LAKE MICHIGAN

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

LAKE MICHIGAN

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

Present-day stream temperatures (estimated)

Late 21st century stream temperatures (projected)

Cold

Thermal class (July mean)

Cold transition

Warm transition

Warm

Very warm

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2014–5186

Prepared in cooperation with the Wisconsin Department of Natural Resources

A Model for Evaluating Stream Temperature Response to 

Climate Change in Wisconsin

A Model for Evaluating Stream Temperature 

Response to Climate Change in Wisconsin

By Jana S. Stewart, Stephen M. Westenbroek, Matthew G. Mitro, John D. Lyons, 

Leah E. Kammel, and Cheryl A. Buchwald

Prepared in cooperation with the Wisconsin Department of Natural Resources

Scientific Investigations Report 2014–5186

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2015

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as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Stewart, J.S., Westenbroek, S.M., Mitro, M.G., Lyons, J.D., Kammel, L.E., and Buchwald, C.A., 2015, A model for 

evaluating stream temperature response to climate change in Wisconsin: U.S. Geological Survey Scientific 

Investigations Report 2014–5186, 64 p., http://dx.doi.org/10.3133/sir20145186.

ISSN 2328-0328 (online)
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................3

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

Approach................................................................................................................................................5

The Soil-Water-Balance Model...................................................................................................................6

Source Data...........................................................................................................................................6

Climate Observations ..................................................................................................................6

Landscape Characteristics ........................................................................................................7

Model Calibration for the Soil-Water-Balance Model....................................................................7

The Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream 

Temperature Model..........................................................................................................................7

Source Data.........................................................................................................................................11

Stream Temperature Observations.........................................................................................11

Climate Observations from Empirical Data............................................................................11

Landscape Characteristics ......................................................................................................14

Groundwater-Recharge Projections from the Soil-Water-Balance Model .....................14

Climate Projections from General Circulation Models........................................................17

Model Development and Application for the Integrated Soil-Water-Balance and 

Artificial Neural Network version 1 Stream Temperature Model .................................18

Artificial Neural Networks .......................................................................................................18

Training and Validation..............................................................................................................18

Model Predictions and Projections for Current and Future Climate Conditions.............20

Results and Discussion...............................................................................................................................22

Model Performance............................................................................................................................22

Model Predictions for Current Conditions......................................................................................26

Model Projections for Future Climate Conditions .........................................................................26

Change in the Amount of Stream Habitat Summarized by Thermal Class .......................31

Cold-Water Streams.........................................................................................................31

Cold-Transition Streams ..................................................................................................31

Warm-Transition Streams ...............................................................................................31

Warm-Water Streams......................................................................................................31

Very Warm Streams..........................................................................................................31

Change in the Distribution of Stream Habitat Summarized by Thermal Class ................31

Change in Absolute Temperature............................................................................................34

Change in Thermal Class..........................................................................................................38

Data and Model Limitations ..............................................................................................................50

Applications of the Integrated Soil-Water-Balance and Artificial Neural Network 

version 1 Stream Temperature Model ........................................................................................51

Summary and Conclusions.........................................................................................................................58

References Cited..........................................................................................................................................60

Appendix 1 (Available as download from web page) ............................................................................64

Appendix 2 (Available as download from web page) ............................................................................64
iv

Figures

 1. Map showing location of study area in Wisconsin and portions of 

Michigan and Minnesota ............................................................................................................4

 2–3. Schematic diagrams showing: 

2. Conceptual modeling approach for evaluating stream temperature 

 response to climate change in Wisconsin.....................................................................5

3. Approach and components of the Soil-Water-Balance Model ..................................8

4–5. Map showing: 

4. Ratio of Soil-Water-Balance predicted recharge to recharge calculated 

 based on measured streamflow records........................................................................9

5. Results of the Soil-Water-Balance Model for Wisconsin, 1970–2000......................10

 6. Schematic diagram showing the approach and components of an Artificial 

Neural Network stream temperature Model integrated with a Soil-Water-Balance 

Model and General Circulation Models..................................................................................12

7–8. Map showing: 

7. Location of 371 stream temperature monitoring sites used for training and 

 validation of the Integrated Soil-Water-Balance and Artificial Neural 

 Network version 1 stream temperature model............................................................13

8. Location of 160 air temperature climate stations used for time-series 

 clustering and for training of the Integrated Soil-Water-Balance and 

 Artificial Neural Network version 1 stream temperature model ..............................15

9–10. Graph showing: 

9. Average daily air temperature for six air temperature time-series groups 

 averaged over 19 years for the summertime period...................................................16

10. Soil-Water-Balance time series of accumulated potential groundwater 

 recharge used for input to the Integrated Soil-Water-Balance and 

 Artificial Neural Network version 1 stream temperature model ..............................17

11. Schematic diagram showing the Artificial Neural Network architecture with 

five input layers, three hidden layers, and a single output layer........................................20

12. Graphs showing simulations of stream temperature for eight validation sites, 

representing 25th and 75th percentiles, based on percent model error for four 

thermal classes from the integrated Soil-Water-Balance and Artificial Neural 

Network version 1 stream temperature Model .....................................................................25

13. Plots showing percent stream length for stream temperature thermal classes 

under current and future climate conditions for 10 General Circulation Models............30

14–15. Maps showing: 

14. Distribution of stream temperature thermal classes by individual stream 

 segment, predicted for current climate conditions and projected for future 

 mid-21st century climate conditions for 10 General Circulation Models ................32

15. Distribution of stream temperature thermal classes by individual stream 

 segment, predicted for current climate conditions and projected for future 

 late-21st century climate conditions for 10 General Circulation Models................33

16–17. Plots showing:

16. Projected absolute change in stream temperature summarized by 

 percent stream length for future climate conditions for 10 General 

 Circulation Models relative to current climate conditions ........................................34

17. Projected absolute change in stream temperature for future climate 

 conditions for 10 General Circulation Models relative to current

 climate conditions ............................................................................................................35
v

18–27. Maps showing: 

18. Projected absolute change in stream temperature for future mid-21st 

 century climate conditions for 10 General Circulation Models relative 

 to current climate conditions..........................................................................................46

19. Projected absolute change in stream temperature for future late-21st 

 century climate conditions for 10 General Circulation Models relative 

 to current climate conditions..........................................................................................47

20. Projected change in stream temperature thermal class for cold-water 

 streams from current to future mid-21st century climate conditions for 

 10 General Circulation Models .......................................................................................48

21. Projected change in stream temperature thermal class for cold-water 

 streams from current to future late-21st century climate conditions for 

 10 General Circulation Models .......................................................................................49

22. Projected change in stream temperature thermal class for cold-transition 

 streams from current to future mid-21st century climate conditions for 

 10 General Circulation Models .......................................................................................52

23. Projected change in stream temperature thermal class for cold-transition 

 streams from current to future late-21st century climate conditions for 

 10 General Circulation Models .......................................................................................53

24. Projected change in stream temperature thermal class for warm-transition 

 streams from current to future mid-21st century climate conditions for 

 10 General Circulation Models .......................................................................................54

25. Projected change in stream temperature thermal class for warm-transition

 streams from current to future late-21st century climate conditions for 

 10 General Circulation Models .......................................................................................55

26. Projected change in stream temperature thermal class for warm-water 

 streams from current to future mid-21st century climate conditions for 

 10 General Circulation Models .......................................................................................56

27. Projected change in stream temperature thermal class for warm-water 

 streams from current to future late-21st century climate conditions for 

 10 General Circulation Models .......................................................................................57

Tables

 1. Water temperature criteria for classifying Wisconsin streams into 

thermal classes and subclasses .................................................................................... 2

 2. Static landscape variables used as model predictors of stream temperature 

in Wisconsin ................................................................................................................................14

3. List of 10 General Circulation Models used in this study, run with the 

A1B emissions scenario, including their originating group, country, 

model identification, and model code .....................................................................................19

 4. Variables used to calibrate the Integrated Soil-Water-Balance and Artificial 

Neural Network version 1 Model and the average absolute sensitivity ...........................22

 5. Summary of performance statistics for the models used to estimate stream 

temperature for 254 sites and 371 sites in Wisconsin ..........................................................23

 6. Summary of residuals for the Integrated Soil-Water-Balance and Artificial 

Neural Network version 1 Model used to estimate stream temperature for 

371 sites in Wisconsin................................................................................................................23

 7. Percent model error by thermal class for the Integrated Soil-Water-Balance 

and Artificial Neural Network version 1 Model used to estimate stream 

temperature for 371 sites in Wisconsin ..................................................................................24
vi

 8. Statistical measure of prediction accuracy for eight validation sites representing 

the 25th and 75th percentile for cold, cold-transition, warm-transition, and 

warm-water sites for the Integrated Soil-Water-Balance and Artificial Neural 

Network version 1 Model ..........................................................................................................24

 9. Predictions of stream temperature thermal class and projected change 

summarized by length and as a percentage of total length for current and 

future climate conditions for 10 General Circulation Models .............................................27

10. Projections of absolute change in stream temperature summarized by length 

and as a percentage of total length for current and future climate conditions for 

10 General Circulation Models .................................................................................................36

11. Projections of change in stream temperature thermal class summarized by 

length and as a percentage of total length for 10 General Circulation Models 

for the mid-21st century and late-21st century......................................................................39

Conversion Factors and Datums 

SI to Inch/Pound

Multiply By To obtain

Length

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft)

kilometer (km) 0.6214 mile (mi)

Area

square kilometer ( km2

) 0.3861 square mile (mi2)

Flow rate

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

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

°F=(1.8×°C)+32

Vertical coordinate information is referenced to National Geodetic Vertical Datum 

of 1988 (NGVD 88).

Horizontal coordinate information is referenced to either the North American Datum 

of 1927 (NAD 27) or the North American Datum of 1983 (NAD 83).
vii

Abbreviations used in this report

ANN artificial neural network

ANNv1 artificial neural network version 1 stream temperature model 

 (Stewart and others, 2006)

APWL accumulated potential water loss

AWC available water-holding capacity 

CGCM General Circulation Model: CGCM3.1 (T63); Canadian Centre for 

 Climate Modelling and Analysis, Canada

CNRM General Circulation Model: CNRM-CM3; Météo-France / Centre 

 National de Recherches Météorologiques, France

CRP Conservation Reserve Program

CSIRO General Circulation Model: CSIRO-Mk3.5; CSIRO Atmospheric 

 Research, Australia

DSI Data Series Index

ECHO General Circulation Model: ECHO-G; Meteorological Institute of the 

 University of Bonn, Meteorological Research Institute of KMA, and 

 Model and Data group, Germany/Korea

FGOALS General Circulation Model: FGOALS-g1.0; LASG / Institute of 

 Atmospheric Physics, China

GCM General Circulation Model

GDD growing degree-day

GFDL General Circulation Model: GFDL-CM2.0; U.S. Dept. of Commerce / NOAA / 

 Geophysical Fluid Dynamics Laboratory, USA

GIS geographic information system

GISS General Circulation Model: GISS-AOM; NASA / Goddard Institute for 

 Space Studies, USA

GUI graphical user interface

HSG hydrologic soils group

INGV General Circulation Model: INGV-ECHAM4; Instituto Nazionale di 

 Geofisica e Vulcanologia, Italy

IPCC Intergovernmental Panel on Climate Change

IPSL General Circulation Model: IPSL-CM4; Institut Pierre Simon Laplace, France

MIROC General Circulation Model: MIROC3.2(hires); Center for Climate System 

 Research (The University of Tokyo), National Institute for Environmental 

 Studies, and Frontier Research Center for Global Change (JAMSTEC), Japan 

MSE mean square error

NCDC National Climatic Data Center
viii

NED National Elevation Data

NHD National Hydrography Dataset

NLCD National Land Cover Database

PDF probability density function

PEST parameter estimation software

PME percent model error

r Pearson’s correlation coefficient

R2 coefficient of determination

RMSE root mean square error

SSURGO Soil Survey Geographic Database

SWB soil-water-balance

SWB-ANNv1 Integrated Soil-Water-Balance and Artificial Neural Network version 1 Model

USGS U.S. Geological Survey

UWCCR University of Wisconsin Center for Climatic Research

WDNR Wisconsin Department of Natural Resources

WICCI Wisconsin Initiative on Climate Change Impacts
ix

Acknowledgments

Ed Roehl (Advanced Data Mining, Inc.), Paul Conrads and Judith Thomas (U.S. Geological Survey (USGS)), and Alex Martin and Christopher Smith (Wisconsin Department of 

Natural Resources (WDNR)) are acknowledged for their assistance in developing and reviewing methods, and deriving and managing geographic information system data. Funding for this 

study was provided in part by the USGS National GAP Analysis Program, Great Lakes Aquatic 

GAP project, and the Federal Aid in Sportfish Restoration, Project F-95-P, studies SSMP and 

SSCN.
x
A Model for Evaluating Stream Temperature Response to 

Climate Change in Wisconsin

By Jana S. Stewart,1 Stephen M. Westenbroek,1 Matthew G. Mitro,2 John D. Lyons,2 Leah E. Kammel,1 and 

Cheryl A. Buchwald1

 

1

 U.S. Geological Survey.

2

 Wisconsin Department of Natural Resources.

Abstract

Expected climatic changes in air temperature and 

precipitation patterns across the State of Wisconsin may alter 

future stream temperature and flow regimes. As a consequence 

of flow and temperature changes, the composition and distribution of fish species assemblages are expected to change. 

In an effort to gain a better understanding of how climatic 

changes may affect stream temperature, an approach was 

developed to predict and project daily summertime stream 

temperature under current and future climate conditions for 

94,341 stream kilometers across Wisconsin. The approach 

uses a combination of static landscape characteristics and dynamic time-series climatic variables as input for an Artificial 

Neural Network (ANN) Model integrated with a Soil-WaterBalance (SWB) Model. Future climate scenarios are based on 

output from downscaled General Circulation Models (GCMs). 

The SWB model provided a means to estimate the temporal 

variability in groundwater recharge and provided a mechanism to evaluate the effect of changing air temperature and 

precipitation on groundwater recharge and soil moisture. The 

Integrated Soil-Water-Balance and Artificial Neural Network 

version 1 (SWB-ANNv1) Model was used to simulate daily 

summertime stream temperature under current (1990–2008) 

climate and explained 76 percent of the variation in the daily 

mean based on validation at 67 independent sites. Results were 

summarized as July mean water temperature, and individual 

stream segments were classified by thermal class (cold, cold 

transition, warm transition, and warm) for comparison of current (1990–2008) with future climate conditions. 

Integrating the SWB Model with the ANN Model 

provided a mechanism by which downscaled global or 

regional climate model results could be used to estimate the 

potential effects of climate change on future stream temperature on a daily time step. To address future climate scenarios, 

statistically downscaled air temperature and precipitation 

projections from 10 GCMs and 2 time periods were used with 

the SWB-ANNv1 Model to project future stream temperature. 

Projections of future stream temperatures at mid- (2046–65) 

and late- (2081–2100) 21st century showed the July mean 

water temperature increasing for all stream segments with 

about 80 percent of stream kilometers increasing by 1 to 

2 degrees Celsius (°C) by mid-century and about 99 percent 

increasing by 1 to 3 °C by late-century. Projected changes in 

stream temperatures also affected changes in thermal classes 

with a loss in the total amount of cold-water, cold-transition, 

and warm-transition thermal habitat and a gain in warm-water 

and very warm thermal habitat for both mid- and late-21st 

century time periods. The greatest losses occurred for coldwater streams and the greatest gains for warm-water streams, 

with a contraction of cold-water streams in the Driftless Area 

of western and southern Wisconsin and an expansion of warmwater streams across northern Wisconsin. Results of this study 

suggest that such changes will affect the composition of fish 

assemblages, with a loss of suitable habitat for cold-water 

fishes and gain in suitable habitat for warm-water fishes. In 

the end, these projected changes in thermal habitat attributable 

to climate may result in a net loss of fisheries, because many 

warm-water species may be unable to colonize habitats formerly occupied by cold-water species because of other habitat 

limitations (e.g., stream size, gradient). Although projected 

stream temperatures may vary greatly, depending on the emissions scenario and models used, the results presented in this 

report represent one possibility. The relative change in stream 

temperature can provide useful information for planning for 

potential climate impacts to aquatic ecosystems. Model results 
2 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

can be used to help identify vulnerabilities of streams to 

climate change, guide stream surveys and thermal classifications, prioritize the allocation of scarce financial resources, 

identify approaches to climate adaptation to best protect and 

enhance resiliency in stream thermal habitat, and provide 

information to make quantitative assessments of statewide 

stream resources.

Introduction

Water temperature is an important determinant of where 

fish and other aquatic organisms live in streams. Most fish are 

ectotherms, which exchange heat with and are generally the 

same temperature as their surrounding aquatic environment. 

The thermal environment in which a given species of fish exists can be defined by lower and upper lethal limits, and within 

these bounds are optimal temperatures for feeding, growth, 

and reproduction. Knowledge of how water temperature varies 

temporally and spatially within and among streams is critical 

to understanding how fish species are distributed in streams. 

In temperate regions such as Wisconsin, stream fishes 

typically encounter water temperatures in the range of 

0–30 degrees Celsius (°C). At any given time of year, water 

temperatures may vary within and among streams. Useful 

metrics for classifying streams can be derived from summertime water temperatures. Lyons and others (2009) classified Wisconsin streams into cold-water, cold-transition, 

warm-transition, and warm-water thermal classes based on the 

presence (or absence) of fish species, species abundance, and 

summertime water temperature metrics (June–August mean, 

July mean, and maximum daily mean) (table 1).

Cold-water and cold-transition streams can support high 

abundances of cold-water fishes such as brook trout Salvelinus fontinalis and brown trout Salmo trutta. Cold-water 

fishes are less abundant in warm-transition streams and absent 

from warm-water streams during summertime but may occur 

in warm-water streams during colder seasons. Warm-water 

and warm-transition streams can support high abundances 

of warm-water fishes such as fathead minnows Pimephales 

notatus and smallmouth bass Micropterus dolomieu. Warmwater fishes are less abundant in cold-transition streams and 

absent from cold-water streams. Summertime water temperature is therefore an important factor in explaining fish distribution patterns in streams of the Laurentian Great Lakes region 

(Wehrly and others, 2003; Chu and others, 2008; Steen and 

others, 2008; Lyons and others, 2009, 2010). Understanding 

the distribution of stream temperatures across all streams in a 

region will help in understanding how fish species are distributed. 

Water temperature in streams is affected by many factors 

operating at multiple spatial and temporal scales, often with 

complex interactions. Air temperature, for example, is a significant climatic determinant of water temperature in streams 

in Wisconsin and other temperate regions (Magnuson and 

others, 1979; Stewart and others, 2006; Westenbroek, 2010b). 

However, stream temperatures in Wisconsin are highly heterogeneous as compared to air temperatures across the landscape. 

Streams or even stream reaches in close proximity to one 

another and under similar climate conditions may exhibit different temperature characteristics because of local variation 

in geology and groundwater input. Wehrly and others (1998, 

2006) have developed models to identify landscape effects on 

stream temperature. 

Given the important role that air temperature plays in 

the list of factors that determine stream temperature, resource 

managers are concerned that changes in climate will impact 

stream temperatures and fish distribution. Wisconsin has on 

average become warmer and wetter over the past 60 years, 

and this warming trend is predicted to continue and increase, 

with the statewide average air temperature increasing by up to 

3–4 °C by the year 2050 (WICCI, 2011). These increases in air 

temperature along with changes in the timing and amount of 

precipitation are expected to alter thermal and hydrologic regimes of Upper Midwestern streams over the coming decades 

(Magnuson and others, 1997; Mosheni and others, 1999), 

affecting the distribution of fish and other aquatic species 

(Mosheni and others, 2003; Lyons and others, 2009, 2010). 

Current and future management of statewide stream resources 

would greatly benefit from an improved understanding of the 

current distribution of stream thermal habitat and the fish communities that live there. 

Table 1. Water temperature criteria for classifying Wisconsin streams into thermal classes and subclasses

(Lyons and others, 2009). 

[deg C, degrees Celsius; <, less than; >, greater than] 

Thermal class Subclass July mean

(deg C)

June-August mean

(deg C)

Maximum daily mean

(deg C)

Cold water < 17.5 < 17 < 20.7

Cold transition 17.5 - 19.5 17.0 - 18.7 20.7 - 22.6

Warm transition 19.5 - 21 18.7 - 20.5 22.6 - 24.6

Warm water > 21 > 20.5 > 24.6

very warm* > 24

*Very warm thermal subclass was added for purpose of estimating climate-change effects on warm-water streams.
Introduction 3

One limitation to stream and fisheries resource 

management in Wisconsin and elsewhere is the relatively 

small number of streams that can be physically sampled in a 

given year, whether sampling involves deploying data loggers 

to measure continuous stream temperature data or surveying 

fish populations. Modeling is a tool resource managers may 

use to make inferences from sampled stream sites to unsampled stream sites to help address those limitations. 

To help gain a better understanding of statewide stream 

resources, an Artificial Neural Network (ANN) model was developed for Wisconsin using water temperature data collected 

at 254 stream sites over the summertime period for 1990–2002 

(Stewart and others, 2006; Westenbroek and others, 2010b). 

The model was applied to stream segments statewide to 

predict daily summertime stream temperature and classify 

streams into summer thermal classes (Lyons and others, 2009) 

and will be referred to as Artificial Neural Network version 1 

stream temperature model (ANNv1) throughout this report. 

ANN models also have been used to successfully predict 

water temperature in other regions of North America (Chenard 

and Caissie, 2008; McKenna and others, 2010; Risley and 

others, 2003). 

Lyons and others (2010) used the ANNv1 predictions to 

predict and project current and future distributions of 50 fish 

species in Wisconsin streams. In order to simulate stream 

temperature under three future climate-warming scenarios, 

Lyons and others (2010) adjusted July mean water temperature 

by 0.8 °C (low), 2.4 °C (medium), and 4 °C (high) to represent 

air temperature increases of low = 1 °C, medium = 3 °C, and 

high = 5 °C, based on Pilgrim and others (1998). A key limitation to this effort was the oversimplification of the relation 

between air and water temperature as a single statewide ratio 

and lack of any connection between precipitation, groundwater, stream recharge, and water temperature. 

As Lyons and others (2010) demonstrated, stream 

temperature models can provide a means to make inferences to 

the potential impacts climate change may have on the stream 

environment and fish populations therein. However, new 

modeling efforts are required to improve how site-specific 

stream environmental landscape characteristics can be combined with continuous climate data to make projections on 

how stream temperature may respond to changes in climatic 

variables under future conditions. Resource managers tasked 

with developing adaptation strategies to protect streams and 

fisheries opportunities can use such models to help prioritize 

the allocation of scarce financial resources and make quantitative assessments of statewide stream resources.

Purpose and Scope

The purpose of this study was to develop models for 

predicting stream temperatures in all Wisconsin streams and 

to evaluate how stream temperatures may respond to climate 

change. This report describes the development of an Integrated 

Soil-Water-Balance and Artificial Neural Network version 1 

(SWB-ANNv1) Model to predict stream temperature from 

continuous climate time series and watershed-landscape 

characteristics under current climate conditions and project 

future stream temperature through integration with results of 

GCMs. The development of the SWB-ANNv1 model builds 

upon ANNv1 (Stewart and others, 2006), and the integration 

of the Soil-Water-Balance (SWB) model is an enhancement to 

this earlier modeling effort (Westenbroek and others, 2010b). 

The integration of SWB with the ANN provides a means to 

link changing climate patterns and precipitation amounts over 

time to stream temperature and potential groundwater recharge. Stream temperature is an important factor in determining the ecological status of temperate region streams in terms 

of which fish species can and cannot live and persist in those 

streams. The results of this study can be used subsequently to 

update stream fish models for predicting or projecting presence and absence of 50 fish species in Wisconsin streams 

under current and future climate scenarios (Lyons and others, 

2010). 

This study also is relevant to the mission of the 

U.S. Geological Survey (USGS) and its core science strategies 

with priorities to identify climate change impacts on fish and 

wildlife species. The resulting research and products can help 

provide the scientific foundation by which policymakers, 

resource managers, and the public make informed decisions 

about the management of natural resources on which they and 

others depend (Burkett and others, 2013). 

Study Area

The study area includes 94,341 km of streams 

(n = 38,423 segments) across the entire State of Wisconsin 

(1:100,000 scale U.S. National Hydrography data) and for 

two bordering watersheds: the Menominee River Basin (Upper Peninsula of Michigan) and the St. Croix River Basin 

(Minnesota) (fig. 1). Wisconsin includes rivers that drain to 

the Mississippi River Basin to the south and west, and the 

U.S. Great Lakes Basin, to the north (Lake Superior) and east 

(Lake Michigan). The proximity to the Great Lakes has a 

strong influence on Wisconsin’s climate and plays a major role 

in seasonal climate variations. The landscape is dominated 

by forested lands in the north, agricultural lands in the central 

and southeast, and major urban centers in the southeast portion of the State. The many rivers and lakes and other glacial 

landforms are common features of Wisconsin’s landscape, 

as glaciers once blanketed all but portions of western and 

southwestern Wisconsin. The unglaciated southwestern part 

of the State is commonly referred to as the Driftless Area 

and is characterized by rugged topography and groundwaterdominated streams that support thriving cold-water fisheries 

for brook trout and brown trout. Cold-water streams also exist 

as part of the glaciated landscape in other parts of the State; 

however, warmer thermal classes of streams tend to be more 

prevalent in those areas (Trout Unlimited, 2005; Lyons and 

others, 2009).
4 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Study area

Basin

Driftless area

Lakes and streams

States

County boundary

EXPLANATION

L

A

K

E

M I C H I G A N

L A K E S U P E R I O R

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

WISCONSIN

0 20 40 60 KILOMETERS

0 20 40 60 MILES

42°

44°

46°

92° 90° 88°

St. Croix River Basin

Bayfield Peninsula

UPPER PENINSULA

Menominee River Basin

Base from U.S. Geological Survey (USGS) digital data, 1:2,000,000.

Figure 1. Location of study area in Wisconsin and portions of Michigan and Minnesota.
Introduction 5

Approach

An approach was developed to predict stream 

temperature under current climate conditions and to project 

how stream temperature may change under future climate 

conditions. The approach uses a combination of static watershed landscape characteristics and dynamic time-series 

climatic variables as input for the SWB-ANNv1 model. Future 

climate scenarios are based on output of downscaled GCMs. 

The SWB-ANNv1 model was developed in order to simulate 

summertime mean daily stream temperature as a continuous 

time series for confluence-to-confluence stream segments using data collected at 371 stream temperature monitoring locations across Wisconsin. The SWB-ANNv1 model was applied 

across the study area to predict current and project future daily 

summertime stream temperature for all 94,341 km of stream. 

The summary variable July mean water temperature was used 

in this report to classify stream segments into thermal classes 

and for comparison to assess the effects of projected future 

climate on stream temperature (Lyons and others, 2009).

This study builds upon ANNv1 developed by Stewart and 

others (2006) that used water temperature data collected at 

254 stream sites over the summertime period for 1990–2002 

(Westenbroek and others, 2010b). The ANN model is a nonlinear model that uses neural network algorithms to link dynamic climate signals and static watershed landscape characteristics to predict time series of stream temperature. The static 

variables provide a link to the spatial variability of stream 

temperature across the State, associated with the changing 

landscape, while the dynamic time-series climate variables 

provide a link to the temporal component of stream temperature, associated with climate patterns. The approach involves 

time-series clustering, a technique that was initially used to 

predict hourly stream temperatures in western Oregon (Risley 

and others, 2003) and by Roehl and others (2006) to generate 

spatially continuous water-level predictions for a Florida aquifer. Stewart and others (2006) used a slightly modified timeseries clustering approach than these other studies for ANNv1 

because most of the Wisconsin stream temperature data were 

temporally discontinuous, having been measured during different summers over a 13-year period (1990–2002). The key 

climate signals in the ANNv1 model were 6 air temperature 

time-series variables obtained by clustering air temperature 

time-series data measured at 156 weather stations across the 

State into 6 groups. A key limitation to the approach taken in 

development of ANNv1 was the absence of any link between 

precipitation and stream temperature. 

This limitation was addressed by integrating a deterministic 

SWB model that uses precipitation and air temperature along with 

landscape characteristics as inputs to track soil moisture and generate a time-series estimate of potential groundwater recharge at a 

daily time step (Westenbroek and others, 2010a and b; Dripps and 

Bradbury, 2007; Hart and others, 2009). In addition to the SWB 

enhancement, the spatial and temporal extent of stream temperature measurements used in ANNv1 was expanded by including 

additional monitoring sites and extending the simulation period 

from the year 2002 to 2008. 

Future stream temperature will not only be influenced 

by changes in air temperature but also by changes in base 

flow that may be attributable to changes in precipitation. The 

amount of groundwater-derived base flow can play a key role 

in determining stream temperature and has been shown to 

be of critical importance to the viability of cold-water trout 

fisheries, particularly in the upper Midwest (Gaffield and others, 2005; Zorn and others, 2002; Wehrly and others, 2006). 

The SWB model provided a means to estimate the temporal 

variability in groundwater recharge and provided a mechanism 

to evaluate the influence of changing air temperature and precipitation on groundwater recharge and soil moisture through 

the integration of GCMs downscaled for Wisconsin. Integrating the SWB model with the ANN model in turn provided a 

mechanism by which results from downscaled GCMs could be 

integrated to estimate the potential effects of climate change 

on stream temperature (fig. 2). 

OUTPUT

MODEL

INPUT

EXPLANATION

GCMs = General Circulation Models

SWB = Soil-Water-Balance Model

ANN = Artificial Neural Network Model

SWB–ANN = Integrated SWB and ANN Model

Estimated stream temperature

• Current (Climate observations)

• Future (GCMs Downscaled climate)

SWB

SWB–ANN

CLIMATE

Figure 2. Conceptual modeling approach for evaluating 

stream temperature response to climate change in 

Wisconsin. 
6 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

To address future climate scenarios, this study used 

statistically downscaled air temperature and precipitation projections from the University of Wisconsin Center for Climatic 

Research (UWCCR) for 10 GCMs. The UWCCR used a process known as statistical downscaling to relate the large-scale 

atmospheric conditions predicted by GCMs to the value of 

observed climate data at a given point. To allow for simulation 

of local climate variability and extremes while also simulating 

the large-scale weather pattern, the UWCCR related the largescale GCM results to a probability density function of values 

at each of 170 climate observing stations (Notaro and others, 

2011). This procedure is reported to reduce the variance and 

extremes that often occur when interpolating raw GCM data 

(Notaro and others, 2011).

 Statistical downscaling of daily air temperature and 

precipitation was available for three time periods—late-20th 

century-baseline historical hindcast (1961–2000), mid-21st 

century (2046–65), and late-21st century (2081–2100)—and 

three different future greenhouse-gas emissions scenarios 

(B2 scenario (low emissions), A1 scenario (high emissions), 

and the A1B scenario (moderate to high emissions) (Notaro 

and others, 2011)). Changes in stream temperature in future 

years will likely reflect realized changes in greenhouse-gas 

emissions; future stream temperatures described in this report 

assume that future carbon emissions develop as envisioned 

in the A1B emissions scenario. The A1B emissions scenario 

is a middle-of-the-road greenhouse-gas emissions scenario 

developed by the Intergovernmental Panel on Climate Change 

(IPPC) (IPCC, 2007). This scenario assumes continued use 

of fossil fuels and a continued and steady upward trajectory 

of carbon emissions over the next few decades, from about 

400 parts per million today to about 550 parts per million by 

mid-century. The three time periods—1961–2000, 2046–65, 

and 2081–2100—are treated as stationary periods, even 

though greenhouse-gas emissions are continuing to change 

through each timespan. This study considers only a single 

emissions scenario and single statistical realization owing 

to limited resources and time constraints. Climate data from 

UWCCR in the form of projected future daily air temperature 

and precipitation served as input for the SWB-ANNv1 model 

to estimate the effect of 10 GCMs on stream temperature.

The following sections describe the development of the 

SWB model and the integration of groundwater-recharge 

estimates from the SWB model into the ANN model (SWBANNv1) to generate daily time-series estimates of stream 

temperature across Wisconsin. Both estimates were made 

under current and future climate conditions, using empirical 

climate observations for current conditions and statistically 

downscaled air temperature and precipitation projections from 

10 GCMs for future conditions. The SWB-ANNv1 model 

was applied to all stream segments statewide for current and 

future time periods. Model results are then presented, showing 

how stream temperature is projected to change across GCMs, 

future time periods, and thermal classes of streams.

The Soil-Water-Balance Model

The USGS SWB software (Westenbroek and others, 

2010a) was used to supply estimates of spatially explicit 

groundwater-recharge over time for use in the SWB-ANNv1 

stream temperature model. The USGS SWB model code 

estimated potential groundwater recharge for a grid of cells on 

a daily basis. The model simulated the major components of a 

water budget, including the processes of interception, runoff, 

evapotranspiration, snowfall, and snowmelt. Soil moisture 

is determined by calculating the net gain or loss of water 

to the soil in a given grid cell, and then by consulting the 

Thornthwaite-Mather soil moisture-retention tables; the tables 

allow one to estimate how much moisture may be extracted 

from a soil given the history of precipitation and evapotranspiration to which it has been exposed (Thornthwaite and Mather, 

1957). The difference between the inputs and outputs of water 

for each cell, including the change in soil moisture storage, 

was assumed to be potential recharge. More detail about 

model formulation, parameterization, and calibration of the 

SWB model may be found in Westenbroek and others (2010a).

Source Data

Application of the SWB model required a tabular or 

gridded climate dataset, along with four gridded datasets 

describing landscape characteristics. The following sections 

describe how these source data were prepared for use with the 

SWB model.

Climate Observations

An interpolated climate dataset was created to encompass 

all Wisconsin streams and for streams outside of Wisconsin 

in two bordering watersheds: the St. Croix (Minnesota) and 

Menominee (Michigan) River Basins. Data from more than 

1,000 meteorological stations were extracted from the Data 

Series Index (DSI)-3200 daily surface database maintained 

by the National Climatic Data Center (NCDC) for the time 

period 1950–2008 (National Oceanic and Atmospheric 

Administration, 2011). Due to the grid-based nature of SWB, 

the selected stations extended beyond the study area, covering 

Wisconsin and parts of Michigan, Minnesota, Illinois, Indiana, 

and Iowa. Data elements included maximum and minimum 

daily air temperature, total daily precipitation, daily snowfall, 

and cumulative snow depth. Air temperature and precipitation data elements were used as SWB input and snow data 

elements were used in SWB verification. The input for this 

gridded dataset was nearly identical to that used by Serbin and 

Kucharik (2009). Because their model domain did not extend 

beyond Wisconsin, it was necessary for us to include additional meteorological stations and create a similar grid for a 

slightly larger model domain. 
The Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 7

Grids were prepared for each of the five climate variables 

by means of a custom R script (R Development Core Team, 

2011), in which a thin-plate spline—a two-dimensional 

smoothing technique—was calculated for each set of daily 

climate data (Fields Development Team, 2006) for the 

purposes of data interpolation and smoothing. Data were 

discarded from the analyses if there were duplicate records, 

if daily values were flagged as “accumulated” or “missing,” 

or if data values fell outside of realistic data ranges (e.g., a 

maximum air temperature greater than 49 °C, a minimum 

air temperature less than −34 °C, or total daily precipitation 

greater than 508 millimeters (mm)).

In addition, daily precipitation totals were adjusted on the 

basis of the recorded time of observation. A station at which 

precipitation values are recorded at 8:00AM is possibly more 

representative of the precipitation that fell during the 16 hours 

of the previous calendar day than the 8 hours of the recorded 

date. Thus, precipitation values were adjusted to account for 

the number of hours actually represented by the value on the 

recorded day. For example, 22.9 mm of precipitation recorded 

at a station with an observation time of 8:00AM would result 

in 15.2 mm of that precipitation amount reallocated to the previous day, retaining 7.7 mm for the current day. The resulting 

data were prepared for use in SWB model calibration.

Landscape Characteristics

Landscape-characteristic grids for SWB model input 

included land cover from the 2001 National Land Cover 

Database (NLCD), available water-holding capacity 

(AWC), and hydrologic soils group (HSG) from the Natural 

Resources Conservation Service Soil Survey Geographic 

Database (SSURGO), and a flow-direction grid derived from 

a hydrologically corrected version of the National Elevation 

Data (NED) (U.S. Geological Survey, 2003, 2004a; U.S. 

Department of Agriculture, 2009).

The source-data grids for the landscape characteristics 

were obtained at 30 meter (m) resolution; SWB model grid 

resolutions tested for this project ranged from 400 to 1,600 m. 

Generalization of the source-data grids to the SWB grids was 

performed as follows: for land cover, flow direction, and HSG 

grids, an SWB grid cell was assigned the value contained in 

the majority of the underlying input grid cells; for the AWC 

grid, an SWB grid cell was assigned a value equal to the 

simple mean of underlying grid cells.

Model Calibration for the Soil-Water-Balance 

Model

An initial SWB model for Wisconsin was created by 

combining the four landscape characteristics grids and the 

climate grids with a lookup table, which was populated with 

textbook values for the runoff curve number, rooting depth, 

and snow parameter values (Cronshey and others, 1986) for 

each combination of HSG and land-cover type. 

The SWB model was calibrated by use of parameter 

estimation software (PEST) (Doherty, 2009) in two steps. The 

first calibration step optimized the SWB model snow parameters to maximize model agreement with first-order climate 

station snowfall observations and included rain and snowfall 

correction factors and the assumed temperatures at which precipitation falls as entirely rain or snow. The second calibration 

step optimized SWB model runoff curve number, maximum 

infiltration rates, and rooting depth parameters to maximize 

model agreement with independently calculated groundwaterrecharge values for Wisconsin. The relation between each of 

these data types and the SWB code is shown in figure 3.

The estimates of recharge used in the calibration process 

were generated by Gebert and others (2007) by performing 

base-flow separation analysis on stream discharge records for 

the period 1970–99. For the calibration work, we chose a subset (n = 44 gaging stations) of the basin recharge estimates that 

were judged to have the least amount of difference between 

groundwater and surface-water divide boundaries. Figure 4 

shows the ratio of the SWB model predicted recharge to the 

recharge calculated by Gebert and others, 2007, and figure 5 

shows SWB model output (recharge, inches per year) generated with calibrated snow, runoff, and soil depth parameters.

Model simulations were run at three resolutions (400, 

800, and 1,600 m) for the period 1989–2000 to determine 

optimal cell size. The finer resolution simulations did not appreciably improve predictions; therefore, the 1,600 m cell size 

was selected for SWB model simulation. The SWB simulations were then run for the 1,600 m cell size for the period 

1990–2008 to match up with the period of stream temperature 

observations and SWB-ANNv1 model simulation.

The Integrated Soil-Water-Balance and 

Artificial Neural Network version 1 

Stream Temperature Model

The SWB-ANNv1 model (fig. 6) was built upon the 

ANNv1 stream temperature model developed by Stewart and 

others (2006) for Wisconsin as described in the Approach 

section of this report. The spatial and temporal extent of the 

ANNv1 model was expanded in this study by including additional stream measurement sites (from 254 in ANNv1 to 371 

sites in this study) and extending the simulation period from 

2002 to 2008. The approach and methods used in development of ANNv1 and this study were nearly identical with the 

following exception: an SWB component, described in this 

report, was added as an enhancement to incorporate groundwater-recharge estimates under current conditions and to 

provide a link to global climate models as a means to simulate 

future stream temperature conditions under different climate 
8 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Soil-water-balance code

Soil and land-use lookup table

Landscape characteristics

· Land cover

· Hydrologic soil group

· Flow direction 

· Available water-holding capacity

Climate data

(tabular or gridded)

Recharge to groundwater

(gridded data)

0

5

10

15

20

25

30

35

40

2 4 6 8 10 12 14 16

Soil water retention table

(Thornthwaite and others, 1957)

Maximum soil-moisture capacity, in inches

Soil-moisture retained, in inches

Accumulated potential water loss, in inches

Figure 3. Approach and components of the Soil-Water-Balance Model (Westenbroek and others, 2010a). 
The Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 9

0 20 40 60 80 100 MILES

0 40 80 20 60 100 KILOMETERS

EXPLANATION

Recharge, in inches per year 

Ratio of predicted to calculated 

recharge

High: 11.8

Low: 0.01

Base from U.S. Geological Survey (USGS), EROS Data Center, Grayscale 

North American Shaded Relief - 1-Kilometer Resolution; September 2005.

Soil-Water-Balance model

1.05

0.78

0.74 0.95 0.67

2.37

0.72

0.64

0.58

0.25

0.46 0.7

0.26 0.37

0.56

0.49

0.38

1.29

3.15

0.53

0.980.38

0.5

1.09

0.95

0.78

0.43

0.82 1.19

0.84

1.15

1.09

0.96

1.15

1.06

0.75

1.05

1

1

0.95

0.95

0.72

2.38

1.4

1.46

0.51

0.91

0.45

41° 

42° 

43° 

44° 

45° 

46° 

47° 

94° 93° 92° 91° 90° 89° 88° 87° 

L

A

K

E

M I C H I G A N

L A K E S U P E R I O R

Figure 4. Ratio of Soil-Water-Balance predicted recharge to recharge calculated based on 

measured streamflow records (Gebert and others, 2007).
10 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

EXPLANATION

Recharge, in inches per year 

Soil-Water-Balance Model

High: 11.8

Low: 0.01

Base from U.S. Geological Survey (USGS), EROS Data Center, Grayscale

North American Shaded Relief - 1-Kilometer Resolution; September 2005.

0 20 40 60 80 100 MILES

0 40 80 20 60 100 KILOMETERS

41° 

42° 

43° 

44° 

45° 

46° 

47° 

94° 93° 92° 91° 90° 89° 88° 87° 

L A

K

E

M I C H I G A N

L A K E S U P E R I O R

Figure 5. Results of the Soil-Water-Balance Model for Wisconsin, 1970–2000.
The Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 11

scenarios (Roehl and others, 2006; Stewart and others, 2006, 

Westenbroek and others, 2010a and b). The output from SWB 

in the form of accumulated potential groundwater recharge, 

served as an additional ANN input variable in this study, in 

contrast to ANNv1. A detailed schematic of the SWB-ANNv1 

model approach is shown in figure 6. The calibrated SWBANNv1 model was applied to all stream segments in the study 

area to estimate stream temperature statewide under current 

and future climate conditions.

Source Data

Development of the SWB-ANNv1 model utilized five 

input datasets including (1) empirical stream temperature 

time-series observations, (2) empirical climate time-series observations, (3) geographic information system (GIS)-derived 

landscape characteristics, (4) SWB estimates of groundwater 

recharge, and (5) climate time-series projections from downscaled GCMs. The following sections describe how these 

source data were prepared for development of the SWBANNv1 model.

Stream Temperature Observations

Water temperature was measured each half hour from 

June 1 to August 31 at 371 stream sites for 1990–2008 by the 

Wisconsin Department of Natural Resources (WDNR) and the 

USGS. The data were discontinuous in that some stream sites 

were sampled over a single summer and others were sampled 

multiple summers over the 19-year period. The SWB-ANNv1 

stream temperature model was developed using 243 of the 

254 stream sites used in ANNv1, 11 of the ANNv1 sites 

were dropped in this study after they were determined to be 

outliers during model calibration, an additional 128 sites were 

added, and the time period was extended from 2002 to 2008. 

Most streams were wadeable (drainage area < 1,600 square 

kilometers (km2

)), with the exception of 11 sites with drainage 

areas ranging from 1,784 to 15,923 km2

. Stream sites were 

fairly evenly distributed across the full range of stream thermal classes with 25 percent cold, 18 percent cold-transition, 

20 percent warm-transition, and 37 percent warm-water sites 

(Lyons and others, 2009). Time series of mean daily water 

temperature were calculated for each site and served as the 

response variable (fig. 7; appendix 1).

Sites were selected that had at least 62 out of 92 days of 

measurements during a single summertime (June–August) 

period. Temperature measurements outside of three standard 

deviations from the mean for the entire period of measurement at a given site were considered outliers and were deleted 

(Wagner and others, 2011). Most water temperature sites 

(243 of 371) had only a single summer of data; the remaining 

128 sites had from 2 to 17 summers of water temperature measurements for a total of 67,356 discrete daily stream temperature measurement data points.

Climate Observations from Empirical Data

Climatic data were acquired from the NCDC for weather 

stations across the study area (National Oceanic and Atmospheric Administration, 2011). Climate stations with data collected during 1990–2008 and with the most complete record 

during the summertime (June–August) period were identified. 

Daily time series were compiled and consisted of data from 

7 weather stations for air pressure, 160 stations for air temperature, 13 stations for dew point, 160 stations for precipitation, 

and 13 stations for solar radiation. Mean daily values were 

calculated for all variables with the exception of precipitation, 

in which case total daily precipitation was calculated.

With as many as 160 air temperature and precipitation 

climate stations, it was necessary to simplify the dataset to 

a more manageable number of climate variables for model 

development (Roehl and others, 2006; Stewart and others, 

2006; Westenbroek and others, 2010b). “Time-series clustering” is a data-mining technique that can optimally segment a 

large collection of time-series signals into a smaller number of 

dynamically similar “groups.” A cross-correlation of Pearson 

coefficients (r) was calculated for each of the climate timeseries variables (e.g., air temperature, precipitation), with 

individual climate stations each representing a separate time 

series; then the k-means clustering technique was applied to 

the cross-correlation matrix to determine the ideal number of 

clusters or groups for each climate variable. The k-means clustering technique provided in the Data Miner Software Kit of 

Weiss and Indurkhya (1997) was implemented, which is based 

on the algorithm of Hartigan and Wong (1979). For k number 

of groups, the k-means algorithm optimizes which members of 

the overall group should be in groups 1 through k. The optimal 

partitioning of groups is determined by using the root mean 

square error (RMSE) as a measure of the difference in distance 

between each member and the mean of the group such that 

movement of any point from one group to another will not 

decrease the RMSE for either group. The k-means clustering 

technique was repeated for a range of group sizes (k values), 

and a mean RMSE for all groups was computed and plotted 

for each k value. The optimal number of groups was selected 

at the inflection point between a sharp vertical decline in mean 

RMSE and a horizontal plateau, or in some cases where a 

more gradual reduction in RMSE occurred with increasing 

number of groups. The mean time series for each climate 

variable group was determined by calculating the mean daily 

value of all climate station members within a group. 

The resulting time series were decorrelated by calculating 

an average time series for each group (average of all climate 

station members), assigning one group to be a reference time 

series (i.e., the group with the largest number of members), 

and calculating differences from the averages on a daily time 

step for the other groups. This greatly reduced the number of 

time-series variables (e.g., air temperature from 160 stations to 

6 time-series groups) while preserving a semblance of spatial 

and temporal variability. All climate variable time-series 

groups with the exception of air temperature were subsequently 
12 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

SWB–ANN

Stream temperature time series

OUTPUT

MODEL

INPUT

Input

layer

Output

layer

Hidden

layer

Soil-water-balance time series

Soil-water-balance accumulated recharge

Air temperature time series

Air temperature clusters

Climate observations

(National Climate Data Center)

Downscaled climate

GCM

(General Circulation Models)

CURRENT TIME PERIOD

CLIMATE TIME SERIES

FUTURE TIME PERIOD

Static landscape characteristics

EXPLANATION

GCMs = General Circulation Models

SWB = Soil-Water-Balance Model

ANN = Artificial Neural Network Model

SWB–ANN = Integrated SWB and ANN Model

Figure 6. Approach and components of an Artificial Neural Network stream temperature Model integrated with a 

Soil-Water-Balance Model and General Circulation Models.
The Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 13

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42°

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92° 90° 88°

0 20 40 60 KILOMETERS

0 20 40 60 MILES

!(

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Study area

Lake and streams

Counties

States

Cold

Cold transition

Warm transition

Warm

Training site

Validation site

 Model partition

Stream temperature sites

 Thermal class, July mean 

EXPLANATION

L A K E S U P E R I O R

L A

K E

M I C H I G A N

MICHIGAN

MINNESOTA

IOWA

ILLINOIS

WISCONSIN

Figure 7. Location of 371 stream temperature monitoring sites used for training and validation of the Integrated 

Soil-Water-Balance and Artificial Neural Network version 1 (SWB-ANNv1) stream temperature model.
14 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

dropped after they did not help to improve model performance 

during ANNv1 model calibration. The six remaining air 

temperature time-series groups served as variables for model 

training for both ANNv1 and the SWB-ANNv1 model (figs. 8 

and 9; appendix 2). 

Landscape Characteristics

The 1:100,000 scale National Hydrography Dataset 

(NHD) served as the framework to which all of the landscape 

characteristics were attributed (U.S. Geological Survey, 2004b). 

Watershed boundaries were delineated using the 30-m NED 

for every confluence to confluence stream reach; static landscape variables were derived using a GIS for the entire upstream contributing area, 60-m riparian buffer, and the stream 

network (U.S. Geological Survey, 2004a). The landscape 

variables included drainage area, land cover, geology, Darcy 

groundwater potential (Baker and others, 2003a and b), annual 

streamflow exceedance, topography, geographic location, and 

network position as described in Brenden and others (2006). 

Pearson’s correlation coefficient (r ≥ 0.75) was used to identify 

and cull highly correlated variables to reduce dimensionality of 

the dataset; for highly correlated pairs, we chose the variable 

more strongly correlated with water temperature, resulting in 

20 static landscape variables for model development. 

Because the stream temperature time series were 

discontinuous among years, clustering and classification were 

used to identify the best landscape variables to explain the 

interannual variability in stream temperature and further reduce the list of variables for use in model training (Risley and 

others, 2003; Roehl and others, 2006). This approach helped 

determine the variables that best discriminated stream temperature sites across multiple summers and also sites with similar 

thermal characteristics (Stewart and others, 2006; Brenden and 

others, 2006). 

Clustering and classification involved three steps: 

(1) stream temperature time series were clustered to group 

measurement sites with similar patterns into time-series 

groups, (2) classification models were developed to determine 

the smallest set of landscape variables that best discriminated 

each group within a single summer, and (3) a scoring procedure was developed to determine those landscape variables 

that best discriminated site groups across multiple summers. 

This process reduced the list of candidate static landscape 

variables to 10 (Westenbroek and others, 2010b; Brenden and 

others, 2006). All 10 variables were used in calibration of 

ANNv1 but 2 variables were dropped for calibration of SWBANNv1 resulting in 8 variables, because they were either spatial scale dependent (e.g., downstream link; Shreve, 1967) or 

they did not seem to improve model performance (e.g., percent 

fines; table 2).

Groundwater-Recharge Projections from the 

Soil-Water-Balance Model

The SWB model tracked and output a variety of variables 

of potential use in stream temperature prediction including 

growing degree-day (GDD), accumulated potential water loss 

(APWL), running sum of unmet potential evapotranspiration, 

soil moisture, and potential recharge. All of these variables 

except potential recharge had “lag-time” associated with them, 

Table 2. Static landscape variables used as model predictors of stream temperature in Wisconsin (Brenden and others, 2006). 

[Spatial unit defines the spatial scale over which the values apply; WT, total upstream watershed; CH, local channel; RT, total upstream 60 meter riparian 

buffer; USGS, U.S. Geological Survey]

Static variable (code, units) Spatial unit Mean Minimum Maximum Standard 

deviation

Source

Drainage area 

(AREAKM, square kilometers)

WT 310.2 0.7 15,923.40 1,460.30 Computed from 

(USGS, 2004a)

Sinuousity 

(SINUOUS, unitless)

CH 1.3 1.0 4.2 0.3 Computed from 

(USGS, 2004b)

Urban - land cover 

(URBWT, percent)

WT 12.6 0.0 100.0 19.9 (USGS, 2003)

Agriculture - land cover 

(AGWT, percent)

WT 42.9 0.0 95.3 30.2 (USGS, 2003)

Open water - land cover 

(WATWT, percent)

WT 1.5 0.0 29.7 3.8 (USGS, 2003)

Wetland - land cover 

(WETWT, percent)

WT 7.6 0.0 53.3 10.4 (USGS, 2003)

Darcy - groundwater delivery 

(DARWT, meters day-1)

WT -87.5 -749.0 5.2 98.6 (Baker and others, 

2003a)

Darcy - groundwater delivery 

(DARRT, meters day-1)

RT 77.6 -43.7 474.2 88.2 (Baker and others, 

2003a)
The Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 15

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Base from U.S. Geological Survey (USGS) digital data, 1:2,000,000.

L

A

K

E

M I C H I G A N

L A K E S U P E R I O R

42°

44°

46°

92° 90° 88°

0 20 40 60 KILOMETERS

0 20 40 60 MILES

(!

(!

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(!

Study area

Lake and streams

County boundary

States

1

2

3

4

5

6

Air temperature station 

time-series group

EXPLANATION

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

WISCONSIN

Figure 8. Location of 160 air temperature climate stations used for time-series clustering and for training of the 

Integrated Soil-Water-Balance and Artificial Neural Network version 1 (SWB-ANNv1) stream temperature model. 

Six air temperature station time-series groups are indicated by color.
16 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

such that the value on a given day was highly correlated to 

the value on the preceding day. The accumulation of potential 

recharge is useful in that it serves as perhaps a better indicator 

of general groundwater availability during the course of a 

summer season. In order to provide a more stable indicator of 

general groundwater availability, a running sum of the daily 

potential recharge was calculated (beginning on January 1st of 

each year) as well as mean annual recharge for each cell in the 

SWB model for the period 1990–2008. The summed potential 

recharge grid was used in SWB-ANNv1 model calibration 

because it addressed both the spatial and temporal components 

of recharge, unlike mean annual recharge where recharge 

values were averaged over the entire year. Time series of 

potential recharge were generated for every grid cell in the 

SWB model domain.

Day (1990–2008 average)

Air temperature, in degrees Celsius

June

10

12

14

16

18

20

22

24

26

July August

1

2

3

4

5

6

EXPLANATION

Air temperature 

time-series group

Figure 9. Average daily air temperature for six air temperature time-series groups averaged over 19 years (1990–2008) 

for the summertime (June–August) period. 

In order to take advantage of the dynamic nature of the 

SWB model and reduce the number of daily time series of 

potential recharge to a more manageable number, the model 

domain was divided into 16 different relatively homogenous 

spatial landscape units based on a combined hill-climbing/

iterative minimum distance method (Rubin, 1967; Forgy, 

1965). The landscape units were derived using a GIS and 

represented a combination of landscape characteristics likely 

to affect groundwater recharge and included quaternary 

geology, HSG, land cover, and NED (Fullerton and others, 

2003; U.S. Department of Agriculture, 2009; U.S. Geological 

Survey, 2003 and 2004a). 

An average time series of mean daily accumulated 

potential recharge was extracted from the SWB model for 

each of the 16 spatial landscape units. Accumulated potential 
The Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 17

recharge starting with January 1st were summed for all days 

leading up to June 1st, to match up with the beginning of the 

SWB-ANNv1 model calibration period; values for subsequent days were added to the total on a daily time step for the 

summertime (June–August) period.

One of the 16 SWB time series was dropped from further 

analysis because it represented the land-cover class of water. 

The remaining 15 SWB time series were tested for crosscorrelation using Pearson’s correlation coefficient to determine 

if some of the SWB time-series signals were similar to one 

another (r ≥ 0.85); highly correlated time series and time series 

with poor spatial representation across the landscape were 

dropped, leaving 3 SWB model accumulated daily potential 

recharge time-series groups for use in the SWB-ANNv1 model 

calibration. These 3 time series of accumulated daily potential 

recharge are referred to as Soil-Water-Balance groups 2, 6, and 

12 in figure 10. 

Climate Projections from General Circulation 

Models

Downscaled climate data were acquired from UWCCR 

for the A1B scenario and 10 GCMs for 3 time periods 

(late 20th century-baseline (1961–2000), mid-21st century 

(2046–65), and late-21st century (2081–2100)) as daily grids 

with a 0.1 × 0.1 degree resolution (or about 8 × 8 km). Air 

temperature and precipitation were extracted from the daily 

grids and used as input to the SWB-ANNv1 model to simulate future summertime mean daily stream temperatures for 

all 30 GCM-time period combinations (10 GCMs × 3 time 

periods) for all stream segments in the study area. 

In order to make use of the downscaled GCM data in the 

SWB-ANNv1 model, the downscaled results were distributed 

to each grid cell within the study area using a smoothing 

procedure. The R package “fields” (Fields Development Team, 

0

1

2

3

4

5

6

7

8

9

10

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

EXPLANATION

Year (summer (June–August) period)

Recharge, in inches

Soil-Water-Balance group 2 

Soil-Water-Balance group 6 

Soil-Water-Balance group 12 

Variation of estimated accumulated 

potential groundwater recharge 

for a given year. 

Figure 10. Soil-Water-Balance time series of accumulated potential groundwater recharge used for input to the Integrated 

Soil-Water-Balance and Artificial Neural Network version 1 (SWB-ANNv1) stream temperature model. 
18 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

2006) was used to apply a kernel smoothing algorithm to the 

GCM output to produce a set of grids with the same projection 

and resolution as the SWB model domain (1,600 m × 1,600 m 

grid cell size). 

Projections of air temperature were generated for each 

of the 6 air temperature time-series groups for the 30 GCMtime period combinations. Air temperature time series were 

extracted from each of the GCMs for grid cells that matched 

the location of the 160 climate stations used in SWB-ANNv1 

model calibration. Daily averages were then generated for 

each of the six air temperature time-series groups, followed 

by decorrelation of group averages on a daily time step. This 

resulted in 30 time series (3 time periods × 10 GCMs) for each 

of the 6 air temperature groups. The results were assembled 

into 30 data files of projected daily air temperature; each data 

file included values for all 6 groups for a specific time period 

and GCM.

Future projections of accumulated daily potential 

recharge were derived for each SWB time series by running 

the SWB model with air temperature and precipitation estimates from the 10 GCMs (table 3) and 3 time periods (1961–

2000, 2046–65, and 2081–2100). Accumulated daily potential 

recharge time series were then extracted for the 3 SWB groups 

required for SWB-ANNv1 model input, resulting in 30 time 

series (3 time periods × 10 GCMs). The results were assembled into 30 SWB data files of daily accumulated potential 

recharge; each data file included values for all 3 SWB time 

series for a specific time period and GCM. 

Model Development and Application for the 

Integrated Soil-Water-Balance and Artificial 

Neural Network version 1 Stream Temperature 

Model

Modeling highly dynamic hydrologic systems on a 

statewide scale is challenging because the systems vary 

discontinuously both spatially and temporally. Stream 

temperature models come in many different varieties, but 

may be lumped into two groups: deterministic and statistical 

(Benyahya and others, 2007). Deterministic stream temperature models generally calculate a segment-by-segment energy 

balance and require detailed data on physical characteristics 

of the stream (Allen, 2008; Cox and Bolte, 2007), data that 

are largely unavailable statewide. Statistical models, such as 

ANNs, are attractive in that they generally require much less 

site-specific data to implement; however, building representative empirical models requires sufficient data to capture 

diverse causes and effects. We chose to use ANN models because they are able to handle non-linear relations, interactions 

among predictors, and discontinuous time-series climate data, 

and are relatively quick to develop while still having high 

predictive power (Conrads and others, 2013; McKenna and 

others, 2010; Risley and others, 2003; Roehl and others, 2006; 

Stewart and others, 2006; Westenbroek and others, 2010b). 

Artificial Neural Networks

ANN models are empirical; they are developed directly 

from data. These models are a multivariate, nonlinear curve 

fitting technique with a flexible mathematical structure capable 

of describing complex nonlinear relations between input 

and output datasets. The structure of ANN models is loosely 

based on the biological nervous system and contains interconnected units that are analogous to neurons (Hinton, 1992). 

The neurons perform a simple “transfer function” whereby the 

input layer neurons are connected to all hidden layer neurons 

and all hidden layer neurons are connected to all output layer 

neurons. Each connection has a weight associated with it; the 

output of a neuron is the simple combination of the values it 

receives through its input connections, the associated weights, 

and the neuron’s transfer function (fig. 11). An ANN model is 

“trained” by iteratively adjusting its weights to minimize the 

error by which it maps inputs to outputs for a dataset composed of input/output vector pairs. Prediction accuracy can be 

measured by metrics such as the coefficient of determination 

(R2

) and RMSE, both during and after training. 

In developing ANN models, it is customary to split 

datasets into “training” and “validation” datasets. Training datasets are used for model development, and validation 

datasets are used for model testing to provide an independent 

evaluation of model performance. For a large dataset with 

broad representation over the range of historical behaviors, 

a small percentage of the dataset (10–25 percent) may be 

selected for the training dataset; for a limited dataset, a larger 

percentage (75–100 percent) may be used in the training 

dataset. To prevent overfitting, the ANN models can be conservatively trained using a method referred to as “stop training.” 

Stop training allows the modeler to stop the training process 

before the ANN model has fit the data to the maximum extent 

possible. Adjustments to architectural and training parameters 

also allow the modeler to control the geometric complexity 

of the surface that the ANN model fits to the data. The datamining software used for this application writes R2

 and RMSE 

to the graphical user interface (GUI) during training, and an 

inflection in the rate of change in these parameters indicates 

a transition from a generally linear, multivariate surface fit to 

a progressively nonlinear fit. This inflection point was used 

to trigger stop training. In general, a high-quality predictive 

model can be obtained when the data ranges are well distributed throughout the state space of variables describing the 

physical system of interest, the input variables selected by the 

modeler share mutual information about the output variables, 

and the functional form “prescribed” or “synthesized” by the 

model to “map” (correlate) input variables to output variables 

is a good one.

Training and Validation

A single SWB-ANNv1 model was developed to simulate 

daily summertime stream temperature (June 1 to August 31) 
The Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 19

for 1990–2008. The model was developed using the iQuest®

(ADMi, 2011) data-mining software (Version 2.03C DM 

Rev31). Model input comprised static landscape variables 

and dynamic climate and SWB time series. The data matrix 

for SWB-ANNv1 model simulation was organized with each 

row representing a site on a particular day and the columns 

representing input and output variables. The data were stacked 

or concatenated by site, and time-series signals (air temperature, SWB, and stream temperature) were matched by calendar 

day. The SWB-ANNv1 model built upon the approach and 

results of the ANNv1 by using the same methodology and 

data sources; however, it expanded the spatial and temporal 

extent of stream temperature sites and observations and added 

the SWB component as an enhancement and a link to future 

climate projections. 

The SWB-ANNv1 model was trained with 90 percent of 

the available data (n = 304 sites; 60,618 measurement days); 

the remaining 10 percent were reserved for model validation 

(n= 67 sites; 6,738 measurement days) (fig. 7). Independent 

training data included sites with the highest information 

content that represent the breadth of behavior in the data; data 

with redundant or similar information were reserved for the 

independent validation dataset. Both training and validation 

sets included sites covering the range of thermal conditions, 

from cold-water to warm-water sites (Lyons and others, 2009). 

Sites with multiple years of measurements were assigned to 

the training set, whereas sites with a single summer of data 

were set aside for model validation. A number of candidate 

models were trained and evaluated for their statistical accuracy 

using measures of R2

 and RMSE. 

The model development process involved training the 

SWB-ANNv1 model iteratively by starting with a candidate 

pool of static and dynamic input variables followed by adjusting learning rates, the number of hidden layer neurons, and 

model weights to maximize the R2 and minimize the mean 

square error (MSE) across training and validation sets. In 

Table 3. List of 10 General Circulation Models used in this study, run with the A1B emissions scenario, including their originating 

group, country, model identification, and model code (Notaro and others, 2011).

Originating group(s) Country Model identification Model code

Canadian Centre for Climate Modelling and Analysis Canada CGCM3.1 (T63) CGCM

Météo-France / Centre National de Recherches 

Météorologiques 

France CNRM-CM3 CNRM

Commonwealth Scientific and Industrial Research 

Organisation (CSIRO) Atmospheric Research 

Australia CSIRO-Mk3.5 CSIRO

Meteorological Institute of the University of Bonn, 

Meteorological Research Institute of the Korea 

Meteorological Administration (KMA), and 

Model and Data Group 

Germany / Korea ECHO-G ECHO

National Key Laboratory of Numerical Modeling for 

Atmospheric Sciences and Geophysical Fluid Dynamics /

 Institute of Atmospheric Physics (LASG / IAP) 

China FGOALS-g1.0 FGOALS

U.S. Department of Commerce / National Oceanic and 

Atmospheric Administration / Geophysical Fluid Dynamics 

Laboratory 

USA GFDL-CM2.0 GFDL

National Aeronautics and Space Administration / 

Goddard Institute for Space Studies 

USA GISS-AOM GISS

Instituto Nazionale di Geofisica e Vulcanologia Italy INGV-ECHAM4 INGV

Institut Pierre Simon Laplace France IPSL-CM4 IPSL

Center for Climate System Research (The University of 

Tokyo), National Institute for Environmental Studies, and 

Frontier Research Center for Global Change (JAMSTEC)

Japan MIROC3.2 (HiRes) MIROC
20 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

addition to the use of “stop training” to prevent overfitting, we 

also slowed the training rates by a factor of 10 (e.g., .075 to 

.0075) when the training and (or) testing R2

 values began to 

stabilize. We limited the number of hidden layer neurons to a 

maximum value of 3. Each time training rates were adjusted, 

model performance (R2

) and input-output sensitivities were 

used to evaluate the stability of the model input variables and 

to remove those static variables with the least amount of influence on the output variable. The model was trained using standard back-error propagation (Rumelhart and others, 1986) by 

which the neural network software calculated an output value, 

compared it to the actual measured target value, determined 

the error, and readjusted model weights to reduce the error. 

This iterative process continued until the error was minimized, 

at which time no learning was taking place. This approach to 

model development is a common and widely used method for 

determining error weights and training a neural network. 

The ability of the model to predict daily mean stream 

temperature was evaluated using four ”goodness-of-fit” statistics for the 67 model validation sites and plots of measured 

and predicted stream temperatures. The importance of individual variables was evaluated using model sensitivity reports. 

;

;

;

;

;

;

x1

x2

x3

y1

x4

Input

layer

Hidden

layer

Output

layer

wi

“Weights”

control

connections

wi+n

(Output time-series 

examples)

(Input time-series and 

static landscape characteristics)

Neurons with linear 

transfer functions

Neurons with nonlinear 

transfer functions

x5

t

t Figure 11. Artificial Neural Network architecture with five input 

layers, three hidden layers, and a single output layer.

The computed statistics included R2, MSE, RMSE, and 

percent model error (PME). The R2

 indicated how much of 

the overall variability in the data was explained by the model 

and how well it captured the overall trend in the data; the MSE 

and RMSE provided a measure of prediction accuracy (i.e., 

whether the model underpredicted or overpredicted and the 

magnitude of that discrepancy); and the PME statistic divided 

the RMSE by the range of the measured data to determine the 

percent of error over the full range of modeled data. We also 

evaluated PME for each of four stream thermal classes (cold, 

cold transition, warm transition, and warm) defined by Lyons 

and others (2009). Each site was first assigned to a thermal 

class based on calculated average July mean, all site days were 

then grouped by thermal class and model partition (training 

and validation). PME was then calculated for all daily predictions within each thermal class and model partition group.

Model Predictions and Projections for Current 

and Future Climate Conditions

The calibrated SWB-ANNv1 model was applied to all 

stream segments (n = 38,243) in the study area using the 
The Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 21

dynamic (air temperature and SWB) and static (landscape 

characteristics) input variables to predict mean daily water 

temperature for each summertime date (June 1–August 31) for 

1990–2008 for a total of 1,748 daily water temperature predictions for each stream segment (92 days per year for 19 years). 

The process was expedited by means of a custom R script 

(R Development Core Team, 2011). The daily predictions 

were summarized to generate a number of water temperature 

variables shown to be important for explaining fish distribution patterns in streams of the Laurentian Great Lakes region 

(Lyons and others, 2009, 2010). Water temperature variables 

included July mean, summertime (June–August) mean, 

summertime maximum daily mean, maximum of the 19 yearly 

July means, maximum of the 19 yearly summertime maximum 

daily means, and number of days when stream temperature 

exceeded a maximum threshold. These summary variables 

were generated for use in fish species occurrence models and 

for use in estimating the effects of projected future climate 

scenarios on stream temperature (Lyons and others, 2010). The 

summary variable July mean water temperature was used in 

subsequent analyses in this report to classify stream segments 

into thermal classes and for comparison to assess the effects of 

projected future climate on stream temperature. We used the 

cold, cold transition, warm transition, and warm-water thermal 

classes identified by Lyons and others (2009), then further 

subdivided the warm-water thermal class into warm and very 

warm in order to capture projected impacts of climate change 

on warm-water streams (table 1). 

We used the model calibration period 1990–2008 to 

represent what we considered “current” conditions along with 

climate observations extracted from the DSI-3200 daily surface database maintained by the NCDC (National Oceanic and 

Atmospheric Administration, 2011). 

Future stream temperature estimates were made for 

three time periods (late 20th century (1961–2000), mid-21st 

century (2046–65), and late 21st-century (2081–2100)) using 

climate projections from 10 GCMs. This required running 

the SWB-ANNv1 model 30 times, each time replacing the air 

temperature and SWB time series with the appropriate data to 

represent the time period and GCM. The daily estimates were 

summarized to generate the average July mean stream temperature for each stream segment for the 30 GCM-time period 

combinations.

Stream temperature projections derived from the 

10 GCMs for future time periods (2046–65 and 2081–2100) 

were referenced to late 20th century baseline (1961–2000) 

GCM-based projections, representing the “current” time period (WICCI, 2011). In contrast, the statewide stream temperature estimates representing “current” (1990–2008) conditions 

were based on actual daily air temperature observations. In 

order to evaluate change in stream temperature from current 

to future time periods, it was necessary to adjust the future 

stream temperature projections for 2046–65 and 2081–2100 

so they could be referenced to observed current conditions 

(1990–2008) rather than modeled GCM-based “current” conditions for the 20th century baseline (1961–2000). Model projections of stream temperature under future conditions based 

on projections from GCMs may be biased. Climate models 

capture general global trends reasonably well, but significant 

local biases in air temperature and precipitation may be present in any given model (Haerter and others, 2011). A bias correction factor was applied to bring GCM-based projections of 

stream temperatures in line with stream temperatures projected 

from observed climate data for 1990–2008.

The bias correction factor represented the difference in 

degrees Celsius between GCM-based “current” and the “observation” based “current” July mean stream temperature. The 

GCM-modeled time period 1961–2000 baseline for current 

climate conditions and the 1990–2008 time period of stream 

temperature observations overlapped for the years 1990–2000. 

Therefore, 1990–2000 served as the baseline for calculation of 

the bias correction factor.

Bias correction factors were calculated separately for 

each combination of stream segment and GCM. Bias correction factors were calculated and applied as follows:

1. July mean stream temperature was calculated for stream 

temperature model outputs run with either the GCM-generated dynamic air temperature data for 1990–2000 or the 

observed air and stream temperature data for 1990–2000. 

2. Bias correction factors were calculated as the GCMderived July mean stream temperature minus the July 

mean stream temperature derived from observed air 

temperature data.

3. Bias correction factors were subtracted from projected 

stream temperatures derived from models using GCM 

projections of air temperatures for 2046–65 and 

2081–2100. 

As an example, if projections of July mean stream 

temperatures based on models using GCM-generated air temperature input data were 2 °C higher than July mean stream 

temperatures based on observed air and stream temperature 

data, then the bias correction factor would be +2 °C. Therefore, projected stream temperatures based on GCMs for future 

time periods (mid- and late-21st century) would be corrected 

by subtracting 2 °C.

After correcting the GCM-derived July mean stream 

temperature for each stream segment using the bias correction factor, the resulting stream temperatures were classified 

into 1 of 5 thermal classes (table 1) for each of the 10 runs of 

the SWB-ANNv1 model for both time periods. Results were 

summarized statewide by GCM and time period using the two 

metrics, July mean stream temperature and July mean thermal 

class. A “GCM average” July mean stream temperature was 

calculated for each stream segment by averaging the values 

of the bias-corrected GCM-derived July mean stream temperatures that resulted from the 10 SWB-ANNv1 model runs 

using the GCM-climate source data. The July mean thermal 

class was then determined for each July mean “GCM average” 

value. Both the “GCM average” and individual results from 

running the SWB-ANNv1 model using each of the 10 GCM 
22 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

datasets as climate input were used for comparison of current 

and future stream temperature projections. In subsequent 

sections of this report, individual results from the 10 SWBANNv1 model runs with GCM climate source data will be 

referred to by the GCM model code (table 3), and the average 

of those results will be referred to as the GCM average.

Results and Discussion

Model Performance

The best model predictors of daily stream temperature 

were the six decorrelated air temperature time series, three 

SWB time series of accumulated potential groundwater recharge and eight static landscape variables. The sensitivity of 

the variables in the final model indicated that the daily stream 

temperature was most sensitive to two of the static variables, 

Darcy (network watershed; a measure of groundwater delivery) and drainage area, followed by one of the dynamic air 

temperature time-series groups and the static variable open 

water (table 4). 

The R2

 for the training and validation data were 0.71 and 

0.76 for the SWB-ANNv1 model compared to 0.60 and 0.67 

for ANNv1, a nine percentage point improvement (Stewart 

and others, 2006; Westenbroek and others, 2010a). Evaluations of daily predictions for the SWB-ANNv1 model resulted 

in an RMSE of 1.9 and 1.5 for training and validation data, 

respectively, and a PME of 8.8 percent for both training and 

validation data, respectively (table 5), which also are improvements over ANNv1. Nearly one-half (49.2 percent) of summertime (June–August) mean stream temperature predictions 

using model validation sites were within 1 °C of observed 

values, 80.5 percent were within 2 °C, and 95.1 percent were 

within 3 °C (table 6). Nearly one-half (47.4 percent) of July 

mean predictions also were within 1 °C of observed values, 

77.2 percent were within 2 °C, and 93.3 percent were within 3 

°C (table 6) for model-validation sites. 

The range of measured values for model-validation 

sites was smallest for cold-water (about 11 °C) and largest 

for the warm-water sites (about 17 °C). This pattern also was 

observed for the training sites. Percent model error (which 

is a function of the range of measured values) by thermal 

class ranged from about 10 percent for warm water to about 

14 percent for cold water, for both validation and training sites 

(table 7). The PME also was summarized for two validation 

sites representing the 25th and 75th percentiles for each of 

the four thermal classes (cold, cold transition, warm transition, and warm) (table 8). The PME interquartile range was 

about 14 to 28 percent for the cold-water sites, about 10 to 

17 percent for cold-transition sites, about 12 to 18 percent for 

warm-transition sites, and about 12 to 17 percent for warmwater sites. 

Table 4. Variables used to calibrate the Integrated Soil-Water-Balance and Artificial Neural Network version 1

(SWB-ANNv1) Model and the average absolute sensitivity.

[Spatial unit defines the spatial scale over which the values apply; WT, total upstream watershed; na, not applicable; RT, total upstream 

60 meter riparian buffer; CH, local channel] 

Variable (code, units) Spatial 

unit Variable type Average absolute sensitivity

Groundwater delivery - Darcy (DARWT, meters day-1) WT static 0.210

Drainage area (AREAKM, square kilometers) WT static 0.161

Air temperature cluster 6 (AT6, degrees Celsius) na dynamic 0.157

Open water (WATWT, percent) WT static 0.143

Wetland (WETWT, percent) WT static 0.071

Agricultural land cover (AGWT, percent) WT static 0.046

Urban land cover (URBWT, percent) WT static 0.038

Groundwater delivery - Darcy (DARRT, meters day-1) RT static 0.034

Air temperature cluster 3 (AT3, degrees Celsius) na dynamic 0.032

Sinuousity (SINUOUS, unitless) CH static 0.021

Air temperature cluster 1 (AT1, degrees Celsius) na dynamic 0.021

Air temperature cluster 4 (AT4, degrees Celsius) na dynamic 0.019

Groundwater recharge - Soil-water-balance cluster 6 (SWB6, inches) na dynamic 0.011

Groundwater recharge - Soil-water-balance cluster 1 (SWB1, inches ) na dynamic 0.010

Air temperature cluster 2 (AT2, degrees Celsius) na dynamic 0.010

Air temperature cluster 5 (AT5, degrees Celsius) na dynamic 0.009

Groundwater recharge - Soil-water-balance 8 (SWB8, inches ) na dynamic 0.007
Results and Discussion 23

Table 5. Summary of performance statistics for the models used to estimate stream temperature for 254 sites (1990–2002) and 

371 sites (1990–2008) in Wisconsin.

[R2, coefficient of determination; RMSE, root mean square error; deg C, degree Celsius; PME, percent model error = root mean square error of the model 

predictions divided by the range of measured data; ANNv1, Artificial Neural Network version 1 stream temperature Model (Stewart and others, 2006); 

SWB-ANNv1, Integrated Soil-Water-Balance and Artificial Neural Network version 1 Model]

Model name Time period Model 

partition

Measured data, in degrees Celsius Number 

of sites

Number of 

observations R2 RMSE 

(deg C)

PME 

(percent) Minimum Maximum Range*

ANNv1 1990–2002 Training 7.4 30.5 23.1 223 25,472 0.60 2.3 9.8

validation 9.8 28.3 18.5 31 2,799 0.67 2.0 11.0

SWB-ANNv1 1990–2008 Training 7.4 30.8 23.4 304 60,618 0.71 1.9 8.8

validation 10.1 28.5 18.4 67 6,738 0.76 1.5 8.8

*

Difference in maximum and minimum measured values.

Table 6. Summary of residuals (absolute value) for the Integrated Soil-Water-Balance and Artificial Neural Network 

version 1 (SWB-ANNv1) Model used to estimate stream temperature for 371 sites in Wisconsin (1990–2008). 

[percent, percent of measured observations; <, less than; >, greater than]

Summer (June–August) mean July mean

Training Validation Training Validation

Degrees Celsius

Number 

of observationsPercent

Number 

of observationsPercent

Number 

of observationsPercent

Number 

of observationsPercent

< 1 degree 24,009 39.6 3,313 49.2 7,789 37.8 1,107 47.4

> 1 - 2 degrees 18,039 29.8 2,106 31.3 6,131 29.8 696 29.8

> 2 - 3 degrees 10,955 18.1 982 14.6 3,801 18.5 376 16.1

> 3 - 4 degrees 5,191 8.6 283 4.2 1,918 9.3 135 5.8

> 4 - 5 degrees 1,889 3.1 51 0.8 753 3.7 19 0.8

> 5 - 6 degrees 431 0.7 2 0.03 159 0.8 0 0

> 6 - 7 degrees 72 0.1 1 0.01 36 0.2 0 0

> 7 - 8 degrees 19 0.03 0 0 11 0.1 0 0

> 8 - 9 degrees 11 0.02 0 0 2 0.01 0 0

> 9 - 10 degrees 2 0.003 0 0 0 0 0 0

Total 60,618 6,738 20,600 2,333
24 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Table 7. Percent model error by thermal class for the Integrated Soil-Water-Balance and Artificial Neural Network 

version 1 (SWB-ANNv1) Model used to estimate stream temperature for 371 sites in Wisconsin (1990–2008). 

[PME, percent model error = root mean square error of the model predictions divided by the range of measured data]

Thermal class

Training Validation

Number of 

observations

Percent of 

observations

Range of 

measured 

values*

PME

(percent)

Number of 

observations

Percent of 

observations

Range of 

measured 

values

PME

(percent)

Cold water 13,640 22.5 15.8 13.7 1,976 29.3 10.5 14.5

Cold transition 11,447 18.9 18.4 10.5 1,275 18.9 12.2 10.6

Warm transition 9,039 14.9 16.5 10.4 1,733 25.7 13.5 11.5

Warm water 26,492 43.7 20.2 9.5 1,754 26.0 16.7 10.0

*Difference in maximum and minimum measured values.

Table 8. Statistical measure of prediction accuracy for eight validation sites representing the 25th and 75th percentile for cold, 

cold-transition, warm-transition, and warm-water sites for the Integrated Soil-Water-Balance and Artificial Neural Network 

version 1 (SWB-ANNv1) Model (1990–2008). 

[R2, coefficient of determination; MSE, mean square error; deg C, degrees Celsius; RMSE, root mean square error; PME, percent model error = root mean 

square error of the model predictions divided by the range of measured data]

Site 

number Thermal class Year measured

Inner 

quartile 

range 

(percentile)

Number of 

observations R2 MSE (deg C)

RMSE 

(deg C)

Range of 

measured 

data 

(deg C)*

PME

(percent)

420 Cold water 2008 25th 92 0.66 0.5 0.7 5.0 13.8

426 Cold water 2007 75th 92 0.8 6.0 2.4 8.7 28.2

228 Cold transition 1998 25th 92 0.85 0.7 0.8 8.7 9.5

353 Cold transition 2000 75th 84 0.77 0.8 0.9 5.1 17.3

287 Warm transition 2004 25th 92 0.77 1.3 1.1 9.5 11.9

242 Warm transition 2000 75th 92 0.72 2.7 1.6 8.9 18.4

20 Warm water 1999 25th 78 0.76 1.3 1.1 9.3 12.2

46 Warm water 1999 75th 91 0.74 2.4 1.5 9.3 16.6

*Difference in maximum and minimum measured values.

Predicted stream temperature appeared to track the daily 

time-series pattern for all eight validation sites representing 

the 25th and 75th percentiles by thermal class (fig. 12). The 

measured and predicted daily temperatures for the 25th percentile sites appeared to match closely with no bias. For the 

75th percentile sites that are classified as cold-water, coldtransition, or warm-transition, however, predicted values were 

biased high; temperature values for the cold-water, coldtransition, and warm-transition classes were overpredicted 

when compared to measured values (fig. 12). Conversely, 

the 75th percentile values for sites classified as warm water 

appear to be biased low. The PME statistic provides a measure of the percent error across the range of measured data, 

where the R2 provides a measure of prediction accuracy and 

how well it captured the overall trend in the data. This can 

be observed in figure 12 where sites with similar R2

 values 

(i.e., warm-transition sites; site 287, 25th percentile, R2 = 0.77, 

PME = 11.9; site 242, 75th percentile, R2 = 0.72, PME = 18.4) 

have very different PME values. For these warm-transition 

sites, the measured versus predicted graphs follow a similar 

overall trend for both sites as indicated by the R2; however, for 

site 242 (75th percentile) the higher PME (18.4 percent) can 

be observed by viewing the magnitude of differences between 

the graph lines across the full range of measured values when 

compared to the graph for site 287 (25th percentile). A similar 

pattern was observed for the cold-water, cold-transition 

and warm-water sites (table 8; fig. 12) when comparing R2

and PME. The PME was greatest for cold-water sites when 

compared to other thermal classes (table 7) indicating a higher 

percent error across the range of measured data.
Results and Discussion 25

Cold (25th percentile): Validation site: 420 

R2 = 0.66, MSE = 0.5, RMSE = 0.7, PME = 13.8 

Cold transition (25th percentile): Validation site: 228 

R2 = 0.85, MSE = 0.7, RMSE = 0.8, PME = 9.5 

Warm transition (25th percentile): Validation site: 287 

R2 = 0.77, MSE = 1.3, RMSE = 1.1, PME = 11.9 

Cold transition (75th percentile): Validation site: 353 

R2 = 0.77, MSE = 0.8, RMSE = 0.9, PME = 17.3 

Warm transition (75th percentile): Validation site: 242 

R2 = 0.72, MSE = 2.7, RMSE = 1.6, PME = 18.4 

Warm (25th percentile): Validation site: 20 

R2 = 0.76, MSE = 1.3, RMSE = 1.1, PME = 12.2 

Warm (75th percentile): Validation site: 46 

R2 = 0.74, MSE = 2.4, RMSE = 1.5, PME = 16.6 

Cold (75th percentile): Validation site: 426 

R2 = 0.8, MSE = 6.0, RMSE = 2.4, PME = 28.2 

5

10

15

20

25

30

6/1 6/20 7/10 7/30 8/19 8/31

0 0

5

10

15

20

25

30

6/1 6/20 7/10 7/30 8/19 8/31

5

10

15

20

25

30

6/1 6/20 7/10 7/30 8/19 8/31

5

10

15

20

25

30

6/1 6/20 7/10 7/30 8/19 8/31

5

10

15

20

25

30

6/1 6/20 7/10 7/30 8/19 8/31

5

10

15

20

25

30

6/1 6/20 7/10 7/30 8/19 8/31

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5

10

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25

30

6/1 6/20 7/10 7/30 8/19 8/31

Stream temperature, in degrees Celsius

Date

EXPLANATION

1998

Measured 

Predicted

EXPLANATION

2000

Measured 

Predicted

EXPLANATION

2008

Measured 

Predicted

EXPLANATION

2007

Measured 

Predicted

EXPLANATION

1999

Measured 

Predicted

EXPLANATION

1999

Measured 

Predicted

EXPLANATION

2004

Measured 

Predicted

EXPLANATION

2000

Measured 

Predicted

Figure 12. Simulations of stream temperature for eight validation sites, representing 25th and 75th percentiles, 

based on percent model error for four thermal classes (cold, cold transition, warm transition, and warm) from the 

integrated Soil-Water-Balance and Artificial Neural Network version 1 (SWB-ANNv1) stream temperature Model.
26 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Model Predictions for Current Conditions

Modeled water temperatures for the current time period 

(1990–2008), as measured by July mean water temperature, 

ranged across stream segments from about 9.0 to 32.0 °C with 

a mean of 18.7 °C and median of 18.8 °C. More than one-half 

of the stream kilometers in the study area (56.7 percent) were 

thermally suitable for supporting cold-water fishes such as 

trout, having thermal classifications of cold (27.1 percent) or 

cold transition (29.6 percent) (table 9; figs. 13, 14, and 15). 

The spatial distribution of streams by thermal class indicated 

a predominance of cold and cold-transition streams in the 

Driftless Area of western and southern Wisconsin and in the 

north along Lake Superior (figs. 1, 14, and 15). The remaining 

stream kilometers were thermally suitable for supporting 

warm-water fishes such as minnow and sunfishes, having 

thermal classifications of warm transition (29.6 percent), warm 

(12.5 percent), and very warm (1.1 percent) (table 9; figs. 13, 

14, and 15). The spatial distribution of streams by thermal 

class indicated a predominance of warm and warm-transition 

streams in the eastern half of Wisconsin, with warm-transition 

streams also prominent across northern Wisconsin adjacent to 

the Upper Peninsula of Michigan (figs. 1, 14, and 15). 

For the Wisconsin portion of the study area (excluding 

the St. Croix River Basin in Minnesota and the Menominee 

River Basin in Michigan), the SWB-ANNv1 stream temperature model classified streams, based on stream length, as 

29.2 percent cold, 30.3 percent cold transition, 27.1 percent 

warm transition, and 13.4 percent warm. The ANNv1 stream 

temperature model, in contrast, classified Wisconsin streams 

as 7.9 percent cold, 45.9 percent cold transition, 28.6 percent 

warm transition, and 17.6 percent warm (Lyons and others, 

2009). Overall, the SWB-ANNv1 model predicted an additional 5.7 percent of stream kilometers as suitable for 

cold-water fishes, as compared to the ANNv1 model, with 

about equal proportions of cold and cold transition stream 

kilometers.

Model Projections for Future Climate Conditions

Future projections of stream temperature were made 

using climate projections downscaled for Wisconsin from 

10 GCMs for the mid-21st century (2046–65) and late-21st 

century (2081–2100). The projections from the individual 

GCMs vary widely; therefore, we provide both the GCM average results as well as the results from individual GCMs as a 

means to show the range of projected values (IPCC, 2007).

Average GCM-based water temperature projections: 

2046–65 time period—Projected water temperatures (July 

mean) for the mid-21st century ranged from about 9.2 to 

33.0 °C for all stream segments, similar to the current time period, however the mean (19.9 °C) and median (20.0 °C), were 

both about 1.0 °C higher when compared to current. Almost 

two-fifths of the stream kilometers in the study area (38.7 percent) were projected to be thermally suitable for supporting 

cold-water fishes at mid-century, having thermal classifications 

of cold (15.5 percent) or cold transition (23.2 percent) (table 9; 

fig. 13). The remaining 61.3 percent of stream kilometers were 

thermally suitable for supporting warm-water fishes, having 

thermal classifications of warm transition (21.3 percent), warm 

(36.8 percent), and very warm (3.2 percent). These projected 

mid-21st century changes represent a loss of thermal habitat 

for cold-water fishes, with a loss of 18 percent of stream kilometers and a concomitant gain of thermal habitat for warmwater fishes.

Average GCM-based water temperature projections: 

2081–2100 time period—During the late-21st century 

projected water temperatures (July mean) ranged from about 

9.3 to 31.7 °C, again similar to the current time period, 

however the mean (20.4 °C) and median (20.5 °C) were both 

1.7 °C higher when compared to current. About one-third of 

the stream kilometers in the study area (33.2 percent) were 

projected to be thermally suitable for supporting cold-water 

fishes at late-century, having thermal classifications of cold 

(11.0 percent) or cold transition (22.2 percent) (table 9; 

fig. 13). The remaining 66.8 percent of stream kilometers were 

thermally suitable for supporting warm-water fishes, having 

thermal classifications of warm transition (18.8 percent), warm 

(42.4 percent), and very warm (5.8 percent). These projected 

late-21st century changes represent a loss of thermal habitat 

for cold-water fishes, with a loss of 23.5 percent of stream 

kilometers and a concomitant gain of thermal habitat for 

warm-water fishes. 

Individual GCM-based water temperature 

projections: 2046–65 and 2081–2100 time period—Among 

SWB-ANNv1 models using climate data from the 10 individual GCMs, the percentage of stream kilometers projected 

to be suitable for cold-water fishes at mid-century ranged from 

a high of 46.7 percent (model CGCM climate data) to a low 

of 25.7 percent (model GFDL climate data) (table 9; fig. 13). 

By late-century, the percentage of stream kilometers projected 

to be suitable for cold-water fishes ranged from a high of 

48.2 percent (model CSIRO climate data) to a low of 23.5 percent (model MIROC climate data) for stream kilometers suitable for cold-water fishes. In the worst-case scenario for coldwater fishes, a comparison of projections using GCM climate 

data to predictions under current climate conditions indicates a 

loss of 30.9 percent of total stream kilometers at mid-century 

(model GFDL climate data) and a loss of 33.2 percent at latecentury (model MIROC climate data) as no longer suitable for 

supporting cold-water fishes. These projected losses based on 

data from individual GCMs represent more than a 10 percent 

reduction in cold-water habitat over the GCM-based average.

Despite the shift from stream kilometers suitable for 

cold-water fishes (lower percentage) to stream kilometers 

suitable for warm-water fishes (higher percentage), the gain in 

stream kilometers occurred only among warm and very warm 

streams (table 9; fig.13); warm-transition streams also suffered losses. There were about 2.9 times as many warm stream 

kilometers projected by mid-century and about 3.4 times as 

many projected by late-century for the GCM average. For very 
Results and Discussion 27

Table 9. Predictions of stream temperature thermal class (Lyons and others, 2009) and projected change summarized by length and as a percentage of total length 

(94,341 kilometers) for current (1990–2008) and future (2046–2065 and 2081–2100) climate conditions for 10 General Circulation Models.

[GCM, General Circulation Model; km, kilometer]

GCM code Thermal class (subclass)

Current time period 

(1990–2008)

Future 

(2046–2065)

Future 

(2081–2100)

Length 

(km)

Length 

(percent 

of total)

Length 

(km)

Length 

(percent 

of total)

Length (percent 

change 

from current)

Length 

(km)

Length 

(percent 

of total)

Length (percent 

change 

from current)

None Cold 25,597 27.1

Cold transition 27,958 29.6Warm transition 27,924 29.6Warm 11,830 12.5Very warm 1,033 1.1

Average of 10 GCMs Cold 14,628 15.5 −42.9 10,417 11.0 −59.3

Cold transition 21,930 23.2 −21.6 20,937 22.2 −25.1

Warm transition 20,076 21.3 −28.1 17,701 18.8 −36.6

Warm 34,719 36.8 193.5 39,822 42.2 236.6

Very warm 2,988 3.2 189.3 5,464 5.8 428.9

CGCM Cold 19,389 20.6 −24.3 15,238 16.2 −40.5

Cold transition 24,611 26.1 −12.0 21,909 23.2 −21.6

Warm transition 27,741 29.4 −0.7 20,261 21.5 −27.4

Warm 20,717 21.9 75.1 33,992 36.0 187.3

Very warm 1,883 2.0 82.3 2,940 3.1 184.6

CNRM Cold 14,748 15.6 −42.4 9,157 9.7 −64.2

Cold transition 22,249 23.6 −20.4 20,827 22.1 −25.5

Warm transition 21,990 23.3 −21.3 17,107 18.1 −38.7

Warm 32,625 34.6 175.8 40,263 42.7 240.3

Very warm 2,728 2.9 164.1 6,988 7.4 576.5
28 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin Table 9. Predictions of stream temperature thermal class (Lyons and others, 2009) and projected change summarized by length and as a percentage of total length (94,341 kilometers) for current (1990–2008) and future (2046–2065 and 2081–2100) climate conditions for 10 General Circulation Models.—Continued [GCM, General Circulation Model; km, kilometer] GCM code Thermal class (subclass) Current time period (1990–2008) Future (2046–2065) Future (2081–2100) Length (km) Length (percent of total) Length (km) Length (percent of total) Length (percent change from current) Length (km) Length (percent of total) Length (percent change from current) CSIRO Cold 18,271 19.4 −28.6 20,543 21.8 −19.7 Cold transition 23,911 25.3 −14.5 24,918 26.4 −10.9 Warm transition 26,274 27.9 −5.9 27,553 29.2 −1.3 Warm 23,808 25.2 101.3 19,590 20.8 65.6 Very warm 2,076 2.2 101.0 1,738 1.8 68.2 ECHO Cold 15,597 16.5 −39.1 8,419 8.9 −67.1 Cold transition 22,002 23.3 −21.3 20,522 21.8 −26.6 Warm transition 18,848 20.0 −32.5 17,071 18.1 −38.9 Warm 34,877 37.0 194.8 40,281 42.7 240.5 Very warm 3,016 3.2 192.0 8,048 8.5 679.1 FGOALS Cold 17,390 18.4 −32.1 11,582 12.3 −54.8 Cold transition 23,182 24.6 −17.1 21,501 22.8 −23.1 Warm transition 19,842 21.0 −28.9 18,244 19.3 −34.7 Warm 31,258 33.1 164.2 39,027 41.4 229.9

Very warm 2,669 2.9 158.4 3,987 4.2 286.0

GFDL Cold 5,120 5.4 −80.0 5,834 6.2 −77.2

Cold transition 19,181 20.3 −31.4 20,098 21.3 −28.1

Warm transition 17,269 18.3 −38.2 17,277 18.3 −38.1

Warm 44,236 46.9 273.9 41,226 43.7 248.5

Very warm 8,535 9.1 726.2 9,906 10.5 859.0
Results and Discussion 29

Table 9. Predictions of stream temperature thermal class (Lyons and others, 2009) and projected change summarized by length and as a percentage of total length (94,341 kilometers) for current (1990–2008) and future (2046–2065 and 2081–2100) climate conditions for 10 General Circulation Models.—Continued[GCM, General Circulation Model; km, kilometer]

GCM code Thermal class (subclass)

Current time period 

(1990–2008)

Future 

(2046–2065)

Future 

(2081–2100)

Length 

(km)

Length 

(percent 

of total)

Length 

(km)

Length 

(percent 

of total)

Length (percent 

change 

from current)

Length 

(km)

Length 

(percent 

of total)

Length (percent 

change 

from current)

GISS Cold 17,442 18.5 −31.9 11,041 11.7 −56.9

Cold transition 23,099 24.5 −17.4 20,781 22.0 −25.7

Warm transition 20,430 21.6 −26.8 19,268 20.4 −31.0

Warm 30,709 32.6 159.6 39,144 41.5 230.9

Very warm 2,661 2.8 157.6 4,108 4.4 297.7

INGV Cold 16,928 17.9 −33.9 9,787 10.4 −61.8

Cold transition 22,761 24.1 −18.6 20,450 21.7 −26.9

Warm transition 23,591 25.1 −15.5 17,343 18.4 −37.9

Warm 28,582 30.3 141.6 40,258 42.6 240.3

Very warm 2,479 2.6 140.0 6,504 6.9 529.6

IPSL Cold 15,042 15.9 −41.2 12,077 12.8 −52.8

Cold transition 21,842 23.2 −21.9 21,109 22.4 −24.5

Warm transition 18,983 20.1 −32.0 17,204 18.2 −38.4

Warm 35,416 37.6 199.4 38,971 41.3 229.4

Very warm 3,058 3.2 196.0 4,978 5.3 381.9

MIROC Cold 8,102 8.6 −68.3 3,940 4.2 −84.6

Cold transition 20,569 21.8 −26.4 18,235 19.3 −34.8

Warm transition 17,819 18.9 −36.2 16,070 17.0 −42.5

Warm 41,262 43.7 248.8 37,993 40.3 221.2

Very warm 6,589 7.0 537.9 18,103 19.2 1,652.5
30 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

0

5

10

15

20

25

30

35

40

45

50

Cold

Cold transition

Warm transition

Warm

Very warm

GCM 

average

Current CGCM CNRM CSIRO ECHO FGOALS GFDL GISS INGV IPSL MIROC

0

5

10

15

20

25

30

35

40

45

50

GCM 

average

Current CGCM CNRM CSIRO ECHO FGOALS GFDL GISS INGV IPSL MIROC

EXPLANATION

Thermal class (July mean)

Current (1990−2008) and Future (2046−2065)

Current (1990−2008) and Future (2081−2100)

General Circulation Model

Percent stream length

Figure 13. Percent stream length for stream temperature thermal classes under current (1990–2008) and future 

(2046–2065 and 2081–2100) climate conditions for 10 General Circulation Models (GCMs).
Results and Discussion 31

warm streams, there were about 2.9 times as many projected 

by mid-century and about 5.3 times as many projected by 

late-century for the GCM average. These directional shifts 

occurred and varied in magnitude by as much as 15 percent 

in SWB-ANNv1 models using climate data from each of the 

10 GCMs (table 9; fig. 13).

Change in the Amount of Stream Habitat 

Summarized by Thermal Class

The change in the amount of stream habitat was evaluated 

by comparing the percent of stream kilometers lost or gained 

by thermal class from current to future time periods. Losses 

occurred for cold-water, cold-transition, and warm-transition 

streams and gains occurred for the warm-water and very 

warm streams for both mid- and late-century. The greatest and 

comparable losses occurred for cold streams for both mid- and 

late-century and the greatest gains occurred for warm streams 

by mid-century, and for very warm streams by late-century 

based on the GCM average (table 9; fig. 13).

Cold-Water Streams

The GCM average projected a mid-century loss of 

42.9 percent and late-century loss of 59.3 percent of the 

25,597 stream kilometers predicted to be cold under current 

climate conditions. Mid-century projected losses ranged 

from a low of 24.3 percent (model CGCM climate data) to a 

high of 80 percent (model GFDL climate data). Late-century 

projected losses ranged from a low of 19.7 percent (model 

CSIRO climate data) to a high of 84.6 percent (model MIROC 

climate data). This worst-case scenario using model MIROC 

climate data projected only 4.2 percent (3,940 km) of all 

stream kilometers remaining as cold at late-century compared 

to 27.1 percent under current climate conditions.

Cold-Transition Streams

For cold-transition streams, the SWB-ANNv1 model 

GCM averages projected a mid-century loss of 21.6 percent 

and late-century loss of 25.1 percent of the 27,958 stream 

kilometers predicted to be cold transition under current climate 

conditions (table 9; fig. 13). Mid-century projected losses 

ranged from a low of 12.0 percent (model CGCM climate 

data) to a high of 31.4 percent (model GFDL climate data). 

Late-century projected losses ranged from a low of 10.9 percent (model CSIRO climate data) to a high of 34.8 percent 

(model MIROC climate data). 

Warm-Transition Streams

The SWB-ANNv1 model GCM averages projected a 

mid-century loss of 28.1 percent and late-century loss of 

36.6 percent of the 27,924 stream kilometers predicted to be 

warm transition under current climate conditions. Mid-century 

projected losses ranged from a low of 0.7 percent (model 

CGCM climate data) to a high of 38.2 percent (model GFDL 

climate data). Late-century projected losses ranged from a 

low of 1.3 percent (model CSIRO climate data) to a high of 

42.5 percent (model MIROC climate data).

Warm-Water Streams

The SWB-ANNv1 model GCM averages projected the 

greatest gain at mid-century of 194 percent and late-century 

gain of 237 percent of the 11,830 stream kilometers predicted 

to be warm under current climate conditions (table 9; fig. 13). 

Mid-century projected gains ranged from a low of 75.1 percent 

(model CGCM climate data) to a high of 274 percent (model 

GFDL climate data). Late-century projected gains ranged from 

a low of 65.6 percent (model CSIRO climate data) to a high of 

248 percent (model GFDL climate data).

Very Warm Streams

The SWB-ANNv1 model GCM averages projected a 

mid-century gain of 189 percent and late-century gain of 

429 percent of the 1,033 stream kilometers predicted to be 

very warm under current climate conditions (table 9; fig. 13). 

Mid-century projected gains ranged from a low of 82.3 percent 

(model CGCM climate data) to a high of 726 percent (model 

GFDL climate data). Late-century projected gains ranged from 

as little as 68.2 percent (model CSIRO climate data) to as high 

as 1,653 percent (model MIROC climate data).

Change in the Distribution of Stream Habitat 

Summarized by Thermal Class

Maps of the spatial distribution of streams by thermal 

class showed how the distribution of thermal classes were 

projected to change for SWB-ANNv1 GCM averages and 

each individual GCM at mid-century (fig. 14) and late-century 

(fig. 15). Under current climate conditions, cold and coldtransition streams are predominantly located across western 

and southern Wisconsin, including the Driftless Area (fig. 1), 

and in the north along Lake Superior. Warm and warmtransition streams are predominantly located in the eastern 

half of Wisconsin, with warm-transition streams also located 

across northern Wisconsin adjacent to the Upper Peninsula of 

Michigan. At mid- and late-century, based on GCM averages, 

mapped projections showed a contraction of cold streams in 

the Driftless Area and an expansion of warm streams across 

northern Wisconsin as compared to current climate conditions 

(figs. 14 and 15). When considering individual GCMs, the 

range of projected cold-water contraction versus warm-water 

expansion varied among models for both mid- and late-century 

(figs. 14 and 15). 

At mid-century, the map of projections based on model 

CGCM climate data showed the lowest loss of cold, cold transition, and warm transition stream kilometers and the lowest 

gain of warm and very warm stream kilometers (fig. 14). Conversely, the map of projections based on model GFDL showed 

the highest loss of cold, cold transition, and warm transition 

stream kilometers and the highest gain of warm and very 
32 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin Current predictions (1990−2008)

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

GCM_Average

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

CGCM CNRM

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

CSIRO

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

ECHO

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

FGOALS

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

GFDL

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

GISS

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

INGV

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

Future predictions (2046−2065)

IPSL

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

ColdCold transitionWarm transitionWarmVery warmLakesState boundariesCanadian provinces

Thermal class (July mean)

EXPLANATION

EKAL CI M I H A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

MIROC

94 ̊ 48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

94 ̊ 48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

94 ̊ 48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

Base from the U.S. Geological Survey 1:100,000 scale digital line graphs, May 2005.

0 100 MILES0 100 KILOMETERS

Figure 14. Distribution of stream temperature thermal classes (July mean) by individual stream segment, predicted for current (1990–2008) climate conditions and 

projected for future (2046–2065) mid-21st century climate conditions for 10 General Circulation Models (GCMs).
Results and Discussion 33

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

Current predictions (1990–2008) Future predictions (2081–2100)

94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊ 94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

94 ̊

48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

ColdCold transitionWarm transitionWarmVery warmLakesState boundariesCanadian provinces

Thermal class (July mean)

EXPLANATION

0 100 MILES0 100 KILOMETERS

94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

ECHO

94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

FGOALS

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

GFDL

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

94 ̊

48 ̊

46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

GISS

IPSL

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

INGV

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

94 ̊

48 ̊46 ̊44 ̊42 ̊

92 ̊ 90 ̊ 88 ̊

MIROC

EK

AL

CI M

I H

A G N

LAKE SUPERIOR

ILLINOIS

IOWA

MINNESOTA

MICHIGAN

CSIRO CGCM CNRM GCM_Average 

Base from the U.S. Geological Survey 1:100,000 scale digital line graphs, May 2005.

Figure 15. Distribution of stream temperature thermal classes (July mean) by individual stream segment, predicted for current (1990–2008) climate conditions and 

projected for future (2081–2100) late-21st century climate conditions for 10 General Circulation Models (GCMs).
34 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

warm stream kilometers (fig. 14). At late-century, the map of 

projections based on model CSIRO climate data showed the 

lowest loss of cold, cold transition, and warm transition stream 

kilometers and the lowest gain of warm and very warm stream 

kilometers (fig. 15). Conversely, the map of projections based 

on model MIROC climate data showed the highest loss of 

cold, cold transition, and warm transition stream kilometers 

and the highest gain of very warm stream kilometers (the gain 

for warm stream kilometers was slightly higher for projections based on model GFDL climate data, 249 percent) versus 

model MIROC climate data (221 percent) (fig. 15).

Change in Absolute Temperature

All stream segments were projected to become warmer, 

by mid- and late-century for all SWB-ANNv1 model results 

based on climate data from each of the GCMs (table 10; 

figs. 16 and 17). On average, about 80 percent of stream 

kilometers were projected to increase by 1 to 2 °C in July 

mean stream temperature by mid-century; the other 20 percent 

were projected to increase by less than 1 °C. By late-century, 

about 99 percent were projected to increase more than 1°C by 

late-century, with 31 percent of those increasing by more than 

2 °C. Increases in stream temperature were projected to be 

greater at late-century than at mid-century for SWB-ANNv1 

models based on climate data from 8 of the 10 GCMs. The 

projected change was about equal for future time periods using 

model CSIRO climate data; for model GFDL climate data, 

projected increases were slightly greater at mid-century as 

compared to late-century.

The maximum change in July mean stream temperature 

projected by SWB-ANNv1 models varied based on climate 

data from different GCMs. Projections based on climate data 

from two GCMs projected mid-century maximum changes in 

July mean stream temperatures less than 1 °C, from six GCMs 

projected maximum changes between 1 and 2 °C, and from 

two GCMs projected maximum changes between 2 and 3 °C 

(table 10). For the late-century time period, SWB-ANNv1 

2081–2100

2046–2065

General Circulation Model

Percent stream length

0

10

20

30

40

50

60

70

80

90

100

0

10

20

30

40

50

60

70

80

90

100

GCM Average

CGCM

CNRM

CSIRO

ECHO

FGOALS

GFDL

GISS

INGV

IPSL

MIROC

GCM Average

CGCM

CNRM

CSIRO

ECHO

FGOALS

GFDL

GISS

INGV

IPSL

MIROC

Temperature, in 

degrees Celsius 

> 4 to 5 

> 3 to 4 

> 2 to 3 

> 1 to 2 

> 0 to 1 

0

EXPLANATION

Temperature, in 

degrees Celsius 

> 4 to 5 

> 3 to 4 

> 2 to 3 

> 1 to 2 

> 0 to 1 

0

EXPLANATION

Figure 16. Absolute change in stream temperature summarized by percent stream length 

for future (2046–2065 and 2081–2100) climate conditions for 10 General Circulation Models 

(GCMs) relative to current (1990–2008) climate conditions. 
Results and Discussion 35

EXPLANATION

ColdCold transitionWarm transitionWarm

Thermal class

CGCM

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

CNRM

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

CSIRO

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

ECHO

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

FGOALS

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

GFDL

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

INGV

Difference in July mean, future minus current, in degrees Celsius

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

IPSL

July mean stream temperature, in degrees Celsius

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

MIROC

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

GISS

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

GCM Average

5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

10 15 20 25 30 35

2046–2065 time period2081–2100 time period

Model prediction 

Figure 17. Projected absolute change in stream temperature for future (2046–2065 and 2081–2100) climate conditions for 10 General Circulation 

Models (GCMs) relative to current (1990–2008) climate conditions.
36 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Table 10. Projections of absolute change in stream temperature summarized by length and as a percentage of total 

length (94,341 kilometers) for current (1990–2008) and future (2046–2065 and 2081–2100) climate conditions for 10 General 

Circulation Models. 

[GCM, General Circulation Model; km, kilometer; >, greater than] 

GCM code Change 

(degrees Celsius)

Future (2046–2065) Future (2081–2100)

Length (km) Length (percent of total) Length (km) Length (percent of total)

GCM Average 0 0 0 0 0

> 0 to 1 19,287 20.4 1,062 1.1

> 1 to 2 75,054 79.6 64,069 67.9

> 2 to 3 0 0 29,210 31.0

> 3 to 4 0 0 0 0

> 4 to 5 0 0 0 0

CGCM 0 0 0 0 0

> 0 to 1 94,341 100 26,368 27.9

> 1 to 2 0 0 67,973 72.1

> 2 to 3 0 0 0 0

> 3 to 4 0 0 0 0

> 4 to 5 0 0 0 0

CNRM 0 0 0 0 0

> 0 to 1 21,351 22.6 680 0.7

> 1 to 2 72,990 77.4 54,548 57.8

> 2 to 3 0 0 39,113 41.5

> 3 to 4 0 0 0 0

> 4 to 5 0 0 0 0

CSIRO 0 0 0 0 0

> 0 to 1 94,284 99.9 94,341 100

> 1 to 2 57 0.1 0 0

> 2 to 3 0 0 0 0

> 3 to 4 0 0 0 0

> 4 to 5 0 0 0 0

ECHO 0 0 0 0 0

> 0 to 1 36,352 38.5 610 0.6

> 1 to 2 57,989 61.5 49,123 52.1

> 2 to 3 0 0 44,397 47.1

> 3 to 4 0 0 211 0.2

> 4 to 5 0 0 0 0

FGOALS 0 0 0 0 0

> 0 to 1 53,790 57 1,244 1.3

> 1 to 2 40,551 43 87,125 92.4

> 2 to 3 0 0 5,972 6.3

> 3 to 4 0 0 0 0

> 4 to 5 0 0 0 0
Results and Discussion 37

Table 10. Projections of absolute change in stream temperature summarized by length and as a percentage of total 

length (94,341 kilometers) for current (1990–2008) and future (2046–2065 and 2081–2100) climate conditions for 10 General 

Circulation Models.—Continued

[GCM, General Circulation Model; km, kilometer; >, greater than] 

GCM code Change 

(degrees Celsius)

Future (2046–2065) Future (2081–2100)

Length (km) Length (percent of total) Length (km) Length (percent of total)

GFDL 0 0 0 0 0

> 0 to 1 278 0.3 290 0.3

> 1 to 2 17,241 18.3 31,647 33.5

> 2 to 3 76,822 81.4 61,406 65.1

> 3 to 4 0 0 998 1.1

> 4 to 5 0 0 0 0

GISS 0 0 0 0 0

> 0 to 1 54,565 57.8 1,612 1.7

> 1 to 2 39,775 42.2 92,017 97.5

> 2 to 3 0 0 712 0.8

> 3 to 4 0 0 0 0

> 4 to 5 0 0 0 0

INGV 0 0 0 0 0

> 0 to 1 56,135 59.5 1,039 1.1

> 1 to 2 38,206 40.5 56,342 59.7

> 2 to 3 0 0 36,960 39.2

> 3 to 4 0 0 0 0

> 4 to 5 0 0 0 0

IPSL 0 0 0 0 0

> 0 to 1 28,232 29.9 1,863 2.0

> 1 to 2 66,109 70.1 67,280 71.3

> 2 to 3 0 0 25,198 26.7

> 3 to 4 0 0 0 0

> 4 to 5 0 0 0 0

MIROC 0 0 0 0 0

> 0 to 1 493 0.5 266 0.3

> 1 to 2 52,657 55.8 6,033 6.4

> 2 to 3 41,191 43.7 50,661 53.7

> 3 to 4 0 0 36,524 38.7

> 4 to 5 0 0 857 0.9
38 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

models projected a maximum change in July mean stream 

temperature less than 1 °C using climate data from one GCM, 

a maximum change between 1 and 2 °C for climate data from 

one GCM, maximum changes between 2 and 3 °C for climate 

data from five GCMs, maximum changes between 3 and 4 °C 

for climate data from two GCMs, and a maximum change 

between 4 and 5 °C for climate data from one GCM (table 10).

The average change in July mean stream temperature 

between the current time period and mid-century, across all 

stream segments and for all GCM climate data, ranged from 

0.63 °C (model CGCM climate data) to 2.25 °C (model GFDL 

climate data); the minimum change ranged from 0.07 °C 

(model GISS climate data) to 0.41 °C (model GFDL climate 

data); and the maximum change ranged from 0.87 °C (model 

CGCM climate data) to 2.95 °C (model GFDL climate data) 

(fig. 17). Between the current time period and late-century, the 

average change in July mean stream temperature, across all 

stream segments and for all GCM climate data, ranged from 

0.53 °C (model CSIRO climate data) to 2.77 °C (model MIROC climate data); the minimum change ranged from 0.09 °C 

(model CSIRO climate data) to 0.41 °C (model GFDL climate 

data); and the maximum change ranged from 0.77 °C (model 

CSIRO climate data) to 4.28 °C (model MIROC climate data).

Stream segments in the cold thermal class showed the 

greatest amount of variation in warming (fig. 17). In comparisons of July mean stream temperatures between the current 

time period and mid-century or late-century, the “coldest” 

streams within the cold thermal class warmed the least and 

the “warmest” streams within the cold thermal class warmed 

the most. For those stream segments classified as cold for 

the current time period, as the July mean stream temperature 

approached the 17.5 °C thermal threshold between cold and 

cold transition (table 1), the projected difference in July 

mean stream temperature became greater. As stream segment 

temperature predictions increased past 17.5 °C the projected 

difference became less and began to plateau, as can be seen 

by the flattening of the graphed points in figure 17. Maps 

of the spatial distribution of temperature change from the 

current time period to the mid-21st century showed that for 

projections based on GCM averages, in general there are 

smaller changes in the southwestern portion of the State and 

along Lake Superior (i.e., changes between 0 and 1 °C) and 

larger changes in the eastern and northern portions of the State 

(i.e., changes between 1 and 2 °C) (fig. 18). The spatial distribution of temperature change for SWB-ANNv1 model projections based on climate data from individual GCMs ranged 

from changes only between 0 and 1 °C statewide (model 

CGCM climate data) to about 81 percent of streams changing 

between 2 and 3 °C (model GFDL climate data), with the 

remainder changing less and largely confined to the Driftless 

Area and Lake Superior shoreline (table 10; fig. 18).

Maps of the spatial distribution of temperature change 

from the current time period to the late-21st century (fig. 19) 

showed largely the same pattern as projected for mid-century 

(fig. 18) but with a wider range of temperature change among 

SWB-ANNv1 models based on climate data from individual 

GCMs and a larger change when based on GCM averages. For 

the SWB-ANNv1 model GCM averages, the greatest change 

of 2 to 3 °C was projected to occur predominantly across the 

north and to a lesser extent across the eastern half of the State. 

Projections based on model CSIRO climate data showed the 

least amount of change, with all streams projected to change 

between 0 and 1 °C. Projections based on model MIROC 

climate data showed the most change, with about 54 percent of 

stream segments across the State changing between 2 and 3 °C 

and about 39 percent of stream segments predominantly across 

the north and to a lesser extent the east projected to change 

between 3 and 4 °C (table 10; fig. 19).

Change in Thermal Class

The effect of temperature change on fish distribution may 

be understood by evaluating changes in thermal classes of 

streams. Projected changes in stream temperature for both the 

mid- and late-21st century time periods indicated that streams 

either remained in the same thermal class or changed to a 

warmer thermal class, either one or two classes warmer, but 

never changed to a colder thermal class (table 11). On average, 

and for all individual GCMs, there were fewer streams projected in cold, cold-transition, and warm-transition thermal classes 

in future time periods and more projected in warm and verywarm thermal classes. Such changes in thermal classes would 

shift the composition of fish communities across Wisconsin 

(Lyons and others, 2010).

Stream segments classified as cold for the current time 

period either remained cold or changed to cold transition by 

mid-century and late-century for GCM averages (table 11). 

The loss of 43 percent of cold stream segments by mid-century 

and 59 percent by late-century for projections based on GCM 

averages (table 9) translated solely to gains for the cold-transition thermal class (table 11). The spatial distribution of these 

cold transition gains, while necessarily confined to the original 

predicted distribution of cold thermal class streams, occurred 

largely on the periphery of the Driftless Area (figs. 1, 20, and 

21). However, for SWB-ANNv1 models based on climate 

data from individual GCMs, two (models GFDL and MIROC 

climate data) projected a small percentage of stream segments 

changing from cold to warm transition by mid-century and 

late-century (table 11).

Stream segments classified as cold transition for the 

current time period either remained cold transition or changed 

to warm transition or warm by mid- and late-century for 

SWB-ANNv1 models based on GCM averages (table 11). 

Those stream segments that changed thermal class, however, 

predominantly changed to warm transition. At mid-century, 

the loss of cold-transition streams as projected by models 

using climate data based on GCM averages resulted in about 

60 percent of cold-transition stream kilometers changing to 

warm transition and 0.7 percent changing to warm. At latecentury, the loss of cold-transition streams resulted in about 
Results and Discussion 39

Table 11. Projections of change in stream temperature thermal class (Lyons and others, 2009) summarized by length and as 

a percentage of total length (94,341 kilometers) for 10 General Circulation Models for the mid-21st century (2046–2065) and 

late-21st century (2081–2100).

[GCM, General Circulation Model; km, kilometer] 

GCM code Change in thermal class

Future (2046–2065) Future (2081–2100)

Length (km) Length (percent of total) Length (km) Length (percent of total)

GCM 

average

Cold (no change) 14,628 15.5 10,417 11.0

Cold to cold transition 10,969 11.6 15,180 16.1

Cold to warm transition 0 0 0 0

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 10,961 11.6 5,758 6.1

Cold transition to warm transition 16,790 17.8 17,701 18.8

Cold transition to warm 207 0.2 4,499 4.8

Cold transition to very warm 0 0 0 0

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 3,286 3.5 0 0

Warm transition to warm 24,638 26.1 27,924 29.6

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 9,874 10.5 7,398 7.8

Warm to very warm 1,955 2.1 4,431 4.7

Very warm (no change) 1,033 1.1 1,033 1.1

CGCM Cold (no change) 19,389 20.6 15,238 16.2

Cold to cold transition 6,208 6.6 10,358 11.0

Cold to warm transition 0 0 0 0

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 18,402 19.5 11,551 12.2

Cold transition to warm transition 9,555 10.1 16,327 17.3

Cold transition to warm 0 0 80 0.1

Cold transition to very warm 0 0 0 0

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 18,186 19.3 3,934 4.2

Warm transition to warm 9,738 10.3 23,990 25.4

Warm transition to very warm 0 0 0 0
40 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Table 11. Projections of change in stream temperature thermal class (Lyons and others, 2009) summarized by length and as 

a percentage of total length (94,341 kilometers) for 10 General Circulation Models for the mid-21st century (2046–2065) and 

late-21st century (2081–2100).—Continued

[GCM, General Circulation Model; km, kilometer] 

GCM code Change in thermal class

Future (2046–2065) Future (2081–2100)

Length (km) Length (percent of total) Length (km) Length (percent of total)

CGCM, 

continued

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 10,979 11.6 9,922 10.5

Warm to very warm 851 0.9 1,907 2.0

Very warm (no change) 1,033 1.1 1,033 1.1

CNRM Cold (no change) 14,748 15.6 9,157 9.7

Cold to cold transition 10,849 11.5 16,421 17.4

Cold to warm transition 0 0 19 0.02

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 11,400 12.1 4,405 4.7

Cold transition to warm transition 16,557 17.6 17,088 18.1

Cold transition to warm 0 0 6,465 6.9

Cold transition to very warm 0 0 0 0

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 5,433 5.8 0 0

Warm transition to warm 22,491 23.8 27,924 29.6

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 10,134 10.7 5,874 6.2

Warm to very warm 1,695 1.8 5,955 6.3

Very warm (no change) 1,033 1.1 1,033 1.1

CSIRO Cold (no change) 18,271 19.4 20,543 21.8

Cold to cold transition 7,326 7.8 5,054 5.4

Cold to warm transition 0 0 0 0

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 16,585 17.6 19,864 21.1

Cold transition to warm transition 11,372 12.1 8,094 8.6

Cold transition to warm 0 0 0 0

Cold transition to very warm 0 0 0 0
Results and Discussion 41

Table 11. Projections of change in stream temperature thermal class (Lyons and others, 2009) summarized by length and as 

a percentage of total length (94,341 kilometers) for 10 General Circulation Models for the mid-21st century (2046–2065) and 

late-21st century (2081–2100).—Continued

[GCM, General Circulation Model; km, kilometer] 

GCM code Change in thermal class

Future (2046–2065) Future (2081–2100)

Length (km) Length (percent of total) Length (km) Length (percent of total)

CSIRO, 

continued

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 14,902 15.8 19,459 20.6

Warm transition to warm 13,022 13.8 8,465 9.0

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 10,786 11.4 11,125 11.8

Warm to very warm 1,043 1.1 705 0.7

Very warm (no change) 1,033 1.1 1,033 1.1

ECHO Cold (no change) 15,597 16.5 8,419 8.9

Cold to cold transition 10,000 10.6 17,128 18.2

Cold to warm transition 0 0 50 0.1

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 12,003 12.7 3,394 3.6

Cold transition to warm transition 15,524 16.5 17,021 18.0

Cold transition to warm 431 0.5 7,543 8.0

Cold transition to very warm 0 0 0 0

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 3,324 3.5 0 0

Warm transition to warm 24,600 26.1 27,924 29.6

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 9,846 10.4 4,815 5.1

Warm to very warm 1,983 2.1 7,015 7.4

Very warm (no change) 1,033 1.1 1,033 1.1
42 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Table 11. Projections of change in stream temperature thermal class (Lyons and others, 2009) summarized by length and 

as a percentage of total length (94,341 kilometers) for 10 General Circulation Models for the mid-21st century (2046–2065) and 

late-21st century (2081–2100).—Continued

[GCM, General Circulation Model; km, kilometer] 

 

GCM code Change in thermal class

Future (2046–2065) Future (2081–2100)

Length (km) Length (percent of total) Length (km) Length (percent of total)

FGOALS Cold (no change) 17,390 18.4 11,582 12.3

Cold to cold transition 8,207 8.7 14,015 14.9

Cold to warm transition 0 0 0 0

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 14,975 15.9 7,486 7.9

Cold transition to warm transition 12,983 13.8 18,042 19.1

Cold transition to warm 0 0 2,430 2.6

Cold transition to very warm 0 0 0 0

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 6,859 7.3 202 0.2

Warm transition to warm 21,065 22.3 27,722 29.4

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 10,193 10.8 8,875 9.4

Warm to very warm 1,637 1.7 2,954 3.1

Very warm (no change) 1,033 1.1 1,033 1.1

GFDL Cold (no change) 5,120 5.4 5,834 6.2

Cold to cold transition 19,025 20.2 19,528 20.7

Cold to warm transition 1,452 1.5 235 0.2

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 156 0.2 570 0.6

Cold transition to warm transition 15,817 16.8 17,042 18.1

Cold transition to warm 11,984 12.7 10,345 11.0

Cold transition to very warm 0 0 0 0
Results and Discussion 43

Table 11. Projections of change in stream temperature thermal class (Lyons and others, 2009) summarized by length and 

as a percentage of total length (94,341 kilometers) for 10 General Circulation Models for the mid-21st century (2046–2065) and 

late-21st century (2081–2100).—Continued

[GCM, General Circulation Model; km, kilometer] 

 

GCM code Change in thermal class

Future (2046–2065) Future (2081–2100)

Length (km) Length (percent of total) Length (km) Length (percent of total)

GFDL, 

continued

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 0 0 0 0

Warm transition to warm 27,924 29.6 27,924 29.6

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 4,328 4.6 2,957 3.1

Warm to very warm 7,502 8.0 8,873 9.4

Very warm (no change) 1,033 1.1 1,033 1.1

GISS Cold (no change) 17,442 18.5 11,041 11.7

Cold to cold transition 8,155 8.6 14,556 15.4

Cold to warm transition 0 0 0 0

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 14,944 15.8 6,225 6.6

Cold transition to warm transition 13,014 13.8 19,259 20.4

Cold transition to warm 0 0 2,474 2.6

Cold transition to very warm 0 0 0 0

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 7,416 7.9 9 0.01

Warm transition to warm 20,508 21.7 27,915 29.6

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 10,201 10.8 8,755 9.3

Warm to very warm 1,628 1.7 3,075 3.3

Very warm (no change) 1,033 1.1 1,033 1.1
44 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Table 11. Projections of change in stream temperature thermal class (Lyons and others, 2009) summarized by length and 

as a percentage of total length (94,341 kilometers) for 10 General Circulation Models for the mid-21st century (2046–2065) and 

late-21st century (2081–2100).—Continued

[GCM, General Circulation Model; km, kilometer] 

 

GCM code Change in thermal class

Future (2046-2065) Future (2081-2100)

Length (km) Length (percent of total) Length (km) Length (percent of total)

INGV Cold (no change) 16,928 17.9 9,787 10.4

Cold to cold transition 8,668 9.2 15,805 16.8

Cold to warm transition 0 0 6 0.01

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 14,092 14.9 4,645 4.9

Cold transition to warm transition 13,865 14.7 17,337 18.4

Cold transition to warm 0 0 5,975 6.3

Cold transition to very warm 0 0 0 0

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 9,726 10.3 0 0

Warm transition to warm 18,198 19.3 27,924 29.6

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 10,384 11.0 6,359 6.7

Warm to very warm 1,446 1.5 5,471 5.8

Very warm (no change) 1,033 1.1 1,033 1.1

IPSL Cold (no change) 15,042 15.9 12,077 12.8

Cold to cold transition 10,555 11.2 13,520 14.3

Cold to warm transition 0 0 0 0

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 11,287 12.0 7,590 8.0

Cold transition to warm transition 16,152 17.1 16,930 17.9

Cold transition to warm 519 0.5 3,437 3.6

Cold transition to very warm 0 0 0 0
Results and Discussion 45

Table 11. Projections of change in stream temperature thermal class (Lyons and others, 2009) summarized by length and 

as a percentage of total length (94,341 kilometers) for 10 General Circulation Models for the mid-21st century (2046–2065) and 

late-21st century (2081–2100).—Continued

[GCM, General Circulation Model; km, kilometer] 

 

GCM code Change in thermal class

Future (2046-2065) Future (2081-2100)

Length (km) Length (percent of total) Length (km) Length (percent of total)

IPSL, 

continued

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 2,831 3.0 274 0.3

Warm transition to warm 25,093 26.6 27,650 29.3

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 9,804 10.4 7,884 8.4

Warm to very warm 2,025 2.1 3,946 4.2

Very warm (no change) 1,033 1.1 1,033 1.1

MIROC Cold (no change) 8,101 8.6 8,419 8.9

Cold to cold transition 17,489 18.5 17,128 18.2

Cold to warm transition 6 0.006 50 0.1

Cold to warm 0 0 0 0

Cold to very warm 0 0 0 0

Cold transition to cold 0 0 0 0

Cold transition (no change) 3,080 3.3 3,394 3.6

Cold transition to warm transition 17,813 18.9 17,021 18.0

Cold transition to warm 7,064 7.5 7,543 8.0

Cold transition to very warm 0 0 0 0

Warm transition to cold 0 0 0 0

Warm transition to cold transition 0 0 0 0

Warm transition (no change) 0 0 0 0

Warm transition to warm 27,924 29.6 27,924 29.6

Warm transition to very warm 0 0 0 0

Warm to cold 0 0 0 0

Warm to cold transition 0 0 0 0

Warm to warm transition 0 0 0 0

Warm (no change) 6,274 6.6 4,815 5.1

Warm to very warm 5,556 5.9 7,015 7.4

Very warm (no change) 1,033 1.1 1,033 1.1
46 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin GCM_Average 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊

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Figure 18. Projected absolute change in stream temperature for future (2046–2065) climate conditions for 10 General 

Circulation Models (GCMs) relative to current (1990–2008) climate conditions.
Results and Discussion 47Figure 19. Projected absolute change in stream temperature for future climate conditions (2081–2100) for 10 General Circulation Models (GCMs) relative to current (1990–2008) climate conditions.

GCM_Average

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48 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin Cold (no change) Cold to cold transition Cold to warm transition

Cold to warmCold to very warm

Thermal change

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CGCM CNRM CSIRO

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Base from the U.S. Geological Survey 1:100,000 scale digital line graphs, May 2005.

Figure 20. Projected change in stream temperature thermal class for cold-water streams from current (1990–2008) to 

future (2046–2065) climate conditions for 10 General Circulation Models (GCMs).
Results and Discussion 49Figure 21. Projected change in stream temperature thermal class for cold-water streams from current (1990–2008) to future (2081–2100) climate conditions for 10 General Circulation Models (GCMs). Base from the U.S. Geological Survey 1:100,000 scale digital line graphs, May 2005.

Cold (no change)Cold to cold transitionCold to warm transitionCold to warmCold to very warm

Thermal change

EXPLANATION

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0 50 100 MILES0 50 100 KILOMETERS

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Cold streams - Thermal class change - current (1990–2008) to future (2081–2100)

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50 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

63 percent of stream kilometers changing to warm transition and 16 percent changing to warm (table 11). The spatial 

distribution of the change in stream segments at mid-century 

from cold transition to warm transition occurred across the 

State but with a heavier concentration of changed stream segments along the southern border of the State (fig. 22). At latecentury, additional stream segments changed to warm transition across the southern part of the State, and changes to warm 

stream segments occurred across the northern part of the State 

(fig. 23). Among models based on climate data from the 10 individual GCMs, at mid-century 6 projected only changes from 

cold transition to warm transition and the other 4 projected 

additional changes to warm (table 11; fig. 22). At late-century 

only one model, using model CSIRO climate data, projected 

changes solely to warm transition, and nine projected changes 

to both warm transition and warm (table 11; fig. 23).

The greatest projected change in thermal class was 

for warm-transition stream segments, of which 88 percent 

of stream kilometers were projected to change to warm by 

mid-century and 100 percent were projected to change to 

warm by late-century for the GCM average (table 11). The 

SWB-ANNv1 model using climate data from 8 of the 10 

individual GCMs projected some warm-transition stream segments to remain as such at mid-century, ranging from about 

10 percent of stream kilometers (model IPSL climate data) 

to about 65 percent (model CGCM climate data). Despite 

SWB-ANNv1 model projecting a 100 percent change from 

warm transition to warm at late-century for the GCM average, 

projections based on climate data for five individual GCMs 

showed some stream segments remaining as warm transition at 

late-century (table 11). The SWB-ANNv1 model using climate 

data from model CSIRO projected about 70 percent of stream 

kilometers remaining as warm transition; however, the use of 

climate data from model CGCM projected about 14 percent 

remaining and the use of climate data from three other GCMs 

projected less than 1 percent remaining (table 11). Maps of the 

spatial distribution of thermal class change, or lack thereof, 

among warm-transition stream segments showed changes 

occurring throughout the State at both mid- and late-century 

(figs. 24 and 25).

Stream segments classified as warm using current climate 

data mostly remained warm at mid-century (83 percent of 

stream kilometers) and late-century (63 percent of stream 

kilometers) with the remainder changing to very warm, as 

projected by the SWB-ANNv1 model GCM average (table 

11). The SWB-ANNv1 model using climate data from each of 

the 10 GCMs projected some change in thermal classes among 

stream segments, from warm to very warm. At mid-century, 

SWB-ANNv1 models projected from about 7 percent (model 

CGCM climate data) to about 63 percent (model GFDL climate data) of stream kilometers changing from warm to very 

warm (table 11). At late-century, SWB-ANNv1 models 

projected from about 6 percent (model CSIRO climate data) 

to about 75 percent (model GFDL climate data) of stream 

kilometers changing from warm to very warm (table 11). 

Maps of the spatial distribution of stream segments remaining warm and changing to very warm showed these changes 

occurring throughout the State at both mid- and late-century 

(figs. 26 and 27).

Data and Model Limitations

Model output of stream temperatures for mid- and late21st century time periods were considered projections of what 

could happen rather than predictions of what will happen. 

Projections are probabilistic statements about the future concerning what is possible under certain conditions as described 

in the model should those conditions be realized in the future. 

For example, our models assumed the A1B emissions scenario 

for the remainder of the 21st century. The A1B emissions 

scenario is a “middle-of-the-road” scenario, developed by the 

Intergovernmental Panel on Climate Change (IPCC, 2007), 

which assumes a balanced approach to energy production 

between fossil and non-fossil fuels. Should carbon emissions 

increase at a slower rate (B2 emissions scenario) or a faster 

rate (A1 emissions scenario), then the climate input data used 

in our model would not accurately represent future conditions. 

Predictions of what changes in climate will occur are inherently difficult to make because predictions of realized future 

emissions of greenhouse gases are uncertain.

Model projections were further constrained by the use of 

statistical downscaling to project future climate conditions at a 

scale appropriate for the study area of Wisconsin. The UWCCR used statistical downscaling to relate climate trends at the 

global scale to climate conditions at the State level in Wisconsin (Notaro and others, 2011). In this application of downscaling, large-scale air temperature and precipitation variables 

from GCMs were statistically related to local climate conditions in Wisconsin. The UWCCR validated this technique 

using historical climate data for Wisconsin (WICCI, 2011). 

Researchers at the UWCCR are continuing work on downscaling additional climatological parameters, which may be of 

relevance to our understanding of climate change impacts on 

stream temperature. Such parameters include evapotranspiration, humidity, and solar radiation. Future advances in our 

understanding of climate change at local versus global scales 

may lead to improvements in our ability to relate changes in 

climate to changes in stream temperature.

Additional model assumptions critical to understanding 

climate impacts on stream temperature include changes in land 

use and streamflow. Land use was assumed to remain constant 

at current conditions. Although land use is expected to change 

over time, the extent to which land use will change is difficult 

to predict. For example, land use may change in response to 

economic conditions. In recent years, increases in commodity 

prices and demand for ethanol have led to the rotation of protected land out of the Conservation Reserve Program (CRP) 

and into agricultural production (Streitfeld, 2008; Allen and 

Vandever, 2012). If environmentally sensitive CRP land is 
Applications of the Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 51

returned to corn production, there is the potential for increased 

surface-water runoff and less infiltration into groundwater, 

which may affect stream temperatures (Panuska and others, 

2007; Marshall and others, 2008).

Future changes in urbanization also may affect how 

changes in climate impact stream temperature. Urbanization is 

expected to increase over time, but predictions of such change 

are inherently uncertain. Wang and others (2003) measured 

urbanization as the percent of connected impervious area in a 

watershed. Urbanization may impact stream temperature in a 

number of ways. Impervious surfaces may limit groundwater 

recharge and reduce stream base flow and may increase 

surface-water input to streams, including warmer thermal 

inputs following precipitation events during summertime. 

Wang and others (2003) found that streams in watersheds with 

levels of connected imperviousness in the threshold region 

of 6–11 percent can experience major changes in thermal 

conditions as a result of minor changes in urbanization. Any 

changes in urbanization, as well as other forms of land use, 

may affect how changes in climate impact stream temperatures.

Streamflow also may change over time as a result of 

climate change, and changes in streamflow may impact 

stream temperature. UWCCR projections of climatic change 

in precipitation for Wisconsin are uncertain; projections from 

individual climate models indicate changes both positive and 

negative to streamflow may occur in the future, depending on 

the time of year. Increases in precipitation may positively impact groundwater recharge and help maintain lower summertime stream temperatures, particularly in cold-water streams. 

However, increases in precipitation during warmer summertime months may lead to increases in warm surface runoff that 

may increase stream temperatures. The interaction of precipitation and land use will be important in determining how these 

factors impact stream temperature as climate changes occur. 

Unpublished data for cold-water streams in the Driftless Area 

of Wisconsin shows how stream temperature relates to precipitation events. Streams heavily influenced by groundwater 

remained consistently cold during the absence of precipitation 

events in summer 2012, whereas spikes in stream temperature 

closely tracked the many precipitation events that occurred 

in summer 2010 (Matthew Mitro, Wisconsin Department of 

Natural Resources, oral commun., [2013]).

Applications of the Integrated SoilWater-Balance and Artificial Neural 

Network version 1 Stream Temperature 

Model

The SWB-ANNv1 stream temperature model described 

in this report represents an important advance over ANNv1 

described by Stewart and others (2006). The development and 

integration of the SWB model with the ANN model allowed 

for the parameterization of the connection between precipitation, groundwater, and stream temperature. This approach also 

provided a way to link projections of future changes in climate 

to groundwater recharge and ultimately to stream temperature. 

The thermal predictions for streams from the SWB-ANNv1 

model under current climate conditions and projections under 

future climate scenarios will enhance the ability of fisheries 

managers to make appropriate recommendations and decisions 

pertaining to stream management.

The SWB-ANNv1 stream temperature model will serve 

as an important tool for fisheries management because of the 

importance of water temperature to fish and the ability of the 

model to make inferences about temperature and fish assemblages in all stream segments across Wisconsin. Fish assemblages in streams vary in relation to differences in thermal 

conditions in streams (Lyons and others, 2009). However, 

the thermal characteristics of many Wisconsin streams are 

unknown. The stream temperature model will serve as an 

important tool in mapping and quantifying streams by thermal class, guiding stream surveys, mapping distributions of 

stream fishes, and making management decisions pertaining to 

stream-habitat protection and restoration to support important 

fisheries.

Wisconsin is recognized as an important cold-water 

State from the perspective of both trout fisheries and fish 

biodiversity. Brook trout are the only native salmonid found 

in cold-water streams in Wisconsin. However, Wisconsin is 

at the southern edge of the brook trout’s distributional range, 

where the species is at increased risk to changes in climate. 

The SWB-ANNv1 stream temperature model estimates can be 

used in fish species occurrence models to project those streams 

that may have suitable habitat for brook trout under future 

climate scenarios (Lyons and others, 2010; Mitro and others, 

2010a; WICCI, 2011). 

In addition to cold-water streams, Wisconsin hosts a 

diversity of streams across a continuous thermal gradient, 

which can be categorized into discrete thermal classes, each 

represented by fish assemblages adapted to particular thermal 

conditions and potentially threatened by changes in climate. 

Warm-water and warm-transition streams have almost a completely different fish fauna compared to cold-water and coldtransition streams (Lyons and others, 2010). Lyons and others 

(2009) identified the thermal guild for 99 fish species found 

in Wisconsin and Michigan streams. There were 65 species 

classified as warm water, 26 as transitional (i.e., cold transition 

or warm transition), and 8 as cold water. Warm-water streams, 

while being small in number, support a significantly higher 

number of fish species than cold-water and transitional streams 

combined. SWB-ANNv1 model predictions may be helpful in 

identifying the small percentage of streams that may be critical 

to preserving warm-water fish species diversity in Wisconsin 

streams and in identifying potential impacts of climate change 

on these streams.
52 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Base from the U.S. Geological Survey 1:100,000 scale digital line graphs, May 2005.

Cold-transition streams - Thermal class change - current (1990–2008) to future (2046–2065)

Cold transition to cold Cold transition (no change)Cold transition to warm transitionCold transition to warmCold transition to very warm

Thermal change

EXPLANATION

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Figure 22. Projected change in stream temperature thermal class for cold-transition streams from current (1990–2008) to 

future (2046–2065) climate conditions for 10 General Circulation Models (GCMs). 
Applications of the Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 53Figure 23. Projected change in stream temperature thermal class for cold-transition streams from current (1990–2008) to future (2081–2100) climate conditions for 10 General Circulation Models (GCMs). 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ Cold transition GCM_Average CGCM CNRM CSIRO ECHO FGOALS GFDL GISS INGV IPSL MIROC

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Cold-transition streams - Thermal class change - current (1990–2008) to future (2081–2100)

Cold transition to coldCold transition (no change)Cold transition to warm transitionCold transition to warmCold transition to very warm

Thermal changeLakesState boundariesCanadian provinces

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Other streams

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54 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Figure 24. Projected change in stream temperature thermal class for warm-transition streams from 

current (1990–2008) to future (2046–2065) climate conditions for 10 General Circulation Models (GCMs). 

Warm transition to coldWarm transition to cold transitionWarm transition (no change)Warm transition to warmWarm transition to very warm

Thermal change

EXPLANATION

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Warm-transition streams - Thermal class change - current (1990–2008) to future (2046–2065)
Applications of the Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 55Figure 25. Projected change in stream temperature thermal class for warm-transition streams from 

current (1990–2008) to future (2081–2100) climate conditions for 10 General Circulation Models (GCMs).

Warm transition to coldWarm transition to cold transitionWarm transition (no change)Warm transition to warmWarm transition to very warm

Thermal change

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56 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Figure 26. Projected change in stream temperature thermal class for warm-water streams from current (1990–2008) to 

future (2046–2065) climate conditions for 10 General Circulation Models (GCMs). 

Warm to coldWarm to cold transitionWarm to warm transition Warm (no change) Warm to very warm

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EXPLANATION

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Applications of the Integrated Soil-Water-Balance and Artificial Neural Network version 1 Stream Temperature Model 57Figure 27. Projected change in stream temperature thermal class for warm-water streams from current (1990–2008) to future (2081–2100) climate conditions for 10 General Circulation Models (GCMs). Warm to cold Warm to cold transition Warm to warm transition Warm (no change) Warm to very warm Thermal change EXPLANATION Other streams Lakes State boundaries Canadian provinces 0 50 100 MILES 0 50 100 KILOMETERS 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ 94 ̊ 48 ̊ 46 ̊ 44 ̊ 42 ̊ 92 ̊ 90 ̊ 88 ̊ Warm GCM_Average CGCM CNRM CSIRO ECHO FGOALS GFDL GISS INGV IPSL MIROC

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58 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

The Wisconsin Initiative on Climate Change Impacts 

(WICCI) (WICCI, 2011) produced the first adaptive assessment for Wisconsin to address the vulnerabilities and sensitivities of natural resources to climate change impacts and to 

propose adaptation strategies to build resiliency and lessen 

the impacts. The ANNv1 stream temperature model (Stewart 

and others, 2006; Westenbroek and others, 2010b) played an 

integral role in identifying the vulnerabilities and sensitivities 

of Wisconsin streams and stream fishes to potential warming scenarios associated with changes in climate (Lyons and 

others, 2010; Mitro and others, 2010a; WICCI, 2011). The 

SWB-ANNv1 model will further advance our understanding 

of climate impacts on Wisconsin streams and aid in the development of adaptation strategies managers can use to protect 

fisheries.

An important initial use of the SWB-ANNv1 model 

has been as a tool to understand current and future distributions of trout and smallmouth bass as part of the development 

of a master plan for managing WDNR land holdings and 

easements along streams in the Driftless Area of Wisconsin 

(WDNR, 2013). The Driftless Master Plan is a forwardlooking document, and the use of SWB-ANNv1 model 

predictions (current time period) and projections (mid-21st 

century time period) represents the first time a WDNR master 

plan explicitly addresses climate change impacts on streams 

as an important factor in making decisions on agency land 

management (WDNR, 2013). The plan includes the identification of where trout and smallmouth bass are currently found 

in streams and where they are likely to be in the future given 

changing climate conditions. The plan ultimately will guide 

land-protection goals, objectives, and strategies to ensure 

public access to desired fisheries recognizing the threat posed 

by climate change to the existence of such fisheries in some 

streams.

Thermal predictions (current climate conditions) and 

projections (future climate scenarios) for streams will enhance 

the ability of resource managers to make appropriate recommendations and decisions pertaining to stream and fisheries 

management. One example is the WDNR’s classification of 

streams as “trout waters.” Streams shown by fish surveys to 

support trout are classified as trout streams. Such classification is important from a resource-management perspective in 

that trout water classification affords a stream a higher level of 

protection from activities that may lead to the degradation of 

cold-water thermal habitat. SWB-ANNv1 model predictions 

that more than one-half of Wisconsin’s stream kilometers are 

thermally suitable for trout (as compared to the 24 percent currently classified as trout waters) will be instrumental in supporting efforts to survey and classify additional trout waters. 

Cold stream temperatures are necessary, but not sufficient, to 

support trout. Thermal class predictions can be used to help 

guide stream survey efforts to focus on those streams most 

likely to contain trout and thus warrant trout-classification 

status. 

Another use of SWB-ANNv1 model predictions and 

projections of stream temperatures is to guide the expenditure 

of financial resources on stream habitat projects. Anglers fishing Wisconsin streams are required to purchase a trout stamp, 

in addition to a fishing license, and the trout stamp funds are 

dedicated to trout stream habitat projects (WDNR, 2011). 

Similar to the use of the SWB-ANNv1 model in the Driftless 

master planning process, modeling the impacts of future 

climate scenarios on stream thermal class will be used to guide 

trout stream habitat projects (Mitro and others, 2010a). Mitro 

and others (2010a) describe a triage approach to prioritizing 

fund expenditures on stream habitat projects. Fisheries managers may forgo spending limited funds on streams projected to 

change thermal classes such that trout losses may be inevitable. Streams projected to be resilient to climate change 

impacts on thermal class such that they are likely to remain 

cold-water streams may be best suited to protection efforts. 

Rather, funds may be dedicated to streams in which the persistence of trout may be contingent upon management actions 

likely to build resiliency to climate change impacts on stream 

temperature. Stream-restoration efforts to build resiliency to 

climate impacts may include in-stream habitat work used to 

narrow and deepen the stream channel and reduce bank erosion to help maintain cold groundwater temperatures over the 

course of the stream (Mitro and others, 2010a and b). Riparian 

management to provide shade cover also may help maintain 

cold thermal temperatures in streams (Cross and others, 2013).

Summary and Conclusions 

This study simulated daily summertime water 

temperatures under current (1990–2008) climate conditions 

and projected water temperature under future climate conditions for 94,341 kilometers (km) of streams across Wisconsin 

(1:100,000 scale U.S. National Hydrography Dataset). Water 

temperature is a critical factor in identifying the suitability 

of streams for different species of fish across this geographic 

area. As ongoing changes in climate progress, stream thermal 

conditions and fish distributions are expected to change and 

models may help quantify such change.

A stream temperature model (SWB-ANNv1) to predict 

stream temperatures in all stream segments during the 

summertime (June–August) period was developed by building 

upon an Artificial Neural Network (ANN) version 1 model 

(ANNv1) by Stewart and others (2006). The ANN model is 

an empirical model that captures the dynamics of spatially 

expansive and behaviorally heterogeneous hydrologic systems 

using static landscape data and dynamic climate time-series 

data. ANNv1 methodology was further expanded upon by 

integrating a Soil-Water-Balance (SWB) model with the ANN 

model to parameterize potential groundwater recharge, thereby 

linking precipitation, groundwater, and stream temperature. 

The resulting integrated SWB and ANN version 1 (SWBANNv1) Model was used to predict daily summertime stream 

temperatures using current climate data and to project daily 

stream temperatures at mid- and late-21st century time periods 
Summary and Conclusions 59

(2046–65 and 2081–2100). Mid- and late-century climate 

projections were based on the A1B emissions scenario and the 

downscaled projections of air temperature and precipitation 

amounts from 10 Global Circulation Models (GCMs) (Notaro 

and others, 2011). The July mean stream temperature was 

derived from mean daily stream temperatures and was used to 

identify the thermal classification of each stream segment: cold 

(<17.5 degrees Celsius (°C), cold transition (17.5–19.5 °C), 

warm transition (19.5–21 °C), warm (21–24 °C), and very 

warm (>24 °C) (Lyons and others, 2009).

The SWB-ANNv1 model captured the overall trend in 

daily summertime stream temperature data with a percent 

model error (PME) of 8.8 percent. The SWB-ANNv1 model 

explained 76 percent of the variation in stream temperature, 

as compared to 67 percent for the ANNv1 model, a nine 

percentage point improvement (Stewart and others, 2006). 

The approach for integrating SWB with the ANN model also 

provided a means to evaluate the effect of changing air temperature and precipitation on groundwater recharge and soil 

moisture and in turn provided a mechanism by which downscaled global or regional climate model results could be used 

to estimate the potential effects of climate change on stream 

temperature.

The SWB-ANNv1 model was based on eight static 

landscape variables (six describing the total upstream watershed, one the total upstream 60-meter riparian buffer, and one 

the local channel), six dynamic climate variables describing 

air temperature groups, and three dynamic variables describing 

groundwater recharge. The SWB-ANNv1 model was developed using a training dataset and tested using an independent 

validation dataset. About 47 percent of the July mean stream 

temperature predictions were within 1 °C of observed values, 

about 77 percent were within 2 °C, and about 93 percent were 

within 3 °C. More than one-half of the stream kilometers 

were predicted suitable for cold-water fishes such as trout or 

sculpins for the current time period (27.1 percent cold and 

29.6 percent cold transition). The remaining stream kilometers 

were predicted suitable for warm-water fishes such as minnows and sunfishes (29.6 percent warm transition, 12.5 percent warm-water, and 1.1 percent very warm). Cold and coldtransition streams were predicted to primarily occur in the 

Driftless Area of western and southern Wisconsin and along 

Lake Superior to the north. Warm-transition and warm streams 

were primarily in the eastern half of Wisconsin, with warmtransition streams also prominent across the north. Overall, 

the SWB-ANNv1 model predicted an additional 5.7 percent of 

stream kilometers as suitable for cold-water fishes in Wisconsin, as compared to the ANNv1 model, with about equal 

proportions of cold and cold transition stream kilometers.

Projections of stream temperatures at mid- and latecentury based on climate data from 10 GCMs showed warming for all stream segments. The GCM average projected about 

80 percent of stream kilometers increasing by 1 to 2 °C by 

mid-century and about 99 percent increasing by 1 to 3 °C by 

late-century, with 31 percent of those increasing by more than 

2 °C in the late-century. Stream segments in the cold thermal 

class showed the greatest amount of variation in warming 

with the “coldest” streams warming the least and those approaching the upper end of the cold thermal class warming 

the most, based on July mean stream temperature. This may 

suggest that cold-water streams dominated by groundwater 

contributions may have a higher capacity for maintaining cold 

temperatures than cold-water streams with a lower proportion of groundwater input even under future climate warming 

scenarios.

The effect of temperature change on fish distribution may 

be understood by evaluating changes in thermal classes of 

streams. Projected changes in stream temperature for both the 

mid- and late-21st century time periods indicated that streams 

either remained in the same thermal class or changed to a 

warmer thermal class, but never changed to a colder thermal 

class. On average, and for all individual GCMs, there were 

fewer stream kilometers projected in cold, cold-transition, and 

warm-transition thermal classes in future time periods and 

more projected in warm and very-warm thermal classes. Such 

changes in thermal classes would shift the composition of fish 

communities across Wisconsin, with a loss in the distribution 

of cold-water fishes and increase in the distribution of warmwater fishes. Less than two-fifths of stream kilometers at midcentury and one-third at late-century would be thermally suitable for cold-water fishes resulting in an 18 to 23 percent loss 

of suitable habitat at mid- and late-21st century, respectively, 

based on the GCM averages. These directional shifts occurred 

and varied in magnitude by as much as 15 percent in SWBANNv1 models using climate data from each of the 10 GCMs. 

The range of cold and cold-transition streams is projected to 

contract within the Driftless Area and along Lake Superior, 

and the range of warm streams is projected to expand in the 

east and particularly across the north in Wisconsin.

Projected losses of cold-water stream habitat may result 

in losses of cold-water stream fisheries for species such as 

brook trout and brown trout. Concomitant increases in warmwater stream habitat may benefit many warm-water fishes, 

but warm-water sport fishes like smallmouth bass may not 

replace fisheries for trout because of other habitat limitations. 

Many headwater streams that currently support trout, for 

example, are physically too small to support smallmouth 

bass. Therefore, projected changes in thermal habitat attributable to climate change may result in net losses of fisheries, 

posing a challenge to fisheries and resource managers. The 

SWB-ANNv1 model developed in this study provides a tool 

to resource managers to assist in identifying vulnerabilities in 

streams to climate change impacts; to guide stream surveys 

and classification, land-protection strategies, and expenditures 

of financial resources for habitat restoration; and to aid in 

making strategic decisions concerning approaches to climate 

change adaptation to best protect and enhance resiliency in 

stream thermal habitat.
60 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

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64 A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin

Appendix 1. Stream identification information, location information,

agency collecting stream temperature data, number of summers with stream 

temperature data collection, years of stream temperature data collection, 

July mean stream temperature, stream temperature thermal class, and model 

partition for 371 stream temperature modeling sites.

Available as a seperate download. 

Appendix 2. Climate station identification and location information for 160 air

temperature stations. 

Available as a seperate download. 
Publishing support provided by:

U.S. Geological Survey Science Publishing Network,

Columbus and Raleigh Publishing Service Centers

For more information concerning this publication, please contact:

Center Director,

USGS Wisconsin Water Science Center

U.S. Geological Survey

8505 Research Way

Middleton, Wisconsin 53562 

(608) 821-3810

Or visit the USGS Wisconsin Water Science Center Web site at:

http://wi.water.usgs.gov/
J.S. Stewart and others—A Model for Evaluating Stream Temperature Response to Climate Change in Wisconsin—Scientific Investigations Report 2014–5186

ISSN 2328-0328 (online) 

http://dx.doi.org/10.3133/sir20145186