1. Introduction

Subseasonal variations of precipitation in Canadian winter have a significant impact on societal and economical activities. For instance, a persistent period of excessive precipitation is usually associated with snow storm, freezing rain, and ice conditions. A useful forecast beyond about one week of a persistent anomaly in precipitation is thus of great value. Unfortunately, numerical weather forecasting models have tremendous difficulties in producing a useful extended-range prediction, especially in precipitation.

Beyond about a week, a forecast can no longer rely on the evolution of extratropical cyclones and anticyclones, because of the fast growth of initial error in the highly nonlinear flow.¹ A low-frequency signal source is essential for such an extended-range forecast. There is indication that the Madden–Julian oscillation (MJO), with its intraseasonal time scale, can provide an important signal for subseasonal weather predictions (e.g., Waliser et al. 2003). The MJO is a tropical large-scale oscillation that is dominated by periods of 30–60 days and zonal wavenumber 1 propagating eastward (Madden and Julian 1971). The MJO has a direct impact on the weather in the tropical region, as it organizes convection and precipitation. It has a significant influence on the extratropical atmospheric variability, possibly through Rossby wave propagation (e.g., Ferranti et al. 1990; Matthews et al. 2004; Lin et al. 2009), and thus could provide an important signal source for the extratropical weather forecasts on subseasonal time scales. The impact of the MJO on the extratropical circulation and weather has been of considerable interest. For example, Higgins et al. (2000) and Mo and Higgins (1998) investigated the relationships between tropical convection associated with the MJO and west coast precipitation. Vecchi and Bond (2004) found that the phase of the MJO has a substantial systematic and spatially coherent effect on subseasonal variability in wintertime surface air temperature in the Arctic region. Donald et al. (2006) reported a near-global impact of the MJO on rainfall. Wheeler et al. (2009) documented the MJO impact on Australian rainfall and circulation.

In this study we investigate the connection between the Canadian precipitation and the tropical convection activity of the MJO, and its association with the large-scale atmospheric circulation. Instead of using some existing MJO index such as the real-time multivariate MJO (RMM) of Wheeler and Hendon (2004), the dominant convection patterns associated with the MJO are represented by the two leading modes of the empirical orthogonal function (EOF) analysis that is applied to the pentad outgoing longwave radiation (OLR) in the equatorial Indian Ocean and western Pacific. We choose to use the expansion coefficients of these EOFs to represent the MJO variability because we would like to construct a direct link of Canadian precipitation and Northern Hemisphere circulation to the major patterns of tropical convective activity related to the MJO. In most of the previous studies about the impact of the MJO on midlatitude weather as previously mentioned, composites were often made for different phases of the MJO, thus a simultaneous association between the atmospheric variable and the MJO was obtained. Lin et al. (2009) produced lagged composites of the amplitude of the North Atlantic Oscillation (NAO) with respect to different MJO phases. They found a significant increase of the NAO amplitude about 5–15 days after the MJO-related convection anomaly reaches the tropical Indian Ocean and western Pacific. The development of the NAO is associated with a Rossby wave train in the Pacific and North American region. Cassou (2008) also considered time lags in analyzing the association between the MJO activity and the Northern Hemisphere weather. Here we consider the time-lagged association between the Canadian precipitation and the MJO activity, as the signal of the tropical diabatic forcing associated with the MJO would take about a week to propagate to Canada (e.g., Lin et al. 2009). Such a lagged association would provide useful information for an extended-range MJO-based forecasting of the Canadian precipitation even without a forecast of the MJO itself. It also suggests a clear dynamical connection from the tropical convection to the extratropical North American weather. With this lagged association, Lin and Brunet (2009) revealed that the MJO has a significant influence on wintertime surface air temperature variability in Canada.

Section 2 describes the data used and analysis procedure. In section 3 lagged regressions of the Canadian precipitation with respect to the variability of the leading modes of MJO convection are presented. The extratropical circulation anomaly associated with the MJO is discussed in section 4. Section 5 presents results of numerical experiments that are designed to simulate the atmospheric response to the tropical MJO convection anomalies. Conclusions and a discussion follow in section 6.

2. Data and analysis procedure

Datasets of different sources are used in this study to depict variabilities in precipitation and atmospheric circulation, and to define the state of the MJO. We make use of the adjusted daily total precipitation data at 495 Canadian stations that are provided by the Climate Research Division of Environment Canada. The adjustment methodology follows the steps described in Mekis and Hogg (1999). In Canada, when a station is relocated, a new identification number is often given to the new location and the observations of these two stations can be combined in order to create a long time series. Adjustments obtained from homogeneity tests using information from surrounding stations were applied for the joining of observations from several stations (Vincent and Mekis 2009). Only 219 stations have data up to 31 March 2005. Stations with more than 20% of missing observations during the extended winters (November–March) of 1979–2005 are excluded from the analysis, resulting in 201 stations that are used in the analysis here. These 201 stations are not uniformly distributed. More stations are located near the west coast and southern part of Canada than in the north and northeast (Figs. 1c,d). The gridpoint pentad data of the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP; Xie and Arkin 1997) are also used to describe precipitation and to compare with the station observations.

To represent the atmospheric circulation fields, the daily-average data of the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) global reanalysis (Kalnay et al. 1996) are utilized. Variables used here include geopotential height at 500 and 700 hPa, vertical velocity at 500 hPa, and horizontal winds and specific humidity at 850 hPa. As a proxy for tropical convection, the daily averaged OLR data from the National Oceanic and Atmospheric Administration (NOAA) polar-orbiting series of satellites (Liebmann and Smith 1996) are used. [These data are provided by the NOAA/Office of Oceanic and Atmospheric Research/Earth System Research Laboratory/Physical Sciences Division (OAR/ESRL/PSD), Boulder, Colorado, from their Web site at http://www.cdc.noaa.gov/.]

The horizontal resolution for the NCEP–NCAR reanalysis, the OLR and the CMAP precipitation is 2.5° × 2.5°. The daily values of the NCEP–NCAR reanalysis, the OLR, and the Canadian station data are averaged for five consecutive days to construct pentad data. The pentad data for the Canadian station precipitation are calculated by averaging all the nonmissing data that are available in that pentad. If all data in a pentad are missing, a value of zero is assigned. The analysis is conducted for extended winters from November to March. The period of our analysis starts from 1979, as the OLR data are continuously available starting from that year. For the NCEP–NCAR reanalysis, the OLR, and the CMAP precipitation, 30 extended winter seasons from 1979/80 to 2008/09 are used. For the Canadian station data, however, as data for many stations are available only until 2005, 26 extended winter seasons from 1979/80 to 2004/05 are analyzed. Each extended winter comprises 30 pentads starting from the pentad of 2–6 November and ending at the pentad of 27–31 March. To match the pentad definition of the CMAP precipitation, the 24th pentad of each winter always covers a period from 25 February to 1 March, no matter if it is a leap year or not. Thus, in the case of a leap year, the data for that “pentad” is actually an average for 6 days.

The seasonal cycle, which is the time mean of the 30-yr (26 yr) pentad climatology, is first removed for each grid point (station). The mean for each winter is then removed in order to eliminate interannual variability. The resulting pentad perturbation represents an intraseasonal variability.

The climatology and standard deviation of the precipitation intraseasonal variability are illustrated in Fig. 1. The CMAP data and the station observations seem to agree well over Canada. Maximum values of average precipitation and variability are located mainly along the west coast region on the west side of the Rockies, which are likely associated with topography as well as abundant moisture supply from the eastern Pacific. Relative high values of precipitation and variability can also be found near the east coast.

To represent the MJO and identify the tropical convection patterns, an EOF analysis is performed on the pentad OLR anomaly for the extended winter from 1979/80 to 2008/09. The area used here is 20°S–20°N and 60°E–150°W where the tropical convection and its variability are strong. The spatial distributions of the two leading modes that explain 11% and 10% of the total variance of pentad mean, respectively, are shown in Fig. 2. EOF1 shows a large area of above-normal convection anomaly centered near the Maritime Continent (Fig. 2a). A dipole structure of convection anomalies, enhanced convection in the eastern Indian Ocean and reduced convective activity in the western Pacific, characterizes EOF2 (Fig. 2b). The principal components (PCs) of the two EOFs have a significant power spectrum peak at around 10 pentads (not shown). The cross correlation between PC1 and PC2 reaches its maximum (0.57) when PC2 leads PC1 by 2 pentads, and its minimum (−0.38) when PC2 lags PC1 by 2 pentads, implying a sequence of appearance of +EOF2, +EOF1, −EOF2, and −EOF1 separated by about 2 pentads. The above features indicate that the two leading EOFs together represent the eastward-propagating MJO disturbance, in agreement with previous studies that performed similar EOF analysis of OLR data (e.g., Lau and Chan 1985; Ferranti et al. 1990). In fact, the longitudinal distributions of these two leading EOFs are very similar to the OLR components of the combined EOF analysis of Wheeler and Hendon (2004). PC1 and PC2 are highly correlated with their RMMs. The correlation between PC1 and RMM1 is 0.62, and that between PC2 and RMM2 is −0.76. Therefore, an impact analysis for the MJO using the OLR PCs should reach similar conclusions comparing to the one that is based on RMMs. Here we choose PC1 and PC2 to represent the MJO variability instead of RMM1 and RMM2 because we would like to construct a direct link of Canadian precipitation and Northern Hemisphere circulation to the major patterns of tropical convective activity related to the MJO. As will be seen in section 5, such tropical convection patterns contribute significantly in forcing the extratropical circulation anomaly.

In an attempt to see the influence of the tropical MJO convection on the Canadian winter precipitation and Northern Hemisphere circulation anomalies, lagged regressions between the two leading OLR PCs and the extratropical atmospheric anomalies are calculated. As PC2 leads PC1 and PC1 leads a negative phase of PC2 by about two pentads, an evolution of global atmospheric anomalies in relation to the MJO could be visualized just by analyzing the simultaneous regressions or composites with respect to PC1 and PC2, as done in many previous studies (e.g., Ferranti et al. 1990; Jones et al. 2004). However, as the MJO is not a perfect periodic oscillation, which is evident from the fact that the lagged correlation between PC1 and PC2 is not close to 1, we analyze here lagged regressions between atmospheric anomalies and PC1 and PC2 separately. In this way, we would have a correct timing of the appearance of midlatitude anomalies with respect to the tropical convection anomaly patterns of the MJO. This will also help to facilitate a comparison with the numerical modeling of midlatitude response to the MJO convective anomalies that takes time to develop as will be presented in section 5.

To describe the relative magnitude of changes associated with the MJO compared to the standard deviation of each variable, the perturbation of each variable is normalized by its own standard deviation during the analysis period. Therefore, in the following discussions, unless specified explicitly, the perturbations are normalized. Because of the skewness of the precipitation distribution, a square root transformation is used for the precipitation pentad data, following Richman and Lamb (1985) and Mo and Higgins (1998). Such a transformation would help to alleviate problems for statistical analysis related to extreme values. The transformed precipitation anomaly at each station or grid point is normalized by its pentad standard deviation.

3. Connection between the MJO and Canadian precipitation

From the last section, we see that the two leading EOFs of the tropical OLR represent reasonably well the MJO convection activity. As PC2 leads PC1 by about two pentads, here we first look at the regression of Canadian precipitation to PC2, which corresponds to a dipole equatorial convection pattern with enhanced convection in the eastern Indian Ocean and reduced convection in western Pacific. The lagged regressions of Canadian station precipitation anomaly with respect to PC2 are presented in Fig. 3, where lag = n means that the precipitation anomaly lags the OLR PC by n pentads. The magnitude represents a precipitation anomaly corresponding to one standard deviation of the PC time series. Those stations with a regression coefficient statistically significant at the 0.05 level according to a Student’s t test are marked with color. The contours are plotted for regressions interpolated from stations to 2° × 2° grid points, and the gray shaded areas are those where the interpolated regression is statistically significant at the 0.05 level. The same lagged regressions are calculated using the CMAP grid precipitation and the result is shown in Fig. 4. The autocorrelation in data has been considered and the effective degree of freedom is reduced when performing the Student’s t test. A test of field significance for the regressions as described in Livezey and Chen (1983) would further help to assess the confidence level. However, comparing to surface air temperature and meteorological variables at upper levels, precipitation data are less spatially coherent. As can be seen, a significant amount of stations and areas have a significant regression. In general, the results of the CMAP precipitation agree reasonably well with the station data over Canada. Significant precipitation anomalies start to appear one pentad after a positive phase of PC2, when above-normal precipitation is observed near the west coast (Figs. 3b and 4b). The maximum increase of precipitation in southwest British Columbia exceeds 0.1 unit corresponding to 1 standard deviation of PC2. Recall that the precipitation anomaly has been normalized by its pentad standard deviation. Therefore, an increase of precipitation by more than 10% of its standard deviation in southwest British Columbia can be expected when a positive PC2 with a one standard deviation magnitude occurs. At lag = 2 (Figs. 3c and 4c) and lag = 3 (Figs. 3d and 4d), the positive precipitation anomaly at the west coast remains, indicating that a persistent excessive precipitation period follows the occurrence of tropical convection pattern of EOF2. At the same time, above-normal precipitation is seen in a large area to the west and south of Hudson Bay with a maximum above-normal precipitation at lag = 3 in south Quebec, and a below-normal anomaly in the northeast coastal region near Newfoundland. From the CMAP result (Figs. 4c,d), negative precipitation anomalies are also observed in the eastern Pacific and California region and the western Atlantic near 35°N. The out-of-phase relationship between the precipitation in British Columbia and California is in agreement with that reported in Mo and Higgins (1998).

For PC1, which corresponds to enhanced equatorial convection centered near 110°E, the lagged regressions of the station and CMAP gridded precipitation are plotted in Figs. 5 and 6, respectively. Again, the results from these two datasets agree reasonably well over Canada. On the simultaneous regression map (Figs. 5a and 6a), significant positive precipitation anomalies are observed in south British Columbia. The above-normal precipitation extends to cover a wide region of south Canada at lag = 1. After that, the signal reduces and disappears (Figs. 5c,d and 6c,d). We know from the last section that PC2 leads PC1 by about two pentads. The significant correlations shown on the simultaneous and lag = 1 regression maps of PC1 (Figs. 6a,b) are consistent with the influence of PC2 at lags 2 and 3 (Figs. 4c,d). From Figs. 6c,d, we also know that the impact of PC2 on Canadian precipitation for lag = 4 and lag = 5 would be weakened (after lag = 3 shown in Fig. 4d). Similarly, the PC1 regression for lags 2 and 3 are consistent, but with an opposite sign, to the regression of PC2 lags 0 and 1, because a negative PC2 follows a positive PC1.

To better quantify the magnitude of precipitation changes associated with the MJO and to assess possible nonlinearity of the association, composites of unnormalized precipitation anomaly are calculated for strong positive and negative phases of PC2. According to a criterion of 1 standard deviation of PC2, 145 positive cases and 157 negative cases are selected. The composites of CMAP gridded precipitation anomaly when precipitation lags PC2 for three pentads (lag = 3) are shown in Fig. 7. Shaded areas represent those where the composite anomaly is different from 0 at a 0.05 significance level according to a Student’s t test. The main feature of Figs. 7a,b is in agreement with Fig. 4d. The maximum precipitation anomaly near the west coast of Canada is about 0.7 mm day⁻¹ for positive cases and 0.9 mm day⁻¹ for negative cases, which is about 30% of its standard deviation (Fig. 1b). The general feature of the precipitation signal associated with PC2 is linear; that is, the precipitation anomaly of a positive PC2 (Fig. 7a) has a similar distribution as that of a negative PC2 but with an opposite sign (Fig. 7b). However, the nonlinearity is not negligible. The positive precipitation anomaly near the west Canadian coast associated with a positive PC2 (Fig. 7a) is weaker and has a smaller extent than the negative precipitation anomaly at the same region associated with a negative PC2 (Fig. 7b). For the precipitation anomaly near the California coast, a positive PC2 has a stronger and larger pattern than a negative PC2. Some nonlinearity can also be found for the precipitation anomalies in other parts of North America.

4. Large-scale circulation anomalies

To understand the precipitation variability in Canada related to the MJO as observed above and have a better confidence of this connection, in this section we examine the extratropical large-scale circulation anomalies corresponding to the tropical MJO convection. As demonstrated in many previous studies, the MJO not only affects the tropical weather, but also influences the global circulation (e.g., Lau and Phillips 1986; Ferranti et al. 1990; Matthews et al. 2004; Lin et al. 2009). The extratropical response to tropical convection, however, is complicated by many factors such as the structure of the background mean flow and interactions with transient eddies (e.g., Ting and Sardeshmukh 1993; Hall and Derome 2000). As discussed in Lin et al. (2009), the development of the NAO follows an MJO-related convection anomaly dipole in the tropical Indian Ocean and western Pacific region. Here we look at how the Canadian precipitation is influenced by the evolution of the extratropical large-scale circulation associated with the MJO convection.

The lagged regressions of 500-hPa geopotential height anomaly with respect to PC2 are presented in Fig. 8. Clearly the development of circulation anomalies over the extratropical North America is linked to tropical forcing of the dipole pattern of PC2. On the simultaneous composite map (Fig. 8a), a dominant feature is that a significant positive height anomaly is formed over the North Pacific centered at 45°N, 180°. Downstream over Alaska and the west coast of Canada, a negative anomaly can be seen. One pentad later (Fig. 8b), the wave pattern shows downstream dispersion with the negative anomaly over northwest Canada undergoing a rapid amplification. By lags +2 and +3 (Figs. 8c,d), significant development of circulation anomalies takes place near the east coast of North America and the North Atlantic, forming a pattern that is similar to a positive NAO. This process is very similar to the evolution of the large-scale extratropical circulation anomalies after MJO phase 3 as reported in Lin et al. (2009), where the MJO phases were defined according to the RMMs of Wheeler and Hendon (2004). Phase 3 of the MJO has a dipole structure of tropical convective activity (e.g., Fig. 3 of Lin et al. 2009), with enhanced convection in eastern Indian Ocean and reduced convection in western Pacific, a pattern that is very similar to our EOF2 of OLR (Fig. 2b).

In contrast to PC2, the lagged regressions of 500-hPa geopotential height anomaly with respect to PC1 show little evidence of pattern amplification over North America (Fig. 9). The lag = 0 and lag = 1 regressions for PC1 (Figs. 9a,b) have a distribution similar to the lag = 2 and lag = 3 regressions for PC2 (Figs. 8c,d), reflecting the fact that PC2 leads PC1 by about 2 pentads. The tropical heating of PC1 itself has a very weak influence on the large-scale extratropical circulation. In the Asian and western Pacific region, the PC1 regression for lags 2 and 3 are similar, but with an opposite sign, to the regression of PC2 at lags 0 and 1, consistent with that a negative PC2 follows a positive PC1.

Changes in large-scale vertical motion could be responsible for precipitation anomalies. To better understand the significant precipitation anomalies in Canada with respect to the MJO, we present regressions of 500-hPa pressure velocity (ω) anomaly with respect to PC2 in Fig. 10. A good correspondence can be found between the vertical motion and precipitation anomalies by comparing Figs. 3 or 4 with Fig. 10. One pentad after a positive phase of EOF2, a significant upward motion anomaly at the coastal region of British Columbia is generated. Upward motion anomalies can also be observed in southeast Canada and the region south of Hudson Bay. At the same time, a downward motion anomaly appears in the northeast over Newfoundland.

Besides vertical velocity, other factors also contribute to precipitation anomalies. Here we look at changes in storm track and moisture transport associated with the MJO. To represent the storm track strength, daily geopotential height data at 700 hPa during each extended winter are bandpass filtered to retain fluctuations with periods between 2 and 6 days. Then the standard deviation of the filtered data is calculated for each pentad. Shown in Figs. 11a,b are lag = 1 and lag = 2 regressions to PC2 for the standard deviation of the bandpass-filtered 700-hPa geopotential height over the North American region. Note that the regressions shown in Fig. 11 are for unnormalized perturbations. As can be seen, in the next two pentads after a positive PC2, synoptic-scale transient activity is increased near the west coast of Canada. To the northeast of Canada, reduced activity of the transients can be observed. The lag = 1 and lag = 2 regressions to PC2 for the moisture flux at 850 hPa are depicted in Figs. 11c,d. The shaded areas represent those where the moisture flux convergence is stronger than 0.4 × 10⁻⁶ g kg⁻¹ s⁻¹. Following a positive PC2, westerly wind blows from the warm ocean into the continent, bringing moist air and producing a strong moisture flux convergence in the coastal region of British Columbia. The lifting effect of the coastal and Rocky Mountains would also contribute to the increased precipitation in this region. Strong southwesterly moisture flux from the southeast United States results in convergence near the Great Lakes and southeast Canada.

5. Numerical model experiments

We have observed that the intraseasonal variability of precipitation in Canada is significantly correlated with the tropical MJO convection. The changes in precipitation can be largely explained by the large-scale circulation anomalies and vertical motion. In this section, numerical experiments are performed to test the hypothesis that the North American atmospheric circulation anomalies and the related changes in precipitation result from a direct response to the MJO convective heating. We use the simple general circulation model (SGCM) as described in Hall (2000). It is a global primitive equation spectral model with no moisture representation. The model has a time-independent forcing that is calculated empirically from observed daily data. This forcing is to maintain a realistic climatology, and is obtained as a residual for each time tendency equation by computing the dynamical terms of the model, together with the dissipation, with daily global analyses and averaging in time. Such a procedure is very similar to that used in Roads (1987), and also in a quasigeostrophic setting by Marshall and Molteni (1993). The resolution used in this study is T31 with 10 vertical levels. This model is able to reproduce large-scales features of the observed climatology and variability reasonably well, and has been used in studies related to remote response to El Niño (Hall and Derome 2000), seasonal prediction (Derome et al. 2005), and intraseasonal variability (Lin et al. 2007).

Here linear integrations are performed using the SGCM, with the approach as described in Hall and Derome (2000) and Lin (2009). The SGCM model is converted into a linear perturbation model on a time-independent basic state, as response to perturbation forcing. The basic state used is the model climate of a long perpetual winter [December–February (DJF)] integration (3600 days) of the nonlinear model, which is very similar to the three-dimensional DJF observational climate. Two experiments are designed to study the model response to a tropical thermal forcing that mimics the EOF1 and EOF2 MJO diabatic heating patterns, respectively. The first one (Exp1) has a single heating at 110°E, while the second (Exp2) has a dipole thermal forcing with a heating at 90°E and a cooling at 165°E. The tropical heating anomaly that is added to the temperature equation, is switched on at t = 0 and persists during the integration. No forcing anomaly is applied to the vorticity, divergence, or mass equations. The heating perturbation represents deep convection in the tropics, and has an elliptical form in the horizontal. The perturbation heating and cooling sources have a semimajor axis of 40° of longitude and a semi-minor axis of 11° of latitude. The magnitude of the heating is proportional to the squared cosine of the distance from the center. The heating anomaly has a vertical profile of (1 − σ) sin(πσ), which peaks at σ = 0.45 with a vertically averaged heating rate of 3.5°C day⁻¹ at the center. This rate is equivalent to a latent heating associated with a precipitation of about 1.5 cm day⁻¹ (Ting and Sardeshmukh 1993). The vertically averaged heating anomalies for the two runs are illustrated in Fig. 12. The linear model is integrated for 15 days starting from an initial state that has no atmospheric perturbation.

The model responses of 500-hPa geopotential height perturbation averaged between days 6 and 10 and between days 11 and 15 are shown in Fig. 13 for the two experiments. The first experiment has a very weak response in the Northern Hemisphere extratropics, with little evidence of Rossby wave propagation. In contrary, the second experiment produces a strong circulation anomaly that takes a two-dimensional Rossby wave form propagating across the Pacific and North America. It is clear that the tropical dipole forcing pattern as shown in Fig. 12b is much more effective in forcing the extratropical atmospheric circulation anomaly than the heating source near 110°E of Fig. 12a. The observed lagged associations between 500-hPa geopotential height and PC2 are simulated in the linear experiment. Figures 13c,d agree quite well with Figs. 8b,c. This suggests that the observed connection between the Northern Hemisphere circulation anomaly and its associated precipitation variability in North America are a direct response to the dipole tropical MJO convection forcing.

To further investigate the sensitivity of the Northern Hemisphere extratropical response to the location of tropical forcing, a series of linear experiments are performed. In these experiments, single heating sources with the same distribution as of Fig. 12a are placed at different longitudes along the equator from 60°E to 150°W at a 10° interval. As the experiment with a heating centered at 110°E has already been made (Exp1 as discussed above), 15 more experiments are conducted. Shown in Fig. 14 are model responses of 500-hPa geopotential height perturbation averaged between days 6 and 10 and between days 11 and 15 for 2 of the experiments: heating sources at 80°E (Figs. 14a,b) and 160°E (Figs. 14c,d). As can be seen, both experiments generate a strong extratropical response. Interestingly, the response patterns of these two experiments are similar but out of phase. The locations of the heating source in these two experiments are close to the heating and cooling centers of the dipole convection pattern of the MJO EOF2 (Fig. 2b). If a cooling instead of heating is placed on the equator at 160°E, the response of the two experiments would be in phase. Therefore, a dipole forcing as of Exp2 discussed above results in a very strong extratropical response that reflects a superposition of the response to the heating on the west and that to the cooling on the east.

An examination of the results of the other experiments with heating sources at different longitudes reveals that a forcing located at a longitude west of 110°E produces a response pattern that is very similar to that at 80°E (Figs. 14a,b), whereas a forcing located to the east of 110°E generates a response very similar to that at 160°E (Figs. 14c,d). To quantitatively describe the amplitude of response to the tropical heating at different longitudinal locations, the 500-hPa geopotential height perturbation averaged between days 11 and 15 for each experiment in the Northern Hemisphere between 20° and 85°N is projected onto that of Exp2 (Fig. 13d). The projection is calculated as a spatial covariance between the height perturbation response and that of Fig. 13d, normalized by the spatial variance of the height field of Fig. 13d. Therefore, it represents a response amplitude for different heating sources when projecting to the pattern of Fig. 13d. The result is presented in Fig. 15 as a function of longitude. As can be seen, a forcing near 110°E has almost no contribution. Maximum contributions come from a heating source near 80°E, and a cooling source near 160°E. Similarly, a cooling source near 80°E and a heating source near 160°E would produce a strong response pattern of negative phase of Fig. 13d. This explains why a dipole convection pattern similar to EOF2 of the tropical OLR as shown in Fig. 2b is so effective in forcing an extratropical circulation anomaly.

This result on the sensitivity of response to the location of tropical forcing in general agrees with previous studies. Using a global barotropic model linearized at about the 300-hPa climatological mean January flow, Simmons et al. (1983) investigated the extratropical response to tropical forcing by specifying idealized vorticity forcing at different locations. They found that the tropical vorticity forcing that is effective in exciting a given North Pacific response changes sign from the west Pacific to the Indian Ocean. The nodal point of sign switch in their study is around 150°E, about 40° to the east of 110°E as in the present study. The difference may be related to the barotropic model they used and the basic state specified. Ting and Sardeshmukh (1993) analyzed the steady linear response to equatorial diabatic heat sources using a global baroclinic model. With the European Centre for Medium-Range Weather Forecasts (ECMWF) DJF basic state, they found that the extratropical response to a heat source at 100°E is out of phase with that to a heat source at 140°E, and the response is very weak when the heat source is placed at 120°E. It is possible to explain this from the angle of extratropical normal mode as in Simmons et al. (1983) and in Ting and Sardeshmukh (1993), where the associated mode of the external forcing has large amplitudes of opposite sign in the tropics with a nodal point near 120°E and the atmospheric perturbation grows by extracting kinetic energy from the basic flow. It is also possible that the structure of basic state plays an important role in determining Rossby wave energy generation and propagation, so that the direct response depends on the relative location of the tropical forcing with respect to the extratropical westerly jet, as discussed in Lin (2009).

From these numerical experiments, it is clear that the dipole tropical heating pattern of EOF2 is more effective than the heating of EOF1 in generating a Rossby wave train that propagates into the extratropical North American region. The impact of the MJO on wintertime precipitation in Canada is likely determined by this process. Although PC1 is significantly correlated with Canadian precipitation at lag = 0 and lag = 1 (Figs. 5a,b), we would argue that the precipitation signal observed in Canada does not result from the tropical forcing centered near 110°E of PC1. Instead, the dipole tropical forcing of PC2 is mainly responsible for the Canadian precipitation anomalies. As shown in the numerical experiments, it takes about one to two weeks for an extratropical response in North America to establish in response to a tropical diabatic forcing in the western Pacific. If the tropical forcing has an impact on Canadian weather, the lagged regressions of lag = 2 and lag = 3 would show significant and increased correlations. This is the case for PC2, but not for PC1. The fact that Fig. 5a is similar to Fig. 3c reflects that PC1 lags PC2 by about two pentads. On the precipitation regression of PC2 at lag 0 (Fig. 3a) some statistically significant anomalies can be found, with already above-normal precipitation near the west coast and dry conditions in the south of Canada. This is consistent, but with an opposite sign, to the regression of PC1 at lag 2 (Fig. 5c). Because a positive PC2 follows a negative PC1, which is preceded by an earlier negative PC2, it is likely that the anomalies on Fig. 3a result from a Rossby wave signal left from the previous MJO cycle.

From Fig. 2a, besides the negative OLR anomaly near 120°E, we can see that EOF1 also has a positive OLR anomaly around 170°W. However, it has a smaller extent and weaker amplitude than that near 120°E. From Fig. 15, it can be seen that a very weak response would be generated if a weak heating is put near 170°W. Therefore the OLR anomaly around 170°W of EOF1 has a limited impact.

6. Conclusions and discussion

In this study we have examined the impact of the MJO on winter precipitation in Canada. Based on pentad data of different sources, a significant connection between tropical convection of the MJO and the Canadian precipitation is found. The occurrence of precipitation anomaly in Canada has a 1–3 pentad lag to the tropical convection activity in the Indian Ocean and western Pacific. After the MJO-related convection displays a dipole structure with enhanced convection over the Indian Ocean and reduced convection over the western Pacific, precipitation in the coastal British Columbia increases significantly. Above-normal precipitation also appears in south Quebec and the region south of Hudson Bay. At the same time, northeast Canada near Newfoundland experiences a reduction in precipitation.

An analysis of the circulation anomalies indicates that the Canadian precipitation variability is linked to the dipole tropical convection anomaly of the MJO through a wave train, a process as discussed in Lin et al. (2009). Changes in vertical motion, storm track activity, and moisture transport, together with the topography of the coastal range and Rocky Mountains are likely to contribute to the precipitation changes in the west coast of British Columbia. On the other hand, the tropical MJO convection centered near the Maritime Continent (110°E) has a very weak connection to the Northern Hemisphere extratropical circulation anomalies, and thus a small impact on Canadian precipitation. The dipole MJO diabatic heat source in the Indian Ocean and western Pacific is thus likely responsible to excite extratropical large-scale circulation anomalies and influence intraseasonal precipitation variability in Canada.

Linear numerical experiments using a primitive equation model with an anomalous thermal forcing that resemble the dipole tropical convection are able to reproduce the observed circulation anomalies in the Northern Hemisphere extratropics, suggesting that the observed circulation anomalies result from the dipole thermal forcing of the MJO. On the other hand, integration with a single thermal forcing near 110°E produces a very week response, again consistent with the observations. The sensitivity of the Northern Hemisphere extratropical response to the location of tropical forcing is further analyzed through a series of linear experiments with an equatorial heat source placed at different longitudes. It is found that a heat source located near 160°E or near 80°E is the most effective in forcing extratropical circulation anomalies.

The time-lagged association between the Canadian precipitation and the MJO convection activity provides important information for an extended-range forecasting of the Canadian precipitation. As the connection has a 5–15-day time lag, an extended-range forecast is possible based on the current observed condition of the MJO. Forecasts of even a longer time scale for Canadian precipitation may also not be out of reach given that the tropical MJO itself has a potential predictability of several weeks (e.g., Waliser et al. 2003). However, the usefulness of the results reported in this study may be limited in several aspects. The signal of the influence of the MJO on Canadian precipitation is modest. It is important to keep in mind that there are many factors that can influence the low-frequency variability of precipitation in winter. The results of the regression and composite analysis presented here just represent an average influence of many MJO events. For an individual case, the signal coming from the tropics could be overwhelmed by other influences such as those from the high-latitude weather. Moreover, previous studies have shown that the atmospheric response to tropical forcing is sensitive to the extratropical basic flow (e.g., Ting and Sardeshmukh 1993). As the winter climate is used as the basic state in the linear integrations, the response should be treated as a response under the climatological condition. With a different basic state, such as that of a specific winter, the response is likely to have a slightly different amplitude and phase. The forcing used in the experiments is stationary. A tropical forcing reflecting the propagating nature of the MJO may produce a more realistic extratropical impact.

In extended-range forecasting, it is important for numerical models to correctly represent and simulate the tropical–extratropical connections as observed in this study. The presented result provides useful information for validating the numerical models.