1EDFXRDS 0.01010

STCHMELV 0.00983

SBSUBSTF 0.00965

1EUGXNET 0.00850

SBSUBSBE 0.00594

SBSUBSTS 0.00540

Input Variable Weight
Appendix B. Model input variable tables and sensitivity analyses 49

Chaotic model input variables—Group 3, northern 

zone

Notes:

Output variable is NAVG24, which is defined in 

equation 5 as the normalized 24-hour hourly moving 

average residual. Input variable labels are defined in 

table 1 and appendix b. Input variables are listed below 

in the order of their importance. Weight, was 

determined through model sensitivity analysis. The 

sum of the weight values equals 1.

Input 

Variable Weight

1TSTD 0.07957

MEANTP 0.04933

1DSTD 0.04886

BASFOREA 0.04406

DENBASFA 0.04013

STCHFORA 0.03689

1SALXEMT 0.02975

DNSTCHFA 0.02795

1ROOXINP 0.02750

1EDFXRDP 0.02662

1SALXEMP 0.02605

1PSTD 0.02344

XCOORD 0.02317

STRMBDEN 0.02256

1ORTXANP 0.02064

LITTLEZ 0.02045

1EDFXRDS 0.02019

1EDFXRDD 0.01928

1ORTXBEP 0.01793

1SSTD 0.01788

1ROOXINT 0.01787

1PEBXLEP 0.01786

1ILLXBOP 0.01781

MIDCHDEN 0.01763

BASBEARS 0.01702

YCOORD 0.01642

OUTMSATC 0.01429

1OSEXURT 0.01420

SBSUBSTC 0.01416

1BANXONS 0.01405

1AURXRAS 0.01352

1BANXOND 0.01326

1EEFXATT 0.01308

1BANXONT 0.01288

1STOXIAP 0.01266

SLOPEPCT 0.01254

STRMRB 0.01244

1ORTXANT 0.01121

BASINKM2 0.01100

BASBEARA 0.01094

1ANNXBLD 0.01068

ROARZ 0.01039

BASBEARC 0.01003

SBSUBSTF 0.00988

SBSUBSBE 0.00974

DEPTH 0.00940

1ORTXBET 0.00938

BASMSLOP 0.00834

STRMCHBE 0.00789

1EDFXRDR 0.00773

Input 

Variable Weight
50 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Chaotic model input variables—Group 3, southern 

zone

Notes:

Output variable is NAVG24, which is defined in 

equation 5 as the normalized 24-hour hourly moving 

average residual. Input variable labels are defined in 

table 1 and appendix B. Input variables are listed below 

in the order of their importance. Weight, was 

determined through model sensitivity analysis. The 

sum of the weight values equals 1.

Input 

Variable Weight

MEANTP 0.06953

1DSTD 0.05887

1TSTD 0.05245

DENBASFA 0.03269

1EDFXRDP 0.03044

1SALXEMP 0.03019

STCHFORA 0.02817

1SSTD 0.02642

1OSEXURT 0.02528

1EDFXRDS 0.02456

STRMBDEN 0.02452

1ROOXINP 0.02378

LITTLEZ 0.02329

1ILLXBOP 0.02224

WETTEDWD 0.02175

XCOORD 0.02173

SBSUBSTG 0.02096

1ORTXBEP 0.02087

DNSTCHFA 0.02054

STCHMELV 0.02022

MIDCHDEN 0.01984

YCOORD 0.01921

1SALXEMT 0.01862

1STOXIAP 0.01749

1EDFXRDT 0.01656

1ROOXINT 0.01651

1EUGXNED 0.01638

1EUGXNET 0.01578

ROARZ 0.01568

1EDFXRDD 0.01550

1PSTD 0.01545

1BANXONS 0.01528

1ORTXANP 0.01402

1ORTXANT 0.01343

1PEBXLEP 0.01322

SLOPEPCT 0.01309

BASBEARA 0.01309

1BANXOND 0.01304

BASMSLOP 0.01301

BASOELEV 0.01208

DEPTH 0.01125

1EEFXATT 0.01102

1ORTXBET 0.01059

1ILLXBOT 0.01025

1ILLXBOD 0.00990

1OSEXURP 0.00941

STRMRB 0.00927

1EDFXRDR 0.00921

1ANNXBLD 0.00794

SBSUBSTF 0.00588

Input 

Variable Weight
Appendix B. Model input variable tables and sensitivity analyses 51

Periodic model input variables—Group 1

Notes:

Output variable is NHOURLY, which is defined 

in equation 6 as the normalized 24-hour residual. Input 

variable labels are defined in table 1 and appendix B. 

Labels with parentheses are time lagged in hours. Input 

variables are listed below in the order of their 

importance. Weight, was determined through model 

sensitivity analysis. The sum of the weight values 

equals 1.

Input Variable Weight

NAVG24P 0.08667

NAVG24P(024) 0.06748

2EDFXRDS(006) 0.04437

2OSEXURT 0.03771

DENBASFA 0.02945

2PEBXLEP 0.02703

2BANXONT 0.02529

MEANTP 0.02427

STRMRB 0.02316

MIDCHDEN 0.02281

2SSTD(006) 0.02266

2EDFXRDP 0.02207

2ORTXANP(012) 0.02190

STMSUATC 0.02095

2EUGXNET 0.01952

1EDFXRDT(003) 0.01928

2EDFXRDT(006) 0.01925

1ORTXBET(003) 0.01921

OUTMSATC 0.01893

DNSTCHFA 0.01791

2EDFXRDT 0.01789

2ORTXBET 0.01720

1ROOXINT(003) 0.01714

2ROOXINP(006) 0.01659

BASBEARA 0.01655

1SALXEMT(003) 0.01648

STRMBDEN 0.01616

2OSEXURT(012) 0.01615

NAVG24P(012) 0.01610

1BANXONT(003) 0.01588

1OSEXURT(003) 0.01575

2EDFXRDT(012) 0.01561

2ANNXBLT(006) 0.01515

2PSTD(006) 0.01482

STRMCHBE 0.01479

2EUGXNET(006) 0.01411

2ORTXBEP(012) 0.01408

2PEBXLEP(012) 0.01387

1EEFXATT(003) 0.01343

2EEFXATT 0.01330

Y 0.01326

1EUGXNET(003) 0.01303

1ORTXANT(003) 0.01246

2SSTD 0.01186

2BANXONT(006) 0.01180

2PEBXLET(012) 0.01103

2BANXONT(012) 0.00919

BASMSLOP 0.00864

1ANNXBLT(003) 0.00788

Input Variable Weight
52 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Periodic model input variables—Group 2, northern 

zone

Notes:

Output variable is NHOURLY, which is defined 

in equation 6 as the normalized 24-hour residual. Input 

variable labels are defined in table 1 and appendix B. 

Labels with parentheses are time lagged in hours. Input 

variables are listed below in the order of their 

importance. Weight, was determined through model 

sensitivity analysis. The sum of the weight values 

equals 1.

Input Variable Weight

NAVG24P 0.06882

2TSTD(003) 0.06107

NAVG24P(024) 0.05031

MEANTP 0.04159

2ORTXANP 0.03287

2TSTD(012) 0.02863

2PEBXLET(003) 0.02787

STRMBDEN 0.02445

2OSEXURT 0.02403

BASFOREA 0.02334

2OSEXURT(012) 0.02303

2ORTXANP(012) 0.02292

STRMCHBE 0.02167

2TSTD(006) 0.02138

2STOXIAT(003) 0.02098

2AURXRAT(006) 0.02077

2PEBXLET(012) 0.01999

BASBEARS 0.01999

2EUGXNET(006) 0.01997

2OREXTGT 0.01988

XCOORD 0.01889

2ORTXANT 0.01868

DENBASFA 0.01746

2ORTXBET(012) 0.01677

MIDCHDEN 0.01667

SBSUBSTC 0.01636

2RYEXTNT(003) 0.01613

2STOXIAP 0.01581

YCOORD 0.01488

2EEFXATT 0.01472

2BANXONT 0.01460

STCHFORA 0.01420

2EEFXATT(003) 0.01384

2STOXIAT 0.01365

DNSTCHFA 0.01351

2SALXEMT(003) 0.01316

BASMSLOP 0.01304

STRMRB 0.01302

2RYEXTNT(006) 0.01261

2STOXIAT(006) 0.01246

2EDFXRDT 0.01200

2SALXEMP(006) 0.01089

2STOXIAP(012) 0.01050

2STOXIAT(012) 0.01036

2AURXRAT(003) 0.01025

SLOPEPCT 0.00933

2EEFXATT(006) 0.00910

2ORTXBET(006) 0.00885

2ORTXBET(003) 0.00867

2EEFXATT(012) 0.00827

2ORTXANT(003) 0.00817

Input Variable Weight
Appendix B. Model input variable tables and sensitivity analyses 53

Periodic model variables—Group 2, southern zone

Notes:

Output variable is NHOURLY, which is defined 

in equation 6 as the normalized 24-hour residual. Input 

variable labels are defined in table 1 and appendix B. 

Labels with parentheses are time lagged in hours. Input 

variables are listed below in the order of their 

importance. Weight, was determined through model 

sensitivity analysis. The sum of the weight values 

equals 1.

Input Variable Weight

NAVG24P 0.09582

NAVG24P(024) 0.04803

NAVG24P(012) 0.03511

DENBASFA 0.03360

MIDCHDEN 0.02891

STCHFORA 0.02770

2TSTD(003) 0.02596

MEANTP 0.02263

2EDFXRDT(006) 0.02128

STCHMELV 0.01989

2PEBXLET(003) 0.01885

2EDFXRDT 0.01884

BASMSATC 0.01873

2EDFXRDS 0.01828

2TSTD(006) 0.01753

BASOELEV 0.01711

DNSTCHFA 0.01701

STRMCHBE 0.01633

2OREXTGT(012) 0.01592

BASFOREA 0.01587

XCOORD 0.01559

2EDFXRDT(003) 0.01558

2OSEXURT 0.01519

YCOORD 0.01502

STRMRB 0.01495

2ORTXANT(006) 0.01478

2OSEXURT(012) 0.01444

2TSTD 0.01410

2BANXONT(003) 0.01404

STRMBDEN 0.01396

2ORTXANP(012) 0.01373

2SALXEMT(003) 0.01306

BASMSLOP 0.01295

2EUGXNET(003) 0.01268

2RYEXTNT(003) 0.01240

2EEFXATT 0.01232

2EUGXNET(006) 0.01201

2ORTXANP(006) 0.01200

2OREXTGT 0.01175

2PEBXLET(006) 0.01166

2ROOXINP 0.01163

BASBEARC 0.01160

2PEBXLET(012) 0.01133

2AURXRAT(003) 0.01126

2SSTD 0.01115

2AURXRAT(012) 0.01106

WETTEDWD 0.01102

SBSUBSTG 0.01101

2ORTXANT(012) 0.01052

2ROOXINP(006) 0.00982

2OSEXURT(003) 0.00979

2EDFXRDS(006) 0.00928

2PSTD(012) 0.00896

BASINKM2 0.00883

2EDFXRDP(006) 0.00876

2EDFXRDP 0.00848

2EEFXATT(003) 0.00821

LITTLEZ 0.00814

2DSTD(012) 0.00740

SLOPEPCT 0.00667

Input Variable Weight
54 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Periodic model input variables—Group 3, northern 

zone

Notes:

Output variable is NHOURLY, which is defined 

in equation 6 as the normalized 24-hour residual. Input 

variable labels are defined in table 1 and appendix B. 

Labels with parentheses are time lagged in hours. Input 

variables are listed below in the order of their 

importance. Weight, was determined through model 

sensitivity analysis. The sum of the weight values 

equals 1.

Input Variable Weight

NAVG24P 0.07983

NAVG24P(024) 0.03873

NAVG24P(012) 0.03714

2OREXTGS(006) 0.02645

2TSTD 0.02626

2TSTD(006) 0.02590

DENBASFA 0.02523

NAVG24P(003) 0.02486

STCHFORA 0.02402

2ILLXBOT(006) 0.02030

2EUGXNET(003) 0.01957

2TSTD(012) 0.01952

2OREXTGT(003) 0.01931

XCOORD 0.01910

MEANTP 0.01904

2SSTD(006) 0.01825

NAVG24P(006) 0.01766

2EUGXNET 0.01760

2ORTXANT(012) 0.01691

2BANXONT(003) 0.01670

2ORTXANP(006) 0.01600

BASBEARC 0.01538

2AURXRAT 0.01531

STRMRB 0.01516

DEPTH 0.01491

MIDCHDEN 0.01485

SLOPEPCT 0.01482

2AURXRAT(006) 0.01447

2ORTXANT 0.01436

STRMBDEN 0.01418

2STOXIAT(003) 0.01407

YCOORD 0.01395

2RYEXTNT(003) 0.01383

2OREXTGT 0.01370

BASBEARS 0.01367

2STOXIAP(012) 0.01314

2SALXEMT(006) 0.01313

2EDFXRDS(006) 0.01286

STRMCHBE 0.01258

2SSTD 0.01255

2PEBXLET 0.01237

2SALXEMT(003) 0.01216

STMSUATC 0.01211

2EEFXATT(012) 0.01183

SBSUBSTF 0.01154

SBSUBSTC 0.01152

BASMSATC 0.01110

BASBEARA 0.01108

2RYEXTNT 0.01101

2EDFXRDP(012) 0.01055

DNSTCHFA 0.01038

2BANXONS 0.01017

SBSUBSTS 0.01005

2DSTD(012) 0.00948

2EDFXRDP 0.00928

2BANXONT 0.00915

2OSEXURT(012) 0.00902

WETTEDWD 0.00802

2STOXIAT(006) 0.00743

OUTMSATC 0.00693

Input Variable Weight
Appendix B. Model input variable tables and sensitivity analyses 55

Periodic model input variables—Group 3, southern 

zone

Notes:

Output variable is NHOURLY, which is defined 

in equation 6 as the normalized 24-hour residual. Input 

variable labels are defined in table 1 and appendix B. 

Labels with parentheses are time lagged in hours. Input 

variables are listed below in the order of their 

importance. Weight, was determined through model 

sensitivity analysis. The sum of the weight values 

equals 1.

Input Variable Weight

NAVG24P 0.09025

2TSTD(003) 0.03659

NAVG24P(012) 0.03275

NAVG24P(024) 0.03247

MEANTP 0.02504

2EDFXRDS(006) 0.02483

2OSEXURT 0.02381

MIDCHDEN 0.02380

2ORTXANP 0.02283

DNSTCHFA 0.02150

2EDFXRDT 0.02130

2PEBXLET(003) 0.02059

2OSEXURT(003) 0.02042

2OREXTGS(006) 0.01964

2EDFXRDT(006) 0.01930

DENBASFA 0.01887

2EDFXRDS 0.01739

YCOORD 0.01730

XCOORD 0.01726

NAVG24P(006) 0.01715

STCHFORA 0.01672

STRMBDEN 0.01633

2TSTD(012) 0.01605

2AURXRAT(012) 0.01557

DEPTH 0.01510

2EUGXNET(003) 0.01501

2BANXONS 0.01500

2RYEXTNT(003) 0.01471

BASFOREA 0.01409

2STOXIAP(012) 0.01397

BASMSATC 0.01376

2SSTD(006) 0.01343

2TSTD(006) 0.01330

BASINKM2 0.01322

SLOPEPCT 0.01317

2AURXRAT 0.01315

2AURXRAT(003) 0.01287

SBSUBSTG 0.01203

2STOXIAP 0.01200

2EEFXATT 0.01127

2BANXONT(012) 0.01124

BASBEARA 0.01123

2OREXTGT 0.01108

BASMSLOP 0.01105

2ORTXBET(003) 0.01103

2EEFXATT(012) 0.01101

2ORTXANT 0.01053

2EDFXRDP 0.01025

2SSTD 0.01011

2PEBXLET(012) 0.00951

2ORTXBET(006) 0.00939

2OSEXURT(012) 0.00936

2DSTD(012) 0.00926

2EUGXNET(006) 0.00915

SBSUBSTC 0.00898

STMSUATC 0.00886

2PSTD 0.00793

2ROOXINT(003) 0.00751

2OREXTGT(003) 0.00744

2EDFXRDS(012) 0.00614

BASBEARC 0.00558

Input Variable Weight
56 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

Appendix C. Model operation instructions

1. Downloading model files

From http://oregon.usgs.gov/projs_dir/or185/, click on “Model operation files” to go to the ftp directory. 

From there, download a file named “modelfiles.zip.” This file is a package containing various files used for 

processing the input data and operating the water temperature model. Some additional software and GIS coverages 

that were used in this study could not be included in this package file, because they must be acquired through other 

firms or agencies. Details regarding those firms or agencies are provided below.

2. Assembling model input parameters

Before running the model, the user must assemble the input data that is specific to their basin of interest for 

the 34 stream habitat and basin characteristics parameters listed in table 1. For proper model operation, it is critical 

that the data assembled by the user be within the maximum and minimum extremes shown in the table 1 for each 

parameter.

It is assumed that stream habitat data, the first 12 parameters listed in table 1, will have already been 

collected at and near the outlet of the user’s basin of interest. The habitat data should be collected and assembled 

using EMAP protocols described in (Kaufmann and Robison, 1994, 1998; and Kaufmann and others, 1999).

The next step is to estimate the basin characteristics, which are the remaining 22 parameters listed in table 1. 

Arc Macro Language (AML) scripts are provided in the “modelfiles.zip” file to assist the user in downloading most 

of these parameters from 10-meter digital elevation models (DEMs) and other GIS coverages.

The aml script files are:

“aml.start”

“aml.clip”

“aml.clean”

“aml.basin”

“aml.wipeout”

Instructions for running the scripts are in “README.gis_instructions.txt”

Using these specific scripts is not required if the user has access to other GIS tools or methods. However, a 

user (with some GIS skills) should examine these scripts to understand how the basin characteristic parameters 

were defined and computed for this study. The computed output for most of the basin characteristic parameters is 

provided in the “aml.basin” file. Running this script requires using proprietary forest and air temperature GIS 

coverages that may have to be purchased through non-USGS agencies listed in “README.gis_instructions.txt”. If 

the user already has forest and air temperature data for their basin, they could modify the “aml.basin” file to just 

compute the DEM derived basin characteristic parameters (such as drainage area, elevation, etc.)

Before running the scripts, the latitude and longitude coordinates of the site of interest must be converted into 

Universal Transverse Mercator, Zone 10 (UTM) 1927 North American Datum (NAD27) units. An easy to use 

coordinate conversion tool is available at http://jeeep.com/details/coord/.
Appendix C 57

The X and Y UTM coordinates then must be manually converted into normalized decimal units for use as 

model inputs: XCOOR and YCOOR.

XCOOR = (Xutm - 384,651) / 223, 448

YCOOR = (Yutm - 4,654,955) / 456,853

Values for BASBEARA, BASBEARS, BASBEARC, and STRMCHBE (listed in table 1) can be manually 

estimated from a topographic map. BASBEARA is the angle (0-360 degrees) of the line starting from the location 

on the basin divide that is furthermost away from the outlet and extending to the outlet. STRMCHBE is the is the 

angle (0-360 degrees) of the line that parallels the main stream channel. This line starts from a location one-third of 

the basin length up from the outlet and extends to the outlet.

3. Setting up the models

The water temperature models can be are run within an EXCEL spreadsheet using an EXCEL add-in called 

NNCALC. The NNCALC add-in file, “nncalc32.xll” is not provided in the “modelfiles.zip” package file. However, 

it can be purchased at a nominal price through:

Advanced Data Mining, LLC

3620 Pelham Road, PMB #351,

Greenville, South Carolina, 29615-5044

email: ed.roehl@advdatamining.com

Telephone: 864-676-9790

Having the NNCALC add-in file enables a user to operate the models without purchasing the entire Neural 

Fusion software package. If it is not possible to acquire the NNCALC add-in, a user could conceivably reconstruct 

the temperature models on their own in a spreadsheet using the 22 model text files (ending in *.txt, and listed 

below) and the EXCEL template “model_template.xls” file. The model text files contain the final hidden and 

output layer weights trained for each model. The “model_template.xls” file contains climate data necessary for the 

chaotic and periodic models. Figure 4 shows how the links between the input, hidden, and output layers would have 

to be set up for each model. Figure 9 shows how data would have to be passed from one model to another to 

simulate hourly or 24-hour moving average temperature time series output. However, by using the NNCALC addin the user would only need to assemble the field habitat and basin characteristics data (listed in table 1) and insert 

them into “model_template.xls” to simulate a water temperature time series for their basin of interest. Using the 

NNCALC add-in, the “model_template.xls” spreadsheet is dynamically linked to 22 model files (ending in *.enn 

and listed below). The 22 *.enn files and the “model_template.xls” file need to all reside together in the same 

directory as the NNCALC add-in file “nncalc32.xll”.
58 Estimating Water Temperatures in Small Streams in Western Oregon Using Neural Network Models

4. Running the models

As a suggestion, the user should always make a copy of the “model_template.xls” for every new application. 

The “model_template.xls” file can be easily compromised if certain cells, rows, or columns are deleted by mistake.

4.1--After the required field habitat and basin characteristics data (table 1) for a basin of interest have been 

assembled, they are inserted into the cells in column B of the ‘group-static’ worksheet in the EXCEL template file 

“model_template.xls”

4.2--After the input data are entered, the three group assignment output values will appear in cells C2, D2, and E2. 

The cell with the highest value will be the group assignment for the site of interest. For assignments in groups 2 or 

3, the cells D3 or E3 will indicate if the site of interest is in the northern or southern zone.

The dividing line between the northern and southern zones for group 2 is at:

Latitude (DMS): 44 degrees 34 minutes 12 seconds

Latitude (DD): 44.57

UTM: 4,935,450

YCOOR: 0.613972

The dividing line between the northern and southern zones for group 3 is at:

Latitude (DMS): 44 degrees 18 minutes 0 seconds

Latitude (DD): 44.30

UTM: 4,905,460

YCOOR: 0.548328

4.3--To compute 24-hour moving average and hourly water temperatures, the user must copy cell F2 (MEANTP) 

and then click on the worksheet for their group assignment (group1, group2n, group2s, group3n, or group3s). Once 

inside the group worksheet, the user must click on cell B2 and then click Edit-->Paste Special-->Values-->OK. Do 

not use Edit-->Paste. (“MEANTP”, output from the STATIC model, is the simulated mean water temperature [in 

degrees Celsius] for the entire simulation period [June 21, 1999, to September 20, 1999.])

4.4--Click on cell C2, which shows the results of the chaos model for the first time step. Highlight from C2 to 

C2209, and then click on Edit-->Fill-->Down. While these cells are still highlighted, click on Edit-->Copy. Click 

on cell D2, and then Edit-->Paste Special-->Values-->OK.

4.5--Click on cell E2, which shows the results of the periodic model for the first time step. Highlight from E2 to 

E2209, and then click on Edit-->Fill-->Down. While these cells are still highlighted, click on Edit-->Copy. Click 

on cell F2, and then Edit-->Paste Special-->Values-->OK.

4.6--Click on both cells G2 and H2, which show 24-hour moving average and hourly water temperatures (in 

degrees Celsius), respectively. To complete the time series, highlight and fill down cells G2 to G2209 and cells H2 

to H2209. These simulated temperatures are based on 1999 climatic conditions for the user’s site of interest.

4.7--If the user is interested in simulating water temperatures for resulting different shade scenarios, they should 

repeat steps 4.1 through 4.6 using a new template file and new input values for the shade related parameters (listed 

in table 6).
Appendix C 59

Model files

Files for the 22 models are included in the “modelfiles.zip” file. File names with the *.enn ending are used in 

conjunction with the NNCALC add-in. File names with the *.txt ending are more easily understood text files and 

are included here as a backup alternative if the user is unable to acquire the NNCALC add-in.

Group assignment model:

“groupmod.enn” or “groupmod.txt”

Static model:

“static.enn” or “static.txt”

Chaos models:

“chaosg1.enn” or “chaosg1.txt”

“chaosg2n.enn” or “chaosg2n.txt”

“chaosg2s.enn” or “chaosg2s.txt”

“chaosg3n.enn” or “chaosg3n.txt”

“chaosg3s.enn” or “chaosg3s.txt”

Periodic models:

“perg1.enn” or “perg1.txt”

“perg2n.enn” or “perg2n.txt”

“perg2s.enn” or “perg2s.txt”

“perg3n.enn” or “perg3n.txt”

“perg3s.enn” or “perg3s.txt”

Moving average models:

“mavg1.enn” or “mavg1.txt”

“mavg2n.enn” or “mavg2n.txt”

“mavg2s.enn” or “mavg2s.txt”

“mavg3n.enn” or “mavg3n.txt”

“mavg3s.enn” or “mavg3s.txt”

Hourly models:

“hourg1.enn” or “hourg1.txt”

“hourg2n.enn” or “hourg2n.txt”

“hourg2s.enn” or “hourg2s.txt”

“hourg3n.enn” or “hourg3n.txt”

“hourg3s.enn” or “hourg3s.txt”