The study area comprises the entire Canadian landmass (Fig. 1). The region includes several major river systems including the Great Lakes–St. Lawrence River system, which is one of the largest freshwater resources globally. Topography plays an important role in shaping regional climates, ranging from wet maritime on the coasts to dry continental across the Prairies and Boreal Plain. Snowfall is restricted to winter months (approximately October to April depending on region). The occurrence, intensity, and timing of seasonal P greatly influence the functioning of ecosystems in various terrestrial ecozones in this region (Hogg et al., 2000). Based on the period 1950–2013, mean annual P varied from more than 2460 mm on the west and 1260 mm on the east coastal regions to less than 360 mm in the interior Prairie (southern central) and northern (above 60∘ N) regions (Fig. 2). The long-term monthly (January–December) minimum and maximum Ts ranged from -30 to +15 ∘C (see Sect. 2.2 below for data sources). Characterized by a highly variable hydroclimate and diminishing water resources, southern parts of Canada are home to cities with the highest population densities and support a vibrant agro-based economy that was hard-hit by the most severe and prolonged droughts of 1988, 1999–2005, and 2015, as well as severe floods of 2011, 2013, and 2014 (Wheater and Gober, 2015; Pomeroy et al., 2016).

Many quantitative metrics have been developed and used for identification and monitoring of droughts (Mishra and Singh, 2011; Raible et al., 2017). A variety of these indices measure, in most cases, how much P and T for a given period deviate from historical averages. Examples include the Palmer drought severity index (PDSI; Palmer, 1965), Palmer hydrological drought index (Palmer, 1965), self-calibrated Palmer drought severity index (Wells et al., 2004), standardized precipitation index (SPI; McKee et al., 1993), the SPEI (Vicente-Serrano et al., 2010), and multivariate standardized drought index (Hao and AghaKouchak, 2013). In Canada, most drought analyses (Dibike et al., 2016; Masud et al., 2017) have utilized climate-based indices since the T and P variables are readily available for longer periods and span larger areas, compared to hydrologic variables such as soil moisture and streamflow. In this study, we make use of the SPEI as a meteorological proxy for drought quantification.

As detailed in Vicente-Serrano et al. (2010), the SPEI is a multi-scalar drought index based on a water balance approach that uses the monthly difference between P and potential evapotranspiration (PET) to analyze wet/dry spells over multiple timescales. SPEI involves calculating monthly PET and then subtracting this from the corresponding monthly P to obtain the climatic water balance. Several derivations have been put forth for calculating PET, including the widely used Penman (Penman, 1948), Thornthwaite (Thornthwaite, 1948), Priestley–Taylor (Priestley and Taylor, 1972), and Hargreaves (Hargreaves et al., 1985) methods. However, most of these approaches require long records for solar radiation, Ts, wind speed, and air pressure, which are not readily available in Canada and many regions of the world. Reanalysis products are an alternative data set for historical drought analysis in Canada and could lead to robust estimates of PET based on the Penman–Monteith algorithm (Maidment, 1993). However, they have been found to be uncertain compared to observations (Wong et al., 2017). A more suitable product with close performance to observations is the Global Environmental Multiscale (GEM) numerical weather prediction model output (Côté et al., 1998). However, it is limited in record length (2002–present). Therefore, the Hargreaves method (Hargreaves, 1994) which simply uses Tmin and Tmax for estimating PET is employed in this study. Once PET is calculated, the difference between P and PET for the month j is calculated as in Eq. (1):

Qj=Pj-PETj, where Qjvalues represent monthly water surplus or deficit.

To compute SPEI, the monthly Qjvalues are first standardized with respect to the long-term monthly mean values. The 1-month SPEI is generally representative of meteorological drought, while timescales between 3 and 6 months are considered as an agricultural drought index. Longer scales such as 6 and 12 months are used to represent hydrological drought and are useful for monitoring surface water resources (Beguería et al., 2014; Hayes et al., 2011). To ascertain the variability of spatio-temporal patterns for different types of droughts, the SPEI was used at different timescales, namely, at 1 (SPEI1), 3 (SPEI3), 6 (SPEI6), and 12 (SPEI12) consecutive months from January–December, at 6 months during the warm season (April–September, SPEI6Apr-Sep), and at 12 months during the hydrologic year (October–September, SPEI12Oct-Sep). SPEI1, SPEI3, SPEI6, and SPEI12 account for the sub-annual variability of droughts, while SPEI6Apr-Sep and SPEI12Oct-Sep account for the inter-annual variability. A drought event occurs any time the SPEI is continuously negative and reaches an intensity of -1.0 or less, and it ends when SPEI becomes positive. Whenever a drought event has been detected with a start and termination month, drought properties such as duration, magnitude, and frequency can be determined. SPEI categories are shown in Table 1. Unless indicated, we focus mostly on other SPEI timescales except SPEI1, which at 1 month is mainly a meteorological drought index.

Long-term trends in drought intensity and variability (inter-annual) are analyzed using the SPEI time series at each grid point. This enables investigation of the percentage of grid points with increasing/decreasing trends during the period 1950–2013 based on the ANUSPLIN- and CANGRD-derived SPEI values. Pre-whitening as described in Yue et al. (2002) is first applied to the monthly SPEI anomalies to remove lag-1 autocorrelation, since serial correlation is generally recognized to influence trends in auto-correlated time series, which may distort the power of the Mann–Kendall test. Pre-whitening is limited to a low-order autoregressive model, i.e. AR(1), since it can falsify the structure of variability in time series across timescales (particularly with higher order models) (Razavi and Vogel, 2018). The pre-whitened SPEI values on different timescales are then used for detecting statistically significant (p<0.05) trends on a pixel basis. Further details on Mann–Kendall trends can also be found in Hamed and Rao (1998).

Hydroclimatological data are often characterized by non-linearity and high dimensionality. Thus, the challenging task is to find ways to reduce the dimensionality of the system to as few modes as possible by expressing the data in such a way as to highlight their similarities and differences (Hannachi et al., 2007). The empirical orthogonal function (EOF) analysis (also known as principal component analysis, PCA) is among the most widely and extensively used method in hydroclimate sciences for accomplishing such tasks (Richman, 1986; Wilks, 2011; Preisendorfer and Mobley, 1988). EOF is employed to find hydroclimate subregions that experienced similar drought features during the period 1950–2013. The EOF consists of computing the covariance matrix of the SPEI series with the corresponding eigenvalues and eigenvectors (Uvo, 2003).

Following the rule by North et al. (1982), the sampling errors at 95 % confidence level of the eigenvalues associated with the leading components were estimated in order to establish how many modes to retain for rotation. To achieve more stable and physically explainable patterns, a rotation of the retained components with the varimax procedure (Richman, 1986) was applied. The patterns defined in this way are referred to as rotated empirical orthogonal functions (REOFs). In summary, the REOF (spatial patterns) values indicate the spatial representativeness of each rotated temporal component (RPC; temporal patterns). Subsequently, we obtained the most revealing patterns of drought evolution across Canada and determined the spatial extent of each component series by mapping the factorial matrix values (i.e. correlation between each REOF and the original SPEI series). Finally, the time variability of the selected RPCs of SPEI was examined for possible trends in the identified subregions using linear regression. The slopes of the trends were computed by applying the method of least squares linear fitting to the time series.

After delimitating hydroclimate subregions that experienced similar drought features, the RPC time series corresponding to the REOFs was then analyzed in a time–frequency domain (to reveal dominant oscillations) by means of the continuous wavelet transform (CWT). Subsequently, by utilizing the wavelet coherence (WCO) technique (Grinsted et al., 2004; Torrence and Compo, 1998; Addison, 2016), the relationships between the dominant oscillations and large-scale climate indices that have possibly modulated historical drought patterns across Canada are investigated. The CWT projects the spectral-temporal characteristics of a time series onto a time–frequency plane from which the dominant periodicities and their duration can be distinguished (Fugal, 2009; Grinsted et al., 2004).

The wavelet power spectrum (WPS) is defined as the squared modulus of the CWT (Jiang et al., 2014; Hao et al., 2012), and represents the signal energy at a specific scale (period) and time. From the WPS, the various periodicities and the time intervals of their occurrence can be determined. For a given time series yn, with n =1,2,3,…,N, the CWT is given by

Wns=∑n′=1Nδts0.5yn′ψ*n′-nδts, where Wns are the wavelet coefficients, n is the time index describing the location of the wavelet in time, s is the wavelet scale, and δt is the sampling interval. The function ψ is the mother wavelet, and the asterisk (*) denotes its complex conjugate. The Morlet wavelet was used since it provides a good balance between time and frequency domains and is suitable when the purpose is to extract dominant signals (Grinsted et al., 2004). The statistical significance of the CWT was assessed against a red noise background at a 95 % confidence interval. The CWT function creates a cone of influence (COI) that delimitates a region of the WPS beyond which edge effects become important and the power could be suppressed (Torrence and Compo, 1998).

Wavelet analysis can also be used to identify the covariance between two time series. This can be done using the concept of wavelet coherence (Grinsted et al., 2004). Wavelet coherence (WCO) reveals local similarities between two time series and may be considered a local correlation coefficient in the time–frequency (time period) plane. For climatological time series, WCO can be used to identify their possible teleconnection with large-scale atmospheric drivers. The WCO between two time series can be computed by normalizing and smoothing their cross wavelet spectrum:

WnXYs=WnXsWnY*s, where WnXs and WnYs represent the WPS of the time series xi and yi, respectively. The statistical significance (p<0.05) of the WCO is estimated using Monte Carlo methods with respect to a red-noise spectrum, resulting in significant periodicities of coherence delineated by significance contours. As in the CWT, regions outside of the COI should be interpreted with caution (Torrence and Compo, 1998).

Figure 3 shows the average monthly (January–December) water surplus/deficit (mm) as defined in Eq. (1) for ANUSPLIN and CANGRD. It is evident that, apart from the Pacific/Atlantic maritime, most of the continental Canadian interior experienced moisture deficits, with the Prairie being the most affected region (this region also has the highest climatological Tmin and Tmax, and some of the least mean annual P during the study period – Fig. 2). Other than the coastal areas, there is a general east to west moisture deficit pattern, mostly determined by the P and T pattern. For comparison, 5.8 % (33.3 %) of CANGRD points experienced moisture surplus (deficit), and 4.3 % (41.6 %) for ANUSPLIN. This implies that ANUSPLIN showed a relatively higher tendency towards dryness relative to CANGRD.

Figure 4 depicts the spatial structure of long-term (1950–2013) SPEI trends at various timescales. Only grid points with significant trends are shown. It is noteworthy that significant trends largely occur in spatially isolated blocks. Decreasing trends are observable in the southern parts of the Prairies, the foothills of the Rocky Mountains, and Pacific maritime regions, whereas increasing trends are limited to a small area in the north and parts of the Atlantic coast to the east, similar to the water balance shown in Fig. 3.

Table 2 shows the percentage of grids with decreasing and increasing trends for ANUSPLIN and CANGRD. For both data sets, the percentage generally decreases with increasing SPEI timescale. ANUSPLIN has a higher tendency towards dryness (decreasing trends) unlike CANGRD. Using SPEI12 as an example, 10 % of ANUSPLIN pixels experienced decreasing trends compared to 4 % in the case of CANGRD. Conversely, apart from SPEI1, CANGRD showed a strong tendency towards wetness (increasing trends) relative to ANUSPLIN. These differences can be attributed partly to the inputs (e.g. the number of stations considered for gridding ANUSPLIN is larger than the number of stations of the CANGRD dataset), estimation methods, and spatial resolution, which are different for both data sets (see Sect. 2.2).

Concerning the EOF analysis, and taking into account the percentage of variance explained by each rotated component (REOF), two main patterns were identified for subsequent discussion and analysis. Table 3 presents the explained variances of varimax rotated components relative to the considered SPEI timescales and data sets. The first two components (for both data sets) explain about 28 to 33.9 % of the total variance depending on the timescale, with the minimum and maximum variances observed for SPEI1 and SPEI12, respectively, in the case of ANUSPLIN. For CANGRD, SPEI6Apr-Sep and SPEI12 explained the minimum and maximum variances, respectively.

Figure 5 shows that between the two main components (REOF), the regions with higher correlations (>0.7) do not overlap, with clearly spatially disjunctive structure. For all SPEI timescales, the loading patterns of the first component (REOF1) with a maximum explained temporal variance of 20.6 % (SPEI12, ANUSPLIN) and 19.5 % (SPEI1, CANGRD) highlights mainly the drought evolution on the interior Prairie ecozone of Canada. This semi-arid region is relatively low-lying and characterized by high hydroclimate variability and some of the least annual mean P. The second component (REOF2) explains a maximum variance of around 13.8 % (SPEI3) in the case of ANUSPLIN and 13.1 % (SPEI12Oct-Sep) for CANGRD. REOF2 is mainly representative of the northern central part of Canada (with the least annual mean P), including the Taiga Shield, Taiga Plains, Southern Arctic, and Taiga Cordillera ecozones, with positive correlations across all timescales and data sets. In summary, the foregoing analyses suggest that the Prairies and northern central regions are the leading droughts modes for Canada, in that they are well captured by the two data sets, with high positive loadings at all investigated timescales.

The RPCs of REOF1 and REOF2 for ANUSPLIN and CANGRD, as well as correlation coefficients between the data sets, are shown in Fig. 6. It is evident that the RPCs from the two data sets are strongly correlated (cor>0.75) for all SPEI timescales, except for RPC2 of SPEI3 where cor=0.45 (the centroids of SPEI3 REOF2 in Fig. 5 are slightly different for both data sets). The primary focus is on SPEI6Apr-Sep and SPEI12Oct-Sep, which reflect the agricultural season (when droughts are most critical for rain-fed and irrigated agriculture) and hydrological year in Canada, respectively. Fig. 6 reveals that the Prairies (REOF1 and RPC1) experienced moderate to extreme (Table 1) drought episodes starting in the mid-1950s, early and late 1960s, the 1970s and 1980s, the period from mid-1997–2005, and the summer of 2009. Some of the drought episodes were extremely dry and severe as they were prolonged in time such as the ones in the late 1970s, mid-1980s, and 1997–2005. These identified drought events correspond well with the findings of Bonsal et al. (2011a), who identified large-scale Prairie droughts in 1961, 1967, 1988, and 2001 using ANUSPLIN and CANGRD data. In the northern central region (REOF2 and RPC2), although fewer droughts were detected for the hydrological year (SPEI12Oct-Sep), with the most intense occurring in 2000 (based on the ANUSPLIN data set), the seasonal SPEI series (SPEI6Apr-Sep) detected several drought events in this region. Extremely dry episodes in this region occurred in the early 1960s, 1980s, early 1990s, and 2000s.

Linear trends of the RPCs for the two subregions are depicted in Fig. 7 and Table 4. For the Prairie subregion, both ANUSPLIN and CANGRD showed insignificant decreasing trends for SPEI6, SPEI6Apr-Sep, and SPEI12Oct-Sep. However, in the northern central region, the trend direction is not the same for both data sets at all SPEI timescales. For ANUSPLIN (CANGRD), decreasing (increasing) trends are found in SPEI6Apr-Sep. Conversely, CANGRD (ANUSPLIN) shows decreasing (increasing) trends in SPEI3. Regionally, the SPEI at different timescales tends to display more significant trends in the northern central relative to the Prairies. Most of the trends are significant in the case of CANGRD compared to ANUSPLIN. The apparent differences in trends between the two data sets and subregions may be attributed to the low station density in areas above 60∘ N which can introduce higher uncertainty in the gridded P and T fields (Vincent et al., 2015).

To detect the dominant frequencies in the RPCs of the SPEI series in Fig. 6, the time series were further analyzed using a CWT. The wavelet power spectrum (WPS) of the RPCs is shown in Fig. 8. Periodicities of drought will be identified for SPEI6Apr-Sep and SPEI12Oct-Sep and their relationship to teleconnection indices examined. These two timescales correspond to the warm season and water year, respectively, and represent periods when moisture shortages are most critical for various sectors in Canada. Other SPEI timescales which explain sub-annual variability are included in Fig. 8 for the interested reader. For SPEI6Apr-Sep, from the WPS of RPC1 in Fig. 8, significant inter-annual variability of between 8 and 32 months is evident throughout much of the entire lengths of the SPEI time series. However, it is concentrated most heavily during the mid-1950s, early and late 1960s, the 1970s and 1980s, and the period from mid-1997–2010. For SPEI12Oct-Sep, a strong frequency band is centred mostly around 16–66 months (∼4 years) and is concentrated during the mid-1950s and late 1960s. Moreover, 32–64-month frequencies are dominant in the mid-1980s and the years between 1990 and 2010.

In the northern central region (RPC2), for SPEI6Apr-Sep, a significant periodicity of a cycle of between 8 and 40 months as a dominant period of variability is evident. It is concentrated in the early 1960s, 1980s, late 1990s, and 2000s. For SPEI12Oct-Sep, the WPS indicates a significant high power for relatively low-frequency (16–100 months, i.e. ∼ 7 years) signals, concentrated over the period 1956–1975 and 1995–2013. The foregoing analysis reveals that the Prairie region (REOF1) of Canada is dominated by high-frequency power signals with high cycles of oscillation for both SPEI6Apr-Sep and SPEI12Oct-Sep, while the northern central region (REOF2) is dominated by relatively low-frequency power signals and low cycles of oscillation. The analysis further indicates that significant inter-annual periodicities (<10 years) dominate drought variability over the two identified subregions across Canada. The dominant periodicities and the intervals during which they occurred are summarized in Table 5.

The WCO technique was used to identify both frequency bands and time intervals at which SPEI6Apr-Sep and SPEI12Oct-Sep, and large-scale climate indices are co-varying (Torrence and Webster, 1999). The results of WCO coefficients between the RPCs of SPEI6Apr-Sep and SPEI12Oct-Sep and teleconnection indices are shown in Figs. 9–11. In these plots, the coloured shading represents the magnitude in the coherence as shown in the colour bar, which varies from 0 to 1 and indicates the timescale variability in the correlation between the two time series. As in Fig. 8, the black contours represent the significant regions. The relative phase relationships are shown as arrows, with in phase pointing right (positive correlation) and antiphase pointing left (negative correlation), whereas a vertical upward (downward) arrow indicates that the second time series lags (leads) the first in phase by 90∘. If an association exists between two time series, a slowly varying phase lag would be expected, and the phenomenon would be phase-locked; i.e. the phase arrows point only in one direction for a given wavelength (Grinsted et al., 2004; Gobena and Gan, 2006). For this study, phase angle associations were noted strictly as either being in-phase-locked or antiphase-locked. To simplify and limit the length of the paper, only results for large-scale climate indices with the strongest correlations with frequencies of drought are shown. Other results are included as supplementary material.

Figure 9 illustrates the squared WCO between the temporal patterns of drought and MEI. It is apparent that, for SPEI6Apr-Sep, the MEI had significant coherence with PC1 mainly concentrated in the 8–16-month band and from 1960–1980 in the Prairie region, indicating that the two time series are phase-locked over this time interval. Also, the strongest coherence between PC1 and MEI occurred over the 32–50-month scale, spanning the period 1986–2002. In the case of SPEI6Apr-Sep PC2 (northern central region), discontinuous in-phase coherence patterns were detected in the 2–32-month bands. The dominant high energy coherence occurred in the 16–32-month scale, spanning the period 1985–2005. Similarly, for the hydrological year timescale (SPEI12Oct-Sep), drought in the Prairies (SPEI12Oct-SepPC1) experienced significant high power with the MEI at the 16–32-month scale from 1980 to 2005 based on ANUSPLIN (1986–2005 based on CANGRD), whereas in the northern central region (SPEI12Oct-SepPC2), significant in-phase cross power between drought and the MEI occurred in the 32–64-month period over the years 1978–2000 (in the case of ANUSPLIN). As in Fig. 8, it can be seen that the Prairie region has more short-term periodicities compared to the northern central region. It is also evident that although the MEI co-varied with drought events, the frequency is higher but shorter lived in the Prairies relative to the northern central region.

Figure 10 shows that for both the seasonal (SPEI6Apr-Sep) and annual (SPEI12Oct-Sep) drought time series, sporadic but significant coherence is observed intermittently from year to year with the PDO. For SPEI6Apr-Sep, dominant strong coherence occurred between 16 and 32 months over the period 1988–2003 for the Prairies region, whereas fluctuations were intermittently observed between 1955 and 2000 for SPEI12Oct-Sep over the Prairie and northern central regions ranging from 16 to 64 months. Unlike the PDO, the PNA showed a strong in-phase relationship with drought over Canada (Fig. 11). It is apparent that the PNA co-varied significantly with SPEI6Apr-SepPC1 over most of the years during the study period. Oscillations in the PNA are manifested in the SPEI6Apr-SepPC1 on wavelengths varying from 2 to 108 months (∼9 years), suggesting that the PNA actively mirrors SPEI6Apr-SepPC1. Particularly, the PNA was phase-locked with drought during the period 1980–2001 at the 16–32-month scale. Apart from the late 1990s and early 2000s at the 8–16 month scale, no significant coherence was found between the PNA and SPEI6Apr-SepPC2. Although with less coherence relative to SPEI6Apr-Sep, the PNA also co-varied with SPEI12Oct-Sep, more so for the northern Central region compared to the Prairie region. In the Prairie region, the strongest coherence between SPEI12Oct-SepPC1 and the PNA occurred over the 16–32-month scale, while for the northern central region, significant cross power between the PNA and SPEI12OctApr-SepPC2 occurred over the 32–64-month scale, spanning the periods 1960–1973 and 1985–2000.

The relationship between drought and the AMO is shown in Fig. S3. It is clear that the AMO did not co-vary with SPEI6Apr-Sep over both homogenous drought regions. However, it is important to note that Shabbar and Skinner (2004) found a significant correlation pattern between the winter AMO index and following summer PDSI in the north of the Prairies province. Here, we only made use of the AMO index for the months April–September of each year. For SPEI12Oct-Sep, significant and high energy existed for the Prairie region only (SPEI12Oct-SepPC1), mainly distributed in the 8–64-month (∼5 years) band and spanning the period 1970–2005. For the AO (Fig. S4), in-phase significant coherence existed with SPEI6Apr-Sep PC2 and SPEI12Oct-SepPC1. In the northern central region (SPEI6Apr-Sep PC2), 16–32-month high-energy regions were found over the period 1963–1978, and 8–16-month significant coherence also existed from 1994 to 2002. In the Prairie region (SPEI12Oct-SepPC1), drought was in phase with the AO especially from 1981 to 2003, where significant cross power and coherence were mainly concentrated in the 64–128-month band (based on CANGRD). The results further indicate that the AO was in antiphase with SPEI6Apr-Sep PC1 and SPEI12Oct-SepPC2 during the study period from 1950 to 2013. In terms of the NAO (Fig. S5), sporadic significant coherence is noticed with the seasonal SPEI6Apr-Sep at a higher frequency, ranging between 4 and 20 months and mainly concentrated over the period 1975–1990. There is also statistically significant in-phase coherence between SPEI12Oct-SepPC1 and the NAO in the 70–128-month band in the late 1970s–late 1990s, based on CANGRD.

The foregoing analysis has shown significant covariance between drought variability over Canada and large-scale climate indices, especially the MEI, PNA and PDO. This is in line with previous studies (e.g. Bonsal and Shabbar, 2008, Fleming and Quilty, 2006, Tremblay et al., 2011, and Perez-Valdivia et al., 2012) that have established links between Canadian hydroclimate and teleconnection indices. Furthermore, one should expect most of the climate indices to yield similar findings given that they appear to be interrelated at several timescales (Sheridan, 2003; Gan et al., 2007; Ng and Chan, 2012). We recommend that future studies examine the degree to which such interrelations can affect the findings reported here by eliminating, for example, the influence of the PDO on the MEI via partial wavelet coherence analysis (Ng and Chan, 2012). Also, a lead/lag response of the identified drought frequencies as well their correlations to positive and negative phases of various teleconnections constitute an area for future research. In addition, only one PET estimation method was used in this study and its selection was constrained by data availability during the study period. We recommend the use of other simple or complex methods to calculate PET and assess their impact on drought analysis over Canada since the Hargreaves method has been known to underestimate PET relative to the Penman–Monteith method (McMahon et al., 2013). Furthermore, the Hargreaves method responds only to changes in temperature and can lead to misleading results under global warming. For example, Sheffield et al. (2012) found little change in global drought over the past 60 years (1950–2008). In terms of data sources, the findings reported here should be validated against other data sets such as long-term satellite products as they become available.