Toward a Regional Stream Temperature Model Through Integration ofMulti-Agency Temperature Databases Using Spatial Statistical Models

In a pilot study for a larger regional analysis, the spatial

stream models were applied to a large database (n = 780)

of summer stream temperature measurements compiled for

the 2,500 km Boise River network in central Idaho (Figure

3; Isaak et al. 2010). The temperature measurements were

obtained from numerous resource agencies (IDFG, BOR,

USFS, RMRS, DEQ, Boise City) and encompassed a 13

year period from 1993 – 2006.

Stream temperature predictions from the spatial models fit

to these data were precise and unbiased (Figure 4, bottom

panel). Moreover, these results were considerably more

accurate than a traditional, non-spatial regression model

(Figure 4, top panel). Parameter estimates differed between

the spatial and non-spatial temperature models, indicating

that autocorrelation among temperature observations

biased the results of the non-spatial model.

An Example

South Fork

= Thermograph

= Weather station

= Flow gaging station

= Dam

= Wildfires

Figure 3. Boise River basin in central Idaho. Stream temperatures

were recorded with digital temperature sensors at 518 unique sites

from 1993 - 2006 to yield 780 temperature records (some sites

were sampled more than once). Orange and gray polygons show

perimeters of recent wildfires.

Figure 2. Distance measures relevant to stream networks include

Euclidean distance (1a), symmetric instream distance (1b), and

asymmetric instream distance (1c). Covariance matrices using

instream distances may be calculated in “tail-up” or “tail-down”

configurations (2). Tail-up covariances restrict spatial correlation to

“flow-connected” sites, meaning that water must flow downstream

from one site to another. Tail-down covariances allow spatial

correlation between any two “flow-unconnected” sites, and require

only that two sites occur on a network sharing a common outlet.

Tail-up Tail-down

Flo

w-c

onn

ect

ed

Flo

w-u

nco

nn

ect

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Sp

ati

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ela

tio

ns

hip

Model

(A) (C)

(B) (D)

Flo

w

h

(A)

Euclidean

h

(C)

Flow-connected

(B)

ab

h = a + b

Flow-unconnected

Flo

w

Daniel Isaak, Erin Peterson1, Jay Ver Hoef2, Jeff Kershner3, Jason Dunham4, Brett Roper5, Charles Luce, Dona Horan, Gwynne Chandler, Steve Hostetler6, Seth Wenger7, and David Nagel

U.S. Forest Service, Air, Water, and Aquatics Program, Rocky Mountain Research Station, Boise, ID.1CSIRO Mathematical and Information Sciences, Indooroopilly, Queensland, Australia.

2NOAA National Marine Mammal Laboratory, International Arctic Research Center, University of Alaska Fairbanks, Fairbanks, AK.3U.S. Geological Survey, Northern Rocky Mountain Science Center, Bozeman, MT

4U.S. Geological Survey Forest and Rangeland Ecosystem Science Center, Corvallis, OR.5U.S. Forest Service, Fish and Aquatic Ecology Unit, Logan, UT.

6U.S. Geological Survey, NRP, Water Resources Center, Corvallis, OR.7Trout Unlimited, Boise, ID.

Boise River Temperature Models

Training on left 2007 validation on right

y = 0.68x + 3.82

4

9

14

19

4 9 14 19

Summer Mean

y = 0.55x + 7.79

5

10

15

20

25

30

5 10 15 20 25 30

y = 0.86x + 2.43

5

10

15

20

25

30

5 10 15 20 25 30

Summer Mean

MWMT MWMT

y = 0.93x + 0.830

4

9

14

19

4 9 14 19

Pre

dic

ted

(C

°)

Observed (C°)

Replace with validation

Data from 2007

r2 = 0.68; RMSE = 1.54°C

Training on left 2007 validation on right

y = 0.68x + 3.82

4

9

14

19

4 9 14 19

Summer Mean

y = 0.55x + 7.79

5

10

15

20

25

30

5 10 15 20 25 30

y = 0.86x + 2.43

5

10

15

20

25

30

5 10 15 20 25 30

Summer Mean

MWMT MWMT

y = 0.93x + 0.830

4

9

14

19

4 9 14 19

Pre

dic

ted

(C

°)

Observed (C°)

Replace with validation

Data from 2007

r2 = 0.93; RMSE = 0.74°C

Non-spatial Multiple Regression Model

Mean Summer Stream Temp

Observed ( C)

Predic

ted (

C)

Non-spatial parametersStream Temp =– 0.0064*Ele (m)+ 0.0104*Rad+ 0.39*AirTemp (C)– 0.17*Flow (m3/s)

Spatial parametersStream Temp =– 0.0045*Ele (m)+ 0.0085*Rad+ 0.48*AirTemp (C)– 0.11*Flow (m3/s)

Spatial Multiple Regression Model

Figure 4. Scatterplots of predicted mean summer stream

temperatures versus observed values for a non-spatial multiple

regression model (top panel) and the spatial regression model

(bottom panel). Grey line indicates 1:1 relationship; black line is

simple linear regression between predicted and observed.

Once the spatial model is fit to a stream temperature database,

a variety of outputs can be derived that are useful for research

and management (Isaak et al. 2010; Peterson et al. 2010).

These include: a) spatially continuous maps of stream

temperature for addressing water quality concerns, b)

accurate, local assessments of climate change impacts, c)

thermal habitat maps for aquatic species, and d) spatially-

explicit representations of model precision (Figure 5).

TemperatureIncrease ( C)Temperature ( C)

a b

Mapping UncertaintyTemperature Prediction Precisionc d

A broader-scale application of the spatial models is now

underway using a regional stream temperature database as

part of an National Center for Ecological Analysis and

Synthesis (NCEAS) working group (Peterson et al. 2010;

Figure 6). The NCEAS project brings together a diverse

group of statisticians and regional biologists to focus on

extending the functionality of the spatial models to address a

range of potential applications in stream networks. These

applications include: 1) enhanced computational efficiency, 2)

link functions for logit and Poisson response variables, 3)

block kriging applications, 4) space-time models, 5) Bayesian

applications, and 6) monitoring design optimization.

NCEAS Temperature Project Haak, A.L., Williams, J.E., Isaak, D., Todd, A., Muhlfeld, C., Kershner, J.L., Gresswell, R., Hostetler, S., andNeville, H.M., 2010, The potential influence of changing climate on the persistence of salmonids of theinland west: U.S. Geological Survey Open-File Report 2010–1236, 74 p.

Isaak, D.J., C. Luce, B.E. Rieman, D. Nagel, E. Peterson, D. Horan, S. Parkes, and G. Chandler. 2010. Effects ofclimate change and recent wildfires on stream temperature and thermal habitats for two salmonids in amountain river network. Ecological Applications 20:1350-1371.

Peterson, E.E., D.M. Theobald, and J.M. Ver Hoef. 2007. Geostatistical modeling on stream networks: developingvalid covariance matrices based on hydrologic distance and stream flow. Freshwater Biology 52:267-279.

Peterson, E.E., J.M. Ver Hoef, and D.J. Isaak. 2010. Spatial statistical models for stream networks: synthesisand new directions. NCEAS Working Group Proposal, funded.

Rieman, B. E., D. Isaak, S. Adams, D. Horan, D., Nagel, and C. Luce. 2007. Anticipated climate warming effects onbull trout habitats and populations across the Interior Columbia River basin. Transactions of the AmericanFisheries Society 136:1552-1565.

Ver Hoef, J.M., and E.E. Peterson. 2010. A moving average approach for spatial statistical models of streamnetworks. Journal of the American Statistical Association 105:6-18.

Ver Hoef, J.M., E.E. Peterson, and D.M. Theobald. 2006. Spatial statistical models that use flow and streamdistance. Environmental and Ecological Statistics 13:449-464.

Wenger, S. J., D. J. Isaak, J. B. Dunham, K. D. Fausch, C. H. Luce, H. M. Neville, B. E. Rieman, M. K. Young, D. E.Nagel, D. L. Horan, and G. L. Chandler. 2011. Role of climate and invasive species in structuring troutdistributions in the Interior Columbia Basin. Canadian Journal of Fisheries and Aquatic Sciences.

Wenger, S. J., D. J. Isaak, J. B. Dunham, K. D. Fausch, C. H. Luce, H. M. Neville, B. E. Rieman, M. K. Young, D. E.Nagel, D. L. Horan, and G. L. Chandler, A. F. Hamlet, and M. M. Marqeta. In Review. Projected effects ofclimate change on four trout species in the western U.S. Proceedings of the National Academy ofSciences.

Williams, J.E., A.L. Haak, H.M. Neville, W.T. Colyer. 2009. Potential consequences of climate change topersistence of cutthroat trout populations. North American Journal of Fisheries Management 29:533-548.

Key Literature:

Products from the NCEAS project will include a regional stream

temperature model, at least two peer-reviewed papers (one

applying the temperature model and one synthesizing spatial

model applications), advances in statistical theory for streams, and

computer code for running new spatial model applications. The

temperature database will be archived through the NCEAS

program and become a national dataset available for subsequent

analyses by interested researchers.

Figure 6. The NCEAS project domain consists of all fish-bearing streams

(42,000 stream km) within the Lower Snake Hydrologic Region that

encompasses central Idaho, northeast Oregon, and southeast Washington.

Within this area, more than 6,000 summer stream temperature observations

at almost 2,000 unique sites have been compiled into a regional database

that NCEAS participants will use to develop spatial model applications.

Application of spatial statistical models to regional stream

temperature databases provides a means of accurately

predicting stream temperatures across broad areas that could

be used for a variety of purposes. Moreover, these models are

especially well-suited to “found” databases compiled from

multiple agencies that are often plagued by issues of non-

randomness and spatial autocorrelation. As a result, spatial

stream models provide an integrative modeling platform that is

suitable for broad regional and interagency applications. As

the functionality of the spatial models is expanded through the

NCEAS project, numerous applications beyond stream

temperatures can be envisioned that would also draw on large,

georeferenced stream databases compiled by resource

agencies (e.g., fish distribution and abundance, water quality

parameters). In short, spatial models for streams promise to

significantly advance management effectiveness and current

understanding of stream ecosystems by enhancing predictive

accuracy, guiding future data collection efforts more precisely,

and extracting useful information from existing databases.

Future Applications

A warming climate may bring unprecedented changes to

stream ecosystems, with temperature considerations of

great importance, given that most aquatic organisms are

ecto-thermic and confined to river networks that are easily

fragmented. Recent broad-scale assessments of climate

effects on sensitive fishes (Rieman et al. 2007; Williams et

al. 2009; Haak et al. 2010; Wenger et al., 2011, In Review)

have relied on air temperature as a surrogate for stream

temperature but these two variables are often weakly

correlated in mountain streams (Figure 1). Methods for

directly modeling stream temperatures across broad areas

are needed for conservation and planning purposes.

Introduction

Recently, a new class of spatial statistical model has been

developed that incorporates covariance structures which

account for the unique forms of spatial dependence (e.g.,

longitudinal connectivity, flow-volume, and flow-direction)

inherent to stream networks (Ver Hoef et al. 2006; Peterson

et al. 2007). Moreover, the spatial models can use a mixed

model approach for residual errors, thereby allowing multiple

covariance matrices to be combined in a robust and flexible

covariance structure (Figure 2; Ver Hoef and Peterson 2010).

Spatial Stream Models

Figure 1. Scatterplot showing the relationship between air

temperature and stream temperature. The bias and imprecision of

this relationship may incorporate significant uncertainty to

bioclimatic assessments that rely on air temperature.

The advent of inexpensive and reliable digital sensors in the

1990s made collection of stream temperature data

convenient and numerous resource agencies routinely

collect this information. Large regional databases of summer

temperature measurements (i.e., n > 10,000) now exist in

the northwest US that could be used to build a regional

temperature model. One challenge in working with large

databases compiled from multiple sources is that sample

locations are often non-randomly distributed and strongly

clustered in space. These issues can strongly bias

parameter estimates and stream temperature predictions

unless analytical approaches are applied that account for

spatial dependence among sample locations (i.e.,

autocorrelation).