Temperature Effects of Point Sources, Riparian Shading, and 

Dam Operations on the Willamette River, Oregon

Scientific Investigations Report 2007–5185

Prepared in cooperation with the Oregon Association of Clean Water Agencies 

and the Willamette Partnership

U.S. Department of the Interior

U.S. Geological Survey
Front cover: Photograph of McKenzie River near Coburg, Oregon (U.S. Geological Survey gaging station 

14165500) looking downstream from Coburg Road bridge. (Photograph taken by Glen Hess, U.S. Geological 

Survey, June 19, 2007.)

Back cover: 

Top: Photograph showing Middle Fork Willamette River at Jasper Road near Jasper, Oregon (river mile 

196.5 from mouth of Willamette River) looking upstream from right bank. (Photograph taken by Anna 

Buckley, formerly U.S. Geological Survey, August 7, 2002.)

Middle: Photograph showing Willamette River at Newberg, Oregon (U.S. Geological Survey gaging 

station 14197900) looking downstream from pipeline bridge. (Photograph taken by Roy Wellman, U.S. 

Geological Survey, June 13, 2005.)

Bottom: Photograph showing McKenzie River above Hayden Bridge at Springfield, Oregon (U.S. 

Geological Survey gaging station 14164900) looking downstream toward confluence with Mohawk River. 

(Photograph taken by Doug Cushman, U.S. Geological Survey, September 12, 2005.)
Temperature Effects of Point Sources, 

Riparian Shading, and Dam Operations 

on the Willamette River, Oregon

By Stewart A. Rounds

Prepared in cooperation with the Oregon Association of Clean Water Agencies 

and the Willamette Partnership

Scientific Investigations Report 2007–5185

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2007

For product and ordering information:

World Wide Web: http://www.usgs.gov/pubprod

Telephone: 1-888-ASK-USGS

For more information on the USGS--the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment:

World Wide Web: http://www.usgs.gov

Telephone: 1-888-ASK-USGS

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

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

reproduce any copyrighted materials contained within this report.

Suggested citation:

Rounds, S.A., 2007, Temperature effects of point sources, riparian shading, and dam operations on the Willamette 

River, Oregon: U.S. Geological Survey Scientific Investigations Report 2007–5185, 34 p.
iii

Contents

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

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

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

Purpose and Scope ..............................................................................................................................4

Description of Models...................................................................................................................................5

Code Changes........................................................................................................................................6

Model Modifications ............................................................................................................................6

Methods...........................................................................................................................................................7

Temperature Effects of Point Sources .......................................................................................................8

Heating Signature Summation Issues...............................................................................................9

Point-Source Independence......................................................................................................9

Addition of 95th Percentiles.....................................................................................................10

Adjustments and Strength Factors ..................................................................................................11

Use of the Trading Tool.......................................................................................................................12

Patterns in the Temperature Differences .......................................................................................12

Predictions and Test Results.............................................................................................................13

Temperature Effects of Riparian Shading................................................................................................18

Long Tom River Shading ....................................................................................................................18

Upper Willamette River Shading......................................................................................................19

Temperature Effects of Dam Operations..................................................................................................21

Summary and Conclusions.........................................................................................................................27

Acknowledgments.......................................................................................................................................28

Supplemental Material................................................................................................................................28

References Cited..........................................................................................................................................28

Appendix A. CE-QUAL-W2 Code Changes...............................................................................................31
iv

Figures

Figure 1. Map showing location of the river network, the modeled river reaches, and 

major reservoirs in the Willamette River basin, Oregon .............................. 3

Figure 2. Graph showing comparison of the sum of the individual point-source heating 

signatures to the results from one model run containing all point sources ......... 9

Figure 3. Boxplot showing percentiles from two hypothetical normal distributions, 

A and B, as well as two distributions resulting from the addition of A and B ...... 10

Figure 4. Graphs showing results of hypothetical heat-trading test case 1, showing

7dADM point-source temperature effects from the test case’s model run and 

errors associated with the Trading Tool estimate ....................................... 14

Figure 5. Graphs showing results of hypothetical heat-trading test case 2, showing 

7dADM point-source temperature effects from the test case’s model run 

and errors associated with the Trading Tool estimate ................................. 15

Figure 6. Graphs showing results of hypothetical heat-trading test case 3, showing 

7dADM point-source temperature effects from the test case’s model run 

and errors associated with the Trading Tool estimate ................................. 16

Figure 7. Graphs showing results of hypothetical heat-trading test case 4, showing 

7dADM point-source temperature effects from the test case’s model run 

and errors associated with the Trading Tool estimate ................................. 17

Figure 8. Graph showing thermal effects of restoring riparian vegetation along the 

Long Tom River, as manifested by a water-temperature change in the 

Willamette River ........................................................................... 18

Figure 9. Graphs showing modeled temperature changes associated with shade 

restoration along selected 5-mile reaches of the upper Willamette River, 

from river mile 116.87 near Albany to river mile 176.80 just upstream of the 

McKenzie River confluence ............................................................... 20

Figure 10. Photograph showing aerial view of Cougar Dam and Reservoir, looking south ... 21

Figure 11. Graph showing seasonal water temperature patterns in the South Fork 

McKenzie River upstream and downstream of Cougar Reservoir, prior to the 

construction of a selective withdrawal tower at Cougar Dam, Oregon, 2001 ...... 22

Figure 12. Graph showing seasonal water temperature patterns in the South Fork 

McKenzie River downstream of Cougar Dam in 2001, 2002, and 2006 ............... 23

Figure 13. Modeled changes in the 7-day moving average of the daily maximum 

water-temperature difference in the South Fork McKenzie and McKenzie 

Rivers in response to the construction of a selective withdrawal tower at 

Cougar Dam, Oregon ........................................................................ 24

Figure 14. Modeled changes in the 7-day moving average of the daily maximum watertemperature difference in the South Fork McKenzie, McKenzie, and Willamette 

Rivers in response to the construction of a selective withdrawal tower at 

Cougar Dam, Oregon ........................................................................ 25

Figure 15. Graph showing effects of the Cougar Dam selective withdrawal tower on the 

cumulative heating effects of the modeled point sources.............................. 26
Tables

Table 1. Point sources of heat included in the Willamette River flow and temperature 

models ....................................................................................... 8

Table 2. Locations of tributaries included in the Willamette River flow and temperature 

models that discharge to the Willamette or Coast Fork Willamette Rivers ......... 13

Table 3. Prediction errors of the Trading Tool when used to estimate the effects of 

several hypothetical heat-trading test cases .......................................... 14

Table 4. Cooling effects of several shading scenarios on the Willamette River, Oregon ... 21

Conversion Factors, Datums, and Acronyms and 

Abbreviations

Conversion Factors

Multiply By To obtain

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

acre 4,047 square meter (m2

)

acre-foot (acre-ft) 1,233 cubic meter (m3

)

cubic foot per second (ft3

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

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

°F=(1.8×°C)+32.

Datums

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).
vi

Acronyms and Abbreviations

Acronyms and Abbreviations Meaning

7dADM 7-day moving average of the daily maximum, usually referring to water 

temperature.

7Q10 Lowest 7-day average streamflow that would be expected to occur once 

in 10 years.

ACWA Oregon Association of Clean Water Agencies.

HUA Human Use Allowance, defined in the State of Oregon watertemperature standard as the maximum allowable increase in water 

temperature attributable to anthropogenic influences and quantified as 

0.3°C.

NTP Natural Thermal Potential, defined in the State of Oregon watertemperature standard as the condition which serves as a pseudo-natural 

baseline for comparisons of point-source and non-point-source heating 

effects in the Total Maximum Daily Load.

ODEQ Oregon Department of Environmental Quality.

POMI Point of Maximum Impact, defined as the location of a cumulative 

point-source heating maximum determined on the basis of model 

results.

PSU Portland State University.

TMDL Total Maximum Daily Load, defined either as the maximum allowable 

load of a pollutant that a water body can carry without violating waterquality standards, or more commonly, the plan created by a regulatory 

agency to bring a water body back into compliance with water-quality 

standards.

TSRF Time series output frequency

USACE U.S. Army Corps of Engineers.

USGS U.S. Geological Survey.

Conversion Factors, Datums, and Acronyms and 

Abbreviations—Continued
Abstract

Water temperature is an important factor influencing the 

migration, rearing, and spawning of several important fish 

species in rivers of the Pacific Northwest. To protect these fish 

populations and to fulfill its responsibilities under the Federal 

Clean Water Act, the Oregon Department of Environmental 

Quality set a water temperature Total Maximum Daily Load 

(TMDL) in 2006 for the Willamette River and the lower 

reaches of its largest tributaries in northwestern Oregon. As 

a result, the thermal discharges of the largest point sources of 

heat to the Willamette River now are limited at certain times of 

the year, riparian vegetation has been targeted for restoration, 

and upstream dams are recognized as important influences 

on downstream temperatures. Many of the prescribed pointsource heat-load allocations are sufficiently restrictive that 

management agencies may need to expend considerable 

resources to meet those allocations.

Trading heat allocations among point-source dischargers 

may be a more economical and efficient means of meeting the 

cumulative point-source temperature limits set by the TMDL. 

The cumulative nature of these limits, however, precludes 

simple one-to-one trades of heat from one point source to 

another; a more detailed spatial analysis is needed. In this 

investigation, the flow and temperature models that formed 

the basis of the Willamette temperature TMDL were used to 

determine a spatially indexed “heating signature” for each of 

the modeled point sources, and those signatures then were 

combined into a user-friendly, spreadsheet-based screening 

tool. The Willamette River Point-Source Heat-Trading Tool 

allows the user to increase or decrease the heating signature of 

each source and thereby evaluate the effects of a wide range 

of potential point-source heat trades. The predictions of the 

Trading Tool were verified by running the Willamette flow 

and temperature models under four different trading scenarios, 

and the predictions typically were accurate to within about 

0.005 degrees Celsius (°C).

In addition to assessing the effects of point-source heat 

trades, the models were used to evaluate the temperature 

effects of several shade-restoration scenarios. Restoration 

of riparian shade along the entire Long Tom River, from its 

mouth to Fern Ridge Dam, was calculated to have a small 

but significant effect on daily maximum temperatures in 

the main-stem Willamette River, on the order of 0.03°C 

where the Long Tom River enters the Willamette River, and 

diminishing downstream. Model scenarios also were run 

to assess the effects of restoring selected 5-mile reaches of 

riparian vegetation along the main-stem Willamette River 

from river mile (RM) 176.80, just upstream of the point 

where the McKenzie River joins the Willamette River, to RM 

116.87 near Albany, which is one location where cumulative 

point-source heating effects are at a maximum. Restoration 

of riparian vegetation along the main-stem Willamette River 

was shown by model runs to have a significant local effect on 

daily maximum river temperatures (0.046 to 0.194°C) at the 

site of restoration. The magnitude of the cooling depends on 

many factors including river width, flow, time of year, and 

the difference in vegetation characteristics between current 

and restored conditions. Downstream of the restored reach, 

the cooling effects are complex and have a nodal nature: at 

one-half day of travel time downstream, shade restoration 

has little effect on daily maximum temperature because water 

passes the restoration site at night; at 1 full day of travel time 

downstream, cooling effects increase to a second, diminished 

maximum. Such spatial complexities may complicate the 

trading of heat allocations between point and nonpoint 

sources.

Upstream dams have an important effect on water 

temperature in the Willamette River system as a result of 

augmented flows as well as modified temperature releases 

over the course of the summer and autumn. The TMDL was 

formulated prior to the installation of a selective withdrawal 

tower at Cougar Dam on the South Fork McKenzie River; 

construction was completed early in 2005. Model runs 

were used to evaluate the likely effects of the new tower 

Temperature Effects of Point Sources, Riparian 

Shading, and Dam Operations on the Willamette 

River, Oregon

By Stewart A. Rounds
on downstream water temperatures, which were quantified 

using the 7-day moving average of the daily maximum. The 

changes were determined to be largest in the South Fork 

McKenzie River, with maximum mid-summer warming of 

6.0–6.5°C and maximum cooling of more than 5.0°C in 

October. The effect was diluted in the main-stem McKenzie 

River, with mid-summer warming of as much as 1.5 or 2.0°C 

and autumn cooling of more than 1.5°C. The effects were 

further diminished downstream in the Willamette River, with 

temperature changes as large as 0.4–0.5°C upstream of the 

Santiam River confluence (RM 108.5) and no more than 0.3°C 

downstream of that point.

Introduction

Background

The water-temperature standard for the State of Oregon 

was designed to protect the needs of targeted fish species 

during critical periods when they use rivers for spawning, 

rearing, migration, or other life stages (Oregon Department 

of Environmental Quality, 2007a). Many rivers in western 

Oregon, including the Willamette River and many of its 

tributaries, exceed the maximum water-temperature standard, 

most typically during summer when salmonids are rearing 

or migrating, or during spring or autumn when salmonids 

are spawning. The Federal Clean Water Act requires that 

exceedances of water-quality standards be addressed, and in 

this case a plan of remediation was required for the Willamette 

River under the Act’s Total Maximum Daily Load (TMDL) 

provisions.

In September of 2006, after many years of data collection 

and modeling, the Oregon Department of Environmental 

Quality (ODEQ) finalized the Willamette temperature TMDL 

(Oregon Department of Environmental Quality, 2006a and 

2006b). A large part of the TMDL focuses on the main-stem 

Willamette River and selected major tributaries (Fall Creek 

as well as the Clackamas, Santiam, North Santiam, South 

Santiam, Long Tom, McKenzie, South Fork McKenzie, Coast 

and Middle Fork Willamette, and Row Rivers) as far upstream 

as the first major dam on each tributary (fig. 1). The TMDL 

is meant to regulate several important sources of temperature 

alteration in this system, including upstream and instream 

dams, riparian vegetation, and point-source discharges.

Dams have an important effect on flow and temperature 

in the rivers downstream of those projects (Collier and others, 

1996). The U.S. Army Corp of Engineers built and operates a 

system of 13 dams in the Willamette River basin that provides 

flood control, recreation, power production, and summertime 

flow augmentation for navigation, among other uses. Many 

of these dams are tall enough, and their point of release is 

low enough, that the temperature of water releases in July and 

August typically is far cooler and the temperature of releases 

in September and October typically is far warmer than what 

would occur in the absence of the dam (Sullivan and Rounds, 

2004). The direct temperature effect diminishes with distance 

downstream, though the effect is still measurable for many 

tens of miles or more, depending on various factors. The 

upstream dams in the Willamette River system were given 

monthly temperature targets under the TMDL in an attempt to 

restore a more natural seasonal temperature pattern and ensure 

compliance with the temperature standard at that point and in 

nearby downstream reaches.

A major nonpoint source of heat to the Willamette River 

and its tributaries is a degraded level of riparian shading that 

allows a greater amount of solar radiation to be absorbed 

by adjacent rivers. Under the TMDL, riparian vegetation is 

required to be restored to a more natural level, calculated using 

information on the types of vegetation that typically grow 

on certain surficial geologic units and accounting for some 

natural level of disturbance.

The thermal effects of both point-source discharges and 

riparian shading were assessed for the TMDL by using a set of 

flow and temperature models developed for that application. 

The effects of the point sources were evaluated relative to a 

baseline condition termed Natural Thermal Potential (NTP), 

defined under the State of Oregon water-temperature standard 

(Oregon Department of Environmental Quality, 2007b) as

“the determination of the thermal profile of a water 

body using best available methods of analysis and 

the best available information on the site-potential 

riparian vegetation, stream geomorphology, 

stream flows, and other measures to reflect natural 

conditions.”

Essentially, NTP represents the water temperature that 

would occur in a stream if certain anthropogenic influences 

were either minimized or eliminated. For the Willamette 

temperature TMDL, NTP conditions were defined as the 

water temperatures that would occur in the absence of point 

sources, with restored riparian vegetation, without Portland 

General Electric’s cap and flashboards at Willamette Falls, and 

without the Eugene Water and Electric Board’s hydroelectric 

diversions on the McKenzie River. Water withdrawals for 

municipal, agricultural, and industrial uses were included in 

the NTP baseline conditions, as were the effects of upstream 

dams. A more historic channel shape was not included in the 

TMDL definition of NTP.

Using the Willamette flow and temperature models, NTP 

conditions were defined for a modeled time period in 2001 and 

2002, and the cumulative thermal effects of the largest point 

sources were assessed. That assessment was done only for the 

most critical conditions, when the rivers exceeded the numeric 

criteria of the temperature standard under NTP conditions. 

 Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Figure 1. Location of the river network, the modeled river reaches, and major reservoirs in the Willamette River basin, Oregon.

ORWSC19_0149_fig_01

5

5

WASHINGTON

COLUMBIA

DOUGLAS

LANE

LINN

MARION

POLK

BENTON

CLACKAMAS

MULTNOMAH

YAMHILL

N Fk

M Fk Willamette River

Mohawk

Marys

Middle

Santiam

N

Santiam River

Pudding

River

S

River

River

Clackamas

River

Molalla

Calapooia

River

River

River

River

River

Fork

Coast Fk

Tualatin

River

Santiam

S

River

Yamhill

RIVER

River

Lookout Point

Lake

Foster

Lake

River

Fern

Ridge

Lake

Willamette Hills

Creek

Lake

McKenzie

Cougar

Reservoir

Dorena

Lake

Cottage

Grove

Lake

Long Tom River

COLUMBIA

N Yamhill

Luckiamute

Detroit

Lake

RIVER

SF

McKenzie R

Row

R.

River

Green

Peter

Lake

WILLAMETTE

Middle

N Fk

M Fk Willamette River

Mohawk

Marys

Middle

Santiam

N

Santiam River

Pudding

River

S

River

River

Clackamas

River

Molalla

Calapooia

River

River

River

River

River

Fork

Coast Fk

Tualatin

River

Santiam

S

River

Yamhill

RIVER

River

Lookout Point

Lake

Foster

Lake

River

Fern

Ridge

Lake

Willamette Hills

Creek

Lake

McKenzie

Cougar

Reservoir

Dorena

Lake

Cottage

Grove

Lake

Long Tom River

COLUMBIA

N Yamhill

Luckiamute

Detroit

Lake

RIVER

Fall Creek

Lake

SF

McKenzie R

Row

River

River

Green

Peter

Lake

Santiam

River

WILLAMETTE Middle

Blue River

Lake

Fall

Creek

River Mill

Dam

Big Cliff

Dam Detroit

Dam

Foster

Dam

Cougar

Dam

Fall Creek

Dam

Lookout

Point

Dam

Dexter

Dam

Dorena

Dam

Cottage

Grove Dam

EXPLANATION

River reaches included in the modeling 

 domain—The entire main-stem Willamette

 River and selected major tributaries as 

 far upstream as the first major dam on

 each tributary

Eugene

Cottage

Grove

Albany

Newberg

Portland

West Linn

Corvallis

Wilsonville

Salem

OREGON

WASHINGTON

C

O

A

S

T

R

A

N

G

E

C

A

S

C

A

D

E

R

A

N

G

E

RM 0

RM 20

RM 10

RM 30 RM 40 RM 50

RM 60

RM 70

RM 80

RM 90

RM 100

RM 110

RM 120

RM 130

RM 140

RM 150

RM 160

RM 170

RM 180

RM 190

RM 200

RM 210

RM 170 River mile

Dam

OREGON

Willamette

River Basin

124°00' 123°30' 123°00' 122°30' 122°00' 121°30'

46°

00'

45°

30'

45°

00'

44°

30'

44°

00'

43°

30'

Base map modified from U.S. Geological Survey and other digital data sets (1:2,000,000; 

1:100,000). Projection: Oregon Lambert Conformal Conic, NAD1983, NAVD1988. 

124°00' 123°30' 123°00' 122°30' 122°00' 121°30'

46°

00'

45°

30'

45°

00'

44°

30'

44°

00'

43°

30'

0 10 20 30 40 MILES

0 10 20 30 40 KILOMETERS

Introduction 
Under such conditions, Oregon’s temperature standard 

specifies that NTP temperatures become the applicable 

temperature criteria, and anthropogenic heating effects must 

be limited to a small amount (0.3°C), called the Human Use 

Allowance (HUA). Using this type of analysis and a policy 

decision specifying that 0.23°C of the HUA could be assigned 

to the point sources, ODEQ used the models iteratively to 

determine maximum heat-load allocations for each of the 

permitted point-source facilities.

In the final TMDL, many of the point sources’ heat 

allocations are sufficiently restrictive that accommodating 

current conditions and future growth may be difficult without 

corrective action or an increased heat-load allocation. Several 

different strategies are being proposed in an attempt to 

accommodate existing and future heat loads. One alternative 

is for each point source to find ways to reduce their heat 

load, possibly by decreasing the amount of water discharged. 

For example, many municipalities have programs in which 

treated wastewater is piped to nearby golf courses for use as 

irrigation water. If the heat load contributed by a point source 

could be decreased, then that point source might no longer 

need all of its heat allocation under the TMDL. By accepting 

a lower allocation, a “credit” could be created that might be 

traded or sold to another point source that needs a higher 

allocation. This sort of trading is allowed under the Willamette 

temperature TMDL.

Trading of heat allocations among the dischargers and 

designated management agencies, including direct pointsource trading or point-source to nonpoint-source trading, may 

be an efficient means of meeting the obligations of the point 

sources under the Willamette temperature TMDL while also 

improving the river ecosystem. A framework for creating a 

marketplace for trading “ecosystem service” credits, including 

temperature credits, is being pursued by the Willamette 

Partnership (http://willamettepartnership.org/). Quantitative 

tools are needed, however, to assess the temperature effects 

of any proposed action or trade. In this investigation, the U.S. 

Geological Survey (USGS) worked in cooperation with the 

Oregon Association of Clean Water Agencies (ACWA) and the 

Willamette Partnership to address some of these temperaturerelated issues under the TMDL.

Purpose and Scope

The purpose of this investigation was to develop a 

better understanding of the effects of point and nonpoint 

sources of heat as well as upstream dam operations on water 

temperature in the Willamette River and the lower reaches of 

its largest tributaries. The investigation was geared primarily 

toward quantifying these effects in the context of the thermal 

allocations set by the Willamette temperature TMDL. 

Specifically, the objectives of this investigation were to:

Evaluate the efficacy of various point-source heat 

allocation trading scenarios, including the partial or 

complete removal of selected point-source discharges 

from the river, with the goal of allowing for future 

growth and the efficient use of existing capacity by 

other point sources;

Evaluate the effect of increased point-source 

heat allocations on the temperature regime of the 

Willamette River;

Evaluate the effect of selected riparian shaderestoration projects on the thermal characteristics of 

the Willamette River system; and

Evaluate the effect of changed operations at Cougar 

Dam on downstream water temperatures, including 

the potential effect of those operations on downstream 

point-source heat allocations.

Through these objectives, this investigation was designed 

to develop a better overall understanding of anthropogenic 

influences on water temperature in the main-stem Willamette 

River, and provide information and tools that might be used in 

the development of a heat-trading system that operates within 

the limits set by the Willamette temperature TMDL. This 

report documents the results of this investigation.

Both the spatial and temporal scopes of this investigation 

were aligned with those used in the development of the 

TMDL. The Willamette flow and temperature models, 

developed previously to form the basis for the temperature 

TMDL, were used to simulate the time periods from June 

1 through October 31 of 2001 and from April 1 through 

October 31 of 2002. The models include the entire main-stem 

Willamette River as well as the lower reaches of selected 

tributaries (Clackamas, Santiam, North Santiam, South 

Santiam, Long Tom, McKenzie, South Fork McKenzie, 

Middle and Coast Fork Willamette, and Row Rivers, as well as 

Fall Creek) up to their first major dams (fig. 1); the McKenzie 

River was modeled only up to the point where it is joined 

by the South Fork McKenzie River. By keeping the same 

spatial and temporal domains as those used in the Willamette 

temperature TMDL, the results of this investigation can be 

directly compared to and augment the information and results 

created during the TMDL process.

•

•

•

•

 Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Description of Models

The Willamette flow and temperature models were 

constructed using CE-QUAL-W2, a two-dimensional 

(longitudinal, vertical) model from the U.S. Army Corps 

of Engineers (Cole and Wells, 2002). CE-QUAL-W2 is a 

physically based mechanistic model that simulates gravityand wind-driven flow through a network of interconnected 

river channels or reservoir reaches by using channel geometry 

and slope, bottom friction, wind shear, density effects, and 

upstream/downstream flow or water-level data. Algorithms 

to calculate the effect of hydraulic structures such as weirs, 

pumps, and spillways are included. Horizontal and vertical 

velocities, flow, and stage are simulated.

Water temperature is modeled in CE-QUAL-W2 by 

using a detailed expression of the energy budget of the water 

body. The model includes algorithms to calculate the effects 

of both topographic and vegetative shading. Using latitude, 

longitude, time of day, and the water body’s orientation, the 

model determines at each time step the presence or absence of 

a topographic or vegetative shadow on the water surface, the 

length of any shadow, and the degree to which that shadow 

shields the water body from solar radiation. Model inputs 

include meteorological data, topographic shading angles, 

tree-top elevations, distance to the vegetation, and solarreduction factors associated with the riparian canopy that vary 

by location. This detailed representation of the heat budget and 

the effects of riparian shading was one of the major reasons 

that ODEQ chose to use CE-QUAL-W2 for the Willamette 

temperature TMDL analysis.

In addition to modeling flow and water temperature, 

CE-QUAL-W2 can simulate many water-quality constituents, 

including conservative and nonconservative tracers, 

bacteria, different forms of nitrogen (nitrate and ammonia) 

and phosphorus, multiple phytoplankton and epiphyton 

groups, dissolved oxygen, multiple suspended-sediment 

groups, and dissolved and particulate organic matter. These 

capabilities were not used in the Willamette temperature 

TMDL application but may be used to build on these models 

in the future. CE-QUAL-W2 has open source code, good 

documentation, and a large user community. In addition, it 

has a long history of successful application to a wide range 

of lake, reservoir, estuary, and river systems (Cole and Wells, 

2002). USGS users have found that CE-QUAL-W2 is capable 

of simulating water temperature with a mean absolute error 

of 0.5 to 1.0°C (Bales and others, 2001; Green, 2001; Rounds 

and Wood, 2001; Sullivan and Rounds, 2005 and 2006).

The Willamette modeling suite is composed of nine 

submodels. These models can be linked together by passing 

the output of any upstream models to the input of downstream 

models. Such connections can be made using filters and scripts 

so that the linkages are automatic and transparent. The nine 

submodels include:

Lower Willamette River, with connections to the 

Columbia River

Middle Willamette River, from RM 26.5 (Willamette 

Falls) to RM 85.5 upstream of Salem

Upper Willamette River, as far upstream as the 

confluence of the Coast and Middle Forks

Clackamas River, the lower 26 miles downstream of 

River Mill Dam

Santiam and North Santiam Rivers, downstream of Big 

Cliff Dam

South Santiam River, downstream of Foster Dam

Long Tom River, downstream of Fern Ridge Dam

McKenzie River as far upstream as its confluence with 

the South Fork McKenzie River, plus the South Fork 

downstream of Cougar Dam

Coast and Middle Forks Willamette River, downstream 

of Cottage Grove Dam on the Coast Fork and 

Dexter Dam on the Middle Fork, including the Row 

River downstream of Dorena Dam and Fall Creek 

downstream of Fall Creek Dam.

In general, these models include the entire main-stem 

Willamette River and most of its major tributaries as far 

upstream as the first major dam on each tributary (fig. 1). 

Version 3.12 of CE-QUAL-W2 was used to build all 

submodels. The Santiam and North Santiam River model 

was constructed by USGS (Sullivan and Rounds, 2004). 

The South Santiam River model was constructed by ODEQ 

with assistance from Dr. Scott Wells’ research team at 

Portland State University (PSU). The rest of the models were 

constructed by the PSU modeling team (Annear and others, 

2004a and 2004b; Berger and others, 2004).

All models were calibrated to measured temperatures at 

many locations for June 1 to October 31, 2001, and April 1 to 

October 31, 2002. The summer of 2001 was a drought period, 

with low flows at or near post-dam 7Q10 low-flow levels in 

many of the modeled rivers. The 7Q10 is the lowest 7-day 

average streamflow that would be expected to occur once in 

10 years. Hydrologic conditions in 2002, in contrast, were 

more typical. The models’ water-temperature predictions were 

in good agreement with measured data; mean absolute errors 

generally were less than 1.0°C (Berger and others, 2004; 

Sullivan and Rounds, 2004).

•

•

•

•

•

•

•

•

•

Description of Models 
Code Changes

All submodels originally were calibrated and run 

with a slightly modified form of CE-QUAL-W2, based on 

version 3.12 from August 19, 2003. The PSU modeling team 

made one enhancement to that code, which created several 

new output files. These custom outputs contained the daily 

maximum water temperature from each segment in the model 

at a user-specified output frequency, calculated using either 

the surface temperature, a volume-weighted temperature, 

or a flow-weighted temperature. Having these quantities 

pre-calculated by the model simplified the post-processing 

of model results. Further modifications were made to the 

model code by the USGS for this investigation to make the 

models easier to use and to eliminate some minor problems. 

The details of the USGS code changes are described in 

appendix A. The models used in this investigation are 

available online from the USGS project website (see section, 

“Supplemental Material”).

Model Modifications

After receiving the Willamette models from ODEQ, 

USGS staff performed a detailed review and found a few 

problems that required attention. Several modifications were 

made to the models to correct errors, remove instabilities, and 

make the results more usable.

Point-Source Spreadsheet Errors

For each of the modeled point sources, a spreadsheet 

was crafted by ODEQ staff to calculate the allowable effluent 

flows and temperatures that result from each source’s 

wasteload allocation formula. The resulting time series of 

flow and temperature were used in the Willamette temperature 

models. The spreadsheet calculations, however, were not 

entirely consistent with the TMDL’s final wasteload allocation 

formulas. Two errors were discovered, both of which relate 

to the calculation and use of an adjustment factor (“a”) in the 

point-source flow-scaling equation of the TMDL (see Oregon 

Department of Environmental Quality, 2006b, for more details 

on the TMDL’s point-source allocation framework). USGS 

staff corrected these errors in the point-source spreadsheets, 

and the allowable point-source flows and temperatures were 

recalculated. The changes were largest for those point sources 

that discharge to the Willamette River and its tributaries 

upstream of the Santiam River (river mile [RM] 108.5); the 

modeled point-source discharges increased slightly at certain 

times of the year. For the rest of the point sources, the changes 

were small and typically negligible.

Tri-City WWTP Oversight

The Tri-City wastewater treatment plant (WWTP), 

which discharges to the lower Willamette River at about 

RM 25.5, was inadvertently modeled by ODEQ with flows 

and temperatures calculated for the Wacker Siltronics point 

source. The Tri-City WWTP is a larger source than Wacker, 

with higher flows and somewhat similar temperatures. After 

correcting this error, the modeled cumulative temperature 

effect of the point sources increased slightly in the lower 

Willamette River.

Travel-Time Offsets

The additional flow in a river contributed by a 

point-source discharge has an effect on downstream 

temperatures—the magnitude of which depends on river 

flow and point-source flow. Downstream of dams, increasing 

streamflow through point-source additions can slightly 

modify downstream patterns in the 7-day moving average 

of the daily maximum (7dADM) temperature. Such changes 

in downstream temperature patterns can complicate the 

analysis of cumulative point-source heating effects because 

temperature changes resulting from travel-time modifications 

are complex and difficult to disentangle from the more 

straightforward point-source heating effects. Because of this 

problem, ODEQ modeled most of the point sources with an 

associated upstream withdrawal of the same magnitude in 

an attempt to eliminate the travel-time artifact. The Cottage 

Grove WWTP did not have an associated time-of-travel offset 

(withdrawal) in the original ODEQ model. By adding such an 

offset, a slight travel-time anomaly in the Coast Fork model 

results was eliminated.

Model Instabilities

Two specific model instabilities were identified and 

eliminated. The first occurred in the Coast Fork model and 

affected the simulated 7dADM water temperature for RMs 

195.6–186.4 for April 18–24, 2002. This instability was 

eliminated by reducing the model’s maximum allowable time 

step from April 16–26, 2002. The second instability occurred 

in the upper Willamette model and affected the 7dADM water 

temperature for RMs 94.8–85.5 for October 2–27, 2002. The 

problem was caused by slightly increased flows on day 277, 

and only occurred for model runs that included point sources 

in the Santiam River system. The Santiam sources (WWTPs at 

Jefferson, Stayton, Lebanon, and Sweet Home), though small, 

were large enough to cause the slightly elevated Willamette 

flows that triggered the instability. These sources had not 

been given time-of-travel offsets by ODEQ in the original 

model runs; adding such offsets was sufficient to eliminate the 

instability. By removing these instabilities and their associated 

artifacts in the modeled 7dADM temperatures, the model 

results were more usable.

 Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Upper Willamette Distributed Tributary Temperatures

The temperatures assigned to the distributed tributaries 

(ground water and ungaged tributaries) of the upper 

Willamette model for branches 1-6 were not consistent in 

the ODEQ models. Different temperatures were used for 

the model runs that included point sources, as compared to 

model runs that had no point sources. The distributed tributary 

temperatures in the former were slightly higher than those 

used in the latter, resulting in a small additional temperature 

increase in the “with point sources” model run that was not 

caused by the point sources. This problem was fixed by 

consistently assigning these temperatures to those used in the 

“without point sources” run.

Lower Willamette Timing Artifacts

Because of the relatively large time steps used in the 

lower Willamette River model, different model runs did not 

necessarily calculate their daily maximum water temperatures 

from the same time of day. The maxima could have been 

extracted from model results that were several minutes apart. 

This timing discrepancy led to temperature differences, 

when comparing two model runs, on the order of several 

hundredths of a degree or more, which in turn led to problems 

in subsequent data analysis, particularly when adding together 

the results of many model runs. The solution was to decrease 

the maximum time step in the lower Willamette River model 

from 360 to 60 seconds, and use a slightly different version 

of the model that determined the daily maximum temperature 

by using information from every time step rather than a userspecified number of times per day (see appendix A).

Flow-Weighted Daily Maximum Temperatures

In assessing the heating effects of point and nonpoint 

sources on the river system, ODEQ opted to use daily 

temperature maxima from the river surface for every submodel 

except the upper, middle, and lower Willamette River. In 

those three submodels, the flow-weighted daily maxima were 

used. The lower Willamette River model, however, produces 

some anomalies in the flow-weighted daily maximum water 

temperatures that appear when 7dADM temperatures from 

two different model runs are subtracted. This “noise” is 

compounded when adding the effects from multiple model 

runs, making those results unusable for some purposes. 

Tests showed that the volume-weighted daily maximum 

temperatures, which do not contain this sort of noise, could 

be used in place of the flow-weighted daily maximum 

temperatures for the lower Willamette River without losing 

any pertinent information. In this work, therefore, USGS used 

the volume-weighted daily maxima rather than the flowweighted daily maxima from the lower Willamette River 

model.

Methods

Model results were analyzed using the same general 

method used by ODEQ in the development of the Willamette 

temperature TMDL. That method may be summarized as 

follows:

Determine the 7-day moving average of the daily 

maximum (7dADM) water temperature for every model 

segment and every day simulated in each model run. 

Flow-weighted daily maximum temperatures were used 

for the upper and middle Willamette River models. 

Volume-weighted daily maximum temperatures were 

used for the lower Willamette River model (ODEQ 

used flow-weighted, as discussed previously). Surface 

daily maximum temperatures were used for all other 

submodels.

Subtract the 7dADM temperatures for the “without 

point sources” baseline model run from the 7dADM 

temperatures for the target model run (for example, 

a “with point sources” run) for every model segment 

and every simulated day. The result is a distribution of 

7dADM temperature differences at each location in the 

model. The “without point sources” baseline run typically 

was the Natural Thermal Potential, or NTP, run.

Determine the 95th percentile of the 7dADM temperature 

differences at each location. Data were grouped together 

in several different ways to calculate these percentiles, 

either for all of 2001 and 2002, or by month, or by a 

fish-use designation time period defined in Oregon’s 

temperature standard. In the calculation of the 95th

percentile, data points were included from a particular 

location and time only if they adhered to two particular 

criteria. If the criteria are met, then the data point is 

included; if either is not met, then the data point is 

excluded from the computation of the 95th percentile. 

Those criteria are:

a. The 7dADM temperature from the NTP run at that 

time exceeds the numeric criteria of the temperature 

standard at some point downstream. The focus is 

on the most critical conditions, when the allowable 

temperature increase is most restricted by the 

standard.

b. The modeled daily average flow at the appropriate 

point of maximum impact (POMI) is equal to or 

greater than the post-dam 7Q10 low-flow statistic 

at that location. The POMI is the location of 

a cumulative point-source heating maximum 

determined on the basis of model results. POMI 

locations are at or near Albany in the upper 

1.

2.

3.

Methods 
Willamette River model, in the Newberg pool or at 

Salem in the middle Willamette River model, and 

in the Portland Harbor for the lower Willamette 

River model. Local POMIs were used for the 

Coast Fork and McKenzie River models. 7Q10 flow 

values were obtained from the ODEQ’s Willamette 

temperature TMDL document (Oregon Department 

of Environmental Quality, 2006b).

This analysis method was discussed with ODEQ staff prior to 

its use, and it was agreed that this method was very similar, if 

not identical, to the method used by ODEQ to analyze model 

results for the TMDL.

Note that at least six different common methods can 

be used to compute percentiles, and no good agreement 

exists as to which is preferred. The SAS statistics package 

alone offers five separate methods for calculating percentiles 

(SAS Institute, 1990). ODEQ staff relied on Microsoft©

Excel to compute percentiles, and Excel’s method, though 

related, does not match any of those offered by SAS. Most 

of these percentile methods differ in their assumptions for 

the intervals that surround each ranked data point; as a result, 

the computations differ most when applied at the extremes 

of the distribution, such as at the 5th or 95th percentile. In this 

analysis, the method documented by Helsel and Hirsch (2002) 

and identical to SAS Proc Univariate’s definition 4 was used 

to compute the 95th percentiles. This method is widely applied, 

but may result in slightly higher 95th percentiles with some 

datasets, as compared to those computed by Excel.

Temperature Effects of Point Sources

The Willamette temperature TMDL quantified the 

cumulative heating effects of a set of 27 point-source 

discharges to the Willamette River and selected tributaries, 

set maximum heat-loading limits for each, and provided for 

the potential trading of such heat-load allocations, among 

other things. The TMDL did not provide any tools or spatially 

linked quantifications of individual point-source heating 

effects, however, that might be used to assess potential pointsource heat-allocation trades. To assess the efficacy of such 

trades, the Willamette flow and temperature models were 

used in this investigation to determine individual “heating 

signatures” for each of the 27 modeled point sources listed in 

table 1. Those signatures then were used to create a screening 

tool in which the magnitude of the heating signature for 

each point source can be increased or decreased to simulate 

the effects of potential changes in point-source heat-load 

allocations. The aim of the screening tool was to facilitate 

the evaluation of point-source to point-source heat-allocation 

trading.

The heating signature for each point source was 

determined by running the Willamette temperature models 

under the TMDL’s NTP baseline conditions, but with the 

addition of that single point source at its maximum wasteload 

allocation under the TMDL. The model results then were 

processed as described in the section “Methods” to obtain 

the 95th percentile of the 7dADM temperature differences 

caused by that point source; that 95th percentile as a function 

of downstream distance is the point source’s heating signature. 

The process was repeated with each of the 27 point sources to 

determine each of the 27 heating signatures. A spreadsheetbased screening tool was created to add the heating signatures 

together and thereby estimate the cumulative heating effects of 

all modeled point sources.

Table 1. Point sources of heat included in the Willamette River 

flow and temperature models.

[Locations are provided for point sources that discharge to the 

Willamette or Coast Fork Willamette Rivers. Abbreviations:

RM, river mile; MWMC, Metropolitan Wastewater Management 

Commission; WWTP, wastewater treatment plant; U of O, University 

of Oregon; NA, not applicable]

Entity Location 

(RM)

Receiving 

stream

Cottage Grove WWTP 207.4 Coast Fork

U of O Heat Plant 181.6 Willamette

MWMC (Eugene/Springfield) 177.9 Willamette

Weyerhaeuser Springfield NA McKenzie

Fort James Halsey 147.6 Willamette

Pope and Talbot 147.6 Willamette

Evanite Fiber 132.8 Willamette

Corvallis WWTP 131.0 Willamette

Albany WWTP 118.4 Willamette

Teledyne Wah Chang 117.2 Willamette

Weyerhaeuser Albany 117.2 Willamette

Sweet Home WWTP NA South Santiam

Lebanon WWTP NA South Santiam

Stayton WWTP NA North Santiam

Jefferson WWTP NA Santiam

Salem WWTP 78.9 Willamette

S&P Newsprint 50.2 Willamette

Newberg WWTP 50.0 Willamette

Wilsonville WWTP 38.9 Willamette

West Linn Paper 26.2 Willamette

Blue Heron Paper 26.4 Willamette

Tri City WWTP 25.5 Willamette

Clackamas Fish Hatchery NA Clackamas

Tryon Creek WWTP 20.4 Willamette

Oak Lodge WWTP 20.1 Willamette

Kellogg Creek WWTP 18.7 Willamette

Wacker Siltronics 6.6 Willamette

 Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Heating Signature Summation Issues

Point-Source Independence

The summation of individual point-source heating 

signatures by the screening tool is only valid in predicting 

the cumulative point-source heating effect if the temperature 

changes that result from each point source are largely 

independent of one another. The temperature changes caused 

by many of these point sources, however, do not completely 

dissipate by the time a downstream point source adds its 

heat to the river. To the extent that an upstream point source 

increases the temperature of the river at the location of a 

downstream point-source discharge, the temperature increase 

caused by the downstream source is slightly less than it 

would be in the absence of the upstream source. Therefore, 

the individual point sources are not completely independent, 

and the summation of the individual point-source heating 

signatures will not be a completely accurate prediction of the 

cumulative temperature effect of all point sources if they were 

modeled together; instead, the sum is likely to be slightly 

larger.

The magnitude of this point-source dependence problem 

diminishes as the temperature change associated with each 

point source decreases. Given that the point sources included 

in this investigation all have discharge flows that are small 

relative to the flow in their respective receiving streams, and 

that the temperature increases caused by each point source 

also are small (typically less than a few tenths of a degree 

Celsius), the point-source dependence problem also is likely 

small. Indeed, the effect was estimated for this investigation 

using a range of point-source flows (as much as 1/50th of the 

receiving stream’s flow) and a range of independent pointsource temperature increases (as large as 0.2°C). Under these 

conditions, the point-source dependence error is only on the 

order of a few thousandths of a degree Celsius. This error is 

small compared to the actual discrepancy between the sum 

of the individual point-source heating signatures and the 

cumulative temperature increase as predicted by a model run 

with all point sources included (fig. 2). Most of the observed 

error in using the sum of the point-source heating signatures, 

then, is not a result of point-source dependence issues.

220 200 180 160 140 120 100 80 60 40 20 0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coast Fork Willamette River

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) 

WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

RIVER MILE

Sum of individual point-source heating signatures

Location of tributary

Location of point source

95th percentile of 7dADM water-temperature difference; all sources in one model run

Figure 2. Comparison of the sum of the individual point-source heating signatures to the results from one model run 

containing all point sources. The difference is caused by (a) interdependence among the point-source heating signatures, 

and (b) the fact that the heating signatures, because they are defined as 95th percentiles, are not additive unless pointsource heating effects are completely synchronized in time.

Temperature Effects of Point Sources 
Addition of 95th Percentiles

The summation of the point-source 

heating signatures is complicated by the 

fact that each signature is defined as a 

95th percentile, and such percentiles from 

separate data distributions are only additive 

under certain conditions. This problem is 

illustrated in figure 3, in which two data 

distributions were added together in two 

different ways. In that figure, distributions A 

and B are normal distributions with means 

of 0.15 and 0.10, respectively, and identical 

standard deviations of 0.03. Distributions 

C and D represent the “random sum” and 

the “ranked sum” of A and B, respectively. 

The random sum is defined as the sum of 

members of distributions A and B, chosen 

randomly. In contrast, the ranked sum was 

created by first ranking the members of A 

and B, pairing them according to their ranks, 

and then adding them together. Statistical 

methods dictate that the standard deviation 

of the random sum, distribution C, is the 

square root of the sum of the variances of 

the distributions being added, giving a value 

of 0.042. In contrast, the standard deviation 

of the ranked sum, distribution D, is simply 

the sum of the standard deviations of A and 

B, resulting in a value of 0.06. Regardless 

of whether the distributions are normal, the 

fact remains that the ranked sums produce 

a wider distribution, and therefore have larger 95th

percentiles than those resulting from the random sum. 

One particularly useful result is that the 95th percentile 

of the ranked sum distribution is exactly equal to the 

sum of the 95th percentiles of distributions A and B.

The example using ranked and random sums 

illustrates that 95th percentiles from many datasets are 

only additive when the members of those datasets are 

tied together with similar ranks. Heating signatures 

from different point sources, therefore, may be added 

together only if the temperature changes caused by each 

of the point sources are not random, but “synchronized” 

with one another. So, in order for the sum of the heating 

signatures to be a good prediction of the results from a 

single model run that includes all point sources together, 

the modeled temperature change resulting from each 

point source can not be random relative to those that 

result from other point sources. The temperature change 

caused by a point-source discharge is determined 

by a number of factors, but streamflow and weather 

conditions are prime influences, and those flow and 

weather conditions are likely to be similar across the entire 

model domain. Therefore, when any one point source is 

modeled to have its greatest heating effect on the river, it is 

likely that all other point sources also have large, if not their 

largest, heating effects on the river. In this way, the pointsource heating effects are somewhat synchronized rather than 

random, and their heating signatures, though they are defined 

as 95th percentiles, probably can be added together without 

incurring a large amount of predictive error.

ORWSC19_0149_fig_03 

A B C D

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

 95th

90th

75th

50th

25th

10th

EXPLANATION

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) 

WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

DISTRIBUTION

Figure 3. Percentiles from two hypothetical normal distributions, 

A and B, as well as two distributions resulting from the addition 

of A and B. Distribution C is the random sum, in which members 

of distributions A and B were chosen randomly and added 

together. Distribution D is the ranked sum, in which the members 

of distributions A and B first were ranked, then paired according 

to their ranks and summed. The ranked sum results in the same 

mean but a wider distribution, resulting in larger 95th percentiles. 

The 95th percentile of D is equal to the sum of the 95th percentiles 

of A and B.

10 Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
 Despite the fact that the point-source heating effects 

are largely synchronized, the sum of the 27 point-source 

heating signatures is slightly larger than the 95th percentile 

of temperature increases resulting from a single model 

run containing all 27 point sources (fig. 2). The difference 

probably is because the heating effects from each point source 

are not completely synchronized in time with those from other 

point sources. The flow conditions that occur at each pointsource discharge location have similar seasonal and annual 

patterns, but may not conform to exactly the same patterns 

because of the influence of varying releases from upstream 

dams. Therefore, the heating effects of point sources that 

discharge to the Willamette River upstream and downstream 

of the McKenzie River confluence are affected by slightly 

different patterns in streamflow, which contributes to the 

difference shown in figure 2.

Adjustments and Strength Factors

The sum of the 27 heating signatures may be slightly 

larger than the results from one model run containing all point 

sources, but the difference is small enough that a correction 

factor can be formulated to adjust each of the heating 

signatures until the sum of all signatures is exactly equal to 

the results from that one model run. The formulation of the 

correction factor must be relatively simple and defensible, and 

yet still produce the desired result. One simple and logical 

way to adjust the heating signatures is to decrease each by a 

certain percentage, where the percentage varies as a function 

of location along the river because the required adjustment, as 

a percentage of the model results, also varies across the model 

domain. This adjustment by itself, however, is not enough 

because the sum of the heating signatures also needs to 

collapse to a single heating signature if all but one point source 

is removed from the analysis. If the percentage adjustment 

still remains in that case, then the prediction would be too low. 

So, the correction factor needs to include not only a factor 

that causes a percentage decrease, but also a second term that 

causes the correction factor to gradually be eliminated as any 

one point-source heating signature becomes the dominant 

member of the sum.

In addition to the correction factors, each heating 

signature was assigned a corresponding “strength factor” 

for use in the screening tool. The strength factor is simply a 

multiplicative factor that is used to linearly vary the magnitude 

of a particular heating signature. A strength factor of 1.0 

leaves the point source at its full wasteload allocation as 

specified in the Willamette temperature TMDL. A strength 

factor of 0.0 has the effect of removing that point source from 

the river. A strength factor of 0.5 cuts its effect in half, and a 

factor of 1.5 increases its effect by 50 percent. The strength 

factor may be thought of as a modification to its allowable 

flow, without a change in its temperature.

Accounting for the strength factors and correction 

terms, the resulting framework for the screening tool is 

manifested in the following equations. The sum of the heating 

signatures, multiplied by their strength factors and adjusted 

by a correction factor results in a prediction of the cumulative 

heating effect caused by the point sources:

∆

∆

T s h

T

= − ∑ i i ( ) 1 α ,

where

is the predicted cumulative temperature 

increase or heating effect of the point 

sources at any one location,

s is the strength factor for point source i i ,

is the temperature increase (heating signature) 

at tha

hi

t location caused by point source at its 

full TMDL allo

i

cation, and 

α is a correction factor at that location.

(1)

The correction factor is defined by:

α = β  −















∑

∑

h T

h

i

i

∆ *

, (2)

where ∆T* is the cumulative point-source temperature 

increase (heating effect) as calculated from one model run 

containing all point sources at their full TMDL heat-load 

allocations. The term in parentheses is a fractional adjustment 

and is the same for each point source, but varies by location. 

The second factor in that equation, β, also varies with location 

and is the term that causes the correction factor to become zero 

when any one point source dominates the strength-weighted 

sum of heating signatures; it is defined with the following 

asymptotic formula:

β λ

γ λ

λ

= ( ) −

( ) − + − ( )

















1 5 1

0 5 1 1

.

. ,

where

is the largest fraction of the strength-weighted 

sum of heating signatures resulting from any 

one point source at that location:

(3)

Temperature Effects of Point Sources 11
λ

γ

= ( )

∑

max , s h

s h

i i

i i

and

 is the largest fraction of the non-weighted 

sum of heating signatures resulting from any 

one point source at that location:

(4)

γ = ( )

∑

max . h

h

i

i

(5)

Formulated in this way, the β factor is near 1.0 under most 

conditions and quickly decreases toward 0.0 whenever any one 

point source begins to dominate the strength-weighted sum 

of heating signatures. This means that the adjustment factor 

α typically is equal to a simple percentage reduction and is 

only eliminated when the strength-weighted sum of heating 

signatures approaches the strength-weighted signature from 

just one point source.

Use of the Trading Tool

A spreadsheet-based screening tool was created to 

calculate the sum of the 27 adjusted and strength-weighted 

point-source heating signatures. This screening tool, termed 

the “Willamette Point-Source Heat-Trading Tool” or just 

the “Trading Tool” for short, was crafted to allow resource 

managers, city engineers, plant operators, and regulators to 

quickly and accurately evaluate the thermal effects of potential 

heat-allocation trades among the point sources regulated by the 

Willamette temperature TMDL. By simply selecting a target 

time period and modifying the strength factors associated with 

each point source in an iterative fashion, potential trades can 

be defined and the effects on the temperature of the river can 

be estimated. The latest version of the Trading Tool may be 

downloaded from the project website; the website address is 

listed in section, “Supplemental Material.”

The Trading Tool not only calculates the sum of the 

strength-weighted point-source heating signatures, but also 

provides graphs of the results and several types of metrics 

that might be useful in evaluating potential trades. Graphs 

include the predicted 7dADM temperature difference that 

results from point sources as a function of river mile along 

the Coast Fork Willamette, McKenzie, and Willamette 

Rivers, with a comparison to the TMDL’s fully allocated 

condition, as well as the difference between the two. The tool 

also includes a graph showing the contribution of each point 

source to the total 7dADM temperature difference, and a 

cumulative frequency plot showing the distribution of 7dADM 

temperature differences for the potential trade compared to the 

fully allocated condition.

Several metrics are calculated by the Trading Tool to 

assist in evaluating the effects of a potential trade. A set 

of screening criteria are evaluated, one for each of several 

subreaches of the modeled domain. These criteria help 

to determine whether the potential trade would cause the 

temperature to increase above the level that occurred at 

any of the local points of maximum impact (POMI) for the 

fully allocated condition. Presumably, if the magnitude of 

the cumulative point-source heating effect at any POMI is 

estimated to increase to a level that is higher than what was 

modeled for the TMDL under fully allocated conditions, then 

that trade might not be desirable. In addition to these screening 

criteria, the number of miles of river that are expected to be 

heated or cooled by certain amounts as a result of the trade 

is quantified. Lastly, an integrated heating or cooling effect 

for the river and several subreaches is calculated. This overall 

heating or cooling effect is quantified in terms of “degreemiles,” where one degree-mile is equivalent to a change in 

temperature of one degree over the entire length of one mile 

of river. This metric is useful in providing an overall measure 

of the heating or cooling effect of the trade, regardless of any 

localized temperature changes.

Finally, the changes in point-source heat-load allocations 

are quantified by the Trading Tool in a set of tables that 

mirrors the wasteload allocations provided in the TMDL. 

For each point source, one or two tables show that source’s 

maximum allowable heating effect both in terms of a change 

in temperature of the receiving stream, and as an added heat 

load in millions of kilocalories per day; each of these measures 

is a function of the flow in the river. These tables may prove 

to be particularly useful to permit writers and to engineers and 

planners that need to quantify a potential trade in units that 

they can measure or calculate.

Patterns in the Temperature Differences

The patterns in the predicted cumulative point-source 

temperature effects can be explained primarily by the 

locations of point-source and tributary inflows. The 7dADM 

temperature difference usually increases where a pointsource discharge is located (the upward-pointing triangles in 

figure 2, for example). The magnitude of the increase depends 

on several factors such as the size of the point source, the 

flow in the river at that location, and the temperature of both 

the river and the point-source discharge. Tributary inflows 

(table 2) are notable particularly where they cause the 7dADM 

temperature difference to decrease in response to additional 

flow that dilutes upstream point-source heating effects; this 

is the case for the inflows of the Row River (RM 206.5), the 

Middle Fork Willamette (RM 186.3), and the Santiam River 

(RM 108.5). The McKenzie River inflow at RM 174.9, though 

it contributes a large flow to the Willamette River, shows an 

increase in the 7dADM temperature difference in figure 2; this 

12  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
results from the presence of a point source on the McKenzie 

River upstream. Downstream of point-source inflows, the 

7dADM temperature difference typically diminishes slightly 

with downstream distance as the river dissipates some of the 

heat from the point sources to the atmosphere.

A few anomalies do not follow this pattern of pointsource heating, downstream heat dissipation, and tributary 

dilution. A small increase and decrease in the 7dADM 

temperature difference, a “hump” in the pattern, occurs 

between roughly RMs 150 and 160. This anomaly, which 

does not coincide with any point-source or tributary 

inflow, has more than one potential explanation. First and 

most likely, it may be caused by the fact that point-source 

temperatures often are relatively constant while receiving 

water temperatures can vary over the course of a day. Any 

increase in river temperature at the point-source’s discharge 

location, therefore, also varies and is greatest when the 

receiving water temperature is at its daily minimum. This 

increased daily minimum water temperature at the point of 

discharge then can result in an increased daily maximum 

water temperature at a location approximately one-half day of 

travel time downstream. This effect can only occur when the 

receiving stream has a sufficiently large daily variation in its 

water temperature at the point of discharge, thus making it a 

transient anomaly. In this case, the anomaly between RMs 150 

and 160 is indeed approximately one-half day of travel time 

downstream of the Metropolitan Wastewater Management 

Commission (MWMC) point source at RM 177.9, and the 

anomaly is associated primarily with that point source’s 

heating signature.

Table 2. Locations of tributaries included in the Willamette River 

flow and temperature models that discharge to the Willamette or 

Coast Fork Willamette Rivers.

[RM, river mile]

Tributary Location 

(RM)

Receiving 

stream

Row River 206.5 Coast Fork

Middle Fork Willamette River 186.3 Willamette

McKenzie River 174.9 Willamette

Long Tom River 149.4 Willamette

Marys River 133.4 Willamette

Calapooia River 120.2 Willamette

Luckiamute River 108.7 Willamette

Santiam River 108.5 Willamette

Rickreal Creek 88.8 Willamette

Mill Creek 84.5 Willamette

Yamhill River 55.1 Willamette

Molalla River 35.6 Willamette

Tualatin River 28.4 Willamette

Clackamas River 24.9 Willamette

Johnson Creek 18.1 Willamette

Columbia Slough 0.8 Willamette

A second possible explanation is that this anomaly 

was caused by a slight change in travel time associated with 

the MWMC and possibly the Weyerhaeuser Springfield 

(McKenzie River) point sources upstream. Downstream of 

dams that release relatively constant flows and temperatures, 

the daily maximum temperature of a river tends to exhibit 

a nodal pattern with downstream distance, where the nodes 

are spaced at intervals of approximately one day of travel 

time (Lowney, 2000). The introduction of point sources 

changes the travel time and therefore the distance between 

nodes. When the 7dADM temperature results of two model 

runs are subtracted, this change in the nodal pattern causes 

some interesting patterns to appear downstream of the larger 

point sources. ODEQ staff tried to remove all such traveltime artifacts by artificially withdrawing flow from the river 

upstream of each point source, but it is possible that not all of 

the travel-time artifacts were completely eliminated.

The “hump” in the 7dADM temperature difference 

between RMs 200 and 205 might be another anomaly caused 

by travel-time changes or daily variations in heating effects 

associated with an upstream point source. The hump also 

could be a numerical modeling artifact caused by the large 

change in temperature that occurs just upstream; slight 

numerical anomalies just downstream of abrupt changes 

in temperature are not uncommon in numerical model 

predictions, though improvements in numerical solution 

techniques in CE-QUAL-W2 have minimized or eliminated 

most such artifacts.

Predictions and Test Results

A screening tool such as the Trading Tool is only useful 

if it can be shown to be accurate in its predictions. To test the 

tool’s predictions, four test cases were created and evaluated 

with the Trading Tool. Then, the exact same conditions were 

simulated with the Willamette flow and temperature models. 

By comparing the results, the error associated with the 

Trading Tool estimates can be quantified. The Trading Tool is 

envisioned to be used only as an easy-to-use screening tool to 

quickly define potentially useful point-source heat-allocation 

trades. Each identified trade, then, can be evaluated with the 

Willamette River flow and temperature models. Only if the 

Trading Tool predictions are shown to be accurate over a wide 

range of conditions might its predictions be used without 

verification; at this time, verification runs with the full suite of 

models is still advisable.

The first test case postulates a purely hypothetical heat 

trade between three point sources in the upper Willamette 

River. In this trade, MWMC’s allocation is decreased by 

50 percent by setting its strength factor in the Trading Tool 

to 0.5. In concert with this heat-load decrease, the screening 

tool shows that the heat-load allocations for the cities of both 

Corvallis and Albany might be increased by 50 percent; their 

strength factors were both set to 1.5. All other strength factors 

Temperature Effects of Point Sources 13
were kept at 1.0 to represent their fully allocated condition 

under the TMDL. This test case was modeled with the full 

suite of flow and temperature models by simply changing the 

modeled flow for each of these three point sources; each was 

changed by multiplying their point-source flow time series 

by each source’s strength factor, but leaving the temperature 

associated with each source unchanged. Time-of-travel offset 

withdrawals also were adjusted for each of these point sources, 

as in the TMDL model runs. The resulting comparison shows 

that, for this test case, the Trading Tool predictions agree with 

the model results to within 0.005°C, with a mean error of 

0.001°C and a mean absolute error of 0.002°C (fig. 4, table 3). 

Mean error is a measure of bias in the predictions, and the 

mean absolute error may be thought of as a typical error 

associated with any point along the river. Given the magnitude 

of the temperature changes being modeled, these errors seem 

small enough to be acceptable.

220 200 180 160 140 120 100 80 60 40 20 0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coast Fork Willamette River

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

RIVER MILE

All sources, before trade

Prediction from Trading Tool

Trade 1 model results

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

Prediction error of Trading Tool

Location of tributary

Location of point source

A. Results of hypothetical heat-trading test case 1. Strength factors are 0.5 for the Metropolitan Wastewater Management

 Commission and 1.5 for the Corvallis and Albany wastewater treatment plants.

B. Errors associated with Trading Tool estimate.

Figure 4. Results of hypothetical heat-trading test case 1, showing 7dADM point-source temperature effects from the test 

case’s model run and errors associated with the Trading Tool estimate.

Table 3. Prediction errors of the Trading Tool when used to 

estimate the effects of several hypothetical heat-trading test 

cases.

[A positive mean, minimum, or maximum error indicates that the tool gave 

a result that was larger than that predicted by the Willamette River flow 

and temperature models. All results are based on the 95th percentile of the 

7dADM water-temperature difference, as described in the section, “Methods.” 

Abbreviations: 7dADM, 7-day moving average of the daily maximum; °C, 

degrees Celsius]

Heat-trading

test case

Error (°C)

Mean Mean 

absolute Minimum Maximum

1 0.001 0.002 -0.005 0.005

2 -0.002 0.002 - 0.011 0.004

3 -0.001 0.001 -0.005 0.002

4 -0.003 0.003 -0.014 0.002

14  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Test case 2, also hypothetical, involves four point 

sources upstream of the Santiam River confluence. In this test 

case, Cottage Grove no longer discharges to the Coast Fork 

Willamette River and MWMC removes its discharge from the 

Willamette River (each strength factor = 0.0). Because of this 

decrease in heat inputs upstream, the cities of Corvallis and 

Albany are able to increase their heat discharges, in this case 

by factors of 2.0 and 3.0, respectively. These strength factors 

were set in the Trading Tool to estimate the cumulative pointsource heating effect. The Willamette flow and temperature 

models also were run to determine the result of this change in 

point-source discharges; the flows of the point sources were 

modified while the temperature of those sources were left 

unchanged. A comparison of the results of the models to the 

predictions of the Trading Tool shows that the Trading Tool’s 

predictions were fairly accurate, with a mean error of 

-0.002°C and a mean absolute error of 0.002°C (fig. 5, 

table 3). The tool’s predicted patterns of 7dADM temperature 

effects generally were within 0.005°C of the model results. 

The match was not quite as accurate in the 15 miles or so 

downstream of the McKenzie River confluence (RM 174.9), 

probably due to the different flow conditions that affect the 

point sources discharging to the McKenzie River versus those 

along the Willamette River.

220 200 180 160 140 120 100 80 60 40 20 0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coast Fork Willamette River

RIVER MILE

All sources, before trade

Prediction from Trading Tool

Trade 2 model results

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

Prediction error of Trading Tool

Location of tributary

Location of point source

 A. Results of hypothetical heat-trading test case 2. Strength factors are 0.0 for Cottage Grove and the Metropolitan 

 Wastewater Management Commission, 2.0 for Corvallis, and 3.0 for the Albany wastewater treatment plant.

 B. Errors associated with Trading Tool estimate.

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

Figure 5. Results of hypothetical heat-trading test case 2, showing 7dADM point-source temperature effects from the test 

case’s model run and errors associated with the Trading Tool estimate.

Temperature Effects of Point Sources 15
In test case 3, the predictions of the Trading Tool were 

tested for sources located in the middle Willamette subreach. 

Again, Cottage Grove’s flow was removed from the river 

(strength factor set to 0.0). The city of Salem’s discharge was 

scaled back by 20 percent (strength factor = 0.8). Then, the 

heat-load allocations for the cities of Newberg and Wilsonville 

were doubled (strength factor = 2.0). The Willamette flow and 

temperature models were used to assess this new condition 

by changing the point-source flows as before. For this test 

case, the Trading Tool predicted the change in temperature 

conditions along the Willamette River quite well, with a mean 

error of -0.001°C and a mean absolute error of 0.001°C (fig. 6, 

table 3). The screening tool’s prediction errors in this case 

were well within ±0.005°C for the entire model domain.

For hypothetical test case 4, the Cottage Grove WWTP 

effluent was removed from the river, and Weyerhaeuser 

Springfield traded some of its heat-load allocation with the 

Weyerhaeuser Albany plant downstream. The Springfield 

plant reduced its load by one-half (strength factor = 0.5), 

thus allowing the Albany plant to double its load (strength 

factor = 2.0). The flow and temperature models were run 

with the modified point-source and travel-time offset flows; 

220 200 180 160 140 120 100 80 60 40 20 0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coast Fork Willamette River

Tributary location

Point source location

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

 A. Results of hypothetical heat-trading test case 3. Strength factors are 0.0 for Cottage Grove, 0.8 for Salem, and 2.0 for 

 both Newberg and Wilsonville. 

 B. Errors associated with Trading Tool estimate.

Location of tributary

Location of point source

RIVER MILE

All sources, before trade

Prediction from Trading Tool

Trade 3 model results

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

Prediction error of Trading Tool

Figure 6. Results of hypothetical heat-trading test case 3, showing 7dADM point-source temperature effects from the 

test case’s model run and errors associated with the Trading Tool estimate.

16  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
the results are compared to the predictions of the Trading 

Tool in figure 7, with error statistics listed in table 3. For this 

test case, the mean error and the mean absolute error for the 

tool’s predictions were -0.003°C and 0.003°C, respectively. In 

this case, the Trading Tool accurately predicted the modified 

patterns in the cumulative point-source heating effects, but 

the predictions were biased very slightly negative for most of 

the length of the Willamette River. This inaccuracy is small 

(less than 2 percent), however, compared to the types of 

temperature differences being modeled, so the predictions of 

the Trading Tool still appear to be reliable in this case.

On the basis of these four hypothetical test cases, the 

Trading Tool predictions are sufficiently accurate to be useful 

in its intended purpose as a tool for screening potential pointsource heat-allocation trades. The tool’s prediction errors 

typically are within ±0.005°C, which is small compared to 

both the calculated cumulative point-source heating effects of 

the TMDL and the typical changes in 7dADM temperature 

patterns associated with many potential trades. Though it 

appears that the Trading Tool is both accurate and reliable in 

its predictions, a verification of all potential point-source heatallocation trades with the full suite of Willamette River flow 

and temperature models is still advised.

220 200 180 160 140 120 100 80 60 40 20 0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coast Fork Willamette River

Tributary location

Point source location

RIVER MILE

All sources, before trade

Prediction from Trading Tool

Trade 4 model results

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

Prediction error of Trading Tool

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

 A. Results of hypothetical heat-trading test case 4. Strength factors are 0.0 for Cottage Grove, 0.5 for Weyerhaeuser

 Springfield, and 2.0 for Weyerhaeuser Albany. 

 B. Errors associated with Trading Tool estimate.

Location of tributary

Location of point source

Figure 7. Results of hypothetical heat-trading test case 4, showing 7dADM point-source temperature effects from the test 

case’s model run and errors associated with the Trading Tool estimate.

Temperature Effects of Point Sources 17
Temperature Effects of Riparian 

Shading

The Willamette River flow and temperature models 

were used to assess the effects of restoring riparian vegetation 

along the Long Tom River, and along selected reaches of 

the upper Willamette River. These effects were modeled by 

changing several model inputs: the tree-top elevation, the 

distance from the center of the river to the vegetation, and 

the fraction of solar radiation intercepted by that vegetation. 

These three model inputs vary as a function of location and 

are assigned separately for the vegetation on each bank of the 

river. The characteristics of the riparian vegetation, translated 

into input files for the models, were developed during model 

construction. Current vegetation characteristics were derived 

from aerial photographs and GIS techniques by ODEQ staff, 

then translated into model input files using methods developed 

by PSU, ODEQ, and USGS (Annear and others, 2004a; 

Sullivan and Rounds, 2004). “System potential” vegetation, or 

the potential near-stream land cover, is the mature vegetation 

that should occur at a particular location, based on the soils 

and geologic materials that occur there. ODEQ conducted 

a study of potential near-stream land cover as part of the 

Willamette River temperature TMDL, and the results were 

used to predict the height and shading characteristics of 

system potential vegetation along the banks of all modeled 

river reaches (Oregon Department of Environmental Quality, 

2006c). System potential vegetation was used in the modeling 

of Natural Thermal Potential baseline conditions in the TMDL 

and in this investigation. System potential shade input files 

for the models were used as received from ODEQ; shade files 

representing current conditions were obtained from PSU as 

used in the latest model calibration runs.

Long Tom River Shading

The effect of restoring riparian vegetation along the entire 

Long Tom River, from Fern Ridge Dam to the mouth of the 

Long Tom, was simulated with the Willamette temperature 

TMDL models by switching the shade input files of the Long 

Tom model between current conditions and system potential 

and running the suite of models under those conditions. The 

7dADM water-temperature differences between these two 

model runs then were calculated, and the 95th percentile of 

that difference was computed according to the procedure 

described in section, “Methods.” Plotting these results as 

a function of downstream distance along the Willamette 

River, the effects of cooling the Long Tom River with shade 

restoration are apparent (fig. 8). A maximum cooling of about 

0.034°C was modeled in the Willamette River as a result of 

shade restoration on the Long Tom River; greater cooling 

effects occur in the Long Tom, but its flow is small relative to 

flow in the Willamette and therefore the cooling effect from 

the Long Tom River is diluted when its waters mix with those 

of the Willamette River. Restoring all riparian vegetation 

along the Long Tom River, though probably very beneficial 

for that river, has a limited effect on temperatures in the 

Willamette River. Still, a decrease of about 0.02°C at the upper 

Willamette’s POMI near Albany might enable one or more of 

the point sources upstream of Albany to increase its allowable 

heat load substantially through a point-source to nonpointsource trade.

180 160 140 120 100 80 60 40 20 0

WILLAMETTE RIVER MILE

-0.10

-0.05

0.00

0.05

Range of 7dADM water-temperature difference

Location of tributary

95th percentile of 7dADM water-temperature difference

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) 

WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

Figure 8. Thermal effects of restoring riparian vegetation along the Long Tom River, as manifested by 

a water-temperature change in the Willamette River. Vegetation restoration represents the change from 

current to system potential conditions along the Long Tom River downstream of Fern Ridge Dam.

18  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Upper Willamette River Shading

The thermal effect of restoring riparian vegetation along 

the upper Willamette River upstream of Albany was explored 

through a series of model runs. As in the Long Tom River 

model runs, these scenarios simply modified the model’s 

shade input file for a baseline model run—in this case, the 

fully allocated point-source model run with system potential 

vegetation. In each run, the vegetation characteristics were 

changed from system potential back to current conditions for 

a selected 5-mile reach along the upper Willamette River. The 

results for each model run then were subtracted from those 

for the baseline model run, thus producing an estimate of the 

cooling effect resulting from the restoration of vegetation in 

that reach. Twelve model runs were performed, each with 

5-mile reaches of restored vegetation between RM 116.87, 

near the upper Willamette River’s POMI at Albany, and RM 

176.80, just upstream of the McKenzie River confluence.

The use of a 5-mile restoration reach has interesting 

implications for the Willamette River system. A 5-mile 

restoration reach was selected because typical restoration 

projects may be relatively limited in their spatial extent, yet 

this amount of restoration was thought to be large enough 

to produce measurable results. Given the velocities in the 

Willamette River during summer, however, a parcel of water 

can travel past an entire 5-mile restoration reach in the span of 

a few hours. One-half day downstream of the restoration reach, 

therefore, the 7dADM water temperature is largely unaffected 

by the restoration project because the water traveled past 

the restored reach at night, when increased shading has little 

effect on water temperature. Similarly, the water at a point 

one full day downstream of the restoration project has a 

decreased 7dADM water temperature because some solar 

energy was prevented from entering the water when it passed 

by the project. These facts manifest themselves in a “nodal” 

pattern of cooling downstream of the restored reach, where the 

greatest cooling occurs at or just downstream of the project, 

followed by nodes of decreasing magnitude that are spaced 

roughly at daily travel-time distances downstream. Indeed, 

this pattern was predicted by the model results (fig. 9.). The 

predicted nodal patterns are not perfectly symmetrical and 

smooth because variations in flow cause the spacing between 

nodes to change over time, and only the model results that met 

certain criteria were used in the analysis of the 95th percentiles 

(see the “Methods” section of this report).

The cooling effects predicted in the upper Willamette 

River as a result of any one 5-mile restoration project appear 

to be significant, relative to the types of temperature changes 

specified by the point-source heat allocations in the Willamette 

River temperature TMDL. The maximum 7dADM watertemperature change ranged from -0.046 to -0.194°C (fig. 9, 

table 4). The magnitude of the effect depends on several 

factors, including river width as well as the amount of shade 

that must be added to restore the reach to system potential 

conditions. The modeled cooling effects, however, vary 

greatly with downstream distance. If the aim of riparian shade 

restoration is to cool the upper Willamette River’s pointsource POMI so that one or more point-source heat allocation 

might be increased, then the location of the restoration project 

becomes critical. The shading scenario that produced the 

maximum amount of cooling at any one location (scenario 

UW-H, -0.194°C, table 4) actually produced only a small 

amount of cooling at RM 116.87 (-0.023°C). Scenario UWK, in which the restored reach was located quite close to the 

POMI, produced the greatest cooling there (-0.094°C) among 

this set of shading scenarios.

An alternate means of quantifying the cooling effect of 

riparian shade restoration is to integrate the predicted cooling 

effect over the entire length of the Willamette River. This is 

done by summing the products of reach length and 7dADM 

water-temperature change (95th percentile) for each segment 

in the upper, middle, and lower Willamette River models. 

The result is an overall measure of the modeled heating or 

cooling effect (in units of “degree-miles”) regardless of any 

localized patterns or maxima. Such an integrated value may 

prove to be a useful metric for comparing model results. With 

this metric, it appears that restoring the riparian vegetation in 

the RM 146.92 to 136.80 reach (scenarios UW-G and UW-H, 

table 4), provides the greatest overall cooling to the Willamette 

River (more than 1°C-mile of cooling per mile of restoration), 

among the model runs tested, despite the fact that these model 

runs provide among the least cooling at the upper Willamette 

River’s POMI near Albany.

As a comparison to point-source heating effects, the 

models were used to quantify the effects of restoring riparian 

vegetation along the upper Willamette River for the entire 

length of all 5-mile reaches that were modeled separately. 

This one model run, in which approximately 60 miles (RMs 

176.80–116.87) of riparian vegetation was restored from 

current to system potential condition, was useful in providing 

context relative to the cumulative heating effects of the point 

sources. This model run, denoted as UW-AL in table 4, 

demonstrated that the nonpoint-source heating effects caused 

by less than system potential shading are substantial, with a 

maximum modeled 7dADM temperature change of -0.419°C. 

Clearly, then, the restoration of riparian shading along the 

upper Willamette River might provide opportunities for 

trading heat credits between point and nonpoint sources under 

the Willamette temperature TMDL.

Temperature Effects of Riparian Shading 19
ORWSC19_0149_fig_09

A. RM 176.80 – 171.82

B. RM 171.82 – 166.84

C. RM 166.84 – 161.86

D. RM 161.86 – 156.88

E. RM 156.88 – 151.89

F. RM 151.89 – 146.92

G. RM 146.92 – 141.94

H. RM 141.94 – 136.80

I. RM 136.80 – 131.82

J. RM 131.82 – 126.84

K. RM 126.84 – 121.86

L. RM 121.86 – 116.87

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

180 100120140160 80 0204060 180 100120140160 80 0204060

WILLAMETTE RIVER MILE (RM) WILLAMETTE RIVER MILE (RM)

Extent of reach where riparian 

vegetation was restored

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

Figure 9. Modeled temperature changes associated with shade restoration along selected 5-mile reaches of the upper 

Willamette River, from river mile 116.87 near Albany to river mile 176.80 just upstream of the McKenzie River confluence.

20 Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Table 4. Cooling effects of several shading scenarios on the Willamette River, Oregon.

[Effects were measured relative to the 95th percentile of the 7dADM water temperature difference due to 

changes in shading. Abbreviations: 7dADM, 7-day moving average of the daily maximum; RM, river mile; 

∆T, change in temperature; °C, degree Celsius]

Shading

scenario

Shaded reach

(RM)

Maximum ∆T in 

Willamette River

(°C)

∆T at RM 116.9

(°C)

Integrated change for 

Willamette River

(°C-mile)

UW - A 176.80 –171.82 -0.074 -0.035 -3.432

UW - B 171.82 – 166.84 -0.048 -0.026 -2.655

UW - C 166.84– 161.86 -0.060 -0.052 -3.893

UW - D 161.86– 156.88 -0.088 -0.054 -3.731

UW - E 156.88– 151.89 -0.060 -0.026 -2.954

UW - F 151.89– 146.92 -0.116 -0.014 -4.043

UW - G 146.92–141.94 -0.182 -0.013 -5.977

UW - H 141.94– 136.80 -0.194 -0.023 -5.111

UW - I 136.80– 131.82 -0.127 -0.035 -3.364

UW - J 131.82– 126.84 -0.048 -0.029 -1.467

UW - K 126.84– 121.86 -0.095 -0.094 -2.731

UW - L 121.86– 116.87 -0.046 -0.045 -1.459

UW - AL 176.80– 116.87 -0.419 -0.273 -29.557

Long Tom all in Long Tom -0.034 -0.021 -2.055

Temperature Effects of 

Dam Operations

In addition to assessing 

the effects of point-source heat 

discharges and riparian shading, 

the Willamette River flow and 

temperature models were used to 

assess the thermal effects of changed 

operations at Cougar Dam, which is 

one of the upper boundaries for the 

McKenzie River model. Situated on 

the South Fork McKenzie River and 

completed in 1963, Cougar Dam is 

the second highest dam (452 ft) and 

impounds the fifth largest reservoir 

(219,000 acre-ft) in the Willamette 

River basin (fig. 10).

Cougar Dam controls the 

flow and greatly influences the 

temperature in the South Fork 

McKenzie River downstream of the 

dam. Cougar Reservoir becomes 

thermally stratified in summer, with 

warmer, less-dense water near the surface and colder, moredense water at the bottom (Resource Management Associates, 

2003). Western Oregon’s warm and sunny summer weather 

adds additional heat to the reservoir’s surface, stabilizing its 

stratification throughout the summer. Because the dam was 

built with its major release point at a relatively low elevation, 

the dam historically released relatively cold water from near 

Figure 10. Aerial view of Cougar Dam and Reservoir, looking south. Photograph taken by 

Bob Heims, U.S. Army Corps of Engineers, July 12, 1989.

the bottom of the reservoir in mid-summer. As the reservoir 

was drawn down in autumn to make room for flood-control 

storage, the heat that was captured in the reservoir’s upper 

layer during the summer was released downstream. As a 

result, the seasonal temperature pattern downstream of Cougar 

Dam through 2001 was quite different from the pattern 

upstream of Cougar Reservoir (fig. 11.).

Temperature Effects of Dam Operations  21
ORWSC19_0149_fig_11

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

2001

2

4

6

8

10

12

14

16

18

WATER TEMPERATURE, IN DEGREES CELSIUS

South Fork McKenzie River upstream of Cougar Reservoir (USGS station 14159200)

South Fork McKenzie River downstream of Cougar Dam (USGS station 14159500)

Figure 11. Seasonal water temperature patterns in the South Fork McKenzie River upstream and downstream of Cougar 

Reservoir, prior to the construction of a selective withdrawal tower at Cougar Dam, Oregon, 2001.

The McKenzie River supports the largest remaining wild 

population of Chinook salmon (Oncorhynchus tshawytscha) 

in the upper Willamette River basin (Good and others, 2005), 

and the South Fork McKenzie River provides good spawning 

habitat. The altered temperature pattern downstream of Cougar 

Dam, however, can create problems with regard to the timing 

of migration, spawning, and egg hatching (Caissie, 2006). To 

restore the suitability of this reach for salmonid spawning, 

the U.S. Army Corps of Engineers (USACE) added a sliding 

gate assembly to the intake structure at Cougar Dam. To allow 

for construction, the reservoir was drawn down from 2002 

through 2004; construction was completed in early 2005. 

The new selective withdrawal tower allows dam operators to 

blend warm water from the top of the reservoir with cooler 

water at other levels, or to simply select a depth from which 

to withdraw water, in an attempt to match a downstream 

temperature target. The selective withdrawal tower was used 

successfully in 2005 and 2006 to restore a more-natural 

seasonal temperature pattern to the South Fork McKenzie 

River downstream of Cougar dam (fig. 12).

The time periods modeled as the basis for the Willamette 

temperature TMDL included one summer in which Cougar 

Dam operated without a selective withdrawal tower (2001), 

and one summer during which Cougar Reservoir was drawn 

down for construction (2002). Release temperatures in 2001 

were typical of the pre-selective-withdrawal-tower period, 

with cool releases in mid-summer and warmer releases in 

autumn. In 2002, the greatly reduced storage and shallower 

depth in Cougar Reservoir resulted in a short residence time 

and less stratification that might affect release temperatures. 

As a result, 2002 release temperatures from Cougar Dam 

mirrored the seasonal temperature pattern upstream, with 

limited warming in the smaller reservoir. These measured 

temperatures were used as upstream boundary conditions for 

the South Fork portion of the McKenzie River model used for 

the Willamette temperature TMDL. Cougar Dam’s current and 

future release temperatures, however, are unlikely to resemble 

those that occurred in 2001; therefore, it is instructive to 

explore how these seasonal changes in Cougar Dam release 

temperatures affect downstream temperatures in the McKenzie 

22  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
ORWSC19_0149_fig_12

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

2

4

6

8

10

12

14

16

18

WATER TEMPERATURE, IN DEGREES CELSIUS

South Fork McKenzie River downstream of Cougar Dam 

 (USGS station 14159500)

2001—Last full year of normal dam operation prior to 

 contruction of selective withdrawal tower 

2002—Reservoir was drawn down for construction 

 activities

2006—Construction completed in early 2005

Figure 12. Seasonal water temperature patterns in the South Fork McKenzie River downstream of Cougar Dam in 2001, 

2002, and 2006.

and Willamette Rivers, and whether such changes might affect 

future point-source heat allocations under the Willamette 

temperature TMDL.

To determine the effect of changed operations at Cougar 

Dam on downstream water temperatures, the Willamette flow 

and temperature models were used to answer one simple 

question: “What might the temperatures downstream of 

Cougar Dam have been during 2001 and 2002 if the released 

temperatures during those periods had been equal to those 

measured in 2006?” Release temperatures in 2005 and 2006, 

the first full years after completion of the selective withdrawal 

tower, were similar; the 2006 water temperatures were selected 

because the second year had fewer operational glitches and 

should be more representative of future seasonal patterns. 

Obviously, superimposing 2006 release temperatures upon 

flow conditions from 2001 and 2002 is imperfect. Release 

temperatures are tied somewhat to the flows, as a stratified 

reservoir has a limited supply of warm and cool water. In 

addition, the 2006 release temperatures are tied somewhat 

to the meteorological conditions that occurred during 2006. 

Still, running the 2001 and 2002 models with 2006 release 

temperatures is a good first step toward quantifying the 

thermal effects of changed operations at Cougar Dam. Further 

refinement of these results can be an objective for future 

research.

Imposing 2006 release temperatures on the 2001 modeled 

conditions has a greater effect than when imposed on the 2002 

conditions, for two main reasons. First, differences between 

2001 and 2006 water temperatures are greater than differences 

between 2002 and 2006 water temperatures (fig. 12). Second, 

the amount of water discharged from Cougar Reservoir was 

much less than normal during August–October 2002 because 

the reservoir was drawn down for construction. Late summer 

releases in 2002 were less than 250 ft3/s, while releases during 

that time period in 2001 exceeded 700 ft3/s. The greater flows 

in 2001 have a greater effect on downstream temperatures 

once those flows are mixed into the McKenzie and Willamette 

Rivers.

Temperature Effects of Dam Operations  23
235 230 225 220 215 210 205 200 195 190 185 180 175

RIVER MILE UPSTREAM OF THE MOUTH OF THE WILLAMETTE RIVER

EXPLANATION

OCT SEPT AUG JULY JUNE MAY APR OCT SEPT AUG JULY JUNE

2002 2001

7.0 6.0 5.0 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -5.0 -6.0 -7.0

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

Mouth of 

McKenzie 

River at 

RM 174.9

South Fork 

McKenzie 

River joins

McKenzie

River at

RM 231.1 NOTE: Color scale is not linear

Figure 13. Modeled changes in the 7-day moving average of the daily maximum water-temperature difference in the South 

Fork McKenzie and McKenzie Rivers in response to the construction of a selective withdrawal tower at Cougar Dam, Oregon.

The Willamette River flow and temperature models 

first were used to determine the change in 7dADM water 

temperature downstream of Cougar Dam in the absence of 

point sources. All other conditions, except for the modified 

temperatures released from Cougar Dam, were identical to 

those used in the Willamette TMDL. Results from those model 

runs showed that Cougar Dam’s selective withdrawal tower 

has the greatest effect on water temperatures in the South 

Fork McKenzie River, with mid-summer 7dADM temperature 

increases as large as 6.0–6.5°C and decreases of 5.0°C or more 

in October, as compared to the original 2001 model results 

(fig. 13). As expected, the modeled temperature changes 

for the 2002 model runs were smaller than those for 2001. 

Downstream of the confluence of the South Fork McKenzie 

24  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
220230 210 200 180190 160170 150 140 130 120 110 100 80 70 90 60 50 40 30 20 10 0

EXPLANATION

OCT SEPT AUG JULY JUNE MAY APR OCT SEPT AUG JULY JUNE

2002 2001

6.0 5.0 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -5.0 -6.0

RIVER MILE UPSTREAM OF THE MOUTH OF THE WILLAMETTE RIVER

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

Mouth of 

McKenzie 

River at 

RM 174.9

South Fork 

McKenzie 

River joins

McKenzie

River at

RM 231.1 NOTE: Color scale is not linear

Figure 14. Modeled changes in the 7-day moving average of the daily maximum water-temperature difference in the South 

Fork McKenzie, McKenzie, and Willamette Rivers in response to the construction of a selective withdrawal tower at Cougar 

Dam, Oregon.

River with the McKenzie River, the thermal effects are 

somewhat diluted, though the 7dADM temperature changes in 

the McKenzie River were still large enough to be important, 

relative to the temperature modifications mandated by the 

TMDL. McKenzie River 7dADM temperatures were warmed 

in mid-summer as much as 1.5 or 2.0°C, depending on time 

of year and location, and cooling in autumn was sometimes 

more than 1.5°C. Because of additional dilution and time 

for heat exchange with the atmosphere, the magnitude of the 

temperature effect decreased downstream of the confluence 

of the McKenzie River with the Willamette River (fig. 14). In 

the Willamette River, 7dADM water-temperature changes as 

large as 0.4–0.5°C (warming in summer, cooling in autumn) 

were predicted upstream of the Santiam River confluence 

(RM 108.5). The effect diminished to no more than 0.3°C 

downstream of that point.

Temperature Effects of Dam Operations  25
In addition to imposing 2006 release temperatures, the 

models were run both with and without the point sources to 

determine their cumulative heating effect under the modified 

baseline conditions. As in the TMDL analysis, the cumulative 

heating effect was determined by first calculating the 7-day 

mean of the modeled daily maximum temperature for each 

location in the models and for each day that was simulated. 

Then, the difference in the 7dADM temperature for each day 

and location was calculated by subtracting the without-pointsources results from the with-point-sources results. Finally, the 

95th percentile of the 7dADM temperature-difference data at 

each location was calculated and plotted against downstream 

distance along the McKenzie and Willamette Rivers. These 

results for both the original TMDL point-source model runs 

(“TMDL base case”) and for the model runs where the 2006 

Cougar Dam release temperatures were imposed (“Cougar 

retrofit”) are shown in figure 15.

Although the changed operations at Cougar Dam were 

shown to have a significant effect on downstream temperature 

in the McKenzie River system and potentially measurable 

Figure 15. Effects of the Cougar Dam selective withdrawal tower on the cumulative heating effects of the 

modeled point sources.

240 220 200 180 160 140 120 100 80 60 40 20 0

0.00

-0.05

0.05

0.10

0.15

0.20

0.25

0.30

McKenzie River Willamette River

7-DAY MOVING AVERAGE OF THE DAILY MAXIMUM (7dADM) 

WATER-TEMPERATURE DIFFERENCE, IN DEGREES CELSIUS

Mouth of RIVER MILE UPSTREAM OF MOUTH OF WILLAMETTE RIVER

McKenzie

River at 

RM 174.9

South Fork 

McKenzie

River joins

McKenzie

River at

RM 231.1

95th percentile of 7dADM temperature difference, TMDL base case—Refers to original TMDL 

 assessment using 2001–02 release temperatures from Cougar Dam

95th percentile of 7dADM temperature difference, Cougar retrofit—Refers to the use of 2006 

 release temperatures from Cougar Dam in the with- and without-point-sources model runs

Difference: Cougar retrofit minus TMDL base case

Location of tributary

Location of point source

EXPLANATION

effects in the Willamette River, incorporating the Cougar 

Dam retrofit into the cumulative point-source temperature 

assessment had little effect. The difference between the “base 

case” and “Cougar retrofit” point-source temperature effects 

was determined to be small, ranging from -0.006 to 0.008°C, 

with less than a 0.001°C decrease at the POMI near RM 117 

(fig. 15). The effect is small because the Cougar Dam retrofit 

was incorporated into both the with- and without-point-sources 

model runs. The temperature of the river receiving the pointsource flows was slightly different as a result of the Cougar 

Dam retrofit, but not so different that the cumulative pointsource effects were greatly affected. Because the cumulative 

point-source heating effects were not greatly affected by the 

Cougar Dam retrofit, the point-source heat allocations of 

the Willamette temperature TMDL would not likely change 

appreciably if the Cougar Dam retrofit had been included 

in the TMDL analysis. Only for those point sources closest 

to Cougar Dam, and particularly for those located on the 

McKenzie River, might a more detailed analysis be warranted.

26  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Summary and Conclusions

The Willamette River flow and temperature models 

were used to explore and quantify the thermal effects of 

point-source discharges, riparian shading, and upstream dam 

operations on water temperature in the Willamette River and 

portions of its largest tributaries. The models, which form 

the basis of the Willamette temperature Total Maximum 

Daily Load (TMDL), were reviewed prior to their use, and 

several modifications were made to correct errors, remove 

instabilities, and make the models and their results more 

usable. Model results were evaluated using methods very 

similar to those used in the construction of the TMDL, in 

which the results of a model scenario were compared to model 

results from a baseline scenario and the 95th percentile of the 

7-day moving average of the daily maximum (7dADM) watertemperature difference was calculated as a function of location 

along the modeled river reaches. In this way, the cumulative 

heating effects of one or more point sources or the thermal 

effect of restoring riparian shade along a particular river 

reach, for example, could be quantified relative to a Natural 

Thermal Potential baseline condition. Because the results of 

each model run were evaluated as a difference between that 

run and a baseline model run, any errors that occurred in both 

were largely eliminated via that subtraction. The predicted 

temperature differences, therefore, were expected to be far 

more precise than the modeled prediction of actual river 

conditions, meaning that predicted temperature differences 

as small as hundredths of a degree Celsius might be real and 

useful.

The flow and temperature models first were used to 

examine the cumulative heating effects of the 27 point sources 

included in the TMDL. The models were run for each point 

source separately to quantify the “heating signature” of 

each source. These signatures then were incorporated into 

a spreadsheet-based screening tool in which each signature 

could be linearly increased or decreased using a multiplicative 

“strength factor.” The sum of the strength-weighted pointsource heating signatures was used as an estimate of the 

cumulative point-source heating effect, such that when the 

strength factor for each point source was set to 1.0, the sum 

equaled the results from one model run that included all point 

sources at their full TMDL heat allocation. This screening 

tool allows users to quickly evaluate the effects of potential 

changes to point-source heat allocations, including the trading 

of such allocations among the point sources. Graphs and 

various metrics are calculated to facilitate the evaluation of 

potential heat-load trades. Once a potential trade is identified 

through the use of the screening tool, the modified pointsource conditions can be evaluated with the full suite of flow 

and temperature models. Four test trades were evaluated, 

and the screening tool was shown to accurately predict the 

resulting cumulative point-source heating effects when 

compared to the exact same conditions simulated with 

the Willamette flow and temperature models, with mean 

absolute errors on the order of 0.002 degrees Celsius (°C) and 

maximum prediction errors of roughly plus-or-minus 0.005°C.

The cooling effects of riparian shading were quantified 

with the Willamette River flow and temperature models. 

Model results showed that restoring all riparian shading along 

the Long Tom River could cool the Willamette River at its 

point of inflow by approximately 0.03°C, which is small but 

potentially useful for heat-load trades with some of the point 

sources upstream of Albany. Shade restoration along selected 

5-mile reaches of the Willamette River upstream of Albany 

showed cooling effects as large as 0.19°C at certain locations. 

A 5-mile reach can be traversed in a few hours, however, 

which caused the cooling effects to exhibit a nodal pattern 

with downstream distance. The cooling effect was minimal 

at one-half day of travel time downstream of the restored 

reach because the water passed by that reach during the night 

when shading does not particularly affect the heat budget 

of the river. This pattern in downstream cooling effects has 

potentially important ramifications for heat-load trading and 

the siting of riparian restoration projects.

Finally, the downstream temperature effects of changed 

operations at Cougar Dam on the South Fork McKenzie 

River were evaluated using the TMDL models. Since 2005, 

temperature releases from Cougar Dam have been controlled 

through the use of a selective withdrawal tower; this change 

occurred after the 2001-2002 time period modeled for the 

temperature TMDL. The downstream thermal effects were 

estimated by substituting 2006 measured temperatures 

downstream of Cougar Dam for the measured 2001 and 2002 

temperatures used in the TMDL models. The model results 

showed that the modified operations at Cougar Dam have an 

important effect on downstream temperatures, with warming 

in mid-summer and cooling in autumn. Predicted 7dADM 

temperature shifts in the South Fork McKenzie River were 

greatest, with changes as large as 6.0°C. Downstream, the 

models showed 7dADM temperature changes in the McKenzie 

River of close to 2.0°C at times. In the Willamette River 

upstream of the Santiam River confluence, predicted 7dADM 

temperature changes were as large as 0.5°C, while downstream 

of the Santiam River the changes were less than 0.3°C. 

Although large temperature shifts were apparent as a result of 

the change in operations at Cougar Dam, if those changes also 

were incorporated into the Natural Thermal Potential baseline 

conditions, the modeled cumulative point-source heating effect 

was not significantly altered.

Summary and Conclusions  27
This investigation has helped to quantify the heating 

effects of several important influences on water temperature in 

the Willamette River and several of its major tributaries. Only 

through a detailed understanding of the river’s heat budget and 

the factors that influence it can scientists, resource managers, 

and regulators construct defensible plans for optimizing 

the river’s thermal regime to protect its beneficial uses and 

aquatic resources. The results of this investigation, and the 

tools produced by it, should prove useful as these managers 

and regulators move forward to implement the Willamette 

temperature TMDL.

Acknowledgments

This investigation was the result of a collaboration 

between the USGS and the Oregon Association of Clean 

Water Agencies (ACWA) with additional assistance from the 

Willamette Partnership. Janet Gillaspie, Executive Director 

of ACWA, aided this investigation through her leadership 

and coordination. A group termed the Scenario Development 

Team (SDT) provided useful discussions, insight, information, 

and guidance. The SDT was composed of USGS staff and 

ACWA members as well as representatives from the Oregon 

Department of Environmental Quality (ODEQ), the U.S. Army 

Corps of Engineers (USACE), and the Willamette Partnership. 

Thanks to ACWA members Mark Yeager (city of Albany), 

Steve Downs (city of Salem), Tom Mendes (Metropolitan 

Wastewater Management Commission of Eugene/Springfield), 

Larry Lamperti and Dan Hanthorn (city of Corvallis), Andrew 

Swanson (Clackamas Water Environment Services), Brett 

Arvidson (Oak Lodge Sanitary District), and Garry Ott (city 

of Portland). Thanks also to Jim Britton (USACE), Jim Bloom 

and Neil Mullane (ODEQ), and David Primozich and Charlie 

Logue (Willamette Partnership).

The assistance of Ryan Michie and Jim Bloom and 

their colleagues at ODEQ was greatly appreciated. Their 

willingness to share the final Total Maximum Daily Load 

models and point-source allocation spreadsheets, as well 

as many other pieces of data and information, made this 

investigation possible and greatly added to its collaborative 

nature. I thank them for enduring a number of meetings and 

for their patience in answering my questions and periodically 

providing me with information.

This report benefited from several helpful reviews. For 

their comments and suggestions on the draft manuscript, 

I thank Scott Wright (USGS), Lorraine Flint (USGS), Jim 

Bloom (ODEQ), Chris Berger (PSU), Jim Britton (USACE), 

and Tom Mendes (ACWA).

Supplemental Material

A website has been created to provide additional 

information and supplemental material associated with this 

investigation. Visitors to http://or.water.usgs.gov/proj/will_

temp/ will be able to:

Download this report;

Download the Willamette River flow and temperature 

models used in this investigation, complete with the 

data files to run them;

Download the Willamette River Point-Source HeatTrading Tool;

View selected sets of results;

Download or view selected animations of model 

output; and

Follow links to related information and data.

References Cited

Annear, R.L., McKillip, M.L., Khan, S.J., Berger, C.J., and 

Wells, S.A., 2004a, Willamette River Basin temperature 

TMDL model—Boundary conditions and model setup: 

Portland, Oreg., Portland State University, Department of 

Civil and Environmental Engineering, Technical Report 

EWR-01-04, 530 p.

Annear, R.L., McKillip, M.L., Khan, S.J., Berger, C.J., and 

Wells, S.A., 2004b, Willamette River Basin temperature 

TMDL model—Model scenarios: Portland, Oreg., Portland 

State University, Department of Civil and Environmental 

Engineering, Technical Report EWR-03-04, 944 p.

Bales, J.D., Sarver, K.M., and Giorgino, M.J., 2001, Mountain 

Island Lake, North Carolina—Analysis of ambient 

conditions and simulation of hydrodynamics, constituent 

transport, and water-quality characteristics, 1996-97: U.S. 

Geological Survey Water-Resources Investigations Report 

01-4138, 85 p.

•

•

•

•

•

•

28  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Berger, C.J., McKillip, M.L., Annear, R.L., Khan, S.J., and 

Wells, S.A., 2004, Willamette River Basin temperature 

TMDL model—Model calibration: Portland, Oreg., 

Portland State University, Department of Civil and 

Environmental Engineering, Technical Report EWR-02-04, 

341 p.

Caissie, D., 2006, The thermal regime of rivers—A review: 

Freshwater Biology, v. 51, p. 1389-1406.

Cole, T.M., and Wells, S.A., 2002, CE-QUAL-W2: A twodimensional, laterally averaged, hydrodynamic and waterquality model, version 3.1: U.S. Army Corps of Engineers, 

Instruction Report EL-02-1 [variously paged].

Collier, M., Webb, R.H., and Schmidt, J.C., 1996, Dams and 

rivers—Primer on the downstream effects of dams: U.S. 

Geological Survey Circular 1126, 94 p.

Good, T.P., Waples, R.S., and Adams, P., eds., 2005, Updated 

status of Federally listed ESUs of West Coast salmon and 

steelhead: U.S. Department of Commerce, National Oceanic 

and Atmospheric Administration Technical Memo NMFSNWFSC-66, 598 p., accessed April 2, 2007, at http://www.

nwr.noaa.gov/Publications/Biological-Status-Reviews/

upload/SR2005-allspecies.pdf.

Green, W.R., 2001, Analysis of ambient conditions and 

simulation of hydrodynamics, constituent transport, and 

water-quality characteristics in Lake Maumelle, Arkansas, 

1991-92: U.S. Geological Survey Water-Resources 

Investigations Report 01-4045, 60 p.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in 

water resources: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 4, chap. A3, 510 p.

Lowney, C.L., 2000, Stream temperature variation in regulated 

rivers—Evidence for a spatial pattern in daily minimum and 

maximum magnitudes: Water Resources Research, v. 36, 

no. 10, p. 2947-2955.

Oregon Department of Environmental Quality, 2006a, 

Willamette Basin Total Maximum Daily Load Order 

memorandum: Oregon Department of Environmental 

Quality, accessed March 27, 2007, at http://www.deq.

state.or.us/wq/TMDLs/docs/willamettebasin/willamette/

ordermemo.pdf.

Oregon Department of Environmental Quality, 2006b, 

Willamette Basin Total Maximum Daily Load program 

documents: Oregon Department of Environmental Quality, 

accessed March 27, 2007, at http://www.deq.state.or.us/wq/

TMDLs/willamette.htm.

Oregon Department of Environmental Quality, 2006c, 

Potential near-stream land cover in the Willamette Basin 

for Temperature Total Maximum Daily Loads (TMDLs)—

Willamette TMDL documents, appendix C, section II: 

Oregon Department of Environmental Quality, accessed 

April 13, 2007, at http://www.deq.state.or.us/wq/TMDLs/

docs/willamettebasin/willamette/appxctemp.pdf.

Oregon Department of Environmental Quality, 2007a, Water 

quality standards: Beneficial uses, policies, and criteria for 

Oregon—Temperature: Oregon Administrative Rule 340-

041-0028: Oregon Department of Environmental Quality, 

accessed April 13, 2007, at http://arcweb.sos.state.or.us/

rules/OARs_300/OAR_340/340_041.html.

Oregon Department of Environmental Quality, 2007b, Water 

quality standards: Beneficial uses, policies, and criteria 

for Oregon—Definitions: Oregon Administrative Rule 

340-041-0002(41): Oregon Department of Environmental 

Quality, accessed April 13, 2007, at http://arcweb.sos.state.

or.us/rules/OARs_300/OAR_340/340_041.html.

Resource Management Associates, Inc., 2003, Blue River 

reservoir temperature modeling with HEC-5Q: Suisun City, 

California, Final report to U.S. Army Corps of Engineers, 

Portland District [variously paged].

Rounds, S.A., and Wood, T.M., 2001, Modeling water quality 

in the Tualatin River, Oregon, 1991-1997: U.S. Geological 

Survey Water-Resources Investigations Report 01-4041, 

53 p.

SAS Institute, Inc., 1990, SAS Procedures guide, version 6, 

3rd ed.: Cary, North Carolina, SAS Institute, Inc., 705 p.

Sullivan, A.B., and Rounds, S.A., 2004, Modeling streamflow 

and water temperature in the North Santiam and Santiam 

Rivers, Oregon: U.S. Geological Survey Scientific 

Investigations Report 2004-5001, 35 p.

Sullivan, A.B., and Rounds, S.A., 2005, Modeling 

hydrodynamics, temperature, and water quality in Henry 

Hagg Lake, Oregon, 2000-2003: U.S. Geological Survey 

Scientific Investigations Report 2004-5261, 38 p.

Sullivan, A.B., and Rounds, S.A., 2006, Modeling waterquality effects of structural and operational changes to 

Scoggins Dam and Henry Hagg Lake, Oregon: U.S. 

Geological Survey Scientific Investigations Report 2006-

5060, 36 p.

References Cited  29
This page is intentionally left blank.

30 Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
USGS personnel obtained the Willamette River 

temperature TMDL models and model source code from 

ODEQ staff. ODEQ used CE-QUAL-W2 version 3.12 

from August 19, 2003, for each of the submodels, with 

one modification by the PSU model development team. 

That “Tmax” modification enabled the model to internally 

calculate and output the daily maximum water temperature 

for every segment in the model in three different ways: (a) 

surface-water temperature only, (b) volume-weighted water 

temperature for the entire cross section, and (c) flow-weighted 

water temperature for the entire cross section. ODEQ used 

this “Tmax” version for almost all of its Willamette TMDL 

modeling. The Tmax version was not used on the North 

Santiam and Santiam Rivers; the version used there did not 

have the Tmax code additions, but the model computations 

were otherwise identical.

When USGS staff needed to run the Willamette River 

models, several code changes were necessary to make the 

models easier to use or to eliminate problems. Great restraint 

was exercised in keeping code changes to a minimum, so as 

to ensure that the model calibration would remain unchanged. 

All code changes were checked extensively and are described 

and justified in this appendix. In the end, USGS used its 

“generic Tmax3” version for all Willamette River temperature 

models except the lower Willamette River, where the “generic 

Tmax3a” version was applied. The details behind these 

versions, and the reasons for their use, are described below.

Removal of Visual Interface

The models as provided by ODEQ to USGS contained 

a “visual interface” such that when they were run under 

Microsoft© Windows, a new window opened to display 

selected model inputs and results during the model run. When 

the model run was completed, however, the display window 

did not close itself and did not return control to the operating 

system. Therefore, the model version that contains this 

visual interface was not amenable to unattended operation in 

which batch files are used to run the submodels in sequence, 

passing the output of one model as input to the next model 

downstream without active human intervention.

To enable unattended linkages between submodels, 

USGS staff removed the visual interface from the source code 

obtained from ODEQ. The code modifications were designed 

to create a “generic” version of CE-QUAL-W2. When 

CE-QUAL-W2 is distributed to the public by the PSU model 

development team, two versions typically are provided: the 

“cvf” version with the visual interface, and a generic version 

without the visual interface. This generic version of the model 

code created by USGS was different from the version with the 

visual interface in exactly the same way that the PSU cvf and 

generic versions differ.

This code change has no effect on the model’s 

computations and therefore has absolutely no effect on the 

model results. This was checked by running the cvf and 

generic versions of the Willamette models and comparing their 

output. No significant differences were observed. The minor 

differences that did exist were easily attributable to the use of 

slightly different compilation options.

Artificial Raising and Lowering of the River 

Bottom

The version of CE-QUAL-W2 used in the Willamette 

River temperature models includes a clever bit of coding by 

the PSU model development team that helps sloping river 

models to continue running under a wide range of flow 

conditions. In each of the model’s “water bodies,” the model 

keeps track of a “surface-layer index.” The water surface, 

though, can actually reside in a model layer that is above 

the surface-layer index. To enable the model to continue 

running when a model segment still has flow, but its bottom 

is above the surface layer index, the PSU team added some 

code that tells the model that the river bottom is lower in that 

segment than originally specified. This “trick” works fairly 

well, but was only partially implemented by the PSU model 

development team at the time the Willamette temperature 

models were being developed.

In running one of the Willamette River models under 

slightly different conditions, USGS staff observed that the 

model could crash because this “trick” was not sufficiently 

robust. The trick allows the surface layer index to drop below 

the bottom-most active layer in a model segment, assigning a 

small nonzero width to the next lower layer to keep the water 

flowing in a sloping reach. This originally was not allowed to 

occur if the segment had the largest Z value in the water body 

– if the water surface in that segment was the lowest in the 

water body, relative to the layer boundaries and irrespective of 

slope.

Appendix A. CE-QUAL-W2 Code Changes

Appendix A  31
The code was changed so that all segments in a water 

body could have their bottoms “lowered,” as long as they are 

not lowered past the bottom-most active layer in that water 

body. Without this fix, the original trick is insufficient to keep 

the river from “drying up” under certain conditions, and the 

model could crash unnecessarily. This modification was tested 

originally by the USGS on another river system (the Tualatin 

River), and it was determined to work as intended. The code 

changes were shared with the PSU model development team 

at that time and have since been incorporated into the latest 

public release version of CE-QUAL-W2. So, in the interest of 

keeping the model from crashing unnecessarily, this change 

was made to the code. In the model code, these modifications 

are denoted with the comments “!SR 08/01/05” and “!SR 

08/08/05,” which are the dates of modification for when these 

fixes were made to USGS versions of the code. This change 

does not affect the computations of the model. It simply keeps 

it from crashing.

Minor Bug Fixes

As stated previously, great care was taken to minimize 

the number of code changes that were made to the Willamette 

models, in order to preserve the model calibration and ensure 

that the models were essentially the same as those used to 

develop the TMDL. In a few instances, though, it made sense 

to correct a couple of small coding errors.

First, in the LATERAL_WITHDRAWAL subroutine, 

several fixes were applied. The statement:

IF (KBOT > KB(ID)) KBOT = KB(ID)

incorrectly referenced the most-downstream segment in the 

branch (ID), when it should have referenced the segment 

where the withdrawal is located (I). The line was changed to

IF (KBOT > KB(I)) KBOT = KB(I)

The original statement could result in the improper allocation 

of a withdrawal flow rate as a function of model layer. This 

error was fixed by the PSU model development team in later 

versions, but was never changed in the Willamette models. 

Next, the following code was added:

IF (QWD(JWD) == 0.0) THEN

 KTW(JWD) = KTOP

 KBW(JWD) = KBOT

 RETURN

END IF

This helps to avoid problems with the calculation of KTOP 

and KBOT, and streamlines the code slightly. This might have 

been the source of problems in which the original code would 

hang if the withdrawal flow rate was zero. In any case, the 

change explicitly enables the model to handle withdrawal flow 

rates of zero.

 Elsewhere in the LATERAL_WITHDRAWAL 

subroutine, the distribution of the withdrawal flow rate 

among the relevant model layers utilized values of BHR() and 

BHRKT2() in the original code. These were carry-overs from 

the DOWNSTREAM_WITHDRAWAL routine and were not 

appropriate for a lateral withdrawal. These variables were 

changed to BH() and BHKT2(). These fixes were cleared with 

the PSU development team in 2004. In addition, two further 

slight code modifications were added to help avoid potential 

divide-by-zero errors in this routine. Those fixes are labeled 

with the comment “!SR 09/16/04,” which was the date when 

these errors were originally fixed in other versions of the code.

In the DOWNSTREAM_WITHDRAWAL subroutine, 

two snippets of code were added in an effort to avoid 

divide-by-zero errors, mirroring code that was added to the 

LATERAL_WITHDRAWAL routine. Look for comments 

with the label “!SR 09/16/04.”

Finally, a problem was fixed in the setting of the 

BHKT1(IU-1) variable when segments are being subtracted 

after a layer is subtracted. There was an extra set of 

parentheses in that computation that would cause the water 

depth in that cell to be computed incorrectly. Look for the 

comment “!SR 07/29/05.” This change is inconsequential, 

because segments are never subtracted in the Willamette 

temperature model applications. Still, this was an obvious 

coding error that has since been corrected by the PSU model 

development team.

All changes up to this point were incorporated into the 

USGS model version named “generic Tmax3,” or “Tmax3” 

for short. The effect of these changes was tested, and no 

significant changes to the model output resulted. Most of the 

coding changes were minor, would rarely be invoked, or were 

“defensive” in nature, guarding against divide-by-zero errors, 

for example, and therefore would not normally be expected 

to cause a change in the model results. Mainly, these bug 

fixes serve to keep the model running under extraordinary 

circumstances, and to keep its computations more correct. 

Many more bug fixes and upgrades could be applied to the 

Willamette temperature models (the public release version of 

CE-QUAL-W2 is at version 3.5 as of April of 2007, and the 

Willamette models were built on version 3.12), but a major 

upgrade to the model code would require a re-evaluation of the 

model calibration, which is beyond the scope and need of this 

investigation. The Tmax3 version was used by USGS to run 

all Willamette submodels except the lower Willamette River, 

as explained below.

32  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Daily Water Temperature Maxima in the Lower 

Willamette River

In version Tmax3 and in the original CE-QUAL-W2 

version obtained from ODEQ, the calculations that determine 

the daily maximum surface temperature, the daily maximum 

volume-weighted temperature, and the daily maximum flowweighted temperature for every segment only calculated those 

quantities when the “time series” output was printed. So, if the 

user specified that the model should write time-series output 

20 times per day (time series output frequency (TSRF) = 

0.05), then the modeled temperatures would be queried only 

20 times per day to find the daily maxima. At times, this may 

not be frequent enough. It particularly can be a problem when 

the model time steps are large, such that different model runs 

might not calculate daily maxima using information from the 

exact same times. If the user-specified maximum time step 

is, say, 360 seconds, as it was in the lower Willamette River 

model, then the typical time step might be several minutes, and 

different model runs (no point sources versus all point sources, 

for example) might end up using information from several 

minutes apart in determining the daily maxima, simply due to 

variations in the model’s variable time steps. As a result, two 

different model runs might show daily maximum temperature 

differences of several hundredths of a degree or more, when 

such differences are only an artifact of the number of times 

per day that the model checked to determine whether a daily 

maximum had occurred. This “timing artifact” is not real and 

can be minimized or eliminated in one of several ways.

Simply increasing the number of times per day that the 

model checks for a daily maximum helps to minimize this 

timing artifact. As a test, the lower Willamette River model 

was run with a time-series output frequency of 200 points 

per day (TSRF = 0.005) and the results were compared to 

those from a model run using a time-series output frequency 

of only 20 points per day. The magnitude of the artifact was 

decreased, but not eliminated. Similarly, tests were run using a 

user-specified maximum time step (DLTMAX) of 60 seconds 

rather than 360 seconds for the lower Willamette River model, 

and this also decreased the magnitude of the timing artifact. 

In fact, decreasing the maximum time step to 60 seconds was 

more effective than checking more frequently.

In an attempt to minimize this artifact to the greatest 

extent possible, two things were changed for the lower 

Willamette River model. First, the maximum time step was 

decreased from 360 seconds to 60 seconds. That did not entail 

a code change. Second, a change was made to the model code 

so that the model would determine the daily maximum water 

temperatures (surface, volume-weighted, flow-weighted) using 

information from each and every time step, rather than only a 

certain number of times per day. This change means that the 

daily maximum temperature calculation is no longer tied to 

the TSRF. This new version of the model was named “generic 

Tmax3a” and was used only for the lower Willamette River 

submodel, because that model had the longest time steps and 

was the most susceptible to this timing artifact.

Tests showed that the new Tmax3a code had smaller 

timing artifacts in the computed daily maximum water 

temperatures. Separate tests showed that the Tmax3a version 

did not produce results that were any different from the Tmax3 

version for the upper Willamette model, where the typical time 

step is much smaller.

Appendix A  33
This page is intentionally left blank.

34  Temperature Effects of Point Sources, Riparian Shading, and Dam Operations on the Willamette River, Oregon
Manuscript approved for publication, August 20, 2007

Prepared by the USGS Publishing Network, 

Publishing Service Center, Tacoma, Washington

Bill Gibbs 

Ellen Hardy

Jacqueline Olson

Bobbie Jo Richey

Sharon Wahlstrom

For more information concerning the research in this report, contact 

Director, Oregon Water Science Center 

U.S. Geological Survey, 2130 SW 5th Ave.

Portland, Oregon 97201

http://or.water.usgs.gov
Rounds— Temperature Effects of Point Sources, Riparian Shading, and Dam Operations, Willamette River, Oregon—Scientific Investigations Report 2007–5185