Abstract

Wavelet and rank correlation analysis were used to identify the links between primary Pacific climate variability modes and low-frequency hydroclimatic variability in the South Saskatchewan River basin (SSRB) of southern Alberta. The April–September average streamflow shows strong interdecadal oscillations with dominant scales of 19–22, 41–42, and 62 yr whereas statistically significant wavelet power in the interannual scale was organized on a background scale of approximately 20–25 yr. At interannual scales, strong coherency is observed between streamflow and the Niño-3 index prior to the 1940s, and in the 1950s, 1970s, and 1980s. However, a change in the phase difference from near 0° in the 1950s to near 180° in the 1980s indicates that the relationship between streamflow and the El Niño–Southern Oscillation (ENSO) is not consistent. Streamflow–Pacific–North America pattern (PNA) and streamflow–Pacific decadal oscillation (PDO) relationships at interannual scales also exhibit similar inconsistencies in phase difference. At interdecadal scales, PDO and streamflow exhibited consistently strong coherence with a stable phase difference of 180° for scales >20 yr. From the period of 1913–2001, the median partial correlation between streamflow and PDO|Niño-3 (read as PDO given Niño-3) was −0.36, whereas it was zero between streamflow and Niño-3|PDO, suggesting that PDO is the primary mode of importance in streamflow variability and predictability in the SSRB. Precipitation variability was also dominated by interdecadal oscillations; however, there is less spatial coherence for dominant scales. Correlations between the basin’s winter precipitation and climate indices are also weaker than with streamflow.

1. Introduction

The North and South Saskatchewan River basins are home to about 88% of Alberta’s population, even though they contain only about 13% of the water resources of the province (Alberta Environment 2008). A considerable portion of the annual flow in these basins comes from spring and summer snowmelt originating from the eastern slopes of the Canadian Rockies. Because the Pacific Ocean is a major moisture source for precipitation during the cold season (when most of the snow accumulation takes place), diagnostic analysis of low-frequency hydroclimatic variability and its relationship with the primary modes of Pacific climate variability—such as the El Niño–Southern Oscillation (ENSO), the Pacific–North American (PNA) pattern, and the Pacific decadal oscillation (PDO)—could provide valuable information for Alberta’s water resources managers, particularly with regard to long-range streamflow forecasting.

ENSO teleconnections to western Canada’s hydroclimatic variability are well documented (e.g., Shabbar and Khandekar 1996; Shabbar et al. 1997; Woo and Thorne 2003; Coulibaly and Burn 2004; Gobena and Gan 2006; Gan et al. 2007). Several studies have also investigated the relationships between hydroclimatic data and the PNA pattern (e.g., Moore 1996; Woo and Thorne 2003; Coulibaly and Burn 2004; Gobena and Gan 2006; Gan et al. 2007). The ENSO and PNA climate anomalies exhibit most of their variance at interannual time scales. A few studies have also considered the interdecadal variation in western Canada’s climatic data; for example, Bonsal et al. (2001) investigated the effects of PDO on Canadian surface temperature. More recently, Gobena and Gan (2006) showed that the strength of ENSO–streamflow relationships in western Canada is influenced by interdecadal variations in the PDO mode. Although regional-scale analyses like the aforementioned studies provide useful information for regional water resources management, a basin-scale diagnostic analysis may be required to identify specific climate anomalies that may provide predictive capability for local-scale water resources management. With this in mind, the present study focuses on the interannual to interdecadal precipitation and streamflow variability in the South Saskatchewan River basin (SSRB) of southern Alberta.

It is now well established that certain large-scale climate variability modes such as ENSO are nonstationary (e.g., Torrence and Compo 1998), and these nonstationary features are also manifested in hydroclimatic time series (e.g., Coulibaly and Burn 2004; Mwale et al. 2004). Thus, wavelet analysis is used hereby to identify the dominant scales of the SSRB’s streamflow and precipitation variability. Wavelets use fast-decaying oscillating waveforms for signal decomposition, which makes them suitable for studying the power fluctuation in nonstationary time series in the frequency and time domains simultaneously. Wavelets have been used to study daily streamflow characteristics (Smith et al. 1998), daily rainfall–runoff relationships (Labat et al. 2000; Lafrenière and Sharp 2003), annual and seasonal streamflow variability (Coulibaly and Burn 2004, 2005), seasonal rainfall and sea surface temperature (SST) variability (Mwale et al. 2004), and the temporal characteristics of the Southern Oscillation index (SOI) and the Niño-3 (5°N–5°S, 150°–90°W) SST index (Torrence and Compo 1998).

This study has two objectives: 1) to identify the dominant interannual to interdecadal modes of variability in the hydroclimatic data of the SSRB using wavelet analysis and 2) to investigate the links between the low-frequency components of the basin’s hydroclimate and Pacific climate variability using wavelet coherence and rank correlation. By analyzing streamflow and precipitation independently, the study provides a comprehensive documentation of the low-frequency features of the hydroclimate of the basin. Possible interactions between interannual and interdecadal modes of variability are also investigated. A description of the study area and data is presented in section 2, followed by a brief description of the wavelet method in section 3. The results of the diagnostic analysis are presented in section 4. The paper presents conclusions in section 5.

2. Study area and data description

The study area covers that portion of the SSRB lying within the province of Alberta (Fig. 1), with an approximate land area of 121 095 km2, which is about a quarter of the surface area of the province. As per the 1996 census, the SSRB is home to 46.7% of the population of Alberta, of which 68% reside in the Bow River subbasin, which constitutes only 21% of basin area (Alberta Environment 2002). The basin elevation ranges from about 600 m at the Alberta–Saskatchewan border to more than 3400 m in the Rocky Mountains.

Fig. 1.

Location of precipitation, streamflow, and snow course stations used in the study.

Fig. 1.

Location of precipitation, streamflow, and snow course stations used in the study.

The precipitation and streamflow data used in the study were extracted from the “South Saskatchewan River Basin Historical Weekly Natural Flows” CD-ROM obtained from Alberta Environment (1998). The weekly streamflow data were “naturalized” by adjusting recorded daily streamflow for known human-made modifications—such as municipal use of water, historical irrigation diversions and return flows, and modifications of streamflow by hydroelectric power projects (Alberta Environment 1998). The weekly precipitation data were derived from Environment Canada’s climatic record, with missing values filled from nearby stations. Details of the procedures used to prepare the datasets are available in the technical report provided with the CD-ROM (Alberta Environment 1998). For our study, we selected 13 hydrometric stations (Fig. 1 and Table 1) and 16 precipitation stations (Fig. 1 and Table 2) with data covering the 1913–2001 period.

Table 1.

Summary of streamflow data used in the study. Also shown are periods of locally significant wavelet power spectrum at the 10% level against red-noise background spectrum. The corresponding scale in years is shown in parentheses. The asterisk means the global wavelet power at that scale is statistically significant at the 10% level.

Summary of streamflow data used in the study. Also shown are periods of locally significant wavelet power spectrum at the 10% level against red-noise background spectrum. The corresponding scale in years is shown in parentheses. The asterisk means the global wavelet power at that scale is statistically significant at the 10% level.
Summary of streamflow data used in the study. Also shown are periods of locally significant wavelet power spectrum at the 10% level against red-noise background spectrum. The corresponding scale in years is shown in parentheses. The asterisk means the global wavelet power at that scale is statistically significant at the 10% level.
Table 2.

As in Table 1, but for precipitation data.

As in Table 1, but for precipitation data.
As in Table 1, but for precipitation data.

Mean annual precipitation in the SSRB increases as we move westward from the Alberta–Saskatchewan border—for example from about 265 mm at Empress near the border to 658 mm at Lake Louise in the Canadian Rockies. The total precipitation during the November–March period—when precipitation mostly occurs as snowfall—accounts for about 20% of the annual precipitation in the plains (e.g., at Calgary and Red Deer) to about 48% at Lake Louise. A severe limitation of the precipitation data used in our study is that the stations are located either in the plains or in the valleys of the Rocky Mountains (Table 2), and thus the precipitation data may not properly reflect the precipitation fields in the Cordillera.

Peak flows in the major rivers of the SSRB occur between mid-June and early July. Although the eastern slopes of the Rocky Mountains and the adjacent foothills constitute only about 25% of the entire area of the SSRB (Environment Canada 1974), annual peak flows in the major rivers are generated by a combination of mountain snowmelt and summer rainfall from higher altitudes. The April–September flow constitutes more than 75% of the annual flow for each of the 13 hydrometric stations, thus acting as an integrator of the winter to summer precipitation. To focus on those variables relevant to the major flow season, we considered the November–March (hereafter Nov–Mar) total precipitation (29 October–2 April), the November–August (hereafter Nov–Aug) total precipitation (29 October–27 August), and April–September (hereafter Apr–Sep) average streamflow (3 April–1 October). Note that because the original data were at weekly time steps, the start (end) dates of the aggregation periods do not necessarily coincide with the first (last) day of the month in question.

To investigate the relationships between the SSRB’s hydroclimatic variables and the Pacific climate, we used the Nov–Mar average Niño-3, Nov–Mar average PDO, and December–February average PNA indices. Niño-3, a time series of equatorial Pacific SST anomalies averaged over the 5°S–5°N, 150°–90°W window, is commonly used as a measure of the strength of ENSO. Even though ENSO originates in the equatorial Pacific, its effect is global. ENSO teleconnections to the extratropical Northern Hemisphere primarily occur in the boreal winter when it reaches its mature phase, which is often associated with anomalous central North Pacific lows (Rasmusson and Carpenter 1982). Warm ENSO (El Niño) episodes are associated with negative midtropospheric geopotential height anomalies over the North Pacific, which should lead to strong sea level pressure (SLP) anomalies in the central and North Pacific regions (Horel and Wallace 1981). In the boreal winter, strong negative SLP anomalies over the central North Pacific consistently correspond to ENSO events with Niño-3 ≥2 (Cayan and Peterson 1989).

The PNA pattern represents a quadripole of 700-mb geopotential height anomalies, with opposite anomalies centered over the Aleutian low and western Canada, and the Hawaiian Islands and southeastern United States (Wallace and Gutzler 1981). The positive phase of PNA appears to be favored during El Niño events (Moore 1996; Trenberth and Hurrell 1994). However, extreme phases of PNA can also occur during years with no anomalous tropical SST forcing (e.g., see Gan et al. 2007). There are two theories on how the equatorial Pacific SST forcing is dynamically related to the dominant midlatitude response. The first theory is that the effect of the ENSO forcing is to reorganize the preferred internal modes of variability, such as the PNA pattern (e.g., Molteni et al. 1993; Palmer 1993; Bladé 1999), whereas others (e.g., Straus and Shukla 2000, 2002) argue that the ENSO forcing can produce midlatitude circulation responses that are distinctly different from the internal modes of variability.

The PDO regime represents interdecadal oscillations in the North Pacific climate system. Observational studies indicate that only two complete cycles of PDO have occurred between 1890 and 1998, with alternating cool and warm PDO phases during 1890–1924, 1925–46, 1947–76, and 1977–98 (Mantua and Hare 2001). The PDO index is a time series of the leading principal component (PC1) of the North Pacific SST anomalies poleward of 20°N. Although PDO is an oceanic (SST) variability mode, its signature extends through the depth of the troposphere and is manifested in the midtroposphere as persistence in the PNA pattern (Mantua and Hare 2001).

At the regional scale, El Niño events are associated with the amplification of the western Canadian ridge, which causes enhanced anticyclones and a northward shift in the midlatitude jet stream, leading to relatively dry winter conditions in western Canada (Shabbar et al. 1997). On the contrary, La Niña (cold ENSO) events are typically associated with a weakening of the western Canadian ridge, enhanced westerly flows, and relatively wet conditions in western Canada. The positive PNA phase is also associated with a deeper-than-normal Aleutian low and an enhanced ridge over western Canada. However, Straus and Shukla (2002) showed that geopotential height anomalies over North America during El Niño winters exhibit pronounced meridional gradients, whereas the gradients during positive PNA winters are mainly zonally oriented. Further details on the large-scale atmospheric features relating ENSO and PNA indices to western Canadian precipitation and streamflow variability can be found in Shabbar et al. (1997), Gobena and Gan (2006), and Gan et al. (2007).

3. Wavelet analysis

In the classical Fourier transform, only the frequency ω is a parameter in the basis functions of the form eiωx. These basis functions are globally uniform in time, and thus the Fourier transform does not contain any time dependence of the signal. Wavelets overcome the limitations of the Fourier transform by using fast-decaying waveforms that can be dilated and translated to reveal oscillations at both high and low frequencies. The wavelet transform is mathematically defined as

 
formula

where f (t) is a real signal, ψ(x) is the basic wavelet function satisfying certain admissibility conditions, s is a dilation parameter, b is a translation parameter, and ψ* is the complex conjugate of ψ (Lau and Weng 1995). Visually, the dilation parameter s controls the width and rate of the local oscillation of the basic wave and can intuitively be thought of as controlling the frequency scale, whereas the translation parameter b moves the wavelet through the time domain. Because the frequency resolution depends on the scale s, both high- and low-frequency fluctuations of a process can be captured by varying either the frequency or time scale.

Given that climate time series are observed at discrete points in time, it is appropriate to use a discrete representation of Eq. (1). The continuous wavelet transform of a discrete sample xn is defined as

 
formula

where N is the total number of samples, n refers to the temporal location of the sample, and δt is the sampling interval (Torrence and Compo 1998). The wavelet power spectrum is then defined as |Wn(s, b)|2. To compare the power spectra across several time series, the wavelet power spectrum may be normalized by the variance of the original time series.

An example of the wavelet power spectrum is shown in Fig. 2 for the Apr–Sep streamflow (A–S Q) of the Belly River near Mountain View [Water Survey of Canada (WSC) ID 05AD005]. The top panel in Fig. 2 shows the standardized streamflow time series, whereas the bottom-left panel is its power spectrum based on the Morlet wavelet. The solid contour lines in the power spectrum plot enclose locally significant power of a red-noise spectrum at a significance level, α = 0.1, whereas the dashed line indicates the cone of influence beyond which the power could be suppressed by the edge effects at both ends of the time series due to zero padding (Torrence and Compo 1998). Hence, the power outside the cone of influence should be interpreted with caution. The wavelet power in Fig. 2 is normalized by the variance of the time series for ease of comparison among stations. Considering individual scale power, locally significant interannual oscillations (≈2–8 yr) were observed during the 1920s to the 1950s and the 1970s. Significant interdecadal oscillations are evident at higher scales, particularly at scales near 21, 42, and 62 yr.

Fig. 2.

Wavelet decomposition of the Apr–Sep average streamflow of Belly River near Mountain View. (a) Streamflow anomaly time series. (b) Wavelet power spectrum. (c) Global wavelet power spectrum. The solid lines in (b) enclose regions in the time–frequency domain where the streamflow power was statistically significant against a red-noise spectrum at the 10% level. The dashed line in (b) is the cone of influence outside where the effect of zero-padding may suppress the wavelet power. The dashed line in (c) is the 90% confidence level for the global wavelet power spectrum.

Fig. 2.

Wavelet decomposition of the Apr–Sep average streamflow of Belly River near Mountain View. (a) Streamflow anomaly time series. (b) Wavelet power spectrum. (c) Global wavelet power spectrum. The solid lines in (b) enclose regions in the time–frequency domain where the streamflow power was statistically significant against a red-noise spectrum at the 10% level. The dashed line in (b) is the cone of influence outside where the effect of zero-padding may suppress the wavelet power. The dashed line in (c) is the 90% confidence level for the global wavelet power spectrum.

Various quantities can be derived from the wavelet transform so as to condense the vast quantity of information contained in the wavelet spectrum and facilitate further analysis and interpretation. These include the global wavelet spectrum, scale-averaged wavelet power (SAWP), band-passed signals, and wavelet coherency. The global wavelet spectrum is obtained by averaging in time the local wavelet power spectra for each scale,

 
formula

It is a useful quantity for identifying dominant scales across the entire time series. The global wavelet spectrum for Belly River shows that only interdecadal-scale fluctuations are globally significant at the 10% level (Fig. 2, bottom-right panel).

The SAWP describes the spatial and temporal fluctuations of the wavelet power over a range of scales, s1 and s2, and is defined as

 
formula

where δj is a factor for scale averaging and Cδ is a reconstruction factor (Torrence and Compo 1998). The time-domain signal over the range of scales s1 and s2 can be reconstructed from the wavelet amplitudes via bandpass filtering:

 
formula

where xt is the reconstructed (bandpassed) signal, ψ(0) is a factor to remove the energy scaling, and ℜ stands for the real part of the quantity in brackets (Torrence and Compo 1998).

Scale bands and periods within which streamflow/precipitation exhibits covariance with climate indices can be identified from wavelet coherence, which is defined as (Torrence and Webster 1999)

 
formula

where is the cross-wavelet spectrum of signals X and Y, 〈·〉 is a smoothing operator and 0 ≤ Rn2 (s) ≤ 1. Equation (6) represents the normalized covariance between two time series because the wavelet transform conserves variance. It has been used to study the relationships between Indian rainfall and ENSO (Torrence and Webster 1999), Baltic Sea ice conditions and the Arctic and North Atlantic Oscillation indices (Jevrejeva et al. 2003), and western Canadian precipitation (Gan et al. 2007). In this study, the SAWP, bandpass filtering, and wavelet coherency are used to investigate the spatiotemporal features of interannual to interdecadal oscillations in precipitation and streamflow and their associations with Pacific climate indices.

4. Discussions of results

a. Hydroclimatic variability

For interdecadal scales, the periods of locally significant streamflow and precipitation wavelet power are listed in Table 1 and Table 2, respectively. For each period of significant wavelet power, the scale corresponding to the peak global wavelet spectrum is shown in parentheses in Table 1 and Table 2. For streamflow, the dominant scales are consistently near 19–22, 41–42, and 62 yr (Table 1), whereas the dominant scales of precipitation exhibit a higher degree of variability, and they are also different for the two seasons analyzed (Table 2).

For interannual (2–8 yr) scales, the SAWP computed from the normalized wavelet power spectrum is shown in Fig. 3. Figure 3a is the station–time diagram of the streamflow SAWP for the 13 stations. Figure 3b shows the time-averaged SAWP at individual stations, whereas Fig. 3c is the “basin averaged” SAWP. The peaks in the streamflow SAWP in Fig. 3c correspond to periods during which statistically significant activities were observed at several hydrometric stations in the basin. Spatially coherent streamflow activities occurred with peaks in 1915, 1927, 1950, 1974, and 1993. Significant activities in the 1910s and 1970s occurred at a lesser number of stations than in the 1920s and 1950s, resulting in a suppressed basin-averaged SAWP for the former two periods (Fig. 3c). Although some activity in the 1990s is evident, the power was not significant at any of the 13 stations. Clearly, there was more streamflow activity before the 1950s, and such activities decrease significantly in the second half of the twentieth century.

Fig. 3.

(a) Station–time diagram of the A–S Q SAWP for 13 stations in the SSRB. (b) Time-averaged A–S Q SAWP. (c) Basin-averaged SAWP of the A–S Q, Nov–Aug precipitation, and Nov–Mar precipitation for the SSRB. The wavelet power was averaged over the 2–8-yr scale.

Fig. 3.

(a) Station–time diagram of the A–S Q SAWP for 13 stations in the SSRB. (b) Time-averaged A–S Q SAWP. (c) Basin-averaged SAWP of the A–S Q, Nov–Aug precipitation, and Nov–Mar precipitation for the SSRB. The wavelet power was averaged over the 2–8-yr scale.

The basin-averaged precipitation SAWP for the 2–8-yr scale is also shown in Fig. 3c. Similar to streamflow, coherent activities in the Nov–Mar precipitation (N–M P) and Nov–Aug precipitation (N–A P) were observed in the 1920s, 1950s, 1970s, and 1990s. A comparison of the Nov–Mar and Nov–Aug precipitation SAWPs reveals that the former exhibited more variance in the 1920s and 1990s, whereas the latter exhibited more variance in the 1920s and 1950s. The temporal fluctuation in the streamflow SAWP shows better agreement with the Nov–Aug precipitation SAWP (Pearson’s correlation coefficient ρ = 0.77) than with the Nov–Mar precipitation SAWP (ρ = 0.55). This is not surprising given that the Nov–Aug period integrates a longer period of basin response than the Nov–Mar period. However, there are some mismatches between the temporal locations of significant precipitation and streamflow activities (e.g., in the 1970s and 1990s).

The peaks of the streamflow and precipitation SAWP in Fig. 3 appear to be organized on a background scale of approximately 20–25 yr. These peaks correspond to years when streamflow records at the majority of the gauging stations were in the upper 25% of the distribution. On the other hand, the low points on the SAWP correspond to periods with streamflow in the lower 25% of the distribution. Those years during which at least two-third of the stations recorded streamflow (precipitation) in the extreme 25% of the distribution (i.e., at least 9 stations for streamflow and 11 stations for precipitation) are listed in Table 3. The decrease in streamflow or precipitation variance during the 1920s, 1930s, 1960s, and 1980s was coincident with periods of extensive drought episodes in western Canada (Godwin 1986; Gan 2000). The gradual ascension and recession of the SAWP over the quasi 20–25-yr cycle means that the SAWP may be used as an early indicator of whether an extended drought period is likely to happen up to possibly several years in advance. For instance, the observation of the continuous recession of the SAWP at the end of the time series since 1996 could be used as an indicator for the onset of extensive drought conditions that had occurred in the region during the period of 2001–03.

Table 3.

List of years with streamflow and precipitation in the lower or upper 25% of the distribution with at least two-third of the stations considered in the study. The years are stratified according to the PDO phase.

List of years with streamflow and precipitation in the lower or upper 25% of the distribution with at least two-third of the stations considered in the study. The years are stratified according to the PDO phase.
List of years with streamflow and precipitation in the lower or upper 25% of the distribution with at least two-third of the stations considered in the study. The years are stratified according to the PDO phase.

b. Wavelet analysis of teleconnections

The SAWPs for the Niño-3 and PNA indices are plotted alongside the streamflow and precipitation SAWPs in Fig. 3c. As has been described elsewhere (Torrence and Compo 1998), Niño-3 exhibited interannual oscillations of large amplitude during the pre-1920 and post-1960 periods and a reduced level of activity in between. Despite the weak amplitudes of Niño-3 between 1920 and 1960, 16 moderate-to-strong ENSO events (10 warm and 6 cold) were recorded during the same period (e.g., Shabbar et al. 1997). Although the ENSO events during the period 1939–43 may be attributed to moderate Niño-3 activities observed from the SAWP, the remaining episodes cannot be explained by the Niño-3 SAWP.

The temporal locations of the peaks of the streamflow or precipitation SAWP in the 1910s and 1970s generally agree with significant Niño-3 activities (Fig. 3c). The streamflow or precipitation activities with peak power centered on 1927 and 1950 coincided with ENSO episodes that occurred during the periods of 1925–31 and 1951–54, both of which occurred when the Niño-3 activity was suppressed. The power fluctuations of the PNA index since 1948 closely follow the intense ENSO activities of the 1970s and 1980s, but they do not seem to offer additional information to that of Niño-3.

To provide a more quantitative picture of the links between climate indices and the SSRB’s hydroclimatology, we computed the wavelet coherence between PC1 of the Apr–Sep streamflow and each of the indices (Fig. 4). PC1, which is based on the correlation matrix, explains about 74% of the variance of streamflow at the 13 stations. The contours in Fig. 4 enclose periods of statistically significant coherence based on a red-noise process as determined by a Monte Carlo experiment (Jevrejeva et al. 2003). Note that the existence of significant wavelet power is not a necessity for the two signals to exhibit significant coherence. The phase differences between the two signals for coherences greater than 0.5 are plotted as vectors in Fig. 4, where a right-pointing arrow indicates that the two signals are in phase, whereas a left-pointing arrow indicates an antiphase relationship. Arrows deviating from the horizontal are indicative of lag–lead relationships between the two signals. Despite the generally weak Niño-3 activities between the 1920s and 1960s, streamflow and Niño-3 show high coherency in the 2–8-yr scale prior to the 1940s, in the 1950s, 1970s, and 1980s (Fig. 4a). The inconsistency in the relationship between streamflow and Niño-3 is clearly evident from the phase distribution in the interannual scale, where the phase difference changes from near 210° prior to the 1940s to near 0° in the 1950s and 180° in the 1970s and 1980s (Fig. 4a). Albeit not as strong as for the interannual scale, Niño-3 and streamflow also show significant covariance near the 20-yr scale. The coherency between streamflow and PNA is shown in Fig. 4b. Relatively strong covariance is observed around 1960 and 1970 near the 2-yr scale and in the 1980s near the 5-yr scale. The phase distribution appears to be even more inconsistent than that of Niño-3.

Fig. 4.

Wavelet coherence between streamflow PC1 and (a) Niño-3, (b) PNA, and (c) PDO. The contours indicate the 95% confidence level. The vectors show the phase difference between the two signals where phase difference is shown for coherence greater than 0.5.

Fig. 4.

Wavelet coherence between streamflow PC1 and (a) Niño-3, (b) PNA, and (c) PDO. The contours indicate the 95% confidence level. The vectors show the phase difference between the two signals where phase difference is shown for coherence greater than 0.5.

The coherency between PDO and streamflow is shown in Fig. 4c. The strongest and most consistent covariance between streamflow and PDO occurs for scales greater than about 20 yr. This is not surprising because the PDO regime is an interdecadal oscillatory mode with two dominant scales centered at 15–25 and 60–75 yr, respectively (Mantua and Hare 2001). The phase difference for the interdecadal scale remained stable near 180° (Fig. 4c). There are also periods of significant coherence in the interannual scale but with less consistent phase distribution—for example, from the 1920s to the 1940s near the 2-yr scale. McCabe and Dettinger (2002) stated that the unfiltered PDO index reflects important ENSO episodes in addition to the interdecadal variability of the North Pacific climate. Indeed, some of the periods of significant coherency in the interannual scale appear to coincide with ENSO events recorded in earlier studies.

We further investigated the PDO–streamflow and PDO–precipitation relationships using a low-pass filtered time series. To emphasize the interdecadal components, the streamflow, precipitation, and PDO time series were filtered by using a low-pass cutoff scale of 15 yr in Eq. (5). To facilitate the comparison among different time series, the filtered signals were normalized by the standard deviation of the respective original time series. For streamflow and precipitation, the first principal components of the filtered signals were used as the interdecadal signals. The proportion of variance accounted for by PC1 is 87.5%, 36.7%, and 52.5% for the Apr–Sep streamflow, Nov–Mar precipitation, and Nov–Aug precipitation, respectively.

As seen in Fig. 5, there is a strong agreement between the PDO and streamflow PC1, with an increase in PDO associated with a decrease in streamflow (Pearson’s ρ = −0.93). Between 1930 and 2001, the historical drought years of 1936, 1941, 1977, 1983–85, and 1988 (Table 3) occurred when the PDO signal was in its extreme warm phase. In contrast, the anomalously wet periods of 1948–54 and 1972 (Table 3) coincided with years when the PDO was in its extreme cool phase. It is also noteworthy that the negative interdecadal streamflow signal in 1961 (e.g., historical drought of 1961) was associated with a temporary warming of the PDO signal in the midst of the cool PDO phase of 1947–76. Using Eq. (5) with a low-pass cutoff scale of 8 yr, Gobena and Gan (2006) found a similar sign reversal in southwestern Canadian streamflow that closely followed a sign reversal in the interdecadal PDO signal between 1959 and 1961. The PDO–precipitation relationship after 1930 is broadly similar to that of streamflow (Pearson’s ρ = −0.72 for Nov–Aug and ρ = −0.76 for Nov–Mar).

Fig. 5.

The leading PC of interdecadal A–S Q, N–A P, and N–M P, and the interdecadal component of the PDO index. A low-pass wavelet filter with a cutoff scale of 15 yr was used to reconstruct the signals.

Fig. 5.

The leading PC of interdecadal A–S Q, N–A P, and N–M P, and the interdecadal component of the PDO index. A low-pass wavelet filter with a cutoff scale of 15 yr was used to reconstruct the signals.

El Niño (La Niña) episodes coinciding with extreme positive (negative) values of the interdecadal PDO signal seem to have an enhanced negative (positive) effect on the hydrology of the SSRB (cf. Table 3 and Fig. 5). For instance, the mature El Niño years of 1931, 1940, 1941, and 1983 coincided with periods when the interdecadal PDO signal was more than 0.5 standard deviations above normal. Similarly, the mature La Niña years of 1951 and 1972 coincided with the interdecadal PDO signal in excess of 0.5 standard deviations below normal. On the other hand, the effects of mature El Niño (La Niña) years that occurred during a cool (warm) PDO phase appear to be either muted or are in opposition to the expected response. A good example for the latter case is the 1954 El Niño event that was associated with one of the wettest years in the basin. Apparently, when both PDO and ENSO are active, the resultant hydrologic responses of the SSRB and likely other river basins of western Canada will depend on whether the two climate anomaly modes are in phase, which likely causes more severe extreme events to occur, or out of phase, which often means a relatively modest effect.

Figure 5 suggests that a quasi 22-yr drought cycle is superimposed on a quasi 42-yr cycle. Given that the late-1880s-to-early-1890s drought was described as the worst on record (Godwin 1986), one may argue that multiyear droughts similar to the 1930s and 1980s could happen on a time scale of 40–50 yr. Because the PDO phase shift occurs every 20–30 yr, this means that the region could experience a severe interdecadal drought during every warm PDO phase. Using diatom-inferred lake water salinity levels in the Chauvin Lake of eastern Alberta (52.69°N, 110.10°W) and the 1988/89 regional droughts as a benchmark measure, Leavitt and Chen (2005) predicted that the probability of occurrence of a drought as severe as the 1988 drought by 2030 was 45%, with a mean interarrival time of 60 yr and an average duration of a decade. An extension of the oscillation in Fig. 5 into the future also suggests that the region could face the next major multiyear drought between 2020 and 2030. It is noteworthy that Leavitt and Chen (2005) characterized the 1930s droughts as among the mildest on record, although our results show that the signature of the 1930s drought in the SSRB hydroclimatic variables is at least comparable to that of the 1980s (Fig. 5).

c. Correlation with climate indices

In this section, we use the Spearman rank correlation to examine the value of ENSO and PDO in long-range forecasting. The Spearman correlation is chosen because of its resistance to outliers and its robustness (Wilks 1995). Rank correlations are computed between the streamflow or winter precipitation at each station and the Nov–Mar Niño-3 and PDO indices. Because the climate indices are correlated to one another, partial correlations were also computed so as to assess the relative influence of each climate index. Correlations were assessed for 1913–2001, 1930–2001, and 1950–2001 periods in an attempt to examine the temporal stability of any monotonic relationships. Table 4 shows the number of stations with statistically significant correlations at the 5% and 1% levels. Also shown in Table 4 are the lowest, median, and highest correlations.

Table 4.

Number of streamflow and precipitation stations that exhibit statistically significant Spearman rank correlations with climate indices (top row). The lowest, median, and highest correlations with each index are also shown in parenthesis (bottom row). Correlations significant at the 5% (1%) level are indicated in italics (boldface). The statistics are based on 13 streamflow and 16 precipitation stations.

Number of streamflow and precipitation stations that exhibit statistically significant Spearman rank correlations with climate indices (top row). The lowest, median, and highest correlations with each index are also shown in parenthesis (bottom row). Correlations significant at the 5% (1%) level are indicated in italics (boldface). The statistics are based on 13 streamflow and 16 precipitation stations.
Number of streamflow and precipitation stations that exhibit statistically significant Spearman rank correlations with climate indices (top row). The lowest, median, and highest correlations with each index are also shown in parenthesis (bottom row). Correlations significant at the 5% (1%) level are indicated in italics (boldface). The statistics are based on 13 streamflow and 16 precipitation stations.

From Table 4, it is clear that the PDO shows stronger correlations with the streamflow of the SSRB than Niño-3, both in terms of the number of stations with statistically significant correlations and the correlation magnitudes. The median partial correlations between streamflow and PDO|Niño-3 (read as PDO given Niño-3) for the 1913–2001, 1930–2001, and 1950–2001 periods are −0.36, −0.46 and −0.46, respectively. On the other hand, the median partial correlations between streamflow and Niño-3|PDO for all three data windows are close to zero (Table 4). These results are consistent with that of Gobena and Gan (2006), who showed that basins originating in the Rocky Mountains were more strongly correlated to PDO than to ENSO (represented by SOI). The lack of significant partial correlation between streamflow and Niño-3|PDO likely means that tropical Pacific SST conditions during the mature phase of ENSO provide redundant information once the PDO–streamflow relationship is accounted for.

The correlations between the Nov–Mar precipitation and PDO are also stronger than those with Niño-3 (Table 4). In general, the correlations of Niño-3 and PDO with the SSRB’s precipitation are weaker than those with streamflow, partly because of the high spatial and temporal noise in precipitation as compared to streamflow. For the 1950–2001 period, precipitation at three stations exhibited significant correlations (α = 0.05) with PDO|Niño-3, whereas six stations exhibited significant correlations with Niño-3|PDO. This suggests that the winter-season indices of both climate modes provide some useful information regarding the winter precipitation variability of the SSRB. However, it should be noted that the climate indices are also from the same time window as the Nov–Mar precipitation and as such their value for prediction purposes is limited.

As mentioned in section 2, the precipitation data used in this study come from stations located in the plains or from valley stations in the Rocky Mountains. Therefore, it is worth examining whether the apparent weakness of the SSRB’s streamflow–Niño-3 relationship (as compared to the modest precipitation–Niño-3 relationship) may partly be attributed to the Cordillera snowpack variability not being properly captured by the precipitation data from the plains and foothills. A preliminary analysis of Alberta Environment snow water equivalent (SWE) data from 14 snow pillow stations shows that the partial correlations between the 1 April SWE and PDO|Niño-3 are stronger than those between SWE and Niño-3|PDO (Table 5). The calculations in Table 5 were based on SWE data for the period of 1970–2004 and obtained at locations shown in Fig. 1. Again, from these results, it seems that mountain snowpack, which plays an important role in runoff generation in the major rivers of the SSRB, is primarily forced by the North Pacific winter SST than by the equatorial Pacific climate during the mature phase of ENSO. Our results concur with that of McCabe and Dettinger (2002), who indicated that PDO—not ENSO—is the primary driving force for the 1 April snowpack variability in the western United States. The lack of explicit ENSO effect on the SSRB’s streamflow could be because PDO is a reddened response to ENSO and atmospheric noise (Newman et al. 2003), and thus the unfiltered PDO index may capture the dynamics of Pacific interdecadal variability as well as important ENSO episodes (McCabe and Dettinger 2002).

Table 5.

As in Table 4, but for 1 April SWE based on 14 mountain snow pillow stations.

As in Table 4, but for 1 April SWE based on 14 mountain snow pillow stations.
As in Table 4, but for 1 April SWE based on 14 mountain snow pillow stations.

Alberta Environment uses the current antecedent soil moisture, snow water equivalent, precipitation, snow pillow information, and temperature to determine seasonal runoff by statistical techniques (Alberta Environment 2008). Currently, water supply outlooks for the March–September runoff volume are issued during the first 10 days of each month beginning in February. The improved understanding of the relationships between Pacific climate variability and basin streamflow and precipitation could be used as a basis to objectively incorporate large-scale climate dynamics into seasonal streamflow forecasting in the SSRB. The inclusion of this information into flow forecasting frameworks may lead to improved forecast lead times and/or skills.

One approach to including large-scale climate information in long-range flow forecasting is to statistically predict precipitation and temperature at the desired lead time and then disaggregate the predicted values to drive a hydrologic model (e.g., see Mwale et al. 2004; Mwale and Gan 2005). With regard to the SSRB, the applicability of this approach seems limited because of a number of reasons. First, significant wavelet power fluctuations at the interannual scale were mainly observed at intervals of about 20–25 yr. In the absence of strong interannual persistence of precipitation power, the climate–precipitation relationship may not be strong enough to produce precipitation forecasts that are accurate enough for driving a hydrologic model. Second, modest correlations between precipitation and large-scale climate anomalies are observed only during the winter season (e.g., Shabbar et al. 1997; Gan et al. 2007), whereas the SSRB’s streamflow integrates precipitation over the winter-to-summer period, and thus the effect of the winter precipitation alone, even if accurately predicted, may not yield a marked improvement in streamflow forecasts for the major flow season. Third, the precipitation data from the valley and foothill stations–—where sufficiently long and reliable records are available—do not seem to accurately represent the mountain snowpack variability.

A second and more straightforward approach is to use indices of climate patterns as predictors in statistical regression models, provided that the indices have a lag relationship with the hydroclimatic data. For the SSRB, the use of the winter-season PDO, plus PNA and Niño-3/SOI from earlier seasons (beginning with the initiation of ENSO) as predictors may yield some improvement in the skill and/or lead time of the current regression models. Although tropical Pacific SST indices during mature ENSO periods do not add new information to that contained in the PDO index, the influence of the early stages of ENSO on the SSRB’s streamflow variability cannot be ruled out and warrants further consideration. One limitation of regression-based forecasts is that they do not contain information about forecast uncertainty. In a companion study, a robust regression model based on M estimators is being explored as a basis for ensemble forecasting using a modified nearest-neighbors resampling algorithm (Gobena and Gan 2009).

A third approach could be to use the large-scale climate information as a conditioning variable for resampling appropriate historical precipitation and temperature data as surrogates for future climate and then use the resampled historical data as multiple scenarios for input to a hydrologic model in an ensemble streamflow prediction (ESP) framework (e.g., Hamlet and Lettenmaier 1999). One attractive feature of the ESP approach is that probabilistic statements can be attached to streamflow forecasts. However, the mismatches in the temporal locations of the streamflow and precipitation powers as revealed by the SAWP at the interannual scale may pose problems with regard to the validity of this approach. A case-by-case analysis of the power fluctuations in the streamflow and precipitation in each subbasin is required to establish its applicability to the SSRB. The ESP approach is also being explored in another study (Gobena and Gan 2009, manuscript submitted to J. Hydrol.).

5. Conclusions

In this study, we used wavelet transforms and rank correlation analysis to investigate low-frequency hydroclimatic variability in the SSRB of southern Alberta and its dynamical links with the Pacific climate variability. The results of the study are summarized as follows:

  1. Dominant modes of streamflow variability occur at interdecadal scales oscillating near 19–22, 41–42, and 62 yr. Clusters of significant streamflow activities at interannual scales were also observed at intervals of approximately 20–25 yr. The intensity of the interannual oscillations has been on the decline since 1950. The spatially averaged SAWP of streamflow revealed that the clusters of significant activities at the interannual scales coincide with periods when streamflow was in the upper quartile of the distribution. Conversely, streamflows in the lower quartile of the distribution coincided with periods of low SAWP. The precipitation variability was also dominated by interdecadal oscillation, although the dominant oscillatory modes show more spatial variability than that of streamflow.

  2. As expected, the strongest coherence between streamflow and Niño-3 occurs in the interannual scale. Despite the generally weak Niño-3 activities between the 1920s and the 1960s, the SSRB’s streamflow and Niño-3 showed high coherency in the 2–8-yr scale prior to the 1940s, and in the 1950s, 1970s, and 1980s. However, the relationship is highly inconsistent as observed from the shifting phase distribution in the interannual scale, where the phase difference changed from near 210° prior to the 1940s to near 0° in the 1950s, and close to 180° in the 1970s and 1980s. On the other hand, PDO and streamflow exhibited consistently strong covariance with a rather stable phase difference of 180° for scales greater than about 20 yr.

  3. Streamflows in the lower and upper quartiles showed interdecadal variations that were synchronized with the PDO phase. There were more years with flows in the lower (upper) 25% of the distribution during the warm (cool) PDO phase than during the cool (warm) phase. To a lesser extent, this was also true for winter precipitation. A comparison of the interdecadal components of basin streamflow and precipitation to that of PDO also revealed that there is a strong agreement between the leading precipitation or streamflow PC and the PDO time series. Since 1930, droughts in the region have occurred at quasi 22- and 42-yr modes. The multiyear droughts of the 1930s and 1980s were part of the quasi 42-yr mode that occurred when the interdecadal PDO signal was in its extreme warm phase persistently for several years. The role of PDO in the initiation and/or maintenance of drought in this region deserves further investigation.

  4. The Spearman rank correlation analysis with climate indices averaged over the Nov–Mar season showed that the SSRB’s streamflow is highly influenced by the PDO regime, with all 13 stations having significant correlations at the 1% level. Even though streamflow correlations with Niño-3 were also significant at 5 of the 13 stations, partial correlation analysis showed that tropical Pacific SST during the mature phase of ENSO did not add substantial new information to that already contained in the PDO index. Preliminary analysis indicates that mountain snowpack, which plays a major role in runoff generation in the SSRB, is more strongly correlated to PDO than to Niño-3, thus partly explaining the weak ENSO–streamflow relationship. Even though correlations between the SSRB’s winter precipitation and Niño-3 (PDO) were generally weaker than with streamflow, there are still statistically significant correlations observed at some precipitation stations.

Acknowledgments

Partial support for this work was provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada. The first author was also supported by a graduate teaching assistantship of the University of Alberta. The Niño-3 index was obtained from the Climate Data Library of the International Research Institute (IRI) for Climate and Society at Columbia University (available online at http://ingrid.ldeo.columbia.edu/SOURCES/.Indices/.nino/.EXTENDED/). The PDO and PNA indices were obtained from the Joint Institute for the Study of the Atmosphere and Ocean (JISAO) at the University of Washington (available online at http://www.jisao.washington.edu/data_sets/). The wavelet and wavelet coherence software was provided by C. Torrence and G. Compo (available online at http://paos.colorado.edu/research/wavelets/), and A. Grinsted (available online at http://www.pol.ac.uk/home/research/waveletcoherence/).

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Footnotes

* Current affiliation: BC Hydro, Burnaby, British Columbia, Canada.

Corresponding author address: Thian Gan, NREF 3-033 P. Markin/CNRL, University of Alberta, Edmonton, AB T6G 2W2, Canada. Email: tgan@ualberta.ca