RIVER RESEARCH AND APPLICATIONS
River Res. Applic. 23: 351–359 (2007)
Published online 20 February 2007 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/rra.985
USING WAVELET ANALYSIS TO DETECT CHANGES IN WATER
TEMPERATURE REGIMES AT MULTIPLE SCALES: EFFECTS OF
MULTI-PURPOSE DAMS IN THE WILLAMETTE RIVER BASINy
E. ASHLEY STEELa* and IAN A. LANGEa,b
a
NW Fisheries Science Center, NOAA Fisheries, 2725 Montlake Blvd E, Seattle, WA 98112, USA
b
Department of Economics, Box 353330, University of Washington, Seattle, WA 98195 USA
ABSTRACT
Maintaining the natural complexity of water temperature regimes is a key to maintaining diverse biological communities. Insect
communities, food webs, and fish respond to the magnitude and duration of water temperature fluctuations. Disruption of these
natural patterns has the potential to alter physiological processes, behavioural adaptations, and community structure and
dynamics. We analysed multiple >300-day time series of water temperature from the Willamette River basin, Oregon, to assess
the impact of large multi-purpose dams on water temperature variability at temporal scales ranging from 1 to 32 days, short
temporal scales that are commonly ignored. We applied wavelet analysis to quantify the variability of water temperature at
multiple temporal scales simultaneously. We compared water temperature regimes above and below dams and before and after
dam construction. The advantages of wavelet analysis are the ability to examine all temporal scales simultaneously and
independently as well as the ability to preserve the temporal context of the wavelet coefficients. We were able to detect
significant ( p < 0.0001) reductions in water temperature variability, defined as the variability of the wavelet coefficients, as a
result of dams at the 1-, 2-, 4-, and 8-day scales. There were no significant differences in water temperature variability between
managed and natural flows at the 16- and 32-day scale ( p ¼ 0.80). In addition to the well-documented effects of dams on
seasonal patterns in water temperature or on water temperature extremes, our results demonstrate that dams have significantly
muted the small temporal scale variance in water temperature patterns to which many organisms may have been
adapted. Conserving or restoring natural temperature patterns in rivers will require attention to these small-scale complexities.
Published in 2007 by John Wiley & Sons, Ltd.
key words: water temperature; variability; river regulation; multi-scale; time series
Received 13 October 2006; Accepted 19 October 2006
INTRODUCTION
Water temperature is a primary regulator of aquatic systems, controlling life cycles of aquatic organisms (Ward and
Stanford, 1979), benthic macroinvertebrate community composition (Krno, 1996; Vinson, 2001), and the
distribution and abundance of fishes (Brett, 1971; Schlosser et al., 2000). While few water temperature metrics
attempt to quantify fluctuations and extremes in natural water temperature regimes (Gaines and Denny, 1993), it is
these complex patterns to which many species of fish and macroinvertebrates are likely adapted (Holtby et al.,
1989; Krno, 1996). There have been few attempts to describe and understand information contained in the
variability exhibited in natural phenomena such as streamwater temperature (Kratz et al., 1995).
We used wavelet analysis on long-term water temperature data from the Willamette River basin, Oregon, to assess the
impact of large multi-purpose dams on water temperature patterns. Large dams have the potential to reduce water
temperature variability at all temporal scales (Petts, 1984). Altered water temperature regimes following dam
construction have been identified in many places (Preece and Jones, 2002; Vinson, 2001). Researchers have documented
changes in mean water temperature, reductions in daily water temperature fluctuations, and shifts in seasonal water
temperature patterns as a result of dams and hydropower (Hains, 1997; USACE, 2000; Preece and Jones, 2002). We
examine temporal scales ranging from 1 to 32 days. Current literature does not examine temporal patterns at scales other
*Correspondence to: E. Ashley Steel, NW Fisheries Science Center, NOAA Fisheries, 2725 Montlake Blvd. East, Seattle, WA 98112, USA.
E-mail: ashley.steel@noaa.gov
y
This article is a U.S. Government work and is in the public domain in the U.S.A.
Published in 2007 by John Wiley & Sons, Ltd.
352
E. A. STEEL AND I. A. LANGE
Figure 1. Water temperature for the gauge below Hills Creek Dam on the Middle Fork Willamette displayed over three time periods: (a) 37 years
of data; (b) 10 years of data; (c) 1 year of data. At the largest scale, a change in water temperature is detectable when the dam was built in the late
1950s and early 1960s. Seasonal fluctuations are obvious but smaller scale water temperature fluctuations are undetectable. At the 10-year scale,
the long-term record of water temperature patterns is no longer visible but a sense of within-season fluctuation is detectable. At the 1-year scale,
patterns in seasonal fluctuations are no longer visible but daily variability is easily detectable.
than daily, seasonal, and annual; therefore, we extend current thinking to consider anthropogenic impacts at intermediate
scales. Without a clear understanding of the degree and scale of anthropogenic change in water temperature regimes, our
ability to restore the natural conditions conducive to native species will be limited.
The number of metrics in current use for describing the complex patterns of temperature in streams and rivers is
enormous, yet none of these metrics consider variability at multiple temporal scales. For example, a change in
annual variability might be detectable at very long temporal scales, but no information about monthly or daily
patterns is detectable at this scale (Figure 1). At shorter temporal scales, monthly and daily patterns are detectable
but the long-term context is lost (Figure 1). In our review of 45 primary research papers and 5 major reviews on
water temperature, we identified over 20 metrics including maximum and minimum daily, monthly, and annual
temperature, weighted-mean migration temperature, critical thermal maxima (CTM), water temperature range,
modal preferred temperature, diel water temperature fluctuation, medial lethal time (LT50), daily and maximum
summer temperature, cumulative degree-day, and average spring temperature. None of these indices capture
fluctuations in water temperature at temporal scales between daily and seasonal; however, organisms may be
adapted to water temperature patterns at these intermediate temporal scales.
Our approach is novel in that we explore effects of dams on the variability of thermal regimes at intermediate
time scales and we apply wavelet analyses to describe and quantify water temperature variability at these multiple
scales simultaneously.
METHODS
Study site
We examined the impact of United States Army Corps of Engineers (USACE) multi-purpose dams on water
temperature regimes in the Willamette River and its tributaries. The Willamette River basin is located in northwestern
Published in 2007 by John Wiley & Sons, Ltd.
River Res. Applic. 23: 351–359 (2007)
DOI: 10.1002/rra
WAVELETS TO DETECT WATER TEMPERATURE CHANGES
353
Oregon (Figure 2). The basin is the human population centre of Oregon; the area of the basin comprises 12% of the
State of Oregon and, in 1990, 68% of the total Oregon population live in the Willamette River basin (Hulse et al., 2002).
Annual precipitation ranges from 1000 to 5500 mm, and increases with elevation. Most precipitation falls from
November through March and highest river flows usually occur in December and January. Winters and summers are
both generally mild in the lowlands with winter lows commonly between 1 and 78C and summer highs between 29
and 358C. Agriculture is the dominant land-use in the lower elevations; private and federal forests dominate the higher
elevations of the watershed. There are 13 large USACE multi-purpose dams inside the Willamette River watershed.
These were completed between 1941 and 1968 (USACE, 2004). They are large dams with storage capacities ranging
from 5930 to 477 700 acre feet (1acre feet ¼ 1233.482 m3). For perspective, the median storage capacity of all dams
in the Willamette River basin is 160 acre feet (StreamNet, 2002).
Figure 2. Map of the Willamette River basin, displaying topography and main tributaries. All 13 USACE large multi-purpose dams are
identified as well the USGS gauges used in our analysis. Stream gauges for which pre-impoundment data were available are distinguished; these
enable the temporal comparison (pre-versus post-impoundment) of water temperature regimes.
Published in 2007 by John Wiley & Sons, Ltd.
River Res. Applic. 23: 351–359 (2007)
DOI: 10.1002/rra
354
E. A. STEEL AND I. A. LANGE
One reason for choosing this set of dams is that they are reported to have shifted seasonal water temperature
patterns in the Willamette River basin (Hains, 1997). The large reservoirs store rainfall and spring snowmelt to
ensure adequate summer water supplies. They release unseasonably cold water from the bottom of the dam in
spring and summer. Unnaturally warm water is then released in the fall (USACE, 2000). These seasonal shifts have
had significant negative impacts on salmon populations via alteration of egg emergence and both juvenile and adult
migration timing (USACE, 2000). Shifts in water temperature regimes at temporal scales smaller than these
seasonal patterns have not been documented except for limited references to reductions in daily fluctuations
(USACE, 1982).
Water temperature data
We acquired daily water temperature data from StreamNet (2002) (e.g. Figure 1). Data are originally from
United States Geological Survey (USGS) gauging stations in the Willamette River basin (Figure 2). We identified
two gauges that allowed a comparison of water temperature regimes before and after dam construction (seven time
series of observations) and 12 gauges that allowed comparison of identical time periods above and below dams. At
these gauges, we identified 19 pairs of time series of daily water temperature data that were at least 300 days in
length between 1952 and 1987 (Table I). We allowed up to three consecutive missing data points in a series and a
total of four missing data points per series. Missing data were interpolated from neighbouring observations.
Interpolation of missing observations was necessary to obtain an adequate sample size of long-term records;
however, the interpolation process provides some minimal reduction in observed variability. In two cases, a pair of
dams was analysed together because the dams were located so closely together that there were no gauges between
them, for example data from a gauge above Green Peter and Foster Dams was compared to data from a gauge below
Green Peter and Foster Dams. Altogether, our analyses considered the effects of 10 of the total 13 large
multi-purpose dams in the Willamette River basin (Figure 2). To maximize the robustness of our analysis, we
utilized all 45 available time series; more than one water temperature data series was analysed for most
comparisons (Table I).
Statistical analysis
We used wavelet analysis to assess whether and at what scale the USACE dams have had an effect on water
temperature regimes in the Willamette River basin. Wavelet analysis examines variability at multiple time scales
simultaneously by decomposing a complicated signal into time–frequency space (Torrence and Compo, 1998). A
discrete wavelet transform is an orthonormal square matrix of filters that is pre-multiplied by a time series of length
N. Pre-multiplying the wavelet filter by the time series gives an N1 matrix of wavelet coefficients. The scale of the
analysis (tj) is proportional to the number of observations analysed. Moving from one time scale to the next larger
time scale doubles the number of non-zero elements (L) in the filter; therefore, small scales have more wavelet
coefficients than large scales. It is generally recommended that the maximum scale of analysis require no more than
10% of the observations in the time series (Percival and Walden, 2000).
We used a member of the Daubechies family of filters, the least asymmetric 8 filter (LA(8)). We interpret the
wavelet coefficients generated by this filter as differences of adjacent averages (Percival and Walden, 2000). We
applied the discrete wavelet transformation to each of the 45 available time series independently. We were able to
examine six simultaneous temporal scales: 1-, 2-, 4-, 8-, 16-, and 32-day. We did not examine the next larger scale,
the 64-day scale, because it would have required more than 10% of the observations in our shortest time series
(303 days). To examine variability in water temperature regimes, we calculated the variability in wavelet
coefficients. Wavelet variances were calculated at each of the six available scales. The wavelet variance formula is
essentially the traditional variance formula, with the wavelet coefficients at each scale replacing a traditional time
series. We calculated a 95% confidence interval around the variance at each scale assuming a Gaussian distribution.
Variability at the 1-day scale describes differences in water temperature patterns among each of many days.
Variability at the 2-day scale describes differences in water temperature patterns among multiple pairs of days, and
variability at the 32-day scale describes differences among monthly water temperature patterns.
To assess whether the large dams in the Willamette River basin impact water temperature regimes at temporal
scales smaller than the documented seasonal shifts, we performed an ordinary least squares (OLS) regression with
Published in 2007 by John Wiley & Sons, Ltd.
River Res. Applic. 23: 351–359 (2007)
DOI: 10.1002/rra
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WAVELETS TO DETECT WATER TEMPERATURE CHANGES
Table I. Dams and data used for both the temporal (before and after dam construction) and the spatial (above and below a dam)
comparisons
Dam
River
USGS site
number
(Operation date)
Pre-dam construction
dates
(Nobs)
Post-dam construction
dates
(Nobs)
Missing data
6/22/61–1/1/69;
5/11/81–2/15/86
(2751; 1742)
8/5/71–11/22/76;
2/4/80–1/25/84
(1937; 1452)
8/31/1963
Temporal Comparisons
Hills Creek
MF Willamette
14148000 (1961)
2/2/52–9/30/56 (1699)
Fall Creek
Fall Creek
14151000 (1966)
12/12/53–12/30/55;
1/5/56–3/25/60
(748; 1540)
5/18/55, 11/14–11/16/55
Spatial Comparisons
Detroit/Big Cliff
N. Santiam
14178000 14181500
Blue River
Blue River
14161100 14162200
(1969)
Hills Creek
MF Willamette
14144800 14145500
(1961)
Cottage Grove
CF Willamette
14152500 14157500
(1942)
Green Peter/
Foster
M. Santiam/
S. Santiam
14185900 14187200
(1968/1968)
Dexter/Lookout
Point
MF Willamette
14148000 14150000
(1954/1954)
7/3/59–3/5/62;
7/27/83–10/23/85;
12/12/85–10/15/87
1/22/76–2/5/77;
8/6/86–6/4/87
(381; 303)
3/3/62–9/1/64;
10/1/68–2/9/70;
7/19/72–3/15/77;
9/27/84–12/28/85
(914; 497; 1701; 458)
6/3/67–9/1/69;
12/14/72–1/20/74
(822; 403)
4/10/74–3/22/76;
11/19/76–9/6/78;
6/28/79–1/24/82;
2/5/85–3/4/86
(713; 657; 942; 393)
8/24/55–9/30/56;
6/12/65–1/2/69;
11/1/75–3/17/77;
6/14/83–5/17/85
(404; 1301; 503; 704)
(977; 820; 673)
(1953/1954)
Above: 5/29/85,
7/15/85, 7/31/85
Below: 12/30/75, 2/3/87
Above: 11/11–11/13/63,
12/21/85
Above: 1/20/74
Above: 4/23/76, 2/5/86
Above: 12/21–12/22/55
Table provides river location, USGS site number, and date at which the dam became operational; dam construction can begin years before the
operation date. Dates of data used in all analyses and identification of missing data are provided.
the variance of the wavelet coefficients as the dependent variable. Potential independent variables included
temporal scale, an indicator variable to describe whether the water had passed through a dam, and median year of
sample data. We also tested for significant interactions between these variables. Six t-tests, using a per test
alpha-level of 0.008 for an overall alpha-level of 0.05, were used to identify the temporal scale(s) responsible for
significant differences between water temperature variability of natural versus managed flow regimes. To test
whether water temperature variability is changing over time due to such factors as global climate change or
increased land-use, we conducted an OLS regression using wavelet variances from the natural river flow data as the
dependent variable and median year of sample data as the independent variable.
RESULTS
Small-scale variability in water temperature regimes was significantly reduced in water that had passed through a
large dam (Figure 3). The best model to describe wavelet coefficient variability included temporal scale and the
indicator for whether the water had passed through a dam (Table II). Median year was marginally significant ( p ¼
Published in 2007 by John Wiley & Sons, Ltd.
River Res. Applic. 23: 351–359 (2007)
DOI: 10.1002/rra
356
E. A. STEEL AND I. A. LANGE
Figure 3. Wavelet variance and 95% confidence intervals for each available time series of water temperature data and for all six scales of
analysis. Water temperature data describing water that has not passed through a dam is represented to the left of the dashed line in each panel.
Water temperature data describing water that has passed through a dam is represented to the right of the dashed line in each panel. Data for the
spatial comparison (above and below dams) are identified with a solid circle. Data for the temporal comparison (before and after dam
construction) are identified with a hollow circle. Scales for the six panels are as follows: (a) 1 day, (b) 2 days, (c) 4 days, (d) 8 days, (e) 16 days,
(f) 32 days. Note: order of time series of water temperature data is maintained among panels. Y-axes differ among panels.
Table II. Regression coefficients, standard errors, t-statistics, and p-values for the best model testing whether dams impact water
temperature variability using all available data (spatial and temporal comparisons)
Independent variable
Constant
Scale
I(Dam)
Coefficient
Standard error
t-Statistic
p-value
0.004
0.130
0.183
0.049
0.011
0.038
0.080
11.765
4.751
0.936
0.000
0.000
The independent variable was the variability of wavelet coefficients at each of six scales, calculated independently for each of 45 times series of
daily water temperature data. I(Dam) is an indicator variable to describe water that has passed through a dam, I(Dam) ¼ 1, versus water that has
not, I(Dam) ¼ 0. The adjusted r-squared for this model is 0.38 and the Akaike’s Information Criterion (AIC) is 0.51 as compared to the AIC value
for the null model of 0.96.
0.059) when entered in a model containing scale and the dam indicator. Inclusion of the interaction between year
and scale was significant ( p ¼ 0.01) but provided only a small reduction in Akaike’s Information Criterion (AIC);
year was no longer even marginally significant when the interaction term was included. In all potential models, the
coefficient for the dam indicator remained between 0.18 and 0.19, indicating that variability below dams is
reduced to not quite one-fifth of the natural variability.
T-tests to identify the temporal scales at which the dam effects occurred found significant differences
( p < 0.0001) between variability in water temperature for water that passed through a dam and water that did not at
1-, 2-, 4-, and 8-day scales; differences in water temperature variability were insignificant at the 16-day scale
( p ¼ 0.06) and 32-day scale ( p ¼ 0.80) (Figure 3).
When the spatial and temporal comparisons were considered independently, we found that the effect of dams was
only statistically significant for the spatial (above and below dam) comparisons and not for the temporal
comparisons (before and after construction) (Table III). For the spatial comparisons alone, the coefficient
Published in 2007 by John Wiley & Sons, Ltd.
River Res. Applic. 23: 351–359 (2007)
DOI: 10.1002/rra
357
WAVELETS TO DETECT WATER TEMPERATURE CHANGES
Table III. Regression coefficients, standard errors, t-statistics, and p-values for the best model testing whether dams impact
water temperature variability using (a) only the spatial comparisons and (b) only temporal comparisons
Independent variable
(a)
Constant
Scale
I(Dam)
(b)
Constant
Scale
I(Dam)
Coefficient
Standard error
t-Statistic
p-value
0.255
0.021
0.232
0.036
0.002
0.039
7.125
11.888
5.914
0.000
0.000
0.000
0.203
0.165
0.086
0.123
0.028
0.097
1.645
5.843
0.888
0.108
0.000
0.380
The independent variable was the variability of wavelet coefficients at each of six scales, calculated independently for each times series of daily
water temperature data (n ¼ 38 for the spatial comparisons and n ¼ 7 for the temporal comparisons). I(Dam) is an indicator variable to describe
water that has passed through a dam, I(Dam) ¼ 1, versus water that has not, I(Dam) ¼ 0. The adjusted r-squared for the model including only the
spatial comparisons is 0.38 and the adjusted r-squared for the model including only the temporal comparisons is 0.45.
Table IV. Regression coefficients, standard errors, t-statistics, and p-values for the model testing whether changes in water
temperature variability occurred over time in naturally flowing waters
Independent variable
Constant
Scale
Time
Coefficient
Standard error
t-Statistic
p-value
0.009
0.129
0.003
0.045
0.012
0.002
0.199
11.149
1.316
0.843
0.000
0.191
The independent variable was the variability of wavelet coefficients at each of six scales, calculated independently for each of 22 times series of
daily water temperature data.
describing the effect of dams was 0.23, indicating that variability is reduced by about 75% below the dams. In the
temporal comparisons, water temperature variability was reduced after dam construction but the change was not
statistically significant, likely because of small sample sizes.
We did not detect long-term trends in water temperature variability of naturally flowing waters. There was no
significant effect of year in which the data were collected on wavelet coefficient variability of water temperatures
for naturally flowing waters (Table IV).
DISCUSSION
We found that the large multi-purpose dams in the Willamette basin reduce variability in water temperature regimes
and that these changes are occurring at small temporal scales, on the order of days to weeks. We did not identify
significant changes in monthly variability. Nor did we identify long-term reductions in water temperature
variability that might have resulted from climate change, altered natural flow regimes, or changing patterns of
land-use in the basin. Reduction of small-scale variation below dams has previously been undetected except for
occasional references to reductions in daily variation, for example USACE, 1982. We found that water temperature
variability was reduced not only at daily scales but also at scales that are rarely investigated such as 2-, 4-, and 8-day
scales. Reduction in variability at these time scales represents a potential threat to the diversity and productivity of
macroinvertebrate and fish communities that has yet to be considered. Restoration aimed at improving thermal
regimes in the basin may be incomplete until impacts of these small-scale changes are understood.
Analysing patterns of variability can yield insights into the forces structuring communities and driving rates of
ecosystem processes (Kratz et al., 1987) and can enable detailed understanding of natural systems (Hokanson et al.,
1977; Kratz et al., 1987; Torgersen et al., 2004). Variability is, however, often considered something to manage or
to reduce in fisheries and ecology, rather than as an important ecological parameter describing changes in
Published in 2007 by John Wiley & Sons, Ltd.
River Res. Applic. 23: 351–359 (2007)
DOI: 10.1002/rra
358
E. A. STEEL AND I. A. LANGE
ecological conditions over time (Kareiva and Bergelson, 1997). Ward (1989) described time as the fourth
key dimension in understanding lotic ecosystems; the way to investigate this fourth dimension is through the
analysis of patterns of variability. One of the difficulties in describing or comparing variability is the perceived lack
of available statistical techniques. Wavelet analysis is an ideal tool for investigating variability because the
technique enables analysis at multiple temporal scales simultaneously, acknowledging the hierarchical nature of
time and space scales in ecology (Csillag and Kabos, 2002; Weins et al., 1986).
Potential new insights from the application of wavelet analysis in ecology are being reported in many areas.
Torgersen et al. (2004) applied wavelet analysis to understand the distribution of fish along 230 linear km of stream
network, and were able to identify periodicity at three spatial scales that corresponded to channel condition, reach,
and landscape variables. Wavelet analysis has been applied in terrestrial ecology where it is often used to explore
vegetation patterns across space, for example, investigating the processes determining plant diversity across
landscapes (Brosofske et al., 1999) and decomposing canopy gap structure (Bradshaw and Spies, 1992).
Furthermore, wavelets are a common tool in geophysics for analysing phenomena such as climate oscillations and
wave formation (Torrence and Compo, 1998).
Wavelet analysis has many ideal statistical properties for the analysis of ecological variability. Like Fourier
coefficients, all of the information in the original data is contained in the wavelet coefficients and so the original time
series can be reconstructed from the coefficients. The advantage of wavelet versus Fourier transformations is that it is
computationally more efficient and scale-independent, looking at multiple scales simultaneously (Torrence and Compo,
1998). Confidence intervals can be derived for wavelet coefficients, enabling statistical significance tests across and
within scale. In addition, software for computing wavelets is becoming readily available (Whitcher, 2003). Our analysis
and the applications of wavelet analysis described above suggest its utility in quantifying and comparing complicated
patterns often found in long time series of ecological data or in detailed spatial data collected over large areas.
Human alterations to water temperature regimes occur in many ways; the fine-scale reductions in water
temperature variability documented here are one example of such alterations. Without a clear understanding of the
complexity of natural patterns and the impacts of anthropogenic change, protection and restoration of natural
patterns will be difficult to achieve (Ward et al., 2001). Summary metrics such as mean summer temperature or
7-day maximum temperature can be a useful indicator of shifts in magnitude of water temperature regimes but the
complexities of natural pattern are not captured using these metrics. We suggest that attention to alterations of
pattern in complex natural phenomena such as water temperature regimes can provide insights into ecological
processes and improve our ability to protect and restore these processes.
ACKNOWLEDGEMENTS
We thank Peter Kiffney, Steve Katz, and Tim Beechie at the Northwest Science Center, Seattle, WA, Mindy
Simmons with the NOAA Fisheries regional office in Portland, OR, Anton Westveld, and Don Percival at the
University of Washington, and two anonymous reviewers for their ideas and constructive manuscript revisions.
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DOI: 10.1002/rra