JANUARV 2005 C O U L I B A L Y AND BURN 191

Spatial and Temporal Variability of Canadian Seasonal Streamflo>vs

PAULIN COULIBALY

Department of Civil Engineering and School of Geography and Geology, McMasler University. Hamilton. Ontario. Canada

DONALD H . BURN

Department of Civil Engineering, University of Waterloo, Waterloo. Ontario. Canada

(Manuscript received 9 December 2003, in final form 7 June 2004)

ABSTRACT

Wavelet and cross-wavelet analysis are used to identify and describe spatial and temporal variability inCanadian seasonal streamflows. and to gain insights into the dynamical relationship between the seasonalstreamflows and the dominant modes of climate variability in the Northern Hemisphere, Results fromapplying continuous wavelet transform lo mean seasonal streamflows from 79 rivers selected from ihcCanadian Reference Hydromctric Basin Network (RHBN) reveal striking climate-related features beforeand after the \95ih. The span of available observations. 1911-99. allows for depicting variance and covari-ance for periods up to 12 yr. Scale-averaged wavelet power spectra are used to simultaneously assess thetemporal and spatial variability in each set of 79 seasonal strcamflow time series. The most striking feature,in the 2-3-yr period and in the 3-6-yr period—the 6-!2-yr period is dominated by white noise and is notconsidered further—is a net distinction between the timing and intensity ol' the temporal variability inautumn, winter, and spring-summer streamflows. It is found that the autumn season exhibits the mostintense activity {or variance) in both the 2-3- and the 3-6-yr periods. The spring-summer season corre-sponds to the least intense activity for the 2-3-yr period, but it exhibits more activity than winter for the3-6-yr period.

Cross-wavelet analysis is provided between the seasonal streamtlows and three selected climatic indices:the Pacific-North America (PNA). the North Atlantic Oscillation (NAO), and the sea surface temperatureseries over the Nifio-3 region (ENSO3), The wavelet cross-spectra reveal strong climale-streamflow activity(or covariance) in the 2-6-yr period starting after 1950 whatever the climatic index and the season. Prior to1950, local and weaker 2-6-yr activity is revealed in central and western Canada essentially in winter andautumn, but overall a non-significant streamflow-climate relationship is observed prior to 1950. Correlationanalysis in the 2-6-yr band between the seasonal streamflow and the selected climatic indices revealedstrong positive correlations with the ENSO in the spring-summer and winter seasons for the post-1950period for hoth eastern and western Canada. A similar correlation pattern is revealed in the west with theNAO, while in the east moderate negative NAO correlations are observed only in the aulumn season priorto 1950, After 1950 strong NAO correlations emerge for ail the seasons. The cross-wavelet spectra and thecorrelation analysis in the 2-6-yr band suggest the presence of a change point around 1950 in the east andwest seasonal streamflows.

I. Introduction

Hydrological systems act as sensible spatial and tem-poral integrators of precipitation (rain and snow), tem-perature, and related evaporation over a speeific areaor region. Seasonal variations of streamflows arise fromvariations in precipitation and temperature, which arecontrolled by large-scale fluctuations in atmosphericcirculation patterns. Hence, streamflow records eanserve as a pertinent index of hydroclimatic variability

Corresponding author address: P. Coulibaly, Dept. of Civil En-gineering and School of Geography and Geology, McMaster Uni-versity. Hamilton, ON L8S 4L7, Canada.E-mail; couliba@mcmaster.ca

at a loeal or regional seale. Gaining insight into the finertemporal structures of streamflow variability is essen-tial to the understanding of the complex hydrology-climate relationship and the dynamics of the hydrologiecycle, which in turn will improve our ability in modelinghydrological systems. This typically requires a decom-position of streamflow time series into time-frequencyspace to identify the dominant modes of variability andto determine how these modes vary in time. This hasbeen done by resorting mostly to Fourier transforms(Hameed 1984; Kunhel et al. 1990; Larocque et al.1998). A major limitation of the Fourier analysis is thatit does not retain the location of a particular event intime and space, nor does it perform well on irregularlyspaced events or nonstationary signals (Smith et al.

© 2005 American Meteorological Society

192 JOURNAL OF CLIMATE VOLUME 18

1998). Standard short-term Fourier transform is par-ticularly limited by its window of fixed arbitrary length.It has been recently shown that temporal structures ofrainfall-runoff records cannot be taken into accountadequately using classical spectral or correlation analy-ses (Labat et al. 2(K)0a). As an alternative, wavelettransforms have been proposed. A major property ofthe wavelet transform is its ability to provide a robustapproach to decompose and represent time series into afiner scale-time domain without a window with arbi-trary limited length. Furthermore, it can permit distin-guishing between two signals that have very similarFourier spectra.

Wavelet analysis has been used in geophysies andmeteorology to identify coherent convective stormstructures and characterize their temporal variability(Kumar and Foufoula-Georgiou 1993; Takeuchi et al.1994: Kumar 1996: Szilagyi et al, 1999) or to analyzelocalized variations within geophysical time series in-cluding climatic indices (Shabbar et al. 1997b; Hu el al.1998: Lucero and Rodriguez 1999), In hydrology, wave-let analysis has been recently applied to examine dailyrainfall-runoff relatitjnships in a karstic watershed (La-bat ct al. 20(K)b), and aiso lo characterize daiiy stream-flow in the United States (Smith et al. 1998) and todescribe reservoir inflow variability in northern Quebec(Couiibaly et al, 2000). More recently, wavelet analysishas been used to describe interannual variability insouthern Quebec streamflows (Anctil and Coulibaly2004). The last two studies were not only confined to aspecific region but also limited to about ?() years ofmean annual Hows.

ln this analysis, continuous wavelet transforms areused to allow a finer analysis of the time-varying struc-tures of the seasonal streamflow records and thestreamflow-elimate relationship throughout Canada.The main objectives of this analysis are to deseribe anddocument the seasonal variability in Canadian stream-flows using wavelet and cross-wavelet analysis. Thisstudy also aims to examine the role of the dominantclimatic patterns in the Northern Hemisphere on theseasotial variability of Canadian streamflows. The re-mainder of the paper is organized as follows. A descrip-tion of the study area and the datasets are first pro-vided. The eontinuous wavelet and cross-wavelet analy-sis method is presented next. Results from the waveletanalysis are then reported, and finally some conclusionsare drawn.

2. Study area and datasets

(/. Reference Hydrometric Basin Network(RtlBN)—-Seasonal streamflows

The analysis described herein was performed on sta-tions from the Reference Hydromctric Basin Network(RHBN). a data collection network of natural rivers inCanada identified by Environment Canada for climatic

change researeh. The criteria according to whieh sta-tions were selected for the RHBN are as follows (Har-vey et al. 1999):

1) degree of basin development: Stations that were in-cluded in the network were those that refleel eateh-ments that are pristine or have stable land-use con-ditions.

2) absenee of signifieant regulations or diversions: Acatchment was considered natural if there was nocontrol strueture upstream of the gauging station,while it was considered regulated if there was anupstream control structure.

3) reeord length: A station must have a minimum rec-ord length of 20 years to be ineluded in the RHBN.The present work selected from the RHBN onlythose stations with a record length of at least 35years to ensure an adequate record length for thewavelet analysis.

4) longevity: This criterion was based on the judgmentof the regional staff. A station was excluded fromthe network if it is currently active but was expectednot to have future data collection activities.

5) data accuracy: Data accuracy was assessed qualita-tively by local experts based on knowledge ol' thehydraulic condition of the stations to ensure thatonly stations with good quality data were ineluded inthe network.

Basin sizes in the RHBN range from 3.63 to 145 000km" with a median size of 1170 km^: 10% of the basinshave a drainage area greater than 20 000 knr. and 10%have a drainage area less than 100 km". An analysis ofthe eharacteristies of stations within the RHBN indi-eates certain limitations of the existing network. Thenetwork tends to comprise large basins in the north andsmaller basins in the south, and certain provinces havelarge gaps in spatial coverage.

The current research employs a subset of the RHBNeonsisting of 79 longer-term gauging stations (see Fig.1) to minimize the limited data record problem andallow longer period (up to decadal time scale) anatysis.The subset ofthe RHBN that has been selected tor thiswork suffers from the same limitations outlined abovefor the RHBN as a whole, ln particular, there are alimited number of stations representing the Canadiannorth and there are few stations from the Prairie Prov-inees (or eentral Canada). The median reeord lengthfor the stations analyzed in this work is 49 years, with arange of record lengths from ?5 to S5 years. The catch-ment drainage areas range from 3.63 to 29 900 km"̂ witha median value of 1350 km'. As such, the subsL't of theRHBN is fairly typical of the stations in the RHBN interms of drainage areas, but consists only of the bestavailable streamflow time series with longer recordlengths. The selected sites aUing wilh the station num-bers, drainage basin areas, and locations are listed inTable 1. The regional grouping of sites (Table 1) is

1 JANUARY 2005 C O U L I B A L Y AND BtJRN 193

Fi(i, 1, Location map: Canada RHBN of line 79 flow stations selected.

based on statistical analysis and climatic factors (Har-vey et ai. 1999; Adamowski and Bocci 2001). The hy-drologie variable selected for this researeh is the sea-sonal mean flow, given that the study is mainly con-cerned with the strong seasonal variability inherent toNordie river flows. Owing to the large size of the studyarea, the length of season is region dependent. Henceseasonal division of slreamllow is based on the analysisof all the monthly streamflow available in each region.To illustrate the streamflow division. Fig. 2 shows thedistribution of monthly flow for two stations (02YL001and 02KB001—located in Upper Humber River, New-foundland, and in Petawawa River, Ontario, respec-tively) and the seasonal division of streamtlow adopted.Similar analysis was eondueted for each of the nineclimatic regions. Table 2 presents the seasonal divi-sion of streamflow for eaeh region and the seasonalclimatic indices used in this study and described here-after.

h. Climatic indices

The analysis also includes several climatie patternsthat appear and persist in the Northern Hemisphere.Two of these are the North Atlantie Oscillation (NAO)and the Pacific-North American (PNA), which arefound to be the most prominent and recurrent patternsof atmospheric eirculation variability in ihe NorthernHemisphere (e.g., storm-track and temperaturechanges: Barnston and Livezey 1987; National Re-search Council 1998; Hurrell et al. 2003). The NAO is alarge-seale alternation of atmospheric mass with cen-ters of aetion near the Icelandic low and the Azoreshigh. It is Ihe dominant and persistent mode of atmo-spheric behavior in the North Atlantic throughout the

year explaining on average 32% of the varianee inmonthly sea level pressures (SLP) (Cayan 1992) butwith even greater dominance during the winter. TheNAO index used in this study is from Hurrell (1995)who exploited SLP atiomalies from Lisbon, Portugal,and Stykkisholmur. Iceland, While exhibiting consider-able interannual variability with concentrations of spec-tral power around periods of 2.1, 8. and 24 yr (Cook etal. 1998). the NAO has been in a generally positivephase since about 1970. A signifieant coherent relation-ship between the NAO and the North Atlantic sea sur-face temperature has reeently been found at interan-nual and interdecadal time seales (Higuchi et al. 1999).The signature of the NAO is strongly regional and canbe directly tied to variations in regional precipitation.Therefore the NAO index may be a relevant variable tothe regional hydrology. For example, in a study on in-terannual variability of Canadian snow cover from 1915to 1992 (Brown and Goodison 1996). significant winterNAO-snow cover correlations were observed in On-tario and southern Ouebec. specifically in December.Other studies (Coulihaly et al. 2000; Anetil and Couli-baly 2004) have shown the intluence of the NAO cir-culalion pattern on annual flow in northern and south-ern Quebec.

Another persistent climatic pattern that has to beconsidered in the Northern Hemisphere is the Pacific-North American atmospheric teleconneetion, which isdefined as a measure of atmospheric response to awarm sea surface temperature (SST) anomaly in thecentral equatorial Pacific (Wallace and Gutzler 1981).The PNA has been found to be a dotninant mode ofvariation in the middle latitudes during the wintermonths. It has been shown to be strongly related to

194 J O U R N A L OF CLIMATE VOLUME 18

TABLE 1. Canadian Reference Hydrometric Basin Network gauging stations used in the wavelet anatysis. River drainage area andlocations are included.

Region

1III1111I11222222222222222222233333333333444444

556

77777777777

Station

()2ZM(H)602ZK(H)l02YRO()102ZH(Hn02YOII()I02ZCHX11O2ZFO()102Ya)()l02YUH)l02ZB(H)]02VnH)lOIFBOOIOlFBIHXl01EO(H)101DG()()301CA003OlEFOOl01BU00201AP002OIEC(H)1UlAPfXM01BC)()l)lOIBOIHIIOlBHHIlOlAOUOlOlBEOOlOlAKOOlOlBCOOl01AD(H)2OlADIH).!02PJ()()702OE02702RD0()202NF0O302LB00702KB00102HL(X)4()2Ea)0202GA()1002FBO0702FC00104NA(X)l()4LJ(X)I()4JC()0202EA{X}502AB00SO2AA(X)1

05PB()1406Gt)001O5LH()O5

08NF(H)l08NB005O8NEO87n8NE07708LD0()l08LA0010HNUH)7O8MH()160SKH(K)608MG()0508JE001

Latitude {"N)

47.635047.224748.807847,946949,015347,213947,7467.S0,607549.240647.613950.307846.369446.223345.173344,851746,744244,446745,943646,071943.838345,701946,736147.094746.935845.170047.831745.94547,666747,256947,206946,659245,467248,899446.685844.842245.888144.549444.712843.190644.522544,456448.600649,616749,778945,669448,382248.0122

48.850058.891751.8528

50.886151.483349.425049.907550.938351.655649.459749.083952,843650,335654.4181

Longitude ("W)

Eastern Canada52.837253,568354.224454,285654.853655.329255.441757.151157.362559.(X)9263.622560,976761,136761,981763,665064,185664.591765.170365.366765.370065.601465.826765.837265.907266.466766.881767,322267,484268,593168,956971.288671.655372.211773.914275.543977.308377.329279.281780,454780,930881,326778.109483.263384.530079.378689.307889.6161

Central Canada92.725096.275399.5472

Western Canada116,0431117,1792118.0417118,1253119.6544120.0653120.5019121.4567122.2236122.7994124.2750

Drainagearea (km')

3.63285275764

4400205

1170624

2110205

13 000368357

135096.946.8

1250391668495

11005050

9481340239

2270234

316014 700

1350709642

93201390246

4120712

15201030

1813960368089402410

321187

1550

48704810055 000

4209710

80.5201

308010 200

1850329

115002160

14 600

Ecozone

Boreal ShieldBoreal ShicklBoreal Shick!Boreal SliicIdBoreal ShieldBoreal ShieldBoreal ShieldBoreal ShieldBoreal ShieldBoreal ShieldBoreal ShieldAtlantie MaritimeAtlantic MaritimeAtlantic MaritimeAtlantic MaritimeAtlantic MaritimeAtlantic MaritimeAtlantic MaritimeAilanlic MaritimeAtlantic MaritimeAtlantic MaritimeAtlantic MaritimeAtlantic MaritimeAtlantic MarilimeAtlantic MaritimeAtlantic MaritimeAtlantic MaritimeAtlantic MaritimeAtlantic MarilimeAtlantic MaritimeMixed-wood plainMixed-wood plainBoreal ShieldBoreal ShieldMixed-wood plainBoreal ShieldBoreal ShieldBoreal ShieldMixed-wood plainMixed-wood plainMixed-wood plainBoreal ShieldBoreal ShieldBoreal ShieldBoreal ShieldBoreal ShieldBoreal Shield

Boreal ShieldTaiga ShieldBoreal Plain

Montaine CordilleraMontaine CordilleraMontaine CordilleraMontaine CordilleraMontaine CordilleraMontaine CordilleraMontaine CordilleraPaeifie MaritimeMontaine CordilleraPaeific MaritimeMontaine Cordillera

.lANtlARY 2005 COULIBALY AND BURN 195

TABLE 1. (Continued)

Region

7888888999999y9999

Station

08JB00208MH00608GA0I0OSHA0()3()8HA001()8HBO080SHE(X)607FB001lOCDOOllOCBOOl10BE(K408CE00108CG001O9AE00309BA00109AA00609AC(X)l09BC001

Latitude {°N)

54.009249,242849,395848,727548,879249.289750.014455.720058.788357.234258.855657.900856.738959.930661.994459,599260,852262.8297

Longitude ("W)

125,0050122,5783123.1444123.6697123.7019124.9103126.8425121.2078122.6592122.6942125.3806131.1544131.6736131.7678132.3778133.8133135.7392136.5806

Drainagearea (km^)

360037.3

172209355347181

12 10020 300

21602570

29 30093503320725068106990

49 000

Ecozone

Montaine CordilleraPacific MaritimePaeific MaritimePaeific MarilitnePaeific MaritimePaeific MaritimePaeific MaritimeMontaine CordilleraTaiga Plain. Boreal CordilleraTaiga Plain. Boreal CordilleraBoreal CordilleraBoreal CordilleraMontaine CordilleraBoreal CordilleraBoreal CordilleraBoreal CordilleraBoreal CordilleraBoreal Cordillera

precipitation and temperature within the same seasonin the western United States (Redmond and Koch1991). Strongly positive and negative PNA indices arcassociated with warm events (El Nino) and cold events(La Nina), respectively, and with North American pre-cipitation and temperature anomalies (Yarnal and Diaz1986). It has been ftiund that the pressure anomaliesassociated wilh the different phases of the PNA alterthe normal upper-atmospheric patterns, thus affectingtemperature and precipitation patterns over various re-gions ol" North America (Shabbar et al. 1997a).

In addition to the NAO and PNA indices, indicatorst)f the El Nifio-Southern Oscillation (ENSO) are alsoselected for this study. The ENSO phenomenon is char-acterized as a spreading of warm water off the coast ofSouth Atnerica from the equatorial central Pacific toeastern Pacific and is associated with elimatic anomaliesthroughout the world. The ENSO index used in thisstudy is the monthly mean equatorial Pacific SST timeseries over the Nifio-3 region (S^N-S'S: 90^'-150°W)(Rasmusson and Carpenter 1982). For notational sim-plicity. ENSO3 will be used herein to denote the SSTseries over that region. The influenee of ENSO onstreamflow is well documented (Redmond and Koch1991: Kahya and Draeup 1993: Eltahir 1996) and sub-sequently the use ofthe ENSO-streamflow relationshipfor predictive purposes has been studied extensively inrecent years (Moss et al. 1994; Piechota et al. 1998;Coulibaly et al. 2000; Gutierrez and Draeup 2001).

It is noteworthy that some climatic indices are rela-tively interlinked over some time periods. A complexrelationship has recently been shown between theNAO, ENSO. and PNA patterns (Huang et al. 1998).However, dynamical relationship between elimatic pat-terns remains controversial and warrants further re-search (Diaz ct al. 2001; Hurrell et al. 2003). Therefore,selected climatic patterns are used here as independent

variables in order to assess the specific link betweeneach climatie indictor and the Canadian seasonalstreamflows.

3. Methods

The decomposition of time series into t ime-frequency space permits not only the identification ofthe dominant modes of variability, but also the deter-mination of how these modes vary in time. This can bedone by using either windowed Fourier transform orwavelet transform. However, a major shortcotning ofstandard Fourier transform is that it does not providean accurate time-lVequency localization of dynamicalprocesses. A major advantage of using the wavelettransform over the Fourier transform is that waveletanalysis is scale independent (Kaiser 1994); hence thereis no need for a predetermined scale (or response in-terval) that would limit the frequency range. Continu-ous wavelet transform is more appropriate for geo-physical and hydrological time series because of thewide range of possible dominant frequencies. More-over, it is also an efficient method for analyzing non-stationary signals (Daubechies 1990)—that property isparticularly useful for analyzing complex time-varyingpatterns such as climatic indices and hydrological timeseries.

The wavelet analysis method described herein is lim-ited to the needs of the present study. Emphasis is givento useful practical details for applying the method forhydrologica! lime series analysis. For a more detaileddescription of wavelet analysis in geophysics and hy-drology, readers are referred to other sources, such asTorrence and Compo (1998) and Labat et al. (20()0b).The continuous wavelet transform W,, of a discrete se-quence of observations .v,, is defined as the convolution

196 JOURNAL OF CLIMATE

Region 1 Station 02YL001 (Upper Humber River)

VOLUME 18

winter

A

'/NX1m

1 spring-Sum mar1 •!

Autur

T

nn Wlnler

-

4 5 6 7 8

Mo nth

Region 3 Station 02KB001 (Pelawama Blver)

FIG. 2. Division of seasonal flows based oti longer than 80-yr records.

of -v,, with a scaled and translated wavelet I^T)) thatdepends on a nondimensional time parameter TJ.

I-=0

- n)8t(1)

where n is the loealized time index, .s is the waveletscale. 5? is the sampling period. A' is the number ofpoints in the time series, and the asterik indicates thecomplex conjugate. Since complex wavelets lead tocomplex continuous wavelet transform, the waveletpower spectrum, defined as |W,,(5)|". is a convenientdescription of the tluctuation ot the variance at differ-ent frequencies. Further, when normalized by tj ^(where o^ is the variance), it gives a measure of the

power relalive to white noise since the expectationvalue for a white-noise process is o^ at all n and ,v.Figure 3b illustrates the normalized local waveletpower spectrum of a typical seasonal (autumn) stream-flow time series (Fig. 3a) using the Morlet wavelet—acomplex nonorthogonal wavelet eonsisting of a planewave modulated by a Gaussian;

where w,) is the nondimensional frequency. The advan-tage of Ihe Morlet wavelet over olher candidates, suehas the Mexican hat wavelet, resides in its good defini-tion in the spectral spaee. For w,, - 6 (used here), theMorlet wavelet scale is almost identieal to the corre-

1 .IANUARY2005

TABLE 2. Seasona

East

Central

West

(ENSO.1. NAO.PNA)

I division

Region

1234

67Sy

COULIBALY

of streamflow iuid climatic inijict;s.

Winter

Dec-MarNov-FebDec-FebDec-MarDec-AprDec-MarDt'C-AprNov-MarDec-Apr

Dec-Mar

Spring-summer

Apr-JulyMar-JulyMar-JulyApr-JulyMil y-AugApr-AugMay-AugApr-JulyMay-Scp

Indices*Apr-Jul

Autumn

Aug-NovAug-OctAug-NovAug-NovSej>-NovSef>-NovSep-NnvAug-OctOct-Nov

Aug-Nov

AND BURN 197

* Except for the Oct-Mar average ENSO3 indices, denotedENSO3_OM (OM stands for Oct-Mar period).

sponding Fourier period of the complex exponential,and the terms scale and period may conveniently beused synonymously (Torrcnce and Compo 1998: Tor-rcnce and Webster 1999). Thus, the lel'l axis in Fig. 3bis Ihc equivalent Fourier period corresponding to thewavelet scale (heneelorth called wavelet period), andthe bottom axis is time (in years). The shaded contoursare the normalized variance in excess of 1. 2, and 4.Features with variance larger than expected lOr a white-noise process reveal that the interannual variability isorganized in preferential bands of wavelet periods.

These bands, 2-3, 3-6, 6-12, and beyond 12 years, havebeen reported by other investigators in precipitationand streamt'low time series (Rajagopalan and Lall 1998;Coulibaly et al. 20(K); Anctil and Coulibaly 2{)04). Thissuggests the choice ofthe scale-averaged wavelet powerto further examine fluctuations in power over specificranges of wavelet periods (bands). Scale-averagedwavelet power is defined as the weighted sum of thewavelet power spectrum over scales s^ to S2'.

(3)

where 8; is a factor that dictates the scale resolution(chosen as 0.1), and Q is a reconstruction factor spe-cific to each wavelet form; C?, = 0.776 for the Morlet.This approach also allows increasing the degree of free-dom of the power estimators. In Fig. 3. the dashedcurve depicts the cone of influence of the waveletanalysis (Torrence and Compo 1998). Any peaks out-side the cone of influence have presumably been re-duced in magnitude due to the zero padding necessaryto deal with finite-length observations. For example, itis possible that activity around a period of 16 yr in Fig.3—see, for example Hu et al. (1998) for an explorationof such periods—carries on at both ends of the timeseries instead of diminishing as illustrated. However,for the span of the available streamflow data, it is nolreasonable to consider wavelet periods much beyond 12

1920 1930

Adams River - — Station-OBLDOOl

Time (year)

1940 1950 1960 1970 1980 1990

1930 1940 1950 1960Time (year)

1970 1980 1990

FIG. 3. Adams River (st;iiion OHLDOOl): (a) Time series of seasonal (autumn) slrcanil'low.(b) Normalized local waveiel power spectrum of the autumn strcamllow using ilic Morleiwavelet. The shaded contours arc al normalized variance of 1. 2. and 4. Dashed curve depictsthe cone of influence beyond which the edge effects become important. White contour linesenclose peaks of greater than 95% confidence for a red noise with a lag-1 coefficient a of 0.26.

198 JOURNAL OF CLIMATE VOLUME 18

yr. Three bands of wavelet periods are examined ingreater detail: 2-3. 3-6. and 6-12. The power spectrumproduced tor a given time series is the product of thenatural process involved and noise. The contour lines inFig. 3 identify peaks of greater than ^5% confidence fora red-noise process with a lag-1 coefficient « of 0.26following the Monte Carlo analysis of Torrence andCompo (1998) based on the univariate lag-1 autoregres-sive process. It must not be presumed that regions ofthe power spectrum out of these 95% confidence levelareas are the product of noise only. The natural processis aiso present in these regions, but influences thepower spectrum to a lesser extent. The coefficient a isseries specific and is estimated for each series.

Finally, cross-wavelet transforms are constructed toanalyse the variability of the streamflow-ciimate rela-tionship throughout Canada. The cross-wavelet powerspectrum is defined as

\W';i'''(s)\-\W^(s)Wr(s)l (4)

where W'^'ls) is a the complex conjugate of lV,V(.v). It isnormalized by l/((r^tr^). The 95% confidence level fol-lows the work of Torrence and Compo (1998). TheMorlet wavelet cross-spectra permits one not only todepict the features common to both the climatic indicesand the seasonal streamflows, but also to highlight tem-poral variations in their relationship.

4. Wavelet analysis results

(h Power Hovmoller of Canadianseasonal streamflows

The scale-average wavelet power represents the av-erage varianee (o^) over a range of scales (or a certainband) and provides an efficient way to examine thefluctuations in power over a desired band. By averagingthe wavelet power speetra at multiple locations, onecan simultaneously assess the spatial and temporal vari-ability of the streamflow data. Figure 4a shows a powerHovmoller (Torrence and Compo 1998), a time-longitude diagram of the normalized scale-averagedwavelet power for the streamflows in the 2-3-yr band atthe longitude location of each hydrometric station.Shown in the figure are the results for the autumn,winter, and spring-summer seasons, as defined above.At eaeh longitude, the wavelet power spectrum is com-puted using the Morlet wavelet, and the scale-averagedwavelet power over the 2-3-yr band is calculated. Allscale-averaged wavelet power time series are then com-bined in a two-dimensional contour plot, with 95% con-fidence level eomputed using the lag-1 autocorrelationat each site. To allow the juxtaposition of streamflowfrom watersheds of different sizes, each scale-averagedseries is normalized by tr"" of the original series. Thezonal average of the power Hovmoller (Fig. 4b) gives ameasure of the average 2-3-yr variance of the stream-flows and typically shows the temporal fluctuations of

the streamflows over the entire area. For example, ae-tivities in the 2-3-yr band for autumn account for up to50% of the average variance (0.5 i r ) in the late 1920s,with moderate peaks (0.40 t r ) around 1955 and 1978. Ingeneral, the autumn season streamflows demonstratethe most intense activity in the 2-3-yr band with mod-erate peaks in the I95()s and late 1970s, and a strongerpeak in the 1920s. The winter season also demonstratesa strong peak in the 1920s and more moderate peaks inthe 1930s and early 1980s. The spring-summer seasoncorresponds to the least intense activity with only mod-erate peaks over several time periods.

Figure 5 presents similar results for the 3-6-yr band.Again, the autumn season exhibits the most intenseactivity with peaks in the 1920s. 1950s, and late 1970s.In comparison with the 2-3-yr band, the peaks are gen-erally not as intense. The spring-summer period tendsto exhibit more activity than the winter period for the3-6-yr band in contrast to the results for ihe 2-3-yrband. Note also the very flat power spectrum for thewinter season for the 3-6-yr band. Overall, the moststriking feature, in the 2-3- and the 3-6-yr periods is anet distinction between the timing and intensity of thetemporal variability in autumn, winter, and spring-summer streamflows^—suggesting that these temporalstructures are either driven by diflerent climatic pat-terns or a phenoment)n with significantly diflerent sea-sonal intensity.

Figure 6 presents the results for the 6-12-yr band andreveals very little organized aetivity. This is likely atleast in part an artifact of the limited length of datarecord available for analysis. As such, the 6-12-yr bandwill not be considered in the subsequent analyses.

b. Seasonal streamflows and climatic patterns

To determine coherent spaee-time variability in eachof the three sectors (east, central, west—see Table 1) ofthe study area, principal component analysis is used.Figure 7 depicts the leading principal component forthe stations from the east, central, and west portions ofthe study area. Results are shown for the autumn, win-ter, and spring-summer seasons. Noteworthy for allthree seasons is the apparent change in behavior ataround 1950. The indication of a ehange in responsearound 1950 will be explored further below. The some-what flat response for the central region is again amanifestation of the limited number of long-term gaug-ing stations available in the central region.

To visualize and examine the relationship betweenthe seasonal streamflow and the selected climaticindices. Moriet wavelet cross-spectrum is calculated us-ing the leading principal component of the seasonalfiow and eaeh of the selected climatic indices. Cross-wavelet spectrum permits highlighting of the stream-flow-^limate index covariance distribution across dif-ferent time scales. Figures 8 to II present results forcross-wavelet analysis between climatic indices and sea-sonal streamflow. Results are presented for ENSO3,

1 JANUARY 2005

60

COULIBALY AND BURN

AUTUMN

120 130

eo 100 110WINTER

120 130

70 80 90

SPRING-SUMMER

100 110 120 130

0.5Power

1960

1960 EP

FIG. 4. Time-longitude diagratiis of the seasonal flows in ihe 2-3-yr band, (ii) Hovmoller plot of the normalizedscale-averaged waveiel power. Shaded contotirs al normalized power of 0.2. 0.5, and I. While contotir lines enclosepeaks of greater ihan ').S% confidence computed using the lag-1 aulocorrelalion al each site, (b) Space averagedof the power Hovmoller.

199

200 JOURNAL OF CLIMATE VOLUME IS

Longitude AUTUMN

70 60 90 100 110 120 130

80 90 100 110 120 130

SPRING-SUMMER

60 70 80 90 100 110 120 130

0.5 0Power

FIG. 5. Time-longitude diagrams of the seasonal flows in the 3-6-yr band. Features are identical to Fig. 4.

ENSO3_OM. NAO, and PNA. With the exception of to March average ENSO indices (namely ENSO3_OM)the ENSO3_OM. each climatic index is presented for are commonly used as they cover the period when thethe same seasonal lime period as the corresponding ENSO signals are prominent. Note that the PNA seriesstreamfiow (see also the results in Table 2). The October are available only from 1950. while the others are avail-

1 JANUARY 2003

60 70 80

COULIBALY AND BURN

Longitude AUTUMN

90 100 110 120 130

0.5

Power

60 110

WINTER

120 130

60 70

SPRING-SUMMER

80 90 100 no 120 130

mil

201

1920

1930

1940

1950

1960

1970

1980

1990

FIG. 6. Time-longitude diagrams of the seasonal tlows in the 6-12-yr band. Features are identical

able for the entire study period (1911-99). Each of Figs, and spring-summer, respectively. In each graph, the8-11 shows the wavelet analysis for the climatie index in horizontal axis shows time (years) and the vertical axisthe top row with eross-wavelet analysis results for each shows the wavelet period (years),sector (east, central, west) in the three following rows. The results for ENSO3 (Fig. 8) reveal the expectedThe three columns present results for autumn, winter, intense activity in the roughly 3-7-yr period that ean be

202 JOURNAL OF CLIMATE VOLUME 18

Leading principal component

1910 192D 1S30 194D 1950 1960 1970 1980 1990 2000

1910 1920 1930 1940 1950 1960 t970 19B0 1990 3000Tima t^a ts )

Fici. 7. Time scries of the seasonal flow leading principalcomponent: east, central, west.

anticipated for the ENSO phenomenon. Intense activ-ity is noted in the lySOs and iy90s, the 1970s, and thet940s. Stronger activity is noted for the autumn andwinter seasons in comparison with the spring-summerseason. The eross-waveiet analysis shows activity in theperiod from 1970 onwards with lesser activity noted forthe spring-summer season. The activity in the cross-wavelet plots is concentrated in the roughly 2-7-yr pe-riod.

The results for ENSO3_OM (Fig. 9) are largely simi-lar to those in Fig. 8 for ENSO3. The most noticeabledifference with the ENSO3_OM analysis is the greateractivity in the spring-summer season in comparison tothe ENSO3 analysis. Correlations between ENSO3^OMand ENSO3 (spring-summer), ENSO3 (autumn), andENSO3 (winter) are about 0.83, 0.68, and 0.95. respec-tively, for the 1910-99 period. In general, the waveletcross-spectra (Figs. S and 9) do not show a particularadvantage of using ENSO3_OM rather than the sea-sonal climatic indices.

Figure 10 presents the results for NAO. The topgraphs show that the NAO results differ with the sea-son in terms of the years with greater activity and theperiods where the greatest activity is observed. Gener-ally, the NAO is active in the 2-8-yr period but otherperiods also demonstrate intense activity (e.g., a longerperiod is observed for both the spring-summer and theautumn results). For the cross-wavclct analysis, themain activity is observed in the 2-6-yr period withstronger activity noted for the autumn and winter sea-sons in eomparison to the spring-summer season.

The PNA results in Fig. 11 show areas of intenseactivity over a wider range of periods than was ob-served for the other elimatic indices. In particular, there

is a band of activity, especially tiotieeable in the spring-summer season, at a period of around 16 yr. The cross-wavelet analysis also exhibits intense activity over awider range of periods with great variability in the re-sults for different seasons and for different regions.This indicates thai the PNA can be expected to haveimpacts on streamflow that will vary spatially and sea-sonally.

In general, the wavelet cross-spectra reveal strongeractivity in the 2-6-yr period generally starting after1950, particularly tor the ENSO'-st ream flow and PNA-streamflow relationship. This ean be associated with thewell-documented shift in the atmospheric circulationaround the mid-1970s over the Northern Hemisphere.However, a signifieant statistical relationship is ob-served between 1950 and 1970 in the E N S O -streamflow activity, particularly in autumn (Fig. 8). Forthe NAO-streamflow relationship, there is strong ae-tivity starting around the I9.'i()s (Fig. 10). suggesting apossible role ot the NAO in the 1950s shift in thestreamflows. Only the PNA-streamflow activity ap-pears stronger after 1970 except for the spring-summerseason (Fig. 11). Prior to year 1950. there is only localand weaker 2-6-yr activity in central and westernCanada essentially in winter and autumn (Figs. 8 and9), but overall, there is no statistically signifieantstreamflow-ciimate activity prior to 1950. The cross-wavelet analysis results consistently support the changepoint (around 1950) revealed by the principal compo-nent analysis and suggest that the shift in the seasonalCanadian streamflows around 1950s may more likely berelated to the NAO index. Further discussion on theyear 1950 change point is provided in section 5.

To further examine the dynamic relationship be-tween the seasonal streamflow and the climatic indices,correlation analysis of the 2-6-yr power spectra are ex-ploited. The correlation analysis also aims to assess pos-sible time delay between seasonal indices and stream-Hows in the 2-6-yr band. Table 3 summarizes the resultsof correlation analysis between two elimatic indices andthe streamOow data. The results are presented for eachof the three regions, for the three different seasons, andhave also been summarized for the period before andafter 1950 as well as for the entire period of record.Correlation values (Table 3) for the period after 1950include not only the effects from the period after 1970,but also the effects of the period 1950-70. Thereforeresults in Table 3 should be interpreted along with Figs.8-11. which highlight the temporal variation in the cli-mate-stream flow relationship.

The east region demonstrates positive correlationswith the ENSO in Ihe spring-summer and winter sea-sons for the post-1950 period but much lower correla-tions lor the period prior to 1950. In the period prior to1950, the correlations tend to be negative with largestmagnitudes noted for the autumn season. For the entireperiod of record, there is again a strong positive corre-lation with ENSO in winter and weaker, but still posi-

JANUARY 20()5 COULIBALY AND BURN 203

204 JOURNAL OF CLIMATE VOLUME 18

a:UJ

CO

601a.w

QlLU

JANUARY 2005 C O U L I B A L Y AND BURN 205

o

206 JOLIRNAL OF CLIMATE VOLUME IS

I JANUARY 2005 COULIBALY AND BURN 207

TABLE 3. Correlation analysis results for 2-6-yr band. Correlation values less than 0.30 are considered insignificant.

Indices

ENSO3 OMENS03_winENS03 spr-sumENS03_aut

NAO_winNAO_spr-sumNAO.aut

ENSO3 OMENSO3_winENSO3 spr-sumENSO3_aut

NAO_winNAO_spr-sumNAO_aut

ENSO3 OMENSO3_winENS03 spr-sumENSO3_aut

NAO_winNAO_spr-sumNAO_aut

Spring-summer

-0.05-0.01

0.09-0.08

-0.03-0.22-0.18

-0.15-0.13

0.03-0.04

0.01-0.30-0.05

0.060.100.210.04

0.09-0.23-0.05

^1950 flows

Autumn

-0.42-0.39-0.22-0.17

-0.41-0.57

0.02

0.580.480.370,14

-0.120.33

-0.39

0.110.120.24

-0.01

0.08-0.04-0.17

Winter

-0.13-0.10

0.01-0.12

-0.06-0.32-0.15

0.550.680.420.67

0.380.080.22

0.070.100.240.01

0.02-0.27-0.07

Spring-summer

East0.380.390.350.39

0.750.06

-0.38

Central-0.08-0.16-0,15

0.19

0.010.04

-0.41

West0.320.26

-0.040.73

0.290.49

-0.37

>1950 flows

Autumn

-0.100.01

-0.14-0.13

-0.5-0.07-0.14

0.510.590.420.29

0.230.01

-0.39

0.160.12

-0.080.36

0.520.08

-0.03

Winter

0.480.600.540.24

0.43-0 .2!-0.39

0.450.350.020.78

0.030.72

-0.36

0.320.410.400.20

0.47-0.34-0.52

All

Spring-summer

0.180.160.310.31

0.39-0.15-0.21

0.050.100.170.44

0.16-O.IO-0.23

0.290.190.210.74

0.330.14

-0.22

(1911-99)

Autumn

0.04-O.OI

0.190.27

-0.15-0.17-0.03

0.510.470.520.46

0.260.02

-0.29

0.22O.IO0.240.52

0.47-0.04

0.01

flows

Winier

0.350.330.580.47

0.40-0.24-0.20

0.500.450.200.72

0.170.40

-0.18

0.260.230.460.37

0,36-0.32-0.23

tive, correlations with ENSO in spring-sumtner. Asitnilar pattern emerges for the NAO in the east, al-though there is a positive correlation between the win-ter NAO and post-1950 and entire period streamflowand a negative correlation for the same time periods forthe autumn NAO.

The eentral region demonstrates greater similarity inthe results for the different time periods, as eould beexpected from the results in Fig. 7. Noteworthy is thestrong, positive correlation for the autumn and winterseasons for the ENSO results. Strong, positive eorrela-tions are also observed for the spring-summer and win-ter seasons for the NAO results post-1950.

The west region demonstrates very little eorrelationin the period prior to 1950. In the post-195Q period,notable positive correlations include spring-summerand winter periods for ENSO and correlations for allseasons for the NAO. The entire period shows similareorrelations to those for the post-1950 period, but withsomewhat reduced magnitudes. A striking feature inthe west is the significant change in eorrelations forboth the ENSO3 and the NAO after 1950.

One of the most prominent features of the correla-tion analysis results is the consistently stronger andpositive eorrelations for spring-summer and winter sea-sons for the ENS03 results in western and easternCanada since 1950—suggesting that the change (around1950) observed in Fig. 7 and also suggested by Figs. 8 to11—may also be related to the ENSO. A similar cor-

relation pattern appears for NAO results in the westsinee 1950. while in the east negative correlations areobserved for the autumn season prior to 1950. How-ever, after 1950, strong NAO eorrelations emerge forall seasons in the east—suggesting a significant contri-bution of NAO in the seasonal streamllow variability ineastern and western Canada. Similar conclusions maynot be drawn for central Canada owing to the limitednumber of stations, as discussed earlier.

5. Discussion

The main eharacteristic time scales {2-3- and 3-6-yrperiods) of the seasonal streamflow revealed by theglobal wavelet spectra, along with the dominant pat-terns of the streamflow-ciimate variability identified bythe cross-wavelet speetra. provide important informa-tion that is essential not only to any attempt to inves-tigate the effects of climate change on Canadianstreamflows. but also to improve seasonal streamflowprediction. Striking elements of the wavelet analysisresults are the shift in the streamflows around 1950(Figs. 7 and 4-6) and the absence of a signifieant sta-tistical relationship between the streamllow and the cli-mate indices prior to 1950. While the shift in Canadianannual streamflows around the 1970s has been welldocumented (Couiibaly and Burn 2004; Anetil andCoulibaly 2004; Perreault et al. 2000) and appears con-sistent with the shift in the atmospheric circulation

208 JOURNAL OF CLIMATE VOLUME 18

around 1970s in the Northern Hemisphere, the year1950 change point revealed in the seasonal streamflowsappears more likely related to NAO dynamics. TheNAO-streamflow temporal relationship shown in Fig.10 is consistent with the dynamics of the NAO duringthe last century (I lurrell et al. 2003): high values of theNAO in the early part (1900-30) of llie century, lowvalues during the period 1930-̂ 50 followed by a strongnegative phase (1950-70—with extreme negative indexaround 1960s) and high positive values in the last 30years (1970-2000—wil^h highest values around 1990s).The strong streamllow/NAO activity around 1950 (Fig.10) ean be related to the shift of the NAO toward ex-tremely negative phase, while the activity around year1970 may be due to the seeond shift toward stronglypositive NAO phase. The effect of the NAO on thestreamflow appears partieularly seasonal with a pro-nounced impact on autumn and spring-summer stream-tiows. This appears consistent with the dominant influ-ence that the NAO exerts on temperature, precipita-tion, and storms of the Atlantic sector and surroundingcontinents (Marshall et al. 2001). Although the NAO isthe dominant pattern of the atmospheric circulationvariability over the North Atlantic, it explains only afraction (about 31%) of the total variance—suggestingthat other climatic patterns should be investigated infurther analysis ineluding the combination of climaticindices.

The second striking feature remains the absence ofsignificant impact of climatic indices on the streamflowsprior to 1950. A possible interpretation may include theeffect of global warming. Global mean surface tem-peratures have risen between 0.3" and ().6°C over thepast century, including a warming of 0.2"-0.3''C sincethe 1950s when data are the most reliable (Houghton etal. 1995). Given that global mean temperatures aredominated by temperature variability over the northerncontinents (Terray and Cassou 2000). thus a signifieantpart of the reeent observed warming ean be explainedas a response to observed changes in atmospheric cir-culation—suggesting that the strong streamflow-ciimate activity after 1950 may be indirectly driven bythe effect of global warming on low-frequency climatevariability. Much more research is definitely needed toassert that assumption and to understand how the natu-ral modes of iow-frequency variability tnay be influ-eneed by elimate change. Further investigation shouldalso include the temporal variability of the Canadianprecipitation-climate relationship.

6. Conclusions

The continuous wavelet transform offers an effeetivetool for deseribing and quantifying the spatial and tem-poral variability of seasonal streamflows. Scale-averaged wavelet speetra permit the sitnuttaneous as-sessment of the temporal and spatial variability in eachof the three sets of 79 streamflow time series corre-

sponding to winter, autumn, and spring-sutnnier sea-son. The span of the available streamflow records.1911-99. allows the depiction of seasonal variance (oraetivity) for periods up to 12 years, thus three periods—namely 2-3. 3-6. and 6-12 yr bands—are investigated.It is shown that the Canadian seasonal streamflows areessentially dominated by the 2-.3- and 3-6-yr activitywith net differences between the timing and the inten-sity of the temporal variability in autumn, winter, andspring-summer. The 6-12-yr-band activity is dtiminatedby white noise in all seasons. Cross-wavelet spectra re-vealed strong streamflow-ciimate activity in the 2-6-yrperiod starting after 1950 whatever the climatic indexand the season. Prior to year 1950. only k)eal andweaker 2-6-yr activity is revealed in central and west-ern Canada essentially in winter and autumn. Theseresults consistently support the change point (around1950) revealed by the principal component analysis. Itis found that the shift in the streanifUtw around 1950 ismore likely related to the change in the NAO towardextremely negative phase.

Correlation analysis between streamfiow activity andclimatic pattern power in the 2-6-yr hand revealedstrong positive correlations wilh the ENSO and theNAO in the east region for spring-summer and winterseasons for the post-1950 period. In the period prior to1950, the correlations tend to be negative with largestmagnitudes noted for the autumn season. In the westregion, there arc no significant correlations prior to1950. The major feature in the west is the strong cor-relation with both the ENSO and the NAO after 1950.The most prominent feature of the correlation analysisresults is the consistently stronger and positive F.NSOcorrelations in spring-summer and winter seasons inboth western and eastern Canada since 1950—sug-gesting that the change point revealed around 1950 mayalso be related to the ENSO. The correlation analysis inthe 2-6-yr band also suggests the presence of a changepoint around 1950 in the east and west seasonal stream-flows. However, owing to the limited number of long-term stations available in the central region, similarconclusion cannot yet be drawn. Finally, a striking fea-ture is the overall absence of significant statistical im-pact of the climatic indices on the seasonal streamflowsprior to 1950. This may be related to the reeent rise ofthe global mean temperatures; however, further inves-tigation is needed to understand the relationship be-tween low-frequency variability and climate change.

Acknowledgments. This work was made possiblethrough grants from the Natural Sciences and Engi-neering Research Council of Canada to eaeh author.The authors gratefully acknowledge the student contri-bution of Vanessa Arnold. The main wavelet analysisroutines were provided by C. Torrence and G. P.Compo (available online at http://paos,eolorado.edu/research/wavelets/). The NAO, PNA, and ENSO3 in-dices are available through the NOAA Climate Predic-

1 JANUARY 2005 C O U L I B A L Y AND 209

tion Center (URL http://www.cpc.ncep.noaa.gov/). Theauthors gratefully acknowledge the valuable commentsof anonymous reviewers.

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