## 1. Introduction

In a dynamical seasonal forecast, one seeks signals that come from some slowly varying processes external to the atmosphere. This is usually done either with a coupled atmosphere–ocean model or with an atmospheric model. In the latter case, the slowly varying sea surface temperature (SST), which is predictable at a much longer time scale than the atmosphere alone, is provided. To extract the externally forced signals, an ensemble technique is used, where a set of integrations for the predicted season is carried out using a GCM with the same SST, but with different initial conditions. The average of an ensemble of sufficient size then represents the signal associated with the boundary forcing.

Since only a single realization is available for the real atmosphere, its seasonal average that is used to verify the ensemble prediction contains not only the signal but also variability that is internally generated and largely unpredictable. Thus, one important factor that determines the seasonal predictability is the magnitude of the signal relative to that of the noise (signal-to-noise ratio). The signal-to-noise ratio is normally high in the tropics where most GCMs produce skillful seasonal forecasts. In the extratropical regions, however, only a limited skill is expected even with a perfect numerical model due to a weak forced signal and strong noise level. Most of the forecast skill is found in the North Pacific and North American regions, a skill that is linked to the atmospheric signal forced by the El Niño–Southern Oscillation (ENSO; e.g., Shukla et al. 2000; Derome et al. 2001).

Another important factor that determines the forecast skill is whether or not the GCM responds to a boundary forcing in the same way as the real atmosphere (i.e., if a signal is realistically generated in magnitude and spatial distribution). Numerical models are imperfect, so the atmospheric response to a boundary forcing (e.g., SST anomaly) is biased and model dependent. Besides model improvement, efforts have been made to reduce the model errors through postprocessing of GCM integrations (e.g., Smith and Livezey 1999; Feddersen et al. 1999; Derome et al. 2001; Mo and Straus 2002; Kang et al. 2004). Lin et al. (2005a, hereafter LDB) formulated a statistical approach based on the regression of the forecast model’s leading forced singular value decomposition (SVD) patterns and the historical observations in order to correct the atmospheric response pattern to tropical SST anomalies. This technique was applied to the winter 500-hPa geopotential height forecasts. Significant improvement in the forecast skill for the North Atlantic Oscillation (NAO) was achieved.

In this paper, we apply the systematic error correction method of LDB to seasonal forecasts of Canadian winter precipitation. Predicting precipitation on a seasonal time scale over high-latitude regions remains a challenging task. Canadian weather is influenced by both the Pacific–North American (PNA) pattern and the NAO, the two most important structures of atmospheric low-frequency variability over the Northern Hemisphere (Wallace and Gutzler 1981; Barnston and Livezey 1987). The former is known to be partly associated with the ENSO. In fact, the ENSO variability is observed to be correlated with precipitation anomaly in the United States (e.g., Ropelewski and Halpert 1986) and Canada (Shabbar et al. 1997). The NAO, with its major action centers over the North Atlantic, may have important influences on the weather in eastern Canada. The NAO is considered difficult to predict since the atmospheric internal dynamics plays a dominant role in its variability (Hurrell et al. 2003). Recently, however, the association between the interannual variability of the NAO and tropical Pacific thermal forcing has started to emerge (e.g., Lin et al. 2005b; Li et al. 2006). Some skill in seasonal forecasts of the NAO has been demonstrated (e.g., Derome et al. 2005; LDB; Muller et al. 2005). Skillful PNA and NAO forecasts would likely lead to improved seasonal precipitation predictions in Canada.

In section 2 the models that are used for the seasonal forecasts and the data are briefly described. Large-scale flow patterns over the winter Northern Hemisphere and their association with Canadian precipitation are discussed in section 3. In section 4, the GCM response patterns to tropical Pacific SST anomaly are identified using an SVD analysis. The scheme for postprocessing for the precipitation for the GCM forecasts is introduced in section 5. Section 6 presents the result of forecast skill. Section 7 gives a summary and discussion.

## 2. GCMs and data description

The output of the ensemble forecast experiments conducted under the second phase of the Historical Forecasting Project (HFP2) is analyzed in this study. The HFP is a collaborative project among some Canadian universities and government laboratories, whose objective is to test the extent to which the potential predictability of mean-seasonal conditions could be achieved. The experiment setup of the first phase of HFP (HFP1) and some results were reported in Derome et al. (2001). In HFP2, ensemble historical seasonal hindcast experiments were performed using four atmospheric GCMs; namely, the second and third generation atmospheric GCMs (GCM2 and GCM3) of the Canadian Centre for Climate Modeling and Analysis (CCCma), a reduced-resolution version of the global spectral model (SEF) of Recherche en Prévision Numérique (RPN), and the Global Environmental Multiscale (GEM) model of RPN.

The GCM2 was used in previous studies for climate simulations (e.g., Boer et al. 1984; McFarlane et al. 1992). It is a global spectral model, with a triangular 32 (T32) horizontal resolution and 10 levels in the vertical. GCM3 shares many basic features with GCM2, but with higher resolution (T63, L32) and improved treatment of many parameterized physical processes (more information available online at http://www.cccma.bc.ec.gc.ca/models/gcm3.shtml). The SEF was used in previous studies for global data assimilation and medium-range weather forecasting (Ritchie 1991; Ritchie and Beaudoin 1994). It is also a global spectral model, with a T63 horizontal resolution and 23 levels. The GEM is an operational model at the Canadian Meteorological Centre (Côté et al. 1998a, b). In HFP2, the GEM model was run at a horizontal resolution of 2° × 2° and 50 vertical levels.

An ensemble of 10 parallel integrations of 4-month duration was conducted for the 1969–2003 period using each model starting from the beginning of each month. The initial atmospheric conditions were at 12-h intervals preceding the start of the forecasts, taken from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996). Global SSTs were predicted using the persistence of the anomaly of the preceding month (i.e., the SST anomaly from the previous month was added to the climate of the forecast period). Sea ice (ICE) extents were initialized with the analysis and relaxed to climatology over the first 15 days of integration. The SST and ICE data were taken from the Seasonal Prediction Model Intercomparison Project-2 (SMIP-2) boundary data (more information available online at http://www-pcmdi.llnl.gov/projects/amip/AMIP2EXPDSN/BCS_OBS/amip2_bcs.htm). The snow cover was initialized with the NCEP weekly observations (Dewey and Heim 1982). Coupled ocean–atmosphere models are becoming more common for seasonal and multiseasonal forecasts. For a forecast up to 4 months as in HFP2, however, the persistent SST anomaly is a reasonable approximation.

The 500-hPa geopotential heights of the NCEP–NCAR reanalysis are used here for analysis and calculation of the PNA and NAO indices. The monthly precipitation data that are used for analysis and verification come from the Climatic Research Unit (CRU) at the University of East Anglia, United Kingdom (Mitchell and Jones 2005, more information available online at http://www.cru.uea.ac.uk/cru/data/hrg.htm). This is the CRU TS 2.1 dataset, which comprises monthly grids of observed climate, for the period 1901–2002, and covering the global land surface at 0.5° × 0.5° resolution. The observed grids are based on extensive databases of monthly measurements of climate at individual stations. However, only the data of the same period as the NCEP–NCAR reanalysis (1948–2002) are used. A comparison was made between this dataset and that of Xie and Arkin (1997) in climatology and variability, and a good agreement was found.

In this study only the winter data and forecasts that start from 1 December are analyzed. As the CRU precipitation data end in 2002, 33 winters from 1969/70 to 2001/02 are covered. The seasonal-averaged precipitation over Canada is more controlled by large-scale phenomena in winter, compared to summer when local convection becomes important and thus more difficult to predict. Also in winter, strong westerlies in the tropospheric midlatitudes provide a favorable condition for a northward Rossby wave propagation so that tropical influences can reach high latitudes. Both the PNA and NAO have a larger amplitude in winter than in summer.

## 3. Large-scale atmospheric patterns and Canadian winter precipitation

We first look at the winter precipitation climatology over Canada. Figures 1a,b depict the time average and standard deviation, respectively, of the December–February (DJF) mean precipitation calculated from the CRU data for the 54 winters from 1948/49 to 2001/02. As can be seen, both the time average and standard deviation have much larger values near the coastal regions than the inland. In the west the maximum precipitation and its variability are located in British Columbia, whereas in the east large values of precipitation and its variability are found over the maritime provinces, Québec and Ontario.

A rotated empirical orthogonal function (REOF) analysis (Richman 1986) was conducted using the wintertime (DJF) seasonally averaged 500-hPa geopotential height of the NCEP–NCAR reanalysis over the region 20°–90°N from 1948/49 to 2001/02 (54 winters). The REOF is normally used to find regionalized circulation patterns. The first two modes (REOF1 and REOF2) are displayed in Fig. 2. As is seen, REOF1 and REOF2 well represent the PNA and NAO, respectively. Therefore, to a good approximation, the principal component of REOF1 (PC1) is used to define the observed PNA index, and PC2 to represent the observed NAO index. In fact, our PNA index is correlated with the DJF PNA index derived from the formula in Wallace and Gutzler (1981; more information available online at http://jisao.washington.edu/data_sets/pna/) at 0.89, while our NAO index correlates with the DJF station-based NAO index (Hurrell 1995; more information available online at http://www.cgd.ucar.edu/cas/jhurrell/indices.data.html) at 0.92.

To document the association of Canadian winter precipitation with the large-scale atmospheric patterns, correlations are calculated between the CRU precipitation over Canada and the PNA and NAO indices during the 54 winters (Fig. 3). In the correlation maps, areas shaded denote those with a statistical significance level of 0.05 according to a two-tailed Student’s *t* test. The general feature of precipitation associated with the PNA pattern is a north–south dipole structure over Canada (Fig. 3a). A significant negative correlation occurs in a large area extending from southern British Columbia, across the southern prairies, into southwest Ontario. Over central-northern Canada, significant positive correlations with the PNA index are observed. A similar pattern of precipitation was reported associated with the ENSO (Shabbar et al. 1997). Considering the link between the ENSO and the PNA (e.g., Horel and Wallace 1981), such similarity is not surprising.

Figure 3b shows the correlation between the NAO index and Canadian winter precipitation. Significant negative values are observed over northeastern Canada, that cover most of Newfoundland and Québec. Hurrell (1995) found that during a positive phase of the NAO, increased northwesterly winds west of Greenland result in reduced precipitation over the Canadian Arctic. Here it is evident that there is a significant influence of the NAO on the weather of northeastern Canada. Small areas of negative and positive correlations can also be found with some degree of significance over the southern prairies and northwestern Canada, respectively.

In summary, winter precipitation over large parts of Canada is significantly affected by the PNA and NAO. This implies that the skill of a seasonal precipitation prediction depends on the forecast accuracy of these large-scale atmospheric patterns.

## 4. GCM response patterns to tropical Pacific SST anomalies

As mentioned in the introduction, a seasonal forecast attempts to reproduce signals that come from some slowly varying processes external to the atmosphere. Here we focus on the part of atmospheric response to the SST anomalies in a specific region—the tropical Pacific—which is known to be a major forcing for atmospheric variability on a seasonal time scale.

The ensemble mean Northern Hemispheric 500-hPa geopotential height averaged over two 3-month segments [DJF, which represents months 1–3 of the forecast, and January–March (JFM), which is for months 2–4] are analyzed. For each GCM, an SVD analysis (Bretherton et al. 1992) is conducted of the covariance between the 3-month-averaged ensemble mean height field and the tropical Indian–Pacific (20°S–20°N, 120°E–90°W) SST in the previous November (recall that it is the November SST anomaly that is persisted throughout the DJFM forecasts). The atmospheric patterns of the leading SVDs represent the dominant forced patterns associated with the SST structures in the tropical Indian–Pacific. To facilitate a comparison with the observations, a similar SVD calculation is performed on the observed 500-hPa geopotential height and the same SST. This represents a lagged association between the observed height field and the tropical SST anomaly.

We first look at the observed SVD patterns shown in Fig. 4. In the geopotential height field, SVD1 and SVD2 have similar distributions as the PNA and NAO, respectively, as is clear when comparing with Fig. 2. The temporal correlation between the principal component of the atmospheric component of SVD1 (APC_{1}) and the observed PNA index is 0.90, whereas that between APC_{2} and the observed NAO index reaches 0.93, where the observed PNA and NAO indices for DJF are obtained by projecting the observed DJF 500-hPa height field to the REOF1 and REOF2 as shown in Fig. 2. The SST distribution for SVD1 represents a typical ENSO signal. Thus, a positive PNA in DJF follows an above-normal SST anomaly in the tropical eastern Pacific in November. Probably less familiar is the SST distribution for SVD2, which reveals a negative SST anomaly along the equatorial Pacific with a center in the middle and western tropical Pacific. The SVD analysis indicates that such an SST distribution in November leads to a positive NAO in DJF. In fact, a similar association between the tropical Pacific SST and the NAO was reported in a recent study (Li et al. 2006). The SVD result for JFM is very similar to that of DJF (not shown).

If a seasonal forecast is to be skillful, the above association between the atmosphere and the SST should be reproduced by the GCMs. Figure 5 show the first and second pairs of SVD for the forecasts for GCM3. For SVD1 (Fig. 5a), the forced PNA pattern is similar to the observations in the Pacific and North American region, though some disagreement can be found in the North Atlantic and Europe. The atmospheric component of SVD2, however, is far from the NAO pattern that is observed (Fig. 5b).

The SVD results for the other three models show similar features. The SST distributions of the first two modes have some similarities in the tropics among the four GCMs (as are shown for GCM3 in Figs. 5c,d). The atmospheric responses, however, are quite model dependent and biased (not shown).

Although the spatial distribution of the atmospheric response patterns is model dependent, their corresponding time variations (APC_{1} and APC_{2}) are significantly correlated with the observed PNA and NAO indices, respectively, as listed in Table 1 for both DJF and JFM. This result is striking, indicating that both the PNA and NAO signals are embedded in the ensemble forecasts. The two leading APCs of the GCMs could be used to represent the PNA and NAO indices with a significant skill. As discussed in LDB, a correction scheme taking into consideration the forecast time series of the leading SVDs can effectively improve the forecast skill of the PNA and NAO.

## 5. Precipitation forecasts by postprocessing GCM integrations

As discussed above, the wintertime precipitation in Canada is significantly influenced by the PNA and NAO. We have also seen that the time evolution of the two leading SVD atmospheric components (APCs) of the ensemble forecasts can be used to produce a skillful prediction of the PNA and NAO indices. Here we make use of the two predicted APCs to construct a forecast of the Canadian winter precipitation.

We first look at the association between the two predicted APCs (APC_{1} and APC_{2}) and Canadian winter precipitation. Figures 6a,b depict the correlations of the CRU precipitation over Canada with APC_{1} and with APC_{2}, respectively, where APC_{1} and APC_{2} are averages for the four models. They represent the observed precipitation distributions associated with the two leading forced patterns in the models. Since APC_{1} and APC_{2} are correlated with the observed PNA and NAO indices, respectively, Fig. 6 has many features similar to Fig. 3. Differences between these two figures are quite obvious as well, reflecting the fact that the model-predicted APC_{1} and APC_{2} indices are not perfectly correlated with the observed PNA and NAO indices. The APC_{1} and APC_{2} are forced signals, while the observed PNA and NAO indices contain both forced and atmospheric internal variabilities. The correlation of precipitation with APC_{1} (Fig. 6a) is not as strong as its correlation with the observed PNA index (Fig. 3a), and we note that the correlation with APC_{2} is stronger (Fig. 6b). The negative correlation center that covers most of Newfoundland and Québec in Fig. 3b is shifted to the south in Fig. 6b, and also in Fig. 6b a negative correlation center emerges to the north of Lake Superior. In short, while APC_{1} and APC_{2} are correlated with the observed PNA and NAO indices, respectively, their related precipitation patterns are not very well correlated with those related to the observed PNA and NAO indices.

_{1}, APC

_{2}, and APC

_{3}), where the SVD analysis was performed between the ensemble mean Northern Hemispheric 500-hPa geopotential height averaged over either DJF or JFM and the November tropical Pacific SST, as described in the last section. For each grid point in space, the regression model can be written as

*P*(

*t*) is the seasonal mean of precipitation;

*a*

_{1},

*a*

_{2}, and

*a*

_{3}are the regression coefficients; and

*ϵ*is the residual. The three regression coefficients are calculated using the historical observed precipitation and the APCs of each model by the least squares method in a cross-validation framework (i.e., when computing the regression coefficients for a given forecast year, that year is excluded). Therefore, the statistical model is trained with data that are independent from the prediction data. Here

*ϵ*is considered as noise and is omitted in the calculations (training and forecast). As the GCMs produce their own precipitation forecasts, we will refer to the forecasts obtained through the postprocessing method in (1) as the corrected forecasts. The effect of the number of SVDs used in the correction was discussed in LDB where it was found that SVD1 and SVD2 are the two major contributors, and the third SVD makes limited contributions. Higher-order SVDs are even less important. Therefore, as in LDB, three SVDs are used in the correction scheme. A small number of predictors (i.e., 3) compared to the sample size (i.e., 33) would also eliminate the overfitting problem in the linear regression equation. Note that if all years were used (instead of our cross-validation approach) and the average of the four model forecasts were used, the spatial distributions of

*a*

_{1}and

*a*

_{2}would be as shown in Fig. 6.

## 6. Forecast skill

In this section, we present the forecast skill for Canadian winter precipitation using the above linear regression model (corrected forecast), compared with that of the original GCM-produced ensemble forecast (original forecast). Results for both DJF (months 1–3) and JFM (months 2–4) forecasts are shown. Two metrics are used for the seasonal forecast skill, namely, the correlation skill, which is the temporal correlation between the observations and forecasts over 33 winters, and the mean squared error (MSE) between the forecast and observed fields. The MSE is calculated using the observed and forecast anomalies that are normalized using their respective standard deviations, an approach that was used in Smith and Livezey (1999).

Figure 7 illustrates the correlation skill of DJF precipitation forecasts for the four GCMs. The left panels present that for the original model forecasts, while the right panels show the skill for the corrected forecasts. Areas with a statistical significance level of 0.05 are shaded. As can be seen, very limited forecast skill can be found on the original skill maps, and the skill distribution is model dependent. With the corrected forecasts, significant improvement of forecast skill is achieved for all four GCMs (Figs. 7b,d,f,h). The skill distribution is now consistent among the GCMs, with significant correlation skill mainly over two regions: the area east of the Rockies, and the Québec–Ontario region. For each model, the local maximum correlation skill exceeds 0.5.

The results for the mean squared error are shown in Fig. 8. Similar conclusions as for the correlation skill can be made for the MSE. After the correction, a significant reduction of MSE is achieved for all the four GCMs over similar areas as for the correlation skill improvement.

Recent studies demonstrated that extended-range forecast skill can be improved with a multimodel approach (e.g., Krishnamurti et al. 2000; Palmer et al. 2000). Here we combine the ensemble forecasts by the four GCMs to see if such a superensemble can further improve the precipitation forecast skill. The combination of four model forecasts is done separately for the original forecasts and the corrected forecasts of the normalized precipitation anomalies. The normalization is done separately for each model under the cross-validation framework. The correlation skill and MSE result for the DJF precipitation forecasts are shown in Figs. 9 and 10, respectively. Indeed, the superensemble approach improves the forecast skill for both the original and corrected forecasts. Again the corrected forecast is doing a much better job than the original forecast. The maximum local correlation skill over Québec and Ontario is greater than 0.6, and the local mean squared error is smaller than 1.0.

As for JFM forecasts (months 2–4), significant improvement by the corrected forecasts over the original forecasts is also achieved. The corrected forecasts by the four models all show significant predictive skill over Québec and eastern Ontario, contrary to the original forecasts (not shown). Displayed in Figs. 11 and 12 are the correlation skill and MSE score, respectively, for the four model-combined forecasts.

It is of interest to know the relative importance of the leading SVDs to the Canadian precipitation forecast skill. Specifically, one would ask whether the improved skill comes from the first or the second SVD. This is assessed by keeping only one predictor on the right hand side of (1), either APC_{1} or APC_{2}. Figures 13a,b depict the correlation skills after correcting the ensemble forecasts with APC_{1} and APC_{2}, respectively, for the four model-combined DJF precipitation forecasts. Although APC_{1} is responsible for some skill in the southern prairies (Fig. 13a), most of the skill in the Québec–Ontario region results from APC_{2} (Fig. 13b). APC_{2} is also associated with some precipitation forecast skill in the northern prairies and the region north of Lake Superior.

It is worth noticing that in Fig. 3b we observe a good linear relationship between the observed NAO index and the precipitation over Newfoundland and northeastern Québec, but the correction scheme seems to improve the skill in a region farther south. The reason is that we did not use the observed NAO index to train the regression model and to do the correction, instead we used the forecast APC_{2} index. The forecast APC_{2} index is correlated with the observed precipitation as shown in Fig. 6b, where one can find that the APC_{2}-related signal agrees with our improved forecasts. This indicates that the forecast APC_{2} is not exactly the observed NAO index, although they are significantly correlated.

The principal component of the oceanic component of SVD2 (OPC_{2}) is correlated with the observed DJF precipitation in Canada (Fig. 14). The SVD analysis was that using the November SST and the forecast Z500 for DJF, and OPC_{2} is the average of four models. It is clear that the wintertime precipitation in the Québec–Ontario region is linked to the tropical Pacific SST variability. The same analysis, but with the 500-hPa geopotential height (not shown), indicates that a wave train propagating from the tropical Pacific seems responsible for the precipitation anomaly in eastern Canada.

To assess the effect of the autocorrelation in the time series, calculations of the regression coefficients in (1) were repeated by removing data of 3 yr (the forecast year, the year before, and the year after), that is, extending the cross-validation approach by excluding data of three consecutive years. This turns out to have little effect on the result. Also the correlation skill was repeated with the detrended data. This again produces no change in the conclusions.

## 7. Summary and discussion

Using a statistical postprocessing method on dynamical seasonal forecasts, the seasonal predictive skill for the Canadian wintertime precipitation is assessed. The technique is based on the fact that the seasonal average of Canadian precipitation is significantly influenced by large-scale atmospheric circulation patterns. The PNA and NAO are two of the most important atmospheric patterns. Although their spatial distributions are not well simulated by all the forecast GCMs (particularly the NAO), their time evolutions are reasonably well resolved by the expansion coefficients of the leading SVDs between the ensemble mean (forced) 500-hPa height field and the tropical/subtropical Pacific SST that is used to force the model.

Significant improvement of predictive skill over that of the original forecasts is obtained for all four GCMs. Reliable seasonal precipitation forecasts are achieved in the southern prairies and the Québec–Ontario region for both DJF and JFM.

Shabbar and Barnston (1996) investigated the seasonal forecast skill of Canadian precipitation using canonical correlation analysis. They found some significant correlation skill in winter over a small area along southern Canada. Over the Québec region, they obtained no forecast skill for precipitation. The postprocessed dynamical seasonal forecasts as reported in this study seem to outperform those based on a pure statistical method.

We have taken an indirect approach to correct the Canadian precipitation forecast. Instead of calculating the SVD between the ensemble precipitation and the SST, we made use of the SST-forced 500-hPa geopotential height patterns in the Northern Hemisphere, and then associated these patterns with the Canadian precipitation. It can be argued that finding the leading patterns in the 500-hPa height field in the Northern Hemisphere as a whole gives a more robust result since the PNA and NAO are very large-scale phenomena. A calculation of precipitation correction using an SVD between the ensemble precipitation over Canada and the SST does not provide an impressive skill improvement as discussed in this study (not shown).

In the HFP2, atmospheric GCMs were used to perform seasonal forecasts. The SST anomaly for the forecast period was predicted as a persistence from the preceding month. The seasonal forecast skill thus comes from the signal that is a one-way response to the SST anomaly in such a two-tier system. How the coupling and feedback between the atmosphere and ocean in a coupled model would affect the seasonal predictive skill of precipitation remains to be seen.

By the SVD analysis in this study, the atmospheric signals that are associated with the tropical/subtropical Pacific SST are used in the correction method. It is possible that the winter NAO variability is also linked to other external processes. For example, there is evidence that the winter NAO is linked to the Eurasian snow-cover anomaly (Cohen et al. 2001), the SST anomaly in the North Atlantic (Czaja and Frankignoul 2002), and signals from the stratosphere (Baldwin et al. 2003). Further studies are needed to quantify the relative importance of these processes and how they contribute to improving the NAO-related seasonal forecasts.

## Acknowledgments

We thank members in the Canadian HFP project and the seasonal forecast forum for their contributions. We are grateful to Juan-Sebastian Fontecilla, Normand Gagnon, and Environment Canada for making the HFP2 data available. This research was funded in part by the Canadian Foundation for Climate and Atmospheric Sciences and by the Natural Science and Engineering Research Council of Canada through the Canadian CLIVAR Network.

## REFERENCES

Baldwin, M. P., D. B. Stephenson, D. W. J. Thompson, T. J. Dunkerton, A. J. Charlton, and A. O’Neill, 2003: Stratospheric memory and extended-range weather forecasts.

,*Science***301****,**636–640.Barnston, A. G., and R. E. Livezey, 1987: Classification, seasonality, and persistence of low-frequency atmospheric circulation patterns.

,*Mon. Wea. Rev.***115****,**1083–1126.Boer, G. J., N. A. McFarlane, R. Laprise, J. D. Henderson, and J-P. Blanchet, 1984: The Canadian Climate Centre spectral atmospheric general circulation model.

,*Atmos.–Ocean***22****,**397–429.Bretherton, C. S., C. Smith, and J. M. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data.

,*J. Climate***5****,**541–560.Cohen, J., K. Saito, and D. Entekhabi, 2001: The role of the Siberian high in Northern Hemisphere climate variability.

,*Geophys. Res. Lett.***28****,**299–302.Côté, J., S. Gravel, A. Méthot, A. Patoine, M. Roch, and A. Staniforth, 1998a: The operational CMC-MRB Global Environmental Multiscale (GEM) model. Part I: Design considerations and formulation.

,*Mon. Wea. Rev.***126****,**1373–1395.Côté, J., J-G. Desmarais, S. Gravel, A. Méthot, A. Patoine, M. Roch, and A. Staniforth, 1998b: The operational CMC-MRB Global Environmental Multiscale (GEM) model. Part II: Results.

,*Mon. Wea. Rev.***126****,**1397–1418.Czaja, A., and C. Frankignoul, 2002: Observed impact of North Atlantic SST anomalies on the North Atlantic Oscillation.

,*J. Climate***15****,**606–623.Derome, J., and Coauthors, 2001: Seasonal predictions based on two dynamical models.

,*Atmos.–Ocean***39****,**485–501.Derome, J., H. Lin, and G. Brunet, 2005: Seasonal forecasting with a simple general circulation model.

,*J. Climate***18****,**597–609.Dewey, K. F., and R. Heim Jr., 1982: A digital archive of Northern Hemisphere snow cover, November 1966 through December 1980.

,*Bull. Amer. Meteor. Soc.***63****,**1132–1141.Feddersen, H. A., A. Navarra, and M. N. Ward, 1999: Reduction of model systematic error by statistical correction for dynamical seasonal prediction.

,*J. Climate***12****,**1974–1989.Horel, J. D., and J. M. Wallace, 1981: Planetary scale atmospheric phenomena associated with the Southern Oscillation.

,*Mon. Wea. Rev.***109****,**813–829.Hurrell, J. W., 1995: Decadal trends in the North Atlantic Oscillation: Regional temperature and precipitation.

,*Science***269****,**676–679.Hurrell, J. W., Y. Kushnir, M. Visbeck, and G. Ottersen, 2003: An overview of the North Atlantic Oscillation.

*The North Atlantic Oscillation: Climatic Significance and Environmental Impact, Geophys. Monogr.,*Vol. 134, Amer. Geophys. Union, 1–35.Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project.

,*Bull. Amer. Meteor. Soc.***77****,**437–471.Kang, I-S., J-Y. Lee, and C-K. Park, 2004: Potential predictability of summer mean precipitation in a dynamical seasonal prediction system with systematic error correction.

,*J. Climate***17****,**834–844.Krishnamurti, T. N., C. M. Kishtawai, Z. Zhang, T. LaRow, D. Bachiochi, and C. E. Williford, 2000: Multimodel ensemble forecasts for weather and seasonal climate.

,*J. Climate***13****,**4196–4216.Li, S., M. P. Hoerling, S. Peng, and K. M. Weickmann, 2006: The annular response to tropical Pacific SST forcing.

,*J. Climate***19****,**1802–1819.Lin, H., J. Derome, and G. Brunet, 2005a: Correction of atmospheric dynamical seasonal forecasts using the leading ocean-forced spatial patterns.

,*Geophys. Res. Lett.***32****.**L14804, doi:10.1029/2005GL023060.Lin, H., J. Derome, and G. Brunet, 2005b: Tropical Pacific link to the two dominant patterns of atmospheric variability.

,*Geophys. Res. Lett.***32****.**L03801, doi:10.1029/2004GL021495.McFarlane, N. A., G. J. Boer, J-P. Blanchet, and M. Lazare, 1992: The Canadian Climate Centre second-generation general circulation model and its equilibrium climate.

,*J. Climate***5****,**1013–1044.Mitchell, T. D., and P. D. Jones, 2005: An improved method of constructing a database of monthly climate observations and associated high-resolution grids.

,*Int. J. Climatol.***25****,**693–712.Mo, R., and D. M. Straus, 2002: Statistical-dynamical seasonal prediction based on principal component regression of GCM ensemble integrations.

,*Mon. Wea. Rev.***130****,**2167–2187.Muller, W. A., C. Appenseller, and C. Schar, 2005: Probabilistic seasonal prediction of the winter North Atlantic Oscillation and its impact on near surface temperature.

,*Climate Dyn.***24****,**213–226.Palmer, T. N., C. Brankovic, and D. S. Richardson, 2000: A probability and decision-model analysis of PROVOST seasonal multi-model ensemble integrations.

,*Quart. J. Roy. Meteor. Soc.***126****,**2013–2034.Richman, M. B., 1986: Rotation of principal components.

,*Int. J. Climatol.***6****,**293–335.Ritchie, H., 1991: Application of the semi-Lagrangian method to a multilevel spectral primitive-equation model.

,*Quart. J. Roy. Meteor. Soc.***117****,**91–106.Ritchie, H., and C. Beaudoin, 1994: Approximation and sensitivity experiments with a baraclinic semi-Lagrangian spectral model.

,*Mon. Wea. Rev.***122****,**2391–2399.Ropelewski, C. F., and M. S. Halpert, 1986: North American precipitation and temperature patterns associated with the El Niño/Southern Oscillation (ENSO).

,*Mon. Wea. Rev.***114****,**2353–2362.Shabbar, A., and A. G. Barnston, 1996: Skill of seasonal climate forecasts in Canada using canonical correlation analysis.

,*Mon. Wea. Rev.***124****,**2370–2385.Shabbar, A., B. Bonsal, and M. Khandekar, 1997: Canadian precipitation associated with the Southern Oscillation.

,*J. Climate***10****,**3016–3027.Shukla, J. S., and Coauthors, 2000: Dynamical seasonal prediction.

,*Bull. Amer. Meteor. Soc.***81****,**2593–2606.Smith, T. M., and R. E. Livezey, 1999: GCM systematic error correction and specification of the seasonal mean Pacific-North America region atmosphere from global SSTs.

,*J. Climate***12****,**273–288.Wallace, J. M., and D. S. Gutzler, 1981: Teleconnections in the geopotential height field during the Northern Hemisphere winter.

,*Mon. Wea. Rev.***109****,**784–812.Xie, P., and P. A. Arkin, 1997: Global precipitation: A 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs.

,*Bull. Amer. Meteor. Soc.***78****,**2539–2558.

(a), (b) First two modes of an REOF analysis of DJF 500-hPa height from NCEP–NCAR reanalysis from 1948/49–2001/02, represented as regressions of DJF 500-hPa height onto the corresponding time expansion coefficients. The magnitude corresponds to 1 std dev of the time coefficient. The contour interval is 10 m. Contours with negative values are dashed.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

(a), (b) First two modes of an REOF analysis of DJF 500-hPa height from NCEP–NCAR reanalysis from 1948/49–2001/02, represented as regressions of DJF 500-hPa height onto the corresponding time expansion coefficients. The magnitude corresponds to 1 std dev of the time coefficient. The contour interval is 10 m. Contours with negative values are dashed.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

(a), (b) First two modes of an REOF analysis of DJF 500-hPa height from NCEP–NCAR reanalysis from 1948/49–2001/02, represented as regressions of DJF 500-hPa height onto the corresponding time expansion coefficients. The magnitude corresponds to 1 std dev of the time coefficient. The contour interval is 10 m. Contours with negative values are dashed.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation between the DJF precipitation and (a) the PNA index and (b) the NAO index for the period of 1948/49–2001/02. The contour interval is 0.1. Contours with negative values are dashed. The shaded areas represent correlations with a significance level of 0.05 according to a two-tailed Student’s *t* test.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation between the DJF precipitation and (a) the PNA index and (b) the NAO index for the period of 1948/49–2001/02. The contour interval is 0.1. Contours with negative values are dashed. The shaded areas represent correlations with a significance level of 0.05 according to a two-tailed Student’s *t* test.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation between the DJF precipitation and (a) the PNA index and (b) the NAO index for the period of 1948/49–2001/02. The contour interval is 0.1. Contours with negative values are dashed. The shaded areas represent correlations with a significance level of 0.05 according to a two-tailed Student’s *t* test.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

(a), (b) Observed DJF 500-hPa height and (c), (d) the previous November SST distributions of (a), (c) SVD1 and (b), (d) SVD2. The magnitude corresponds to 1 std dev of each time coefficient. The contour interval is 10 m in (a), (b), 0.3°C in (c), and 0.1°C in (d). The shaded areas in (c) represent SST anomaly values greater than 0.6°C, whereas those in (d) are smaller than −0.1°C.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

(a), (b) Observed DJF 500-hPa height and (c), (d) the previous November SST distributions of (a), (c) SVD1 and (b), (d) SVD2. The magnitude corresponds to 1 std dev of each time coefficient. The contour interval is 10 m in (a), (b), 0.3°C in (c), and 0.1°C in (d). The shaded areas in (c) represent SST anomaly values greater than 0.6°C, whereas those in (d) are smaller than −0.1°C.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

(a), (b) Observed DJF 500-hPa height and (c), (d) the previous November SST distributions of (a), (c) SVD1 and (b), (d) SVD2. The magnitude corresponds to 1 std dev of each time coefficient. The contour interval is 10 m in (a), (b), 0.3°C in (c), and 0.1°C in (d). The shaded areas in (c) represent SST anomaly values greater than 0.6°C, whereas those in (d) are smaller than −0.1°C.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

(a), (b) Forecast DJF 500-hPa height and (c), (d) previous November SST distributions of (a), (c) SVD1 and (b), (d) SVD2 for GCM3. The magnitude corresponds to 1 std dev of each time coefficient. The contour interval is 10 m in (a), 5 m in (b), 0.3°C in (c), and 0.1°C in (d). The shaded areas in (c) represent SST anomaly values greater than 0.6°C, whereas those in (d) are smaller than −0.1°C.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

(a), (b) Forecast DJF 500-hPa height and (c), (d) previous November SST distributions of (a), (c) SVD1 and (b), (d) SVD2 for GCM3. The magnitude corresponds to 1 std dev of each time coefficient. The contour interval is 10 m in (a), 5 m in (b), 0.3°C in (c), and 0.1°C in (d). The shaded areas in (c) represent SST anomaly values greater than 0.6°C, whereas those in (d) are smaller than −0.1°C.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

(a), (b) Forecast DJF 500-hPa height and (c), (d) previous November SST distributions of (a), (c) SVD1 and (b), (d) SVD2 for GCM3. The magnitude corresponds to 1 std dev of each time coefficient. The contour interval is 10 m in (a), 5 m in (b), 0.3°C in (c), and 0.1°C in (d). The shaded areas in (c) represent SST anomaly values greater than 0.6°C, whereas those in (d) are smaller than −0.1°C.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation between the observed DJF precipitation and the four model averaged (a) APC_{1} and (b) APC_{2} for the forecast period. The contour interval is 0.1. Contours with negative values are dashed. The shaded areas represent correlations with a significance level of 0.05 according to a two-tailed Student’s *t* test.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation between the observed DJF precipitation and the four model averaged (a) APC_{1} and (b) APC_{2} for the forecast period. The contour interval is 0.1. Contours with negative values are dashed. The shaded areas represent correlations with a significance level of 0.05 according to a two-tailed Student’s *t* test.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation between the observed DJF precipitation and the four model averaged (a) APC_{1} and (b) APC_{2} for the forecast period. The contour interval is 0.1. Contours with negative values are dashed. The shaded areas represent correlations with a significance level of 0.05 according to a two-tailed Student’s *t* test.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation scores for the DJF precipitation forecasts by (a) GCM2 original, (b) GCM2 corrected, (c) GCM3 original, (d) GCM3 corrected, (e) SEF original, (f) SEF corrected, (g) GEM original, and (h) GEM corrected. The contour interval is 0.1. Contours with negative values are dashed. Areas with statistical significance passing the 0.05 level as estimated by a Student’s *t* test are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation scores for the DJF precipitation forecasts by (a) GCM2 original, (b) GCM2 corrected, (c) GCM3 original, (d) GCM3 corrected, (e) SEF original, (f) SEF corrected, (g) GEM original, and (h) GEM corrected. The contour interval is 0.1. Contours with negative values are dashed. Areas with statistical significance passing the 0.05 level as estimated by a Student’s *t* test are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation scores for the DJF precipitation forecasts by (a) GCM2 original, (b) GCM2 corrected, (c) GCM3 original, (d) GCM3 corrected, (e) SEF original, (f) SEF corrected, (g) GEM original, and (h) GEM corrected. The contour interval is 0.1. Contours with negative values are dashed. Areas with statistical significance passing the 0.05 level as estimated by a Student’s *t* test are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Mean squared error for the DJF precipitation forecast by (a) GCM2 original, (b) GCM2 corrected, (c) GCM3 original, (d) GCM3 corrected, (e) SEF original, (f) SEF corrected, (g) GEM original, and (h) GEM corrected. Areas with MSE smaller than 1.5 are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Mean squared error for the DJF precipitation forecast by (a) GCM2 original, (b) GCM2 corrected, (c) GCM3 original, (d) GCM3 corrected, (e) SEF original, (f) SEF corrected, (g) GEM original, and (h) GEM corrected. Areas with MSE smaller than 1.5 are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Mean squared error for the DJF precipitation forecast by (a) GCM2 original, (b) GCM2 corrected, (c) GCM3 original, (d) GCM3 corrected, (e) SEF original, (f) SEF corrected, (g) GEM original, and (h) GEM corrected. Areas with MSE smaller than 1.5 are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation scores for the DJF precipitation forecast by four model combined ensemble for (a) original and (b) corrected forecasts. The contour interval is 0.1. Contours with negative values are dashed. Areas with statistical significance passing the 0.05 level as estimated by a Student’s *t* test are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation scores for the DJF precipitation forecast by four model combined ensemble for (a) original and (b) corrected forecasts. The contour interval is 0.1. Contours with negative values are dashed. Areas with statistical significance passing the 0.05 level as estimated by a Student’s *t* test are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation scores for the DJF precipitation forecast by four model combined ensemble for (a) original and (b) corrected forecasts. The contour interval is 0.1. Contours with negative values are dashed. Areas with statistical significance passing the 0.05 level as estimated by a Student’s *t* test are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Mean squared error for the DJF precipitation forecast by four model combined ensemble for (a) original and (b) corrected forecasts. Areas with MSE smaller than 1.5 are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Mean squared error for the DJF precipitation forecast by four model combined ensemble for (a) original and (b) corrected forecasts. Areas with MSE smaller than 1.5 are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Mean squared error for the DJF precipitation forecast by four model combined ensemble for (a) original and (b) corrected forecasts. Areas with MSE smaller than 1.5 are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation scores for the DJF precipitation forecast by four model combined ensemble with correction of (a) APC_{1} and (b) APC_{2}. The contour interval is 0.1. Contours with negative values are dashed. Areas with statistical significance passing the 0.05 level as estimated by a Student’s *t* test are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation scores for the DJF precipitation forecast by four model combined ensemble with correction of (a) APC_{1} and (b) APC_{2}. The contour interval is 0.1. Contours with negative values are dashed. Areas with statistical significance passing the 0.05 level as estimated by a Student’s *t* test are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation scores for the DJF precipitation forecast by four model combined ensemble with correction of (a) APC_{1} and (b) APC_{2}. The contour interval is 0.1. Contours with negative values are dashed. Areas with statistical significance passing the 0.05 level as estimated by a Student’s *t* test are shaded.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation between the time series of OPC_{2} and the DJF precipitation in Canada. The contour interval is 0.1. Contours with negative values are dashed. The shaded areas represent correlations with a significant level of 0.05 according to a two-tailed Student’s *t* test.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation between the time series of OPC_{2} and the DJF precipitation in Canada. The contour interval is 0.1. Contours with negative values are dashed. The shaded areas represent correlations with a significant level of 0.05 according to a two-tailed Student’s *t* test.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlation between the time series of OPC_{2} and the DJF precipitation in Canada. The contour interval is 0.1. Contours with negative values are dashed. The shaded areas represent correlations with a significant level of 0.05 according to a two-tailed Student’s *t* test.

Citation: Monthly Weather Review 136, 3; 10.1175/2007MWR2232.1

Correlations between the atmospheric expansion coefficients of the leading forced SVD modes and the observed PNA and NAO indices. A correlation coefficient larger than 0.30 is required to pass a 0.05 significance level, which is shown in boldface.