Wavelet analysis of variability in annual Canadian streamflows



[1] Wavelet analysis is used to identify and describe variability in annual Canadian streamflows and to gain insights into the dynamical link between the streamflows and the dominant modes of climate variability in the Northern Hemisphere. Results from applying continuous wavelet transform to mean annual streamflows from 79 rivers selected from the Canadian Reference Hydrometric Basin Network (RHBN) reveal striking climate-related features before the 1950s and after the 1970s. The span of available observations, 1911–1999, allows for depicting variance for periods up to 12 years. Scale-averaged wavelet power spectra are used to simultaneously assess the interannual and spatial variability in 79 annual streamflow time series. The most striking feature, in the 2–3 year band and in the 3–6 year band (the 6–12 year band is dominated by white noise (since 1950) and is not considered further) is a net distinction between the timing and intensity of the interannual variability in western, central, and eastern streamflows, which is shown to be linked to the regional climatology. It is found that for the 2–3 year band, the Canadian streamflows are depicted mainly by the Pacific North America (PNA) during 1950–1999, and the Northern Hemisphere Annular Mode (NAM) only prior to 1950, and the North Atlantic Oscillation (NAO) after 1970. Similarly, in the 3–6 year band, the streamflows are depicted mostly by the NAO, the sea surface temperature anomalies over the Niño-3 region (ENSO3) and the PNA during the period 1950–1999, and the NAM prior to 1950. Furthermore, strong local correlations between teleconnection patterns and western, central, and eastern streamflows are also revealed in both the 2–3 and 3–6 year bands with striking changes around 1950 and 1970. The correlation analysis in the 2–3 year and 3–6 year bands revealed the presence of two change points in the west and east streamflows occurring around 1950 and 1970.

1. Introduction

[2] Recent advances in the identification of coherent climatic patterns in the atmospheric circulation can be particularly relevant to the interpretation of variations and long-range persistence within hydrological records. Low-frequency climatic fluctuations reflect locally on the interannual variability in hydroclimatic variables (temperature, precipitation, river flow) which are key elements in understanding the underlying dynamics of the hydrologic cycle. Furthermore, a better understanding of the temporal and local/regional connection between low-frequency climatic fluctuations and the variations of river discharge can lead to better hydrologic system modeling (e.g., improved long-range forecast) and hence improved water resources management. However, assessing the changes in atmospheric patterns and their relationships to the Northern Hemisphere hydrologic regime remains a difficult task owing to the coarseness of the ground station network even for a standard variable such as precipitation. The space-time variability of precipitation (solid and liquid) requires a large number of weather stations for a proper characterization of rainfall or snowfall patterns over large areas such as Canadian watersheds. As an alternative, one can resort to river discharge records. Hydrological systems act as spatial and temporal integrators of precipitation over specific watersheds, and hence annual river flow observations can serve as a pertinent index of interannual hydroclimatic variability at a local or regional scale.

[3] This study aims to assess the variability of Canadian annual streamflows and the possible links to the dominant climatic patterns in the Northern Hemisphere. Most previous interannual variability assessment studies are based either on direct correlation analysis to identify strong statistical relationship between the hydroclimatic variable and the teleconnection pattern indices [e.g., Yarnal and Diaz, 1986; Redmond and Koch, 1991] or more recently on nonparametric multitaper method of spectral analysis [Rajagopalan and Lall, 1998], a more direct measure of the occurrence process. All these approaches assume stationary time series, but continuous wavelet analysis has revealed that the interannual variability of phenomena such as El Niño-Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO) are nonstationary processes, since their variance changes in frequency and intensity through time [e.g., Torrence and Compo, 1998; Higuchi et al., 1999; Coulibaly et al., 2000]. Wavelet analysis has been used in geophysics and meteorology to identify coherent convective storm structures and characterize their temporal variability [Kumar and Foufoula-Georgiou, 1993; Takeuchi et al., 1994; Kumar, 1996; Szilagyi et al., 1999] or to analyze localized variations within geophysical time series including climatic indices [Shabbar et al., 1997b; Hu et al., 1998; Lucero and Rodriguez, 1999]. In the field of hydrology, wavelet analysis has been recently applied to examine daily rainfall-runoff relationships in a karstic watershed [Labat et al., 2000] and also to characterize daily streamflow [Smith et al., 1998; Saco and Kumar, 2000] and monthly reservoir inflow [Coulibaly et al., 2000].

[4] The main objectives of this analysis are to describe and document the variability in annual Canadian streamflows using wavelet analysis. This study also aims to examine the role of the dominant climatic patterns in the Northern Hemisphere on the interannual variability of Canadian streamflows. The remainder of the paper is organized as follows. A description of the study area and the data sets are first provided. The continuous wavelet analysis method is presented next. Results from the wavelet analysis are then reported, and finally some conclusions are drawn.

2. Study Area and Data Sets

2.1. Reference Hydrometric Basin Network (RHBN)

[5] The analysis described herein was performed on stations from the Reference Hydrometric Basin Network (RHBN), a data collection network of natural rivers in Canada identified by Environment Canada for climatic change research. The five criteria according to which stations were selected for the RHBN are as follows [Harvey et al., 1999]:

[6] First is the degree of basin development. Stations that were included in the network were those that reflect catchments that are pristine or have stable land-use conditions. As a guideline, a catchment that has less than 10% of its surface area modified from natural conditions was considered to represent pristine conditions.

[7] Second is the absence of significant regulations or diversions. A catchment was considered natural if there was no control structure upstream of the gauging station, and it was considered regulated if there was an upstream control structure.

[8] Third is record length. A station must have a minimum record length of 20 years to be included in the RHBN. This record length was chosen to make sure that underrepresented climatic or geographic areas, which are characterized by minimal data availability, were included in the network. The present work selected from the RHBN only those stations with a record length of at least 35 years to ensure an adequate record length for the wavelet analysis.

[9] Fourth is longevity. This criterion was based on the judgment of the regional staff. A station was excluded from the network if it is currently active but was expected not to have future data collection activities.

[10] Fifth is data accuracy. Data accuracy was assessed qualitatively by local experts based on knowledge of the hydraulic condition of the stations to ensure that only stations with good quality data were included in the network.

[11] The RHBN originally consisted of 255 hydrometric stations. All stations had at least 20 years of record, with an average record length of 38 years. Basin sizes range from 3.63 to 145,000 km2, with a median size of 1170 km2; 10% of the basins have a drainage area greater than 20,000 km2; and 10% have a drainage area less than 100 km2. The RHBN has decreased in size from its original design and currently contains 200 + stations. An analysis of the characteristics of stations within the RHBN indicates certain limitations of the existing network. The network tends to comprise large basins in the north and smaller basins in the south, and certain provinces have large gaps in spatial coverage.

[12] The current research employs a subset of the RHBN consisting of 79 longer-term gauging stations (see Figure 1) to minimize the limited data record problem and allow longer period (up to decadal timescale) analysis. It can be seen that the subset of the RHBN that has been selected for this work suffers from the same limitations outlined above for the RHBN as a whole. In particular, there is a limited number of stations representing the Canadian north and there are few stations from the Prairie Provinces. The median record length for the stations analyzed in this work is 49 years, with a range of record lengths from 35 to 85 years. The catchment drainage areas range from 3.63 to 29,900 km2, with a median value of 1350 km2. As such, the subset of the RHBN is fairly typical of the stations in the RHBN in terms of drainage areas, but consists only of the best available streamflow time series with longer record length. The selected sites along with the station numbers, drainage basin areas, and locations are listed in Table 1. The regional grouping of sites (Table 1) is based on statistical analysis and climatic factors [Harvey et al., 1999; Adamowski and Bocci, 2001]. The hydrologic variable selected for this research is the annual mean flow given that the study is mainly concerned with interannual to decadal variability in the streamflows. Note that using annual mean flow eliminates the strong seasonal variability inherent to Nordic river flows.

Figure 1.

Location map of the 79 Canadian Reference Hydrometric Basin Network (RHBN) flow stations selected.

Table 1. Canadian Reference Hydrometric Basin Network (RHBN) Gauging Stations Used in the Wavelet Analysis
RegionStation NumberLatitudeLongitudeDrainage Area, km2Ecozone
Eastern Canada
102ZM00647.635052.83723.63Boreal Shield
102ZK00147.224753.5683285Boreal Shield
102YR00148.807854.2244275Boreal Shield
102ZH00147.946954.2856764Boreal Shield
102YQ00149.015354.85364400Boreal Shield
102ZG00147.213955.3292205Boreal Shield
102ZF00147.746755.44171170Boreal Shield
102YC00150.607557.1511624Boreal Shield
102YL00149.240657.36252110Boreal Shield
102ZB00147.613959.0092205Boreal Shield
102VC00150.307863.622513000Boreal Shield
201FB00146.369460.9767368Atlantic Maritime
201FB00346.223361.1367357Atlantic Maritime
201EO00145.173361.98171350Atlantic Maritime
201DG00344.851763.665096.9Atlantic Maritime
201CA00346.744264.185646.8Atlantic Maritime
201EF00144.446764.59171250Atlantic Maritime
201BU00245.943665.1703391Atlantic Maritime
201AP00246.071965.3667668Atlantic Maritime
201EC00143.838365.3700495Atlantic Maritime
201AP00445.701965.60141100Atlantic Maritime
201BO00146.736165.82675050Atlantic Maritime
201BQ00147.094765.8372948Atlantic Maritime
201BP00146.935865.90721340Atlantic Maritime
201AQ00145.170066.4667239Atlantic Maritime
201BE00147.831766.88172270Atlantic Maritime
201AK00145.94567.3222234Atlantic Maritime
201BC00147.666767.48423160Atlantic Maritime
201AD00247.256968.593114700Atlantic Maritime
201AD00347.206968.95691350Atlantic Maritime
302PJ00746.659271.2886709Mixedwood Plain
302OE02745.467271.6553642Mixedwood Plain
302RD00248.899472.21179320Boreal Shield
302NF00346.685873.91421390Boreal Shield
302LB00744.842275.5439246Mixedwood Plain
302KB00145.888177.30834120Boreal Shield
302HL00444.549477.3292712Boreal Shield
302EC00244.712879.28171520Boreal Shield
302GA01043.190680.45471030Mixedwood Plain
302FB00744.522580.9308181Mixedwood Plain
302FC00144.456481.32673960Mixedwood Plain
404NA00148.600678.10943680Boreal Shield
404LJ00149.616783.26338940Boreal Shield
404JC00249.778984.53002410Boreal Shield
402EA00545.669479.3786321Boreal Shield
402AB00848.382289.3078187Boreal Shield
402AA00148.012289.61611550Boreal Shield
Central Canada
505PB01448.850092.72504870Boreal Shield
506GD00158.891796.275348100Taiga Shield
605LH00551.852899.547255000Boreal Plain
Western Canada
708NF00150.8861116.0431420Montaine Cordillera
708NB00551.4833117.17929710Montaine Cordillera
708NE08749.4250118.041780.5Montaine Cordillera
708NE07749.9075118.1253201Montaine Cordillera
708LD00150.9383119.65443080Montaine Cordillera
708LA00151.6556120.065310200Montaine Cordillera
708NL00749.4597120.50191850Montaine Cordillera
708MH01649.0839121.4567329Pacific Maritime
708KH00652.8436122.223611500Montaine Cordillera
708MG00550.3356122.79942160Pacific Maritime
708JE00154.4181124.275014600Montaine Cordillera
708JB00254.0092125.00503600Montaine Cordillera
808MH00649.2428122.578337.3Pacific Maritime
808GA01049.3958123.1444172Pacific Maritime
808HA00348.7275123.6697209Pacific Maritime
808HA00148.8792123.7019355Pacific Maritime
808HB00849.2897124.9103347Pacific Maritime
808HE00650.0144126.8425181Pacific Maritime
907FB00155.7200121.207812100Montaine Cordillera
910CD00158.7883122.659220300Taiga Plain, Boreal Cordillera
910CB00157.2342122.69422160Taiga Plain, Boreal Cordillera
910BE00458.8556125.38062570Boreal Cordillera
908CE00157.9008131.154429300Boreal Cordillera
908CG00156.7389131.67369350Montaine Cordillera
909AE00359.9306131.76783320Boreal Cordillera
909BA00161.9944132.37787250Boreal Cordillera
909AA00659.5992133.81336810Boreal Cordillera
909AC00160.8522135.73926990Boreal Cordillera
909BC00162.8297136.580649000Boreal Cordillera

2.2. Selected Climatic Indices

[13] The analysis also includes several climatic patterns that appear and persist in the Northern Hemisphere. Two of these are the North Atlantic Oscillation (NAO) and the Pacific-North American (PNA) that are found to be the predominant patterns for displaying low-frequency variability (interannual to decadal timescales) in the Northern Hemisphere (e.g., storm-track and temperature changes [Barnston and Livezey, 1987; Lamb and Peppler, 1987; National Research Council, 1998]). The NAO is a large-scale alternation of atmospheric mass with centers of action near the Icelandic Low and the Azores High. It is the dominant and persistent mode of atmospheric behavior in the North Atlantic throughout the year, explaining on average 32% of the variance in monthly sea level pressures (SLP) [Cayan, 1992] but with even greater dominance during the winter. The NAO index used in this study is from Hurrell [1995], who exploited SLP anomalies from Lisbon, Portugal, and Stykkisholmur, Iceland. While exhibiting considerable interannual variability with concentrations of spectral power around periods of 2.1, 8, and 24 years [Cook et al., 1998], the NAO has been in a generally positive phase since about 1970. A significant coherent relationship between the NAO and the North Atlantic sea surface temperature has been recently found at interannual and interdecadal timescales [Higuchi et al., 1999]. The signature of the NAO is strongly regional and can be directly tied to variations in regional precipitation. Therefore the NAO index may be a relevant variable to the regional hydrology. For example, in a study on interannual variability of Canadian snow cover from 1915 to 1992 [Brown and Goodison, 1996], significant winter NAO-snow cover correlations were observed in Ontario and southern Quebec specifically in December. Another study [Brown, 1995] has shown that the influence of the NAO circulation pattern on winter snow cover was mainly confined to southern Canada.

[14] Another persistent climatic pattern that has to be considered in the Northern Hemisphere is the Pacific-North American (PNA) atmospheric teleconnection, which is defined as a measure of atmospheric response to a warm sea surface temperature (SST) anomaly in the central equatorial Pacific [Wallace and Gutzler, 1981]. The PNA has been found to be a dominant mode of variation in the middle latitudes during the winter months. It has been shown to be strongly related to precipitation and temperature within the same season in the western United States [Redmond and Koch, 1991]. Strongly positive and negative PNA indices are associated with warm events (El Niño) and cold events (La Niña), respectively, and with North American precipitation and temperature anomalies [Yarnal and Diaz, 1986]. It has been found that the pressure anomalies associated with the different phases of the PNA alter the normal upper atmospheric patterns, thus affecting temperature and precipitation patterns over various regions of North America [Shabbar et al., 1997a].

[15] Station-based indices are now criticized as nonoptimal representations of the time-dependent behavior of their own associated spatial patterns [Wallace, 2000]. For example, rather than using a prescribed station-based NAO index, one may use the leading natural mode of variability as determined from principal component analysis of the hemispheric or global SLP field, based on observations or model control runs. It is noteworthy that there is no guarantee that the computed patterns represent real physical/dynamical modes of the climate system [Hurrell et al., 2003]. Indeed, principal component analysis can reveal only orthogonal patterns. These issues (station-based versus derived leading components) are in the center of recent debate [Wallace, 2000; Ambaum et al., 2001]. Therefore, in this study, two types of climatic patterns are considered. The Northern Hemisphere Annular Mode (NAM), originally called the Arctic Oscillation, is the first principal component of the Northern Hemisphere (20°–90°N) winter SLP field [Thompson and Wallace, 1998, 2000]. The NAM is shown to exert a strong influence on wintertime climate throughout middle- and high-latitude continental regions, affecting not only the mean conditions, but also the day-to-day variability associated with storm intensity and the occurrence of high-latitude blocking [Thomson and Wallace, 2001]. It explains 23% of the extended winter mean (December–March) variance and is largely dominated by the NAO structure in the Atlantic sector [Hurrell et al., 2003]. Serreze et al. [2000] consider the NAO as a major component of the NAM, with cold-season correlation of about 0.8. The NAM pattern, like the NAO, has been generally positive since the early 1970s.

[16] In addition to the NAO, PNA, and NAM indices, indicators of the El Niño-Southern Oscillation (ENSO) are also selected for this study. The ENSO phenomenon is characterized as a spreading of warm water off the coast of South America from the equatorial central Pacific to the eastern Pacific and is associated with climatic anomalies throughout the world. The ENSO index used in this study is the monthly mean equatorial Pacific sea surface temperatures (SST) anomalies over the Niño-3 region (5°N–5°S; 90°W–150°W) [Rasmusson and Carpenter, 1982]. For notational simplicity, ENSO3 will be used herein to denote the SST anomalies over that region. The influence of ENSO on streamflow is well documented [Redmond and Koch, 1991; Kahya and Dracup, 1993; Dracup and Kahya, 1994; Eltahir, 1996; Kiem and Franks, 2001], and subsequently the use of the ENSO-streamflow relationship for predictive purposes has been studied extensively in recent years [Moss et al., 1994; McKerchar et al., 1996; Piechota et al., 1997, 1998; Piechota and Dracup, 1999; Coulibaly et al., 2000; Gutiérrez and Dracup, 2001].

[17] It is noteworthy that some climatic indices are relatively interlinked over some time periods. As indicated previously, the NAM index is considered as a “sister of the NAO” [Serreze et al., 2000]; PNA and ENSO3 are connected as documented previously; and a complex relationship has been recently shown between the NAO, ENSO, and PNA patterns [Huang et al., 1998]. However, the dynamical relationship between climatic patterns remains controversial and warrants further research [Diaz et al., 2001; Hurrell et al., 2003]. Therefore the selected climatic patterns are used here as independent variables in order to assess the specific link between each climatic indictor and the Canadian streamflows.

3. Methods

[18] The decomposition of time series into time-frequency space permits the identification of the dominant modes of variability and how these modes vary in time. This can be done by using either windowed Fourier transform or wavelet transform. However, a shortcoming of standard Fourier transform is that it does not provide an accurate time-frequency localization, nor does it perform well on irregularly spaced events or nonstationary signals [Smith et al., 1998]. A major advantage of using the wavelet transform over the Fourier transform is that wavelet analysis is scale independent [Kaiser, 1994], and hence there is no need for a predetermined scale (or response interval), which would limit the frequency range. Continuous wavelet transform is more appropriate for geophysical and hydrological time series because of the wide range of possible dominant frequencies. Moreover, it is also an efficient method for analyzing nonstationary signals [Daubechies, 1990].

[19] The wavelet analysis method described herein is limited to the needs of the present study. Emphasis is given to useful practical details for applying the method for hydrological time series analysis. For a more detailed description of wavelet analysis in geophysics and hydrology, the readers are referred to other sources, such as Torrence and Compo [1998] and Labat et al. [2000]. The continuous wavelet transform of a discrete sequence of observations xn is defined as the convolution of xn with a scaled and translated wavelet ψ(η) that depends on a nondimensional time parameter η,

display math

where n is the localized time index, s is the wavelet scale, δt is the sampling period, N is the number of points in the time series, and the asterisk indicates the complex conjugate. Since complex wavelets lead to complex continuous wavelet transform, the wavelet power spectrum, defined as ∣Wn(s)∣2, is a convenient description of the fluctuation of the variance at different frequencies. Further, when normalized by σ−2 (where σ2 is the variance), it gives a measure of the power relative to white noise, since the expectation value for a white noise process is σ2 at all n and s.

[20] Figure 2b illustrates the normalized local wavelet power spectrum of a typical streamflow time series (Figure 2a) using the Morlet wavelet, a complex nonorthogonal wavelet consisting of a plane wave modulated by a Gaussian:

display math

where ω0 is the nondimensional frequency. The advantage of the Morlet wavelet over other candidates such as the Mexican hat wavelet resides in its good definition in the spectral-space. For ω0 = 6 (used here), the Morlet wavelet scale is almost identical to the corresponding Fourier period of the complex exponential, and the terms “scale” and “period” may conveniently be used synonymously [Torrence and Compo, 1998; Torrence and Webster, 1999]. Thus the left axis in Figure 2b is the equivalent Fourier period corresponding to the wavelet scale (hereinafter called the wavelet period), and the bottom axis is time (in years). The shaded contours are the normalized variance in excess of 1, 2, and 4. Features with variance larger than expected for a white noise process reveal that the interannual variability is organized in preferential bands of wavelet periods. These bands, 2–3, 3–6, 6–12, and beyond 12 years, have been reported by other investigators in precipitation and streamflow time series [Rajagopalan and Lall, 1998; Coulibaly et al., 2000]. This suggests the choice of the scale-averaged wavelet power to further examine fluctuations in power over specific ranges of wavelet periods (bands). Scale-averaged wavelet power is defined as the weighted sum of the wavelet power spectrum over scales s1 to s2:

display math

where δj is a factor that dictates the scale resolution (chosen as 0.1), and Cδ is a reconstruction factor specific to each wavelet form; Cδ = 0.776 for the Morlet. This approach also allows increasing the degree of freedom of the power estimators. In Figure 2, the dashed curve depicts the cone of influence of the wavelet analysis [Torrence and Compo, 1998]. Any peaks outside the cone of influence have presumably been reduced in magnitude due to the zero padding necessary to deal with finite length observations. For example, it is possible that activity around a period of 16 years in Figure 2 (see, for example, Hu et al. [1998] for an exploration of such periods) carries on at both ends of the time series instead of diminishing, as illustrated. For the span of the available streamflow data, it is thus not reasonable to consider wavelet periods much beyond 12 years. Three bands of wavelet periods are examined in greater detail: 2–3, 3–6, and 6–12.

Figure 2.

Bow River at Banff (station 05BB001). (a) Time series of mean annual streamflows. (b) Normalized local wavelet power spectrum of the streamflows using the Morlet wavelet. The shaded contours are at normalized variance of 1, 2, and 4. The dashed curve depicts the cone of influence beyond which the edge effects become important. The white contour lines enclose peaks of greater than 95% confidence for a red noise with a lag-1 coefficient α of 0.18.

[21] Finally, the power spectrum produced for a given time series is the product of the natural process involved and noise. The contour lines in Figure 2 identify peaks of greater than 95% confidence for a red noise process with a lag-1 coefficient α of 0.18 following the Monte Carlo analysis of Torrence and Compo [1998] based on the univariate lag-1 autoregressive process. It must not be presumed that regions of the power spectrum out of these 95% confidence level areas are the product of noise only. The natural process is also present in these regions but influences the power spectrum to a lesser extent. The coefficient α is series specific and is estimated for each series.

4. Wavelet Analysis Results

4.1. Eastern Canada

[22] The scale-average wavelet power represents the average variance (equation image2) over a range of scales (or a certain band). It provides an efficient way to examine the fluctuations in power over a desired band. By averaging the wavelet power spectra at multiple locations, one can simultaneously assess the spatial and temporal variability of the streamflow data. Figure 3a shows a power Hovmöller [Torrence and Compo, 1998], a time-longitude diagram of the normalized scale-averaged wavelet power of the eastern Canada streamflows in the 2–3 year band at the longitude location of each hydrometric station. At each longitude, the wavelet power spectrum is computed using the Morlet wavelet, and the scale-averaged wavelet power over the 2–3 year band is calculated from equation (3). Then all the scale-averaged wavelet power time series (equation (3)) are combined in a two-dimensional contour plot, with 95% confidence level computed using the lag-1 autocorrelation at each site. To allow the juxtaposition of streamflow from watersheds of different sizes, each scale-averaged series is normalized by σ−2 of the original series. The zonal-average of the power Hovmöller (Figure 3b) gives a measure of the average 2–3 year variance of the streamflows over eastern Canada. It typically shows the temporal fluctuations of the streamflows over the entire area. For example, activities in the 2–3 year band account for up to 45% of the average variance (0.45 equation image2) between 1978 and 1982, with a second moderate peak (0.30 equation image2) between 1955 and 1960. Figure 3c shows the time-averaged 2–3 year power as function of longitude. The longitudinal distribution of the power spectra (Figures 3a and 3c) reveals three local patterns: a low activity zone at 50°–60°W, an intense activity zone at 60°–77.5°W, and a moderate activity region at 77.5°–90°W, corresponding (see Table 1) to region 1 (Boreal Shield: Newfoundland-Labrador and Northern Quebec), region 2 (Atlantic Maritime: Nova Scotia, New Brunswick, and Prince Edward Island) and part of region 3 (Mixedwood plain: Southern Quebec and upper St. Lawrence/Lake Ontario); and region 4 (Boreal Shield: Ontario) and part of region 5 (Boreal/Taiga Shield: western Quebec), respectively. This may suggest that the division of flow stations into climatic regions can be refined by considering the space-time variability of mean annual flows. In general, the eastern Canada streamflows are characterized by locally intense activities in the 2–3 year band with moderate peaks in 1945 and 1955, and stronger peaks in the 1980s. There is no significant structure in that band prior to the 1940s.

Figure 3.

Time-longitude diagrams of the Canadian annual flows in the 2–3 year band. (a) Hovmöller plot of the normalized scale-averaged wavelet power. The shaded contours are at normalized power of 0.2, 0.5, and 1. The white contour lines enclose peaks of greater than 95% confidence computed using the lag-1 autocorrelation at each site. (b) Space-average of the power Hovmöller. (c) Time-average of the power Hovmöller. Each circle corresponds to a flow station location.

[23] Figure 4 illustrates the power Hovmöller for the 3–6 year band of eastern Canada streamflows. The general level of activity is slightly similar to the preceding band (2–3 year), but with different timing. The activity in the 3–6 year band accounts for up to 0.5 equation image2 around 1930s, with a second peak (0.4 equation image2) between 1950 and the late 1960s (Figure 4e). There is an organized activity in that band since the 1930s, with fluctuations differing as a function of longitude until the 1990s. Here again, the longitudinal distribution of the power spectra (Figures 4d and 4f) suggests three regions with low, high, and moderate activity, thus confirming that finer regionalization of the flow stations may be obtained by assessing the low-frequency fluctuations of mean annual streamflows. The timing of the zonal-scale fluctuations in the 2–3 year band (Figure 3b) and the 3–6 year band (Figure 4e) is surprisingly opposite, suggesting that these structures are driven by different climatic phenomena or a combination of climatic patterns. Figure 5 presents the power Hovmöller for the 6–12 year band of eastern Canada streamflows. There is only one significant structure (or peak) in that band, accounting for about 0.25 equation image2 around the 1930s. There has been no organized activity in the 6–12 year band for the last 60 years. It should be noted that caution must be exercised in interpreting the results for the 6–12 year band since many of the stations have record lengths that are shorter than would be desired for this type of analysis.

Figure 4.

Time-longitude diagrams of the annual flows in the 3–6 year band. Features are identical to Figure 3.

Figure 5.

Time-longitude diagrams of the annual flows in the 6–12 year band. Features are identical to Figure 3.

4.2. Central Canada

[24] The limited number of stations with longer records available in central Canada suggests that the wavelet analysis results presented herein are not representative of the entire region and must be interpreted with caution. Figures 35 show the power Hovmöller for the 2–3, 3–6, and 6–12 year bands of central Canada streamflows. In the 2–3 year band, there is a single activity accounting for up to 0.55 around the 1940s, while in the 3–6 year band, there are two intense activities corresponding to a strong peak (0.65 equation image2) in the 1930s and a second strong peak (0.60 equation image2) between 1980 and 1990. In the 6–12 year band, a moderate activity accounts for about 0.50 equation image2 around the 1930s.

[25] Although the longitudinal distribution of the power spectra is questionable because of the limited number of stations, the zonal average still provides a good measure of the temporal fluctuations of the streamflow. In general, there has been no organized activity in the 2–3 and 6–12 year bands in the last 50 years. The 3–6 year band is characterized by a strong activity between 1920 and 1930 followed by a no-activity period (1940–1970), and a second strong activity between 1980 and 1990. Those temporal fluctuations are essentially reflected by one site (station 06GD001 at 96.27°W). Additional streamflow records will be necessary to further assess the spatial and temporal variability of streamflows in central Canada.

4.3. Western Canada

[26] In this analysis, the western Canada streamflows cover regions 7, 8, and 9 (see Table 1) with a total of 29 stations, thus allowing a better space-time variability analysis of streamflows as compared to the central part of Canada. Figure 3 presents the power Hovmöller for the 2–3 year band of western Canada streamflows. The strongest activity in this band is in the 1920s, accounting for up to 0.90 equation image2 (Figure 3b), with a second peak (0.40 equation image2) between 1970 and 1980, and a third peak (0.45 equation image2) in 1998. There is no organized activity in that band between 1925 and 1965. Here the longitudinal distribution of the power spectra (Figures 3a and 3c) suggests three distinct activity zones: an intense activity zone at 116–121W, a moderate activity region at 121–129W, and a no activity zone at 129–136.5W – corresponding approximately (see Table 1) to region 7 (Montaine Cordillera – British Columbia), region 8 (Pacific Maritime – British Columbia), and region 9 (Boreal Cordillera – British Columbia/Yukon Territories) respectively. It appears that some flow stations (actually in region 7 or 9) can belong to neighboring region 8 – suggesting that a refinement of the station division may be possible based on the wavelet analysis of the annual sreamflows. Figure 4 illustrates the power Hovmöller for the 3–6 year band of Western Canada streamflows. The general level of activity is slightly similar to the preceding band (2–3 year), but with different longitudinal distribution and slightly similar timing except for year 1950. The activity in the 3–6 year band is characterized by three moderate peaks (in 1920, 1950, 1970) and a lower peak in 1998 (Figure 4e). The longitudinal distribution of the power spectra (Figure 4d) confirms the three distinct activity zones (116–121W, 121–129W, and 129–136.5W) but with different level of intensity as compared to the activity level in the 2–3 year band. The Boreal Cordillera (region 9) seems dominated by the 3–6 year activity while the Montaine Cordillera (region 7) is more strongly affected by the 2–3 year band activity. Only the Pacific Maritime appears equally affected by both the 2–3 year and the 3–6 year activity. There is no organized structure in the 6–12 year band as indicated by its power Hovmöller (Figure 5). The overall level of activity in that band accounts for only 0.15 equation image2, and thus it consists essentially of white noise. Again, care must be taken in interpreting these results due to the presence of stations with short record lengths.

4.4. Power Hovmöller of Canadian Streamflows

[27] To simultaneously assess the spatial and temporal variability of the annual streamflows throughout Canada, the time-longitude diagrams of the annual flows (from western to eastern Canada), Figures 35 are discussed. It is noteworthy that even an apparently small feature in these figures represents a significant activity. The smaller structure sizes are due to scale reduction to allow juxtaposition of all the 79 stations and to provide a complete overview of the spatial and temporal variability of the streamflows (from west to east). It appears from Figure 3 that organized activity in the 2–3 year band starts after the 1940s except for western Canada, where a strong activity is observed in the 1920s. Moderate activity is revealed between 1950 and 1960, and major (intense) activity is revealed between 1970 and 1990. Conversely, in the 3–6 year band (Figure 4), the major activity is observed between 1950 and 1970 and moderate activity between 1920 and 1930 and between 1980 and 1990. However, in both cases, years 1950 and 1970 can be seen as particular points in the streamflow variability level. A moderate 6–12 year activity is revealed around the 1930s only in the eastern and central Canada streamflows (Figure 5). There has been no organized activity in the 6–12 year band since 1940. In general, the Canadian streamflows appear essentially dominated by the 2–3 and 3–6 year activity. Therefore only the 2–3 and 3–6 year bands are considered herein for the streamflow-climatic pattern study.

4.5. Streamflow and Climatic Patterns

[28] To examine the dynamic relationship between the streamflow and the selected climatic indices, the dominant structures of the interannual variability in the streamflows revealed by the power Hovmöller plots are exploited. Principal component (PC) analysis is used to construct three streamflow time series corresponding to western, central, and eastern Canada streamflows. The west PC series are obtained from the 29 stations located between 110°W and 140°W, the central PC series are constructed from the three stations (between 90°W and 100°W), and the east PC series are obtained for the 47 stations between 40°W and 90°W (see Figure 1). In each case, the leading PC selected (Figure 6) explains at least 70% of the total variance. Specifically, the west leading PC explains 80% of the total variance, while the central and the east PCs explain 95% and 75% of the total variance, respectively. The PC series (Figure 6) reveals three possible time periods in the streamflow variability: one in 1911–1950, a second in 1950–1970, and third in 1970–1999, each characterized by a different trend and level of variability. This raises an interest in investigating further the streamflow power during these three periods. The PC series as shown in Figures 7 and 8 do preserve the main interannual features revealed in the power Hovmöller plots for the 2–3 and 3–6 year bands. Figure 7 shows the 2–3 year scale-average power spectra for the PC streamflow series and the teleconnection patterns considered. Figure 7 reveals a positive correlation between the west streamflow power and the ENSO3 activity particularly after 1950, while a negative correlation with the PNA activity is shown since 1950. Note that the PNA series are available only from 1950, while the others are available for the entire period (1911–1999) considered. To further substantiate the results in Figure 7, correlation analysis results for the 2–3 year band are presented in Table 2, for data before and after 1950, data before and after 1970, and for all available data (1911–1999). Considering the complete data set, the western streamflow activity in the 2–3 year band is essentially depicted by the ENSO3, with a correlation value of 0.52. The west streamflow power is also negatively correlated to the PNA (−0.47) for the period 1970–1999, while there is no correlation with the NAO and the NAM.

Figure 6.

Time series of the flow leading principal component: west, central, east.

Figure 7.

Time series of the scale-averaged wavelet power for the 2–3 year band: west, central, east, and selected climatic indices.

Figure 8.

Time series of the scale-averaged wavelet power for the 3–6 year band: west, central, east, and selected climatic indices.

Table 2. Correlation Analysis Results for the 2–3 Year Band
Climate Indices≤1950≥1950≤1970≥19701911–1999a
  • a

    Except for the PNA index, where time series are available for 1950–1999.


[29] The central streamflow power is negatively correlated to ENSO3 (−0.50) and PNA (−0.55) during 1950–1999 and 1950–1970, respectively. Again, the NAO and the NAM are not correlated to central streamflow power. Conversely, the eastern streamflow power is positively correlated to NAM prior to 1950 (0.53) and negatively correlated with NAO afterward (−0.64), confirming that these “twin patterns” do not have the same temporal distribution of power as shown in Figure 7. East is also correlated to ENSO3 (−0.48) only after 1970, but more correlated to the PNA (0.66) during 1950–1999. Since 1950, the eastern streamflow activity in the 2–3 year band is depicted mainly by the PNA and the NAO, while the central and western streamflow activities are mostly related to the ENSO3 and the PNA. Considering all the data analyzed for the entire period (1911–1999), the Canadian streamflow activity in the 2–3 year band is correlated to the PNA (0.48) during 1950–1999, but before 1950 it is mainly correlated to the NAM (0.62), but with no correlation to the NAO. Conversely, after 1970, the Canadian streamflow power is negatively correlated to the NAO (−0.55), while there is no correlation to the NAM for that period. This may indicate that even though the NAO and the NAM are two representations of the same phenomenon [Wallace, 2000], they are not identical. It has been shown that the NAM index is more strongly coupled to Eurasian winter surface air temperature than the NAO index [Thompson and Wallace, 1998], suggesting that NAM and NAO can have different impacts in a specific region.

[30] Similar analysis is performed for the 3–6 year band (Figure 8 and Table 3). The higher level of activity in the 3–6 year band discussed earlier is reflected in general by stronger correlations with the teleconnection patterns. Here again, the west is correlated to the ENSO3 (−0.48), but also to the NAO (−0.69), and the PNA (−0.59) during 1950–1999. The increasing level of activity in the west (since 1950) is likely related to PNA as indicated by the increasingly strong correlations since 1950. A striking element of the correlation results here is that after 1970, the west is negatively correlated to all the climatic patterns selected, while before 1970, it is correlated only to the PNA. Similarly, after 1950, the west is negatively correlated to ENSO3 and NAO, while there was only a positive correlation to NAO prior to 1950. From these results, one can argue that years 1950 and 1970 may represent changing points in west streamflow activity, and this appears consistent with the recent study of Chen and Rao [2002], who tested the stationarity of midwestern United States hydrologic time series using segmentation analysis and identified change points between 1960 and 1970. Furthermore, the 1970 change point may also be related to the enhancement of the power in the 3–6 year band for both the NAO and the PNA since 1970 (Figure 8), suggesting that change point in streamflow variability may not only reflect sudden changes in intensity of climatic patterns, as shown by the teleconnection indices, but also can be attributed to modifications in the dominant atmospheric circulation modes that affect a specific region. This obviously requires further investigation to be illustrated. Still, in the 3–6 year band, the central streamflow power is highly correlated to the PNA (0.75) prior to 1970 and moderately correlated to the NAO (−0.46) after 1970. Here ENSO3 and NAM are not correlated to the central streamflow power. The eastern streamflow activity is correlated to ENSO3 (−0.66) and NAO (−0.73) since 1950, with stronger correlations (−0.70 and −0.79, respectively) after 1970. East is also strongly correlated to the PNA (−0.84) prior to 1970 and less correlated afterward. Here again, there is a significant enhancement in the intensity level of the teleconnection indices (ENSO3, NAO) after 1950 and 1970, respectively, suggesting two possible change points: a first one in 1950 and a second one in 1970. This is consistent with previous studies in eastern Canada. Shabbar et al. [1997b] identified a detectable cooling in winter surface temperature data from 12 stations in coastal eastern Canada and western Greenland since 1970 that was linked to an enhancement of the negative phase of the NAO index and of the positive phase of the PNA. Perreault et al. [2000] used a Bayesian method to identify a change point in annual reservoir inflows for the Outaouais basin in eastern Canada. They reported a change point around 1979 with approximately 12 years of standard deviation. Although the change point in 1950 suggested by the present results may require further investigation, it is clear from the present analysis that the east and the west 3–6 year bands are negatively correlated to the ENSO3 and NAO since 1950, which was not the case prior to that change point. Similar findings substantiate the 1970 change point in the west and the east (see Table 3). The low activity level in central Canada streamflows is associated with the limited data in this area, as discussed earlier. Additional streamflow records will be needed to assess whether the 1950 and 1970 change points appear in that region.

Table 3. Correlation Analysis Results for the 3–6 Year Band
Climate Indices≤1950≥1950≤1970≥19701911–1999a
  • a

    Except for the PNA index, where time series are available for 1950–1999.


[31] In general, considering the entire data set during 1911–1999, the Canadian streamflow activity in the 3–6 year band is depicted mainly by the NAO (−0.61), the ENSO3 (−0.58), and the PNA (−0.53). Surprisingly, there is no significant correlation with NAM since 1950. In both the 2–3 and 3–6 year bands, the Canadian streamflows are depicted mainly by the PNA and the NAO and by the ENSO especially in the 3–6 year band, which is consistent with the ENSO cycle.

5. Discussion

[32] The wavelet analysis results presented in the previous section reveal clear temporal patterns which can be used to refine streamflow regionalization over the Canadian Reference Hydrometric Basin Network (RHBN). The main characteristic timescales (2–3 and 3–6 year periods) of the annual streamflows revealed by the global wavelet spectra along with the strong climate related correlations identified provide qualitative information that is essential to any attempt to investigate the effects of climate change on streamflows. For example, it is clear from Table 2 that since 1950, the eastern streamflow activity in the 2–3 year band is mostly related to the PNA and NAO, while the central and western streamflows are mainly dominated by the ENSO3 and the PNA. Such streamflow-climate relationship can also be used to improve long-range forecasting, which is an essential part of the development of optimal reservoir planning and operation policies for power generation, water supply, and flood control. For example, the use of the ENSO-streamflow relationship for predictive purposes has shown promising results in recent studies [Piechota et al., 1998; Coulibaly et al., 2000; Gutiérrez and Dracup, 2001]. However, further analysis of the climate-streamflow relationship may be required and should include other methods such as cross-wavelet analysis to highlight the temporal variation in the relationship between streamflows and climate indicators. The integration of the observed temporal structures and the related climatic patterns into streamflow simulation would require a suitable hydrologic model which can take into account all the observed dynamic components of the streamflow.

6. Conclusions

[33] The continuous wavelet transform offers an effective tool for both describing interannual features and quantifying the temporal variability of annual streamflows. Scale-averaged wavelet spectra permit us to simultaneously assess the interannual and spatial variability in 79 streamflow time series. The span of the available streamflow records, 1911–1999, allows depicting the interannual variance (or activity) for periods up to 12 years, and thus three periods, namely, 2–3, 3–6, and 6–12 year bands, are investigated. It is shown that the Canadian streamflows are essentially dominated by the 2–3 and 3–6 year activity with net differences between the timing and the intensity of the interannual variability in western, central, and eastern Canada. The 6–12 year band activity is dominated by white noise in all the regions since 1950. Correlation analysis between streamflow activity and climatic pattern power in both the 2–3 and 3–6 year bands revealed two major change points, namely, 1950 and 1970 in western and eastern streamflows, while it is concluded that central Canada requires additional streamflow records to assess similar change points. In the 2–3 year band, western and central streamflow activity is essentially depicted by the ENSO3 and the PNA since 1950, while the eastern streamflow activity is highly correlated to the NAO and PNA. In general, the Canadian streamflow activity in the 2–3 year band is depicted by the NAM prior to 1950, the PNA since 1950, and the NAO since 1970.

[34] Stronger correlations with the teleconnection patterns are observed in the 3–6 year band. The most striking elements in the 3–6 year band are that since 1970, the west is strongly negatively correlated to all the climatic patterns, while before 1970, it was correlated only to the PNA. Similarly, since 1950 the west and east are highly negatively correlated with the ENSO3 and NAO, which was not the case prior to 1950. In the 3–6 year band, central streamflow is essentially depicted by the NAO since 1970 and by the PNA before 1970. In general, the Canadian streamflow activity in the 3–6 year band is depicted by the NAO, the ENSO3, and the PNA. The correlation analysis results confirm that NAM and NAO can have significantly different impacts in a given region, indicating that the two climatic patterns are not identical. The wavelet analysis results also indicate that streamflow regionalization can be refined based on their wavelet spectra. Further analysis should include monthly streamflows and climatic patterns to assess high-frequency (infra-annual/seasonal) structures.


[35] This work was made possible through grants from the Natural Sciences and Engineering Research Council of Canada to each author. The authors gratefully acknowledge the student contribution of Vanessa Arnold. Main wavelet analysis routines were provided by C. Torrence and G. P. Compo, and are available at http://paos.colorado.edu/research/wavelets/. The NAO, PNA, and ENSO3 indices are available through NOAA's Climate Prediction Center at http://www.cpc.ncep.noaa.gov/. The NAM (or AO) index values are available through D. W. J. Thompson's Annular Modes Web site at URL: http://www.atmos.colostate.edu/ao/.