Toward a Regional Stream Temperature Model Through Integration of
Multi-Agency Temperature Databases Using Spatial Statistical Models
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.
Flow-unconnected
Flow-connected
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.
Replace with validation
5U.S. Forest Service, Fish and Aquatic Ecology Unit, Logan, UT.
6U.S. Geological Survey, NRP, Water Resources
Training
left
2007 validation on right
a
Center,onCorvallis,
OR.
Data
from
2007
h
b
7Trout Unlimited, Boise, ID.
Mean Summer Stream Temp
h
(A)
h=a+b
(B)
(C)
Boise River Temperature Models
Non-spatial
Summerparameters
Mean
Stream Temp =
y = –0.93x
+ 0.830
0.0064*Ele
(m)
+ 0.0104*Rad
+ 0.39*AirTemp (C)
– 0.17*Flow (m3/s)
Model
Introduction
Tail-down
19
(C)
25
20
19
15
5
5
10
15
20
25
Training on left
2007 validation on right
9
4
4
9
14
19
Spatial
Multiple
Regression
Summer
Mean Model
MWMT
2
30
ry ==0.93x
0.93;
RMSE = 0.74°C
+ 0.830
19
Summer Mean
y = 0.55x + 7.79
25
14
20
14
15
9
9
10
4
5 4
30
5
(D)
An Example
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.
30
4
9
14
20
19
25
4
MWMT ( C)
Observed
10
15
20
15
5
25
y = 0.55x + 7.79
25
5
20
19
MWMT
10
15
14
30
10
10
9
30
Figure 4.
summer stream
25
temperatures versus observed values for a non-spatial multiple
regression model (top panel)20and the spatial regression model
(bottom panel). Grey line indicates
1:1 relationship; black line is
15
simple linear regression between predicted and observed.
5
y = 0.68x + 3.82
19
Observed
(C°)
y
=
0.86x + mean
2.43
Scatterplots of predicted
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.
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).
30
9
14
Spatial
parameters
MWMT=
Stream Temp
– 0.0045*Ele (m)
y = 0.86x + 2.43
+ 0.0085*Rad
+ 0.48*AirTemp (C)
– 0.11*Flow (m3/s)
Replace with validation
Data from 2007
14
4
4
0.68x + RMSE
3.82
r2y== 0.68;
= 1.54°C
19
9
10
(B)
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.
Predicted (C°)
(A)
Flow
14
Spatial Relationship
Flow-connected
Flow-unconnected
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.
Tail-up
Non-spatialSummer
MultipleMean
Regression Model
Predicted (C°) Predicted ( C)
Flow
Euclidean
30
5
10
15
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
20 that NCEAS
25
30participants will use to develop spatial model applications.
Observed
(C°)
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) spatiallyexplicit representations of model precision (Figure 5).
a
b
Temperature
Increase ( C)
Temperature ( C)
c
Mapping Uncertainty
d
Temperature Prediction Precision
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.
Future 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 nonrandomness 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.
Key Literature:
NCEAS Temperature Project
Spatial Stream Models
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).
South Fork
= Dam
= Wildfires
= Thermograph
= Weather station
= Flow gaging station
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.
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.
Haak, A.L., Williams, J.E., Isaak, D., Todd, A., Muhlfeld, C., Kershner, J.L., Gresswell, R., Hostetler, S., and
Neville, H.M., 2010, The potential influence of changing climate on the persistence of salmonids of the
inland 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 of
climate change and recent wildfires on stream temperature and thermal habitats for two salmonids in a
mountain river network. Ecological Applications 20:1350-1371.
Peterson, E.E., D.M. Theobald, and J.M. Ver Hoef. 2007. Geostatistical modeling on stream networks: developing
valid 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: synthesis
and 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 on
bull trout habitats and populations across the Interior Columbia River basin. Transactions of the American
Fisheries Society 136:1552-1565.
Ver Hoef, J.M., and E.E. Peterson. 2010. A moving average approach for spatial statistical models of stream
networks. 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 stream
distance. 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 trout
distributions 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 of
climate change on four trout species in the western U.S. Proceedings of the National Academy of
Sciences.
Williams, J.E., A.L. Haak, H.M. Neville, W.T. Colyer. 2009. Potential consequences of climate change to
persistence of cutthroat trout populations. North American Journal of Fisheries Management 29:533548.