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Coherence between atmospheric teleconnections and Mackenzie River Basin lake levels
Journal of Great Lakes Research 37 (2011) 642–649
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Journal of Great Lakes Research j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j g l r
Coherence between atmospheric teleconnections and Mackenzie River Basin lake levels Sergio Sarmiento a,⁎, Akilan Palanisami b, 1 a b
Lone Star College-Cy Fair, USA Dept. of Physics, University of Houston, Houston, TX, 77004, USA
a r t i c l e
i n f o
Article history: Received 1 December 2010 Accepted 17 June 2011 Available online 14 September 2011 Communicated by Ram Yerubandi Keywords: Lake levels Teleconnections Climate variability Mackenzie River Basin Coherence Aleutian Low
a b s t r a c t Lake Athabasca (LA), Great Slave Lake (GSL) and Great Bear Lake (GBL) lie within the Mackenzie River Basin (MRB), with GBL and GSL being the ninth and tenth largest lakes in the world by volume. How these lake levels fluctuate in time is important in management of the Peace-Athabasca delta, the ecology of these lakes, and for estimating sediment flux. The understanding of how the MRB lake levels interact with atmospheric teleconnections at different time scales may permit enhanced prediction of MRB water levels. Here we compare five teleconnections (North Pacific (NP), Pacific North American (PNA), Pacific Decadal (PDO), El Niño (MEI) and Arctic Oscillations (AO)) with lake water levels using a squared coherence analysis to determine over what timescales these teleconnections play statistically significant roles within the basin. The relevance of these interactions is then examined using power spectral analysis. We find PNA plays a considerable role in the southern half of the MRB over the interdecadal timescale. In contrast, PDO, despite having large interdecadal fluctuations, plays little role in the interdecadal lake water level fluctuations. Over the 1.1–3 year timescale, several teleconnections also show coherence with lake levels but are of less importance due to small water level fluctuations over that timescale. The coherence between LA and GSL water levels is also reduced over the 1.1–3 year timescale and may be related to flow regulation by the W. A. C. Bennett dam. © 2011 International Association for Great Lakes Research. Published by Elsevier B.V. All rights reserved.
Introduction The Mackenzie River Basin (MRB) area is very sensitive to climate (Cohen, 1997) and has experienced the highest year to year climate variability (air temperature and lake ice cover) in the winter for the northern hemisphere during the last 50 years (Kistler et al., 2001; Magnuson et al., 2000; Serreze et al., 2000). Studies of climate variability across Canada have used pattern distributions of river and lake ice phenology (Duguay and Lafleur, 2003; Duguay et al., 2006; Howell et al., 2009; Latifovic and Pouliot, 2007; Lenormand et al., 2002), snow (Brown et al., 2007) and temperature (Bonsal and Prowse, 2003; Bonsal et al., 2001) to evaluate spatial–temporal differences. Important differences in the time trends of these parameters have been observed; however, how lake level across the MRB correlates with climate variability is not well understood. The only study pertaining to this topic found a poor linear correlation between Great Slave Lake water levels and teleconnection indexes for the period 1900–2000 (Gibson et al., 2006).
⁎ Corresponding author. Tel.: + 1 281 290 5234. E-mail addresses: [email protected] (S. Sarmiento), [email protected] (A. Palanisami). 1 Tel.: + 1 713 743 7297.
Teleconnections are large-scale atmospheric and oceanic circulation oscillations characterized by persistent coupled anomalies in ocean surface water temperature, geopotential height, and global atmospheric circulation (Bonsal et al., 2006; Ghanbari and Bravo, 2008; Wallace and Gutzler, 1981). They may play an important role in affecting interannual/interdecadal fluctuations in lake level with this impact varying with latitude. The large lakes in the Mackenzie River Basin (MRB) provide a unique opportunity for investigating such impacts. Lake level changes are strongly correlated with climate change (Magnuson et al., 2000) especially for high latitude lakes (Rouse et al., 2008; Rouse et al., 2005; Schertzer et al., 2003). Significant relationships have been established between teleconnections and surface air temperature (Bonsal and Prowse, 2003) and ice break/freeze-up dates across Canada (Bonsal et al., 2006), including some control points for the MRB. Thus teleconnections may provide information useful in predicting lake levels across the MRB; however, no studies have determined the timescales at which teleconnections may influence MRB lake level variability, and this question is the objective of this paper. Better understanding of the effects of individual teleconnections across the MRB could help predict future lake level changes and thereby contribute to water management of the area as well as regional infrastructure/economic planning (Cohen, 1997; Ghanbari and Bravo, 2008). Here we evaluate the response of lakes in the
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Background
the Great Slave sub-basin (MRBB, 2003) due to past uranium mining and to Great Slave Lake and Lake Athabasca because of activities such as pulp and paper mill operation along the Peace and Athabasca rivers (Evans, 2000). Thus understanding and predicting how MRB lake levels fluctuate can have a broad beneficial impact on environmental and economic planning in the region.
Mackenzie River Basin
Climate variability and teleconnections
The MRB is located in Northern Canada covering 15° of latitude across arctic, subarctic and boreal climatic regions (Fig.1) with the presence of permafrost in 75% of the area covered by the MRB (MAGS, 2005). The largest lakes of the basin are Great Bear Lake (GBL), Great Slave Lake (GSL) and Lake Athabasca (LA), which are of glacial origin with the first two ranking as the ninth and tenth largest lakes of the world by volume (Herdendorf, 1982).GBL is the largest lake in Canada and lies within the Arctic Circle. GSL is the second largest lake in Canada with a maximum depth of 614 m. Its main inflow is the Slave River whose headwaters formed by the confluence of the Peace River and the outflow from Lake Athabasca; the Athabasca River is the major river flowing into the Lake Athabasca although the Peace River contributes flow under certain hydrological conditions, primarily ice jamming and bank overflow. The Peace-Athabasca River Delta (PAD), one of the most productive deltas in the world (Pietroniro et al., 2006; Prowse et al., 2006) is situated on the convergence of all four North American flyways for migratory birds, with millions of ducks, geese, swans, gulls, turns and shorebirds using the delta for nesting, rest or feeding during migration (Timoney, 1995). The Peace River has been regulated since 1967 by the W. A. C. Bennett dam (Gibson et al., 2006). Therefore studying LA and GSL lake level variability contributes to better defining the effects of regulation and climate in the basin and also can be used to better manage regional hydroelectric power (Cohen, 1997). Tug and barge traffic (which moves much of the fuel in the region) also depends on water level with lower levels leading to higher transportation costs (Zdan et al., 1997). Conversely, higher flow in and out of the lakes can contribute to greater sediment movement or flux, which plays an important role in the ecology of Great Slave Lake (MRBB, 2003) and the transport of contaminants in multi-lake systems (Lick, 1982). Contaminant flux has been a concern both in
At a regional scale, an evaluation of the influence of the most significant teleconnections on the climate of the Mackenzie River Basin shows the North Pacific variability modes, including the North Pacific storm track and the Aleutian Low Pressure system, to have an influence on the seasonal and interannual climate variability of the basin (Ioannidou and Yau, 2008a; Ioannidou and Yau, 2008b; Szeto et al., 2007). The circumpolar air stream and the western Rocky Mountains also have an influence on the basin water and energy flows. The Aleutian Low Pressure system refers to cyclonic activity over the North Pacific during the cold season and when the baroclinic systems are active (Lackmann et al., 1998; Smirnov and Moore, 1999; Szeto et al., 2007; Trenberth, 1990). Strong Aleutian Lows are associated with stronger southwesterly onshore winds that increase precipitation and latent heat on the western flanks of the Rockies and warm and dry conditions in the MRB, whereas during weak Aleutian Lows, weaker onshore winds lead to colder conditions in the MRB in the winters (Szeto et al., 2007). The teleconnections associated with the strengthening and weakening of the Aleutian Low correspond to the negative phases of North Pacific Oscillation (NP) (Trenberth and Hurrell, 1994), Arctic Oscillation (Thompson and Wallace, 1998; Wang and Ikeda, 2000) as well as the positive phases of El Niño Southern Oscillation (Wolter and Timlin, 1993; Wolter and Timlin, 1998), Pacific Decadal Oscillation (PDO) (Mantua et al., 1997) and Pacific North American Oscillation (PNA) (Wallace and Gutzler, 1981). High correlation coefficients among the Aleutian Low-related indexes for the period 1960–2008 (NOAA, 2009) support strong connections between NP, PDO, and PNA.
Mackenzie River Basin (MRB) to climate variability by identifying the timescales over which climate oscillations (teleconnections) are correlated with changes of lake level.
Fig. 1. Location of the Mackenzie River Basin with Great Bear Lake in the north and Great Slave and Lake Athabasca in the south.
Methodology Lake level heights fluctuate on a variety of timescales, and these temporal fluctuations can be studied using Fourier analysis (Cohn and Robinson, 1976). Unlike the seasonal fluctuations, the origins of large scale fluctuations remain unclear and different sources have been considered (sunspot activity, lunar pedigree cycle, teleconnections) (Cohn and Robinson, 1976). First we studied how much of the lake level variability can be explained by teleconnection fluctuations by examining the coherence (squared coherence) of the lake levels with several different teleconnections important in the region. The analysis of squared coherence, the frequency equivalent of correlation (Ghanbari and Bravo, 2008), provides information on whether fluctuations at time scale T in the teleconnection are consistently lagging (or leading) the lake level fluctuations at time scale T. This lagging or leading property is called the “phase”, and if the phase is random (i.e. the fluctuations at timescale T of the teleconnection sometimes lags and other times leads the timescale T fluctuations of the lake levels), the squared coherence is small. In contrast, if the average phase is large and consistent (large coherence) the squared coherence will also be large. By looking at the coherence, the timescales at which teleconnection fluctuations and lake level fluctuations are correlated can be inferred. After determining the timescales of coherence, we then study their relative importance by using power spectrum analysis i.e., some timescales show small lake level fluctuations, so even if the coherence between the lake level/teleconnection is significant, the overall effect on the lake is not large. The power spectrum estimates which timescales have significant fluctuation within a time series.
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Lake levels Lake water level data were obtained from the hydrometric database of the Water Survey of Canada (http://www.ec.gc.ca/rhc-wsc/). The lake level time series (Fig. 2) are the average of the following gage stations: Yellowknife and Hay River for GSL, Crackingstone Point and Fort Chipewyan for LA and Port Radium and Hornby Bay for GBL. Lake levels were measured at monthly intervals but had several gaps in the time series, mostly ranging from one to four months, with a maximum gap of ten months in GBL. The power spectrum and squared coherence calculations used here (Jenkins and Watts, 1968) require a continuous time series with no gaps. To fulfill this requirement, we tried various interpolation functions (average value, linear, or cubic spline) to fill the gaps. In the resulting analysis, we found little difference when using different interpolation functions, suggesting the type of interpolation function is not critical to the analysis (at least to the level discussed here). This is reasonable as the gaps reflect a loss of information over a short time scale and should not show up strongly at the interannual time scale studied here. As the choice of interpolation did not matter, we arbitrarily choose the cubic spline interpolation for this study. Power spectrum The power spectrum (or periodogram) provides an estimate of the frequency dependence of the fluctuations within a time series, i.e. the relative importance of long period versus short period oscillations can be discerned. Here we used Welch's averaged modified periodogram method of spectral estimation (Welch, 1967) to estimate the spectrum of a time series (x). The time series was first divided into sections of length N which were individually detrended. The sections were chosen to overlap each other by 75%. Breaking the original time series into multiple sections which were analyzed individually and then averaged effectively smoothed the final power spectrum. To
reduce spectral leakage, a window function (W) of length N was used on these smaller sections to smoothly taper the ends of the section (Hamming window). W ðnÞ = 0:54−0:46 cos 2π
n ð0 ≤ n ≤ N Þ N
ð1Þ
where n is the independent index of the window function. The power spectrum of each section was first calculated individually (pxx), 2 N 1 −inð2πf Þ ∑ W ðnÞe xn pxx ðf Þ = 2πN n = 1
ð2Þ
Where xn is the nth data point within the section, f is the frequency and i is the square root of −1. The results from all sections were then averaged to obtain the average power spectrum (Pxx): Pxx ðf Þ = h pxx ðf Þi
ð3Þ
Where the angle brackets denote the average over all sections. To calculate the confidence level of Pxx, we repeated the analysis using a random (Gaussian, white) time series with the same length and variance as the original data series. This was repeated 1000 times, and a distribution of power spectra from the random time series was generated. The power above which only 5% of the random time series power spectra remained was used as the 95% confidence value. This confidence level calculation was repeated individually for each data set for which power spectral analysis was performed. Squared coherence Squared coherence, the frequency domain equivalent of correlation refers to the leading/lagging relationship between two time series in the frequency domain i.e., how consistently synchronized
Fig. 2. Lake Level Time Series for (a) Great Bear Lake, (b) Great Slave Lake and (c) Lake Athabasca for the period 1960–2008. Observed gaps are the result of no recorded gage readings. Data taken from the hydrometric database of the Water Survey of Canada (http://www.ec.gc.ca/rhc-wsc/).
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they are in terms of phase at particular timescales (Ghanbari and Bravo, 2008; Von Storch and Zwiers, 1999). Squared coherence ranges in values between zero and one and measures the timeaveraged phase correlation, with systems that display inconsistent phase correlation resulting in low squared coherence values (Jenkins and Watts, 1968). High coherence values do not require high amplitude fluctuations. Squared coherence analysis has proven to be a useful method at the Laurentian Great lakes to determine the periods at which correlation occurs between lake level time series that display variability across a broad range of periods, and teleconnection indexes (Ghanbari and Bravo, 2008). Coherence does not necessarily mean causality; however significant coherence values support a correlation between changes in both series (Ghanbari and Bravo, 2008). To calculate the squared coherence of two time series (x and y), we followed the method outlined by Von Storch and Zwiers (1999). Briefly, the time series were divided into sections of length N which were individually detrended. The sections were chosen to overlap each other by 75%. A Hamming window was used on the individual sections. The cross spectrum of each individual section was then calculated (pxy): N N 1 −inð2πf Þ −imð2πf Þ pxy ðf Þ = ∑ W ð n Þe x ∑ W ð m Þe y n m 2πN n = 1 m = 1
ð4Þ
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The average cross spectra (Pxy)was then calculated: D E Pxy ðf Þ = pxy ðf Þ
ð5Þ
The squared coherence (Cxy) is then given by:
Cxy ðf Þ =
2 Pxy ðf Þ Pxx ðf ÞPyy ðf Þ
ð6Þ
In the following analysis, section lengths of 20 years with 75% overlap were used, allowing access to the interannual fluctuations with a reasonable degree of confidence. Other window lengths (18, 10 and 6 years) and overlaps also were studied; all trends discussed subsequently were also reflected in these analyses as well. Two different, random time series will also have a finite squared coherence spectrum. So there is the question of whether or not a measured coherence spectrum is significant. To evaluate if the measured spectrum was statistically different from two random time series, 1000 pairs of random (white, Gaussian) time series were generated, and the squared coherence spectrum between these pairs measured (Monte Carlo analysis); 90% of the squared coherence values fell below a certain value, and this value was used for the 90% confidence level shown in the squared coherence figures (Fig. 3). A similar analysis was done to estimate the 95% confidence level. This
Fig. 3. Squared Coherence analysis between monthly lake levels of Great Bear Lake (GBL), Great Slave Lake (GSL), Lake Athabasca (LA) and monthly teleconnection indexes of Pacific Decadal Oscillation (PDO), Pacific North American Oscillation (PNA), North Pacific Oscillation (NPI), Multivariate ENSO Index (MEI), and Arctic Oscillation (AO) during 1960–2008. Horizontal axis represent period in years. Coherence values in the vertical axis with flat parallel lines representing the values statistically significant at the 90% and 95% confidence level. (a) GBL-PDO. (b) GSL-PDO. (c) LA-PDO. (d) GBL-PNA. (e) GSL-PNA. (f) LA-PNA. (g) GBL-NPI. (h)GSL-NPI. (i) LA-NPI. (j) GBL-MEI. (k) GSL-MEI. (l) LA-MEI. (m) GBL-AO. (n) GSLAO. (o) LA-AO.
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method of estimating confidence levels was first described by Thompson (1979). To account for the effects of data gaps and the subsequent interpolation, the same pattern of gaps which occurred in the lake level data was forced onto the random time series used for the Monte Carlo analysis. Including the gap/interpolation in the Monte Carlo analysis only changed the confidence level by a few percent. This is expected as the gaps remove information from the time series and the subsequent simple interpolations used are unlikely to create phase correlation.
projecting the 1000 mb height anomalies poleward of 20°N onto the loading pattern of the AO. The AO index is important since it describes the pressure over the arctic regions. (Thompson and Wallace, 1998; Wang and Ikeda, 2000). Lower than normal pressure over the Arctic leads to stronger westerlies in the upper atmosphere and subsequent warm phases, while the opposite is the case for the cold phase (http:// jisao.washington.edu/ao/). AO data was taken from (http://www.cpc. ncep.noaa.gov/products/precip/CWlink/daily_ao_index/ao.shtml). Results and discussion
Teleconnections The teleconnection index values used in this study were monthly standardized anomalies. The North Pacific Index (associated with NP), is the area-weighted sea level pressure over the region 30°N–65°N, 160°E–140°W; this index provides a measure of the intensity of the mean wintertime Aleutian Low and was obtained from http://www. cgd.ucar.edu/cas/jhurrell/NPndex.html. The PNA Index represents a mode of low-frequency variability in the northern hemisphere. The PNA positive phase is characterized by higher than a normal ridge over the Rockies and a deeper than normal trough over the Aleutian area and the eastern United States (Yin, 1994). The positive phase is associated with a meridional upper-level flow and the negative phase with a zonal upper-level flow. The PNA characterizes the 700 mb atmospheric flow and is an important component in understanding the low-frequency variability of the mean tropospheric flow over North America (Quiring, 2010). The PNA Index derived from the Wallace and Gutzler (1981) method was obtained from http://www. jisao.washington.edu/data_sets/pna/pna19482009. The PDO Index is based on the pattern of Sea-Surface Temperature (SST) in the North Pacific Ocean poleward of 20°N. PDO represents interdecadal oscillations with events that could persist 20 to 30 years unlike El Niño which last between 6 and 18 months; furthermore, PDO is more influential in the North Pacific of North America whereas El Niño effect is stronger in the tropics (Mantua and Hare, 2002) The PDO data were obtained from http://jisao.washington.edu/pdo/PDO.latest. El Niño is the periodic warming in sea-surface temperatures across the central and east-central equatorial Pacific. Multiple indexes have been developed to describe the El Niño Southern Oscillation (ENSO) and due to its complexity, different areas are better characterized by specific indexes. The Multivariate ENSO Index (MEI) was chosen since it better reflects the coupled ocean–atmosphere system at a more global scale (Wolter and Timlin, 1993; Wolter and Timlin, 1998). This index is based on six observed variables over the tropical Pacific: sea-level pressure, zonal and meridional components of the surface wind, seasurface temperature, surface air temperature, and total cloudiness fraction of the sky (Wolter and Timlin, 1998). The MEI data was obtained from: http://www.esrl.noaa.gov/psd/people/klaus.wolter/ MEI/mei.html. The Arctic Oscillation (AO) is the dominant pattern of non-seasonal sea-level pressure (SLP) variations north of 20°N and is calculated by
We begin by looking at the squared coherence between the lakes of the MRB and several different teleconnections at the interannual and interdecadal periods (Fig. 3). The squared coherence was calculated as in Eq. 6 where f is defined as 1/period. The direct effect or lake level response to a given teleconnection was assumed to take place at the periods whose coherence values were significant at the 90% confidence level or higher. In the 1.1–3 year period range, many of the squared coherence analyses displayed periods of significant coherence. In particular, GSL and LA had an almost identical response to PNA at 1.17, 1.53 and 1.66 year periods (Figs. 3e, f). Similarly, El Niño (MEI) also showed significant squared coherence values with GSL and LA levels at the 1.1–3 year timescale, although the El Niño (MEI) coherence values were lower and the statistically significant periods were not identical between the two lakes as it was for PNA (Figs. 3e, f, k, l). Repeating this analysis using annual values instead of monthly values for the time series displays a similar trend of 1.1– 3 year phase correlation (See Fig A.1 in the appendix). For the ten-year period, the results were clearer. Only PNA and El Niño (MEI) displayed significant squared coherence values at the interdecadal timescale. Once again, the PNA squared coherence showed up strongly in the southern two lakes (GSL and LA), whereas El Niño (MEI) was only significant in GSL. The significant phase correlation found at the 1.1–3 year period and the 10-year period led to the next question; how important were the lake level fluctuations at these timescales? To answer this, we used power spectral analysis. The power spectra of all three lakes (Fig. 4) showed greater fluctuation with longer periods, with the 10year period amplitude fluctuations roughly five times larger than the fluctuations at the 1.1–3 year period. Therefore, 1.1–3 year fluctuations were not as important as the 10-year fluctuations, but were still significant. The power spectra of the teleconnections were also analyzed (Fig. 5). Over the timescales studied, no clear trend in fluctuation amplitude versus period was found. As expected, El Niño MEI showed enhanced fluctuations over a 3–5 year period and PDO showed a strong long period amplitude fluctuation. In contrast, the other teleconnections were relatively flat with period over the 1.1–10 year time scale. Squared coherence was also used to examine temporal correlation between the different lakes of the MRB (Fig. 6). The squared coherence was again calculated as in Eq. 6. GSL and LA showed a
Fig. 4. Power Spectrum Analysis of lake levels of (a) Great Bear Lake, (b) Great Slave Lake and (c) Lake Athabasca for the period 1960–2008. The horizontal line represent the values statistically significant at the 95% confidence level.
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Fig. 5. Power Spectrum Analysis of teleconnection indexes for (a) Pacific Decadal Oscillation—PDO, (b) Pacific North American Oscillation—PNA, (c) North Pacific Index—NP, (d) Multivariate ENSO Index—MEI and (e) Arctic Oscillation—AO, for the period 1960–2008. The horizontal line represent the values statistically significant at the 95% confidence level.
very significant coherence (N95% confidence) over the 3.5–10 year period. For the 1.1–3.5 year period, the coherence became more variable, but still significant. In contrast, GSL and GBL showed no significant coherence over the 1.1–10 year time scale. Interdecadal (10 year period) The squared coherence analysis found significant interdecadal correlations between the southern two lakes (GSL and LA) and PNA (Figs. 3e, f). As the 10-year period lake level fluctuations were relatively large (Fig. 4), this timescale was an important player in the overall lake level variability. To look for the origin of the 10-year period coherence we examined the power spectrum of PNA (Fig. 5b) but the PNA power spectrum revealed no particularly strong fluctuations at the 10-year period. Apparently, 10-year period PNA fluctuations have a disproportionately large coherence with the lake levels in the southern half of the MRB. That the two southern lakes
gave a similar response is not unexpected as both lakes are part of the same catchment, with LA outflow feeding into the Peace River which together form the Slave River, the main inflow to GSL. El Niño (MEI) also gave a significant interdecadal squared coherence with GSL, but not with LA. One possible explanation stems from differences in El Niño's influence on the precipitation patterns of the Peace River sub-basin as compared to the Athabasca River sub-basin (MAGS, 2005). Given the 10-year timescale, PDO may also be expected to play a role in the interdecadal lake levels. Surprisingly, PDO displayed little coherence with any of the lakes at this timescale, despite having sizable interdecadal fluctuations (Fig. 5a). Whatever influence PDO has on the basin lake levels cannot be simply explained by phase correlation. In the Laurentian Great Lakes, Ghanbari and Bravo (2008) found that both PNA and PDO were significantly coherent on the interdecadal time scale. As both the MRB and Laurentian basins are within the four centers of geopotential high anomalies that define the PNA index, a similar response of both basins to PNA could be expected. PDO has also been correlated with flow out of the Liard sub-basin (which drains into the Mackenzie River) by Burn et al. (2004), so the lack of coherence between MRB lake levels and PDO is a non-trivial interaction. Intriguingly, muskrat populations have also been found to have an 11 year cycle (Timoney et al., 1997). A connection between this muskrat cycle and the decadal correlations found here is possible, but a squared coherence analysis of the muskrat population oscillations with the teleconnections has not yet been performed. As muskrat trapping is an important economic activity for native inhabitants of the MRB, correlation of muskrat populations with teleconnections could aid in management of this resource. Long inter-annual (3–7 year period)
Fig. 6. Squared Coherence between lake levels of (a) Great Slave Lake and Lake Athabasca and (b) Great Slave Lake and Great Bear Lake. LA sub-basin is part of the larger GSL sub-basin. Coherence values in the vertical axis with flat parallel lines representing the values statistically significant at the 90% and 95% confidence level.
In the 3–7 year timescale, no significant coherence was found between any lake with any teleconnection. This is somewhat surprising as coherence was found at both longer and shorter periods. This lack of significant coherence was not due to small fluctuations of the teleconnections; all of the teleconnections studied here have substantial fluctuations at the 3–7 year timescale (Fig. 5). It is possible that nonlinear interference between different teleconnections was obscuring the squared coherence signal of any particular teleconnection, resulting in low coherence. Another simpler possibility is that teleconnections were not strongly connected with MRB lake levels at
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these timescales. In the Laurentian great lakes, ENSO was found to be strongly correlated with lake levels at this timescale. However, this is not unexpected as the effects of ENSO are known to be region dependent (Redmond and Koch, 1991; Timoney et al., 1997). Short inter-annual (1.1 to 3 year period) Across the MRB, many of the teleconnections examined had a significant squared coherence in the 1.1–3 year periods. At this time scale, the noise due to the monthly variations in the time series must be considered. The squared coherence looks at phase correlation between the time series, and a statistically significant coherence means the fluctuations between time series (even if they are due to ‘noise’) must be phase correlated. It is unlikely that random noise would be phase correlated between two different time series (this point is the foundation of the Monte Carlo confidence interval calculation described previously). Additionally, repeating the analysis with annual values instead of monthly values gave similar trends (appendix), suggesting the correlations were not due to noise in the monthly values. The preponderance of significant coherence values at this timescale (in contrast to the lack of coherence generally found at the 3–7 year periods) was striking; consideration of these teleconnections could aid in short inter-annual lake level prediction. While the lake level fluctuations at this time scale were only ~ 20% as large as the interdecadal fluctuations (Fig. 4), they were still a nontrivial component of the overall lake level fluctuation. The squared coherence between the AO and GBL was significant at 1.53, 1.66, 2.0, 2.8 year periods (Fig. 3m). The lack of significant coherence between AO and GSL and LA (Fig. 3n, o) indicates the effect of this oscillation was restricted to the northern part of the MRB. El Niño (MEI), on the other hand, showed significant coherence with the southern half of the MRB with several periods within a 1.1– 3 year time scale (Figs. 3k,l). As several agencies put forward predictions of ENSO up to 6 months in advance (Piechota et al., 2006) this correlation may be especially suitable as an aid in forecasting of GSL and LA lake levels on this timescale or for calibration of MRB hydrological models. In contrast, the El Niño MEI-GBL coherence was comparatively weak (Fig. 3j). This lack of coherence supports the interpretation of a weak El Niño effect in the northern part of the basin. NP, which represents the intensity of the wintertime Aleutian Low, is the teleconnection with the greatest number of periods that were significantly in coherence with the levels of GBL, GSL and LA (Figs. 3g, h, i). Those periods differ for GBL (1.33, 1.43, 2.2 years), GSL (1.53, 1.66, 2.0, 2.85 years) and LA (1.11 and 1.66 years) suggesting a period dependent lake response to the Aleutian Low across the MRB. Flow regulation effects Human influence on inflow/outflow from the lakes can affect correlations between climate variability and lake levels. The most significant contribution in this regard is from the W.A.C. Bennett Dam, which has regulated the Peace River since 1967 and impact water levels in Great Slave Lake. However, a daily water balance model for GSL for the period 1964–1998 Gibson et al. (2006) found that the primary driving force behind lake level fluctuation to be climatedriven precipitation variability in the Peace-Athabasca basin and not regulation. In this study, GSL water level at any given year was estimated using Peace-Athabasca basin precipitation data from that year and the prior 2 years (coefficient of determination; r 2 = 0.52). Their findings suggest that for periods larger than 3 years, GSL water level can be predicted by precipitation in the Peace-Athabasca basin (although anthropogenic effects may still play a significant role). To investigate the temporal effects of the dam, we examined the squared coherence of the lake levels between LA and GSL (Fig. 6a) with the rationale that Bennett dam regulation should have a stronger
effect on GSL than LA because of the continuous flow of the Peace River into Great Slave Lake via the Slave River. For four year periods and longer, the two lakes had a highly significant phase correlation, suggesting dam regulation had little effect on the GSL lake level fluctuations at this timescale. However for 3.5 year periods and shorter, the coherence was smaller and more variable. Dam activity may play a role in this reduced phase correlation. Conclusions At the interdecadal timescale, relatively large lake level fluctuations were found in the three largest lakes of the MRB. PNA was significantly coherent at the interdecadal timescale with the lake level fluctuations in the southern half of the basin and may have predictive value in this regard. Coherence with El Nino also occurred at this timescale, but the effect was latitude dependent. At the 1.1–3 year timescales, lake level fluctuations were correlated with a number of teleconnections, but the relationship was latitude and period dependent which complicated the use of teleconnections as predictive tools at this timescale. The lake levels of GSL and LA in the southern half of the basin were found to be strongly coherent at the 4–10 year timescale, suggesting they were strongly linked, whereas the coherence of GSL with GBL was weak over all timescales studied. Since Great Bear Lake is not hydrologically connected to Lake Athabasca and Great Slave Lake basins, this lack of coherence with GBL is expected. Supplementary materials related to this article can be found online at doi:10.1016/j.jglr.2011.08.002. References Bonsal, B.R., Prowse, T.D., 2003. Trends and variability in spring and autumn 0 degrees C-isotherm dates over Canada. Clim. Chang. 57, 341–358. Bonsal, B.R., Shabbar, A., Higuchi, K., 2001. Impacts of low frequency variability modes on Canadian winter temperature. Int. J. Climatol. 21, 95–108. Bonsal, B.R., Prowse, T.D., Duguay, C.R., Lacroix, M.P., 2006. Impacts of large-scale teleconnections on freshwater-ice break/freeze-up dates over Canada. J. Hydrol. 330, 340–353. Brown, R., Derksen, C., Wang, L., 2007. Assessment of spring snow cover duration variability over northern Canada from satellite datasets. Remote. Sens. Environ. 111, 367–381. Burn, D.H., Cunderlik, J.M., Pietroniro, A., 2004. Hydrological trends and variability in the Liard River basin. Hydrol. Sci. 49 (1), 53–67. Cohen, S.J., 1997. Mackenzie Basin Impact Study (MBIS). In: Cohen, S.J. (Ed.), Vancouver. Cohn, B.P., Robinson, J.E., 1976. Forecast model for great lakes water levels. J. Geol. 84, 455–465. Duguay, C.R., Lafleur, P.M., 2003. Determining depth and ice thickness of shallow subArctic lakes using space-borne optical and SAR data. Int. J. Remote. Sens. 24, 475–489. Duguay, C.R., Prowse, T.D., Bonsal, B.R., Brown, R.D., Lacroix, M.P., Menard, P., 2006. Recent trends in Canadian lake ice cover. Hydrol. Process. 20, 781–801. Evans, M.S., 2000. The large lake ecosystems of northern Canada. Aquat. Ecosyst. Heal. Manag. 3, 65–79. Ghanbari, R.N., Bravo, H.R., 2008. Coherence between atmospheric teleconnections, Great Lakes water levels, and regional climate. Adv. Water Res. 31, 1284–1298. Gibson, J.J., Prowse, T.D., Peters, D.L., 2006. Hydroclimatic controls on water balance and water level variability in Great Slave Lake. Hydrol. Process. 20, 4155–4172. Herdendorf, C.E., 1982. Large lakes of the world. J. Great Lakes Res. 8, 379–412. Howell, S.E.L., Brown, L.C., Kang, K.K., Duguay, C.R., 2009. Variability in ice phenology on Great Bear Lake and Great Slave Lake, Northwest Territories, Canada, from SeaWinds/QuikSCAT: 2000–2006. Remote. Sens. Environ. 113, 816–834. Ioannidou, L., Yau, M.K., 2008a. Climatological analysis of the Mackenzie River Basin anticyclones: structure, evolution and interannual variability. In: Woo, M.K. (Ed.), Cold Region Atmospheric and Hydrologic Studies. Springer, Berlin, pp. 51–60. Ioannidou, L., Yau, M.K., 2008b. A climatology of the Northern Hemisphere winter anticyclones. J. Geophys. Res. Atmos. 113 17 pp. Jenkins, G.M., Watts, D.G., 1968. Spectral analysis and its applications. Holden Day. Kistler, R., Kalnay, E., Collins, W., Saha, S., White, G., Woollen, J., Chelliah, M., Ebisuzaki, W., Kanamitsu, M., Kousky, V., van den Dool, H., Jenne, R., Fiorino, M., 2001. The NCEP-NCAR 50-year reanalysis: monthly means CD-ROM and documentation. Bull. Am. Meteorol. Soc. 82, 247–267. Lackmann, G.M., Gyakum, J.R., Benoit, R., 1998. Moisture transport diagnosis of a wintertime precipitation event in the Mackenzie River basin. Mon. Weather. Rev. 126, 668–691. Latifovic, R., Pouliot, D., 2007. Analysis of climate change impacts on lake ice phenology in Canada using the historical satellite data record. Remote. Sens. Environ. 106, 492–507.
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Journal of Great Lakes Research j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j g l r
Coherence between atmospheric teleconnections and Mackenzie River Basin lake levels Sergio Sarmiento a,⁎, Akilan Palanisami b, 1 a b
Lone Star College-Cy Fair, USA Dept. of Physics, University of Houston, Houston, TX, 77004, USA
a r t i c l e
i n f o
Article history: Received 1 December 2010 Accepted 17 June 2011 Available online 14 September 2011 Communicated by Ram Yerubandi Keywords: Lake levels Teleconnections Climate variability Mackenzie River Basin Coherence Aleutian Low
a b s t r a c t Lake Athabasca (LA), Great Slave Lake (GSL) and Great Bear Lake (GBL) lie within the Mackenzie River Basin (MRB), with GBL and GSL being the ninth and tenth largest lakes in the world by volume. How these lake levels fluctuate in time is important in management of the Peace-Athabasca delta, the ecology of these lakes, and for estimating sediment flux. The understanding of how the MRB lake levels interact with atmospheric teleconnections at different time scales may permit enhanced prediction of MRB water levels. Here we compare five teleconnections (North Pacific (NP), Pacific North American (PNA), Pacific Decadal (PDO), El Niño (MEI) and Arctic Oscillations (AO)) with lake water levels using a squared coherence analysis to determine over what timescales these teleconnections play statistically significant roles within the basin. The relevance of these interactions is then examined using power spectral analysis. We find PNA plays a considerable role in the southern half of the MRB over the interdecadal timescale. In contrast, PDO, despite having large interdecadal fluctuations, plays little role in the interdecadal lake water level fluctuations. Over the 1.1–3 year timescale, several teleconnections also show coherence with lake levels but are of less importance due to small water level fluctuations over that timescale. The coherence between LA and GSL water levels is also reduced over the 1.1–3 year timescale and may be related to flow regulation by the W. A. C. Bennett dam. © 2011 International Association for Great Lakes Research. Published by Elsevier B.V. All rights reserved.
Introduction The Mackenzie River Basin (MRB) area is very sensitive to climate (Cohen, 1997) and has experienced the highest year to year climate variability (air temperature and lake ice cover) in the winter for the northern hemisphere during the last 50 years (Kistler et al., 2001; Magnuson et al., 2000; Serreze et al., 2000). Studies of climate variability across Canada have used pattern distributions of river and lake ice phenology (Duguay and Lafleur, 2003; Duguay et al., 2006; Howell et al., 2009; Latifovic and Pouliot, 2007; Lenormand et al., 2002), snow (Brown et al., 2007) and temperature (Bonsal and Prowse, 2003; Bonsal et al., 2001) to evaluate spatial–temporal differences. Important differences in the time trends of these parameters have been observed; however, how lake level across the MRB correlates with climate variability is not well understood. The only study pertaining to this topic found a poor linear correlation between Great Slave Lake water levels and teleconnection indexes for the period 1900–2000 (Gibson et al., 2006).
⁎ Corresponding author. Tel.: + 1 281 290 5234. E-mail addresses: [email protected] (S. Sarmiento), [email protected] (A. Palanisami). 1 Tel.: + 1 713 743 7297.
Teleconnections are large-scale atmospheric and oceanic circulation oscillations characterized by persistent coupled anomalies in ocean surface water temperature, geopotential height, and global atmospheric circulation (Bonsal et al., 2006; Ghanbari and Bravo, 2008; Wallace and Gutzler, 1981). They may play an important role in affecting interannual/interdecadal fluctuations in lake level with this impact varying with latitude. The large lakes in the Mackenzie River Basin (MRB) provide a unique opportunity for investigating such impacts. Lake level changes are strongly correlated with climate change (Magnuson et al., 2000) especially for high latitude lakes (Rouse et al., 2008; Rouse et al., 2005; Schertzer et al., 2003). Significant relationships have been established between teleconnections and surface air temperature (Bonsal and Prowse, 2003) and ice break/freeze-up dates across Canada (Bonsal et al., 2006), including some control points for the MRB. Thus teleconnections may provide information useful in predicting lake levels across the MRB; however, no studies have determined the timescales at which teleconnections may influence MRB lake level variability, and this question is the objective of this paper. Better understanding of the effects of individual teleconnections across the MRB could help predict future lake level changes and thereby contribute to water management of the area as well as regional infrastructure/economic planning (Cohen, 1997; Ghanbari and Bravo, 2008). Here we evaluate the response of lakes in the
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643
Background
the Great Slave sub-basin (MRBB, 2003) due to past uranium mining and to Great Slave Lake and Lake Athabasca because of activities such as pulp and paper mill operation along the Peace and Athabasca rivers (Evans, 2000). Thus understanding and predicting how MRB lake levels fluctuate can have a broad beneficial impact on environmental and economic planning in the region.
Mackenzie River Basin
Climate variability and teleconnections
The MRB is located in Northern Canada covering 15° of latitude across arctic, subarctic and boreal climatic regions (Fig.1) with the presence of permafrost in 75% of the area covered by the MRB (MAGS, 2005). The largest lakes of the basin are Great Bear Lake (GBL), Great Slave Lake (GSL) and Lake Athabasca (LA), which are of glacial origin with the first two ranking as the ninth and tenth largest lakes of the world by volume (Herdendorf, 1982).GBL is the largest lake in Canada and lies within the Arctic Circle. GSL is the second largest lake in Canada with a maximum depth of 614 m. Its main inflow is the Slave River whose headwaters formed by the confluence of the Peace River and the outflow from Lake Athabasca; the Athabasca River is the major river flowing into the Lake Athabasca although the Peace River contributes flow under certain hydrological conditions, primarily ice jamming and bank overflow. The Peace-Athabasca River Delta (PAD), one of the most productive deltas in the world (Pietroniro et al., 2006; Prowse et al., 2006) is situated on the convergence of all four North American flyways for migratory birds, with millions of ducks, geese, swans, gulls, turns and shorebirds using the delta for nesting, rest or feeding during migration (Timoney, 1995). The Peace River has been regulated since 1967 by the W. A. C. Bennett dam (Gibson et al., 2006). Therefore studying LA and GSL lake level variability contributes to better defining the effects of regulation and climate in the basin and also can be used to better manage regional hydroelectric power (Cohen, 1997). Tug and barge traffic (which moves much of the fuel in the region) also depends on water level with lower levels leading to higher transportation costs (Zdan et al., 1997). Conversely, higher flow in and out of the lakes can contribute to greater sediment movement or flux, which plays an important role in the ecology of Great Slave Lake (MRBB, 2003) and the transport of contaminants in multi-lake systems (Lick, 1982). Contaminant flux has been a concern both in
At a regional scale, an evaluation of the influence of the most significant teleconnections on the climate of the Mackenzie River Basin shows the North Pacific variability modes, including the North Pacific storm track and the Aleutian Low Pressure system, to have an influence on the seasonal and interannual climate variability of the basin (Ioannidou and Yau, 2008a; Ioannidou and Yau, 2008b; Szeto et al., 2007). The circumpolar air stream and the western Rocky Mountains also have an influence on the basin water and energy flows. The Aleutian Low Pressure system refers to cyclonic activity over the North Pacific during the cold season and when the baroclinic systems are active (Lackmann et al., 1998; Smirnov and Moore, 1999; Szeto et al., 2007; Trenberth, 1990). Strong Aleutian Lows are associated with stronger southwesterly onshore winds that increase precipitation and latent heat on the western flanks of the Rockies and warm and dry conditions in the MRB, whereas during weak Aleutian Lows, weaker onshore winds lead to colder conditions in the MRB in the winters (Szeto et al., 2007). The teleconnections associated with the strengthening and weakening of the Aleutian Low correspond to the negative phases of North Pacific Oscillation (NP) (Trenberth and Hurrell, 1994), Arctic Oscillation (Thompson and Wallace, 1998; Wang and Ikeda, 2000) as well as the positive phases of El Niño Southern Oscillation (Wolter and Timlin, 1993; Wolter and Timlin, 1998), Pacific Decadal Oscillation (PDO) (Mantua et al., 1997) and Pacific North American Oscillation (PNA) (Wallace and Gutzler, 1981). High correlation coefficients among the Aleutian Low-related indexes for the period 1960–2008 (NOAA, 2009) support strong connections between NP, PDO, and PNA.
Mackenzie River Basin (MRB) to climate variability by identifying the timescales over which climate oscillations (teleconnections) are correlated with changes of lake level.
Fig. 1. Location of the Mackenzie River Basin with Great Bear Lake in the north and Great Slave and Lake Athabasca in the south.
Methodology Lake level heights fluctuate on a variety of timescales, and these temporal fluctuations can be studied using Fourier analysis (Cohn and Robinson, 1976). Unlike the seasonal fluctuations, the origins of large scale fluctuations remain unclear and different sources have been considered (sunspot activity, lunar pedigree cycle, teleconnections) (Cohn and Robinson, 1976). First we studied how much of the lake level variability can be explained by teleconnection fluctuations by examining the coherence (squared coherence) of the lake levels with several different teleconnections important in the region. The analysis of squared coherence, the frequency equivalent of correlation (Ghanbari and Bravo, 2008), provides information on whether fluctuations at time scale T in the teleconnection are consistently lagging (or leading) the lake level fluctuations at time scale T. This lagging or leading property is called the “phase”, and if the phase is random (i.e. the fluctuations at timescale T of the teleconnection sometimes lags and other times leads the timescale T fluctuations of the lake levels), the squared coherence is small. In contrast, if the average phase is large and consistent (large coherence) the squared coherence will also be large. By looking at the coherence, the timescales at which teleconnection fluctuations and lake level fluctuations are correlated can be inferred. After determining the timescales of coherence, we then study their relative importance by using power spectrum analysis i.e., some timescales show small lake level fluctuations, so even if the coherence between the lake level/teleconnection is significant, the overall effect on the lake is not large. The power spectrum estimates which timescales have significant fluctuation within a time series.
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Lake levels Lake water level data were obtained from the hydrometric database of the Water Survey of Canada (http://www.ec.gc.ca/rhc-wsc/). The lake level time series (Fig. 2) are the average of the following gage stations: Yellowknife and Hay River for GSL, Crackingstone Point and Fort Chipewyan for LA and Port Radium and Hornby Bay for GBL. Lake levels were measured at monthly intervals but had several gaps in the time series, mostly ranging from one to four months, with a maximum gap of ten months in GBL. The power spectrum and squared coherence calculations used here (Jenkins and Watts, 1968) require a continuous time series with no gaps. To fulfill this requirement, we tried various interpolation functions (average value, linear, or cubic spline) to fill the gaps. In the resulting analysis, we found little difference when using different interpolation functions, suggesting the type of interpolation function is not critical to the analysis (at least to the level discussed here). This is reasonable as the gaps reflect a loss of information over a short time scale and should not show up strongly at the interannual time scale studied here. As the choice of interpolation did not matter, we arbitrarily choose the cubic spline interpolation for this study. Power spectrum The power spectrum (or periodogram) provides an estimate of the frequency dependence of the fluctuations within a time series, i.e. the relative importance of long period versus short period oscillations can be discerned. Here we used Welch's averaged modified periodogram method of spectral estimation (Welch, 1967) to estimate the spectrum of a time series (x). The time series was first divided into sections of length N which were individually detrended. The sections were chosen to overlap each other by 75%. Breaking the original time series into multiple sections which were analyzed individually and then averaged effectively smoothed the final power spectrum. To
reduce spectral leakage, a window function (W) of length N was used on these smaller sections to smoothly taper the ends of the section (Hamming window). W ðnÞ = 0:54−0:46 cos 2π
n ð0 ≤ n ≤ N Þ N
ð1Þ
where n is the independent index of the window function. The power spectrum of each section was first calculated individually (pxx), 2 N 1 −inð2πf Þ ∑ W ðnÞe xn pxx ðf Þ = 2πN n = 1
ð2Þ
Where xn is the nth data point within the section, f is the frequency and i is the square root of −1. The results from all sections were then averaged to obtain the average power spectrum (Pxx): Pxx ðf Þ = h pxx ðf Þi
ð3Þ
Where the angle brackets denote the average over all sections. To calculate the confidence level of Pxx, we repeated the analysis using a random (Gaussian, white) time series with the same length and variance as the original data series. This was repeated 1000 times, and a distribution of power spectra from the random time series was generated. The power above which only 5% of the random time series power spectra remained was used as the 95% confidence value. This confidence level calculation was repeated individually for each data set for which power spectral analysis was performed. Squared coherence Squared coherence, the frequency domain equivalent of correlation refers to the leading/lagging relationship between two time series in the frequency domain i.e., how consistently synchronized
Fig. 2. Lake Level Time Series for (a) Great Bear Lake, (b) Great Slave Lake and (c) Lake Athabasca for the period 1960–2008. Observed gaps are the result of no recorded gage readings. Data taken from the hydrometric database of the Water Survey of Canada (http://www.ec.gc.ca/rhc-wsc/).
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they are in terms of phase at particular timescales (Ghanbari and Bravo, 2008; Von Storch and Zwiers, 1999). Squared coherence ranges in values between zero and one and measures the timeaveraged phase correlation, with systems that display inconsistent phase correlation resulting in low squared coherence values (Jenkins and Watts, 1968). High coherence values do not require high amplitude fluctuations. Squared coherence analysis has proven to be a useful method at the Laurentian Great lakes to determine the periods at which correlation occurs between lake level time series that display variability across a broad range of periods, and teleconnection indexes (Ghanbari and Bravo, 2008). Coherence does not necessarily mean causality; however significant coherence values support a correlation between changes in both series (Ghanbari and Bravo, 2008). To calculate the squared coherence of two time series (x and y), we followed the method outlined by Von Storch and Zwiers (1999). Briefly, the time series were divided into sections of length N which were individually detrended. The sections were chosen to overlap each other by 75%. A Hamming window was used on the individual sections. The cross spectrum of each individual section was then calculated (pxy): N N 1 −inð2πf Þ −imð2πf Þ pxy ðf Þ = ∑ W ð n Þe x ∑ W ð m Þe y n m 2πN n = 1 m = 1
ð4Þ
645
The average cross spectra (Pxy)was then calculated: D E Pxy ðf Þ = pxy ðf Þ
ð5Þ
The squared coherence (Cxy) is then given by:
Cxy ðf Þ =
2 Pxy ðf Þ Pxx ðf ÞPyy ðf Þ
ð6Þ
In the following analysis, section lengths of 20 years with 75% overlap were used, allowing access to the interannual fluctuations with a reasonable degree of confidence. Other window lengths (18, 10 and 6 years) and overlaps also were studied; all trends discussed subsequently were also reflected in these analyses as well. Two different, random time series will also have a finite squared coherence spectrum. So there is the question of whether or not a measured coherence spectrum is significant. To evaluate if the measured spectrum was statistically different from two random time series, 1000 pairs of random (white, Gaussian) time series were generated, and the squared coherence spectrum between these pairs measured (Monte Carlo analysis); 90% of the squared coherence values fell below a certain value, and this value was used for the 90% confidence level shown in the squared coherence figures (Fig. 3). A similar analysis was done to estimate the 95% confidence level. This
Fig. 3. Squared Coherence analysis between monthly lake levels of Great Bear Lake (GBL), Great Slave Lake (GSL), Lake Athabasca (LA) and monthly teleconnection indexes of Pacific Decadal Oscillation (PDO), Pacific North American Oscillation (PNA), North Pacific Oscillation (NPI), Multivariate ENSO Index (MEI), and Arctic Oscillation (AO) during 1960–2008. Horizontal axis represent period in years. Coherence values in the vertical axis with flat parallel lines representing the values statistically significant at the 90% and 95% confidence level. (a) GBL-PDO. (b) GSL-PDO. (c) LA-PDO. (d) GBL-PNA. (e) GSL-PNA. (f) LA-PNA. (g) GBL-NPI. (h)GSL-NPI. (i) LA-NPI. (j) GBL-MEI. (k) GSL-MEI. (l) LA-MEI. (m) GBL-AO. (n) GSLAO. (o) LA-AO.
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method of estimating confidence levels was first described by Thompson (1979). To account for the effects of data gaps and the subsequent interpolation, the same pattern of gaps which occurred in the lake level data was forced onto the random time series used for the Monte Carlo analysis. Including the gap/interpolation in the Monte Carlo analysis only changed the confidence level by a few percent. This is expected as the gaps remove information from the time series and the subsequent simple interpolations used are unlikely to create phase correlation.
projecting the 1000 mb height anomalies poleward of 20°N onto the loading pattern of the AO. The AO index is important since it describes the pressure over the arctic regions. (Thompson and Wallace, 1998; Wang and Ikeda, 2000). Lower than normal pressure over the Arctic leads to stronger westerlies in the upper atmosphere and subsequent warm phases, while the opposite is the case for the cold phase (http:// jisao.washington.edu/ao/). AO data was taken from (http://www.cpc. ncep.noaa.gov/products/precip/CWlink/daily_ao_index/ao.shtml). Results and discussion
Teleconnections The teleconnection index values used in this study were monthly standardized anomalies. The North Pacific Index (associated with NP), is the area-weighted sea level pressure over the region 30°N–65°N, 160°E–140°W; this index provides a measure of the intensity of the mean wintertime Aleutian Low and was obtained from http://www. cgd.ucar.edu/cas/jhurrell/NPndex.html. The PNA Index represents a mode of low-frequency variability in the northern hemisphere. The PNA positive phase is characterized by higher than a normal ridge over the Rockies and a deeper than normal trough over the Aleutian area and the eastern United States (Yin, 1994). The positive phase is associated with a meridional upper-level flow and the negative phase with a zonal upper-level flow. The PNA characterizes the 700 mb atmospheric flow and is an important component in understanding the low-frequency variability of the mean tropospheric flow over North America (Quiring, 2010). The PNA Index derived from the Wallace and Gutzler (1981) method was obtained from http://www. jisao.washington.edu/data_sets/pna/pna19482009. The PDO Index is based on the pattern of Sea-Surface Temperature (SST) in the North Pacific Ocean poleward of 20°N. PDO represents interdecadal oscillations with events that could persist 20 to 30 years unlike El Niño which last between 6 and 18 months; furthermore, PDO is more influential in the North Pacific of North America whereas El Niño effect is stronger in the tropics (Mantua and Hare, 2002) The PDO data were obtained from http://jisao.washington.edu/pdo/PDO.latest. El Niño is the periodic warming in sea-surface temperatures across the central and east-central equatorial Pacific. Multiple indexes have been developed to describe the El Niño Southern Oscillation (ENSO) and due to its complexity, different areas are better characterized by specific indexes. The Multivariate ENSO Index (MEI) was chosen since it better reflects the coupled ocean–atmosphere system at a more global scale (Wolter and Timlin, 1993; Wolter and Timlin, 1998). This index is based on six observed variables over the tropical Pacific: sea-level pressure, zonal and meridional components of the surface wind, seasurface temperature, surface air temperature, and total cloudiness fraction of the sky (Wolter and Timlin, 1998). The MEI data was obtained from: http://www.esrl.noaa.gov/psd/people/klaus.wolter/ MEI/mei.html. The Arctic Oscillation (AO) is the dominant pattern of non-seasonal sea-level pressure (SLP) variations north of 20°N and is calculated by
We begin by looking at the squared coherence between the lakes of the MRB and several different teleconnections at the interannual and interdecadal periods (Fig. 3). The squared coherence was calculated as in Eq. 6 where f is defined as 1/period. The direct effect or lake level response to a given teleconnection was assumed to take place at the periods whose coherence values were significant at the 90% confidence level or higher. In the 1.1–3 year period range, many of the squared coherence analyses displayed periods of significant coherence. In particular, GSL and LA had an almost identical response to PNA at 1.17, 1.53 and 1.66 year periods (Figs. 3e, f). Similarly, El Niño (MEI) also showed significant squared coherence values with GSL and LA levels at the 1.1–3 year timescale, although the El Niño (MEI) coherence values were lower and the statistically significant periods were not identical between the two lakes as it was for PNA (Figs. 3e, f, k, l). Repeating this analysis using annual values instead of monthly values for the time series displays a similar trend of 1.1– 3 year phase correlation (See Fig A.1 in the appendix). For the ten-year period, the results were clearer. Only PNA and El Niño (MEI) displayed significant squared coherence values at the interdecadal timescale. Once again, the PNA squared coherence showed up strongly in the southern two lakes (GSL and LA), whereas El Niño (MEI) was only significant in GSL. The significant phase correlation found at the 1.1–3 year period and the 10-year period led to the next question; how important were the lake level fluctuations at these timescales? To answer this, we used power spectral analysis. The power spectra of all three lakes (Fig. 4) showed greater fluctuation with longer periods, with the 10year period amplitude fluctuations roughly five times larger than the fluctuations at the 1.1–3 year period. Therefore, 1.1–3 year fluctuations were not as important as the 10-year fluctuations, but were still significant. The power spectra of the teleconnections were also analyzed (Fig. 5). Over the timescales studied, no clear trend in fluctuation amplitude versus period was found. As expected, El Niño MEI showed enhanced fluctuations over a 3–5 year period and PDO showed a strong long period amplitude fluctuation. In contrast, the other teleconnections were relatively flat with period over the 1.1–10 year time scale. Squared coherence was also used to examine temporal correlation between the different lakes of the MRB (Fig. 6). The squared coherence was again calculated as in Eq. 6. GSL and LA showed a
Fig. 4. Power Spectrum Analysis of lake levels of (a) Great Bear Lake, (b) Great Slave Lake and (c) Lake Athabasca for the period 1960–2008. The horizontal line represent the values statistically significant at the 95% confidence level.
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Fig. 5. Power Spectrum Analysis of teleconnection indexes for (a) Pacific Decadal Oscillation—PDO, (b) Pacific North American Oscillation—PNA, (c) North Pacific Index—NP, (d) Multivariate ENSO Index—MEI and (e) Arctic Oscillation—AO, for the period 1960–2008. The horizontal line represent the values statistically significant at the 95% confidence level.
very significant coherence (N95% confidence) over the 3.5–10 year period. For the 1.1–3.5 year period, the coherence became more variable, but still significant. In contrast, GSL and GBL showed no significant coherence over the 1.1–10 year time scale. Interdecadal (10 year period) The squared coherence analysis found significant interdecadal correlations between the southern two lakes (GSL and LA) and PNA (Figs. 3e, f). As the 10-year period lake level fluctuations were relatively large (Fig. 4), this timescale was an important player in the overall lake level variability. To look for the origin of the 10-year period coherence we examined the power spectrum of PNA (Fig. 5b) but the PNA power spectrum revealed no particularly strong fluctuations at the 10-year period. Apparently, 10-year period PNA fluctuations have a disproportionately large coherence with the lake levels in the southern half of the MRB. That the two southern lakes
gave a similar response is not unexpected as both lakes are part of the same catchment, with LA outflow feeding into the Peace River which together form the Slave River, the main inflow to GSL. El Niño (MEI) also gave a significant interdecadal squared coherence with GSL, but not with LA. One possible explanation stems from differences in El Niño's influence on the precipitation patterns of the Peace River sub-basin as compared to the Athabasca River sub-basin (MAGS, 2005). Given the 10-year timescale, PDO may also be expected to play a role in the interdecadal lake levels. Surprisingly, PDO displayed little coherence with any of the lakes at this timescale, despite having sizable interdecadal fluctuations (Fig. 5a). Whatever influence PDO has on the basin lake levels cannot be simply explained by phase correlation. In the Laurentian Great Lakes, Ghanbari and Bravo (2008) found that both PNA and PDO were significantly coherent on the interdecadal time scale. As both the MRB and Laurentian basins are within the four centers of geopotential high anomalies that define the PNA index, a similar response of both basins to PNA could be expected. PDO has also been correlated with flow out of the Liard sub-basin (which drains into the Mackenzie River) by Burn et al. (2004), so the lack of coherence between MRB lake levels and PDO is a non-trivial interaction. Intriguingly, muskrat populations have also been found to have an 11 year cycle (Timoney et al., 1997). A connection between this muskrat cycle and the decadal correlations found here is possible, but a squared coherence analysis of the muskrat population oscillations with the teleconnections has not yet been performed. As muskrat trapping is an important economic activity for native inhabitants of the MRB, correlation of muskrat populations with teleconnections could aid in management of this resource. Long inter-annual (3–7 year period)
Fig. 6. Squared Coherence between lake levels of (a) Great Slave Lake and Lake Athabasca and (b) Great Slave Lake and Great Bear Lake. LA sub-basin is part of the larger GSL sub-basin. Coherence values in the vertical axis with flat parallel lines representing the values statistically significant at the 90% and 95% confidence level.
In the 3–7 year timescale, no significant coherence was found between any lake with any teleconnection. This is somewhat surprising as coherence was found at both longer and shorter periods. This lack of significant coherence was not due to small fluctuations of the teleconnections; all of the teleconnections studied here have substantial fluctuations at the 3–7 year timescale (Fig. 5). It is possible that nonlinear interference between different teleconnections was obscuring the squared coherence signal of any particular teleconnection, resulting in low coherence. Another simpler possibility is that teleconnections were not strongly connected with MRB lake levels at
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these timescales. In the Laurentian great lakes, ENSO was found to be strongly correlated with lake levels at this timescale. However, this is not unexpected as the effects of ENSO are known to be region dependent (Redmond and Koch, 1991; Timoney et al., 1997). Short inter-annual (1.1 to 3 year period) Across the MRB, many of the teleconnections examined had a significant squared coherence in the 1.1–3 year periods. At this time scale, the noise due to the monthly variations in the time series must be considered. The squared coherence looks at phase correlation between the time series, and a statistically significant coherence means the fluctuations between time series (even if they are due to ‘noise’) must be phase correlated. It is unlikely that random noise would be phase correlated between two different time series (this point is the foundation of the Monte Carlo confidence interval calculation described previously). Additionally, repeating the analysis with annual values instead of monthly values gave similar trends (appendix), suggesting the correlations were not due to noise in the monthly values. The preponderance of significant coherence values at this timescale (in contrast to the lack of coherence generally found at the 3–7 year periods) was striking; consideration of these teleconnections could aid in short inter-annual lake level prediction. While the lake level fluctuations at this time scale were only ~ 20% as large as the interdecadal fluctuations (Fig. 4), they were still a nontrivial component of the overall lake level fluctuation. The squared coherence between the AO and GBL was significant at 1.53, 1.66, 2.0, 2.8 year periods (Fig. 3m). The lack of significant coherence between AO and GSL and LA (Fig. 3n, o) indicates the effect of this oscillation was restricted to the northern part of the MRB. El Niño (MEI), on the other hand, showed significant coherence with the southern half of the MRB with several periods within a 1.1– 3 year time scale (Figs. 3k,l). As several agencies put forward predictions of ENSO up to 6 months in advance (Piechota et al., 2006) this correlation may be especially suitable as an aid in forecasting of GSL and LA lake levels on this timescale or for calibration of MRB hydrological models. In contrast, the El Niño MEI-GBL coherence was comparatively weak (Fig. 3j). This lack of coherence supports the interpretation of a weak El Niño effect in the northern part of the basin. NP, which represents the intensity of the wintertime Aleutian Low, is the teleconnection with the greatest number of periods that were significantly in coherence with the levels of GBL, GSL and LA (Figs. 3g, h, i). Those periods differ for GBL (1.33, 1.43, 2.2 years), GSL (1.53, 1.66, 2.0, 2.85 years) and LA (1.11 and 1.66 years) suggesting a period dependent lake response to the Aleutian Low across the MRB. Flow regulation effects Human influence on inflow/outflow from the lakes can affect correlations between climate variability and lake levels. The most significant contribution in this regard is from the W.A.C. Bennett Dam, which has regulated the Peace River since 1967 and impact water levels in Great Slave Lake. However, a daily water balance model for GSL for the period 1964–1998 Gibson et al. (2006) found that the primary driving force behind lake level fluctuation to be climatedriven precipitation variability in the Peace-Athabasca basin and not regulation. In this study, GSL water level at any given year was estimated using Peace-Athabasca basin precipitation data from that year and the prior 2 years (coefficient of determination; r 2 = 0.52). Their findings suggest that for periods larger than 3 years, GSL water level can be predicted by precipitation in the Peace-Athabasca basin (although anthropogenic effects may still play a significant role). To investigate the temporal effects of the dam, we examined the squared coherence of the lake levels between LA and GSL (Fig. 6a) with the rationale that Bennett dam regulation should have a stronger
effect on GSL than LA because of the continuous flow of the Peace River into Great Slave Lake via the Slave River. For four year periods and longer, the two lakes had a highly significant phase correlation, suggesting dam regulation had little effect on the GSL lake level fluctuations at this timescale. However for 3.5 year periods and shorter, the coherence was smaller and more variable. Dam activity may play a role in this reduced phase correlation. Conclusions At the interdecadal timescale, relatively large lake level fluctuations were found in the three largest lakes of the MRB. PNA was significantly coherent at the interdecadal timescale with the lake level fluctuations in the southern half of the basin and may have predictive value in this regard. Coherence with El Nino also occurred at this timescale, but the effect was latitude dependent. At the 1.1–3 year timescales, lake level fluctuations were correlated with a number of teleconnections, but the relationship was latitude and period dependent which complicated the use of teleconnections as predictive tools at this timescale. The lake levels of GSL and LA in the southern half of the basin were found to be strongly coherent at the 4–10 year timescale, suggesting they were strongly linked, whereas the coherence of GSL with GBL was weak over all timescales studied. Since Great Bear Lake is not hydrologically connected to Lake Athabasca and Great Slave Lake basins, this lack of coherence with GBL is expected. Supplementary materials related to this article can be found online at doi:10.1016/j.jglr.2011.08.002. References Bonsal, B.R., Prowse, T.D., 2003. Trends and variability in spring and autumn 0 degrees C-isotherm dates over Canada. Clim. Chang. 57, 341–358. Bonsal, B.R., Shabbar, A., Higuchi, K., 2001. Impacts of low frequency variability modes on Canadian winter temperature. Int. J. Climatol. 21, 95–108. Bonsal, B.R., Prowse, T.D., Duguay, C.R., Lacroix, M.P., 2006. Impacts of large-scale teleconnections on freshwater-ice break/freeze-up dates over Canada. J. Hydrol. 330, 340–353. Brown, R., Derksen, C., Wang, L., 2007. Assessment of spring snow cover duration variability over northern Canada from satellite datasets. Remote. Sens. Environ. 111, 367–381. Burn, D.H., Cunderlik, J.M., Pietroniro, A., 2004. Hydrological trends and variability in the Liard River basin. Hydrol. Sci. 49 (1), 53–67. Cohen, S.J., 1997. Mackenzie Basin Impact Study (MBIS). In: Cohen, S.J. (Ed.), Vancouver. Cohn, B.P., Robinson, J.E., 1976. Forecast model for great lakes water levels. J. Geol. 84, 455–465. Duguay, C.R., Lafleur, P.M., 2003. Determining depth and ice thickness of shallow subArctic lakes using space-borne optical and SAR data. Int. J. Remote. Sens. 24, 475–489. Duguay, C.R., Prowse, T.D., Bonsal, B.R., Brown, R.D., Lacroix, M.P., Menard, P., 2006. Recent trends in Canadian lake ice cover. Hydrol. Process. 20, 781–801. Evans, M.S., 2000. The large lake ecosystems of northern Canada. Aquat. Ecosyst. Heal. Manag. 3, 65–79. Ghanbari, R.N., Bravo, H.R., 2008. Coherence between atmospheric teleconnections, Great Lakes water levels, and regional climate. Adv. Water Res. 31, 1284–1298. Gibson, J.J., Prowse, T.D., Peters, D.L., 2006. Hydroclimatic controls on water balance and water level variability in Great Slave Lake. Hydrol. Process. 20, 4155–4172. Herdendorf, C.E., 1982. Large lakes of the world. J. Great Lakes Res. 8, 379–412. Howell, S.E.L., Brown, L.C., Kang, K.K., Duguay, C.R., 2009. Variability in ice phenology on Great Bear Lake and Great Slave Lake, Northwest Territories, Canada, from SeaWinds/QuikSCAT: 2000–2006. Remote. Sens. Environ. 113, 816–834. Ioannidou, L., Yau, M.K., 2008a. Climatological analysis of the Mackenzie River Basin anticyclones: structure, evolution and interannual variability. In: Woo, M.K. (Ed.), Cold Region Atmospheric and Hydrologic Studies. Springer, Berlin, pp. 51–60. Ioannidou, L., Yau, M.K., 2008b. A climatology of the Northern Hemisphere winter anticyclones. J. Geophys. Res. Atmos. 113 17 pp. Jenkins, G.M., Watts, D.G., 1968. Spectral analysis and its applications. Holden Day. Kistler, R., Kalnay, E., Collins, W., Saha, S., White, G., Woollen, J., Chelliah, M., Ebisuzaki, W., Kanamitsu, M., Kousky, V., van den Dool, H., Jenne, R., Fiorino, M., 2001. The NCEP-NCAR 50-year reanalysis: monthly means CD-ROM and documentation. Bull. Am. Meteorol. Soc. 82, 247–267. Lackmann, G.M., Gyakum, J.R., Benoit, R., 1998. Moisture transport diagnosis of a wintertime precipitation event in the Mackenzie River basin. Mon. Weather. Rev. 126, 668–691. Latifovic, R., Pouliot, D., 2007. Analysis of climate change impacts on lake ice phenology in Canada using the historical satellite data record. Remote. Sens. Environ. 106, 492–507.
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