## 1. Introduction

It is known that the Pacific–North American (PNA) teleconnection and the North Atlantic Oscillation (NAO, also known as the local display of the Arctic Oscillation) are the two most important atmospheric patterns of low-frequency variability over the Northern Hemisphere (Wallace and Guztler 1981; Barnston and Livezey 1987). The PNA and NAO explain a significant part of the interannual variance of the extratropical Northern Hemisphere atmospheric variability (Hurrell 1995, 1996). Most studies have focused on the influence of the PNA on the weather and climate over the North Pacific and North America. For the NAO, in addition to its impact on the climate over the North Atlantic and European area, many works have ascribed its influence on the recent climate changes in the Asian monsoon area by modulating the East Asia jet stream (Gong and Ho 2003; Branstator 2002; Watanabe 2004) or by teleconnection patterns (e.g., Li et al. 2008) or by modulating the quasi-biennial oscillation (QBO) wind in the stratosphere (e.g., Chen and Li 2007).

The typical definition of the NAO index is the difference between the normalized sea level pressure (SLP) at Lisbon, Portugal, and that at Stykkisholmur, Iceland (Hurrell 1995). The associated large-scale atmospheric pattern is usually one of the most pronounced modes over the Northern Hemisphere in the winter season. However, the NAO structure may be distorted for other seasons. Folland et al. (2009) showed that the summer NAO is characterized by a more northerly location and a smaller spatial scale and of a weaker amplitude than its winter counterpart. In the study of Portis et al. (2001), the NAO is represented through their concept of a “mobile NAO” where the NAO is defined month by month with the points of maximum anticorrelation of the National Centers for Environmental Prediction (NCEP) reanalysis mean SLP between two regions. Li et al. (2008) found that the recent climate changes over southwestern China in spring can be influenced by a teleconnection pattern that extends from the North Atlantic eastward to the Urals and ends over northern China. Although this teleconnection pattern has a close relationship to the NAO, its association to the surface temperature over China cannot be well reproduced by the typically defined NAO index, indicating that different downstream-extension mechanisms are involved.

The seasonal forecast is known to be a boundary forcing problem and the potential predictability of the atmospheric mean state is determined by slowly evolving boundary conditions, most notably the SST. However, in the extratropics, only limited forecast skill is expected due to the strong unpredictable atmospheric noise level. The PNA pattern associated with the tropical Pacific SST is believed to be the dominated source of seasonal forecast skill in the North Pacific and North American regions (Shukla et al. 2000; Derome et al. 2001). For the NAO, both observational and model studies indicate that part of it can be connected to the tropical forcing (Pozo-Vazquez et al. 2001; Wu and Hsieh 2004; Lin et al. 2005b; Li et al. 2006; Jia et al. 2009). Most of the above-mentioned studies, however, dealt with winter seasons.

While *often* global SST forcing *is* used in the numerical seasonal forecasts, in this study, we focus on the leading atmospheric patterns associated with the tropical Pacific Ocean, which is known to be a major forcing area for the atmospheric variability on a seasonal time scale, and investigate their influence on the climate over China. Four seasons [December–February (DJF) for winter, March–May (MAM) for spring, June–August (JJA) for summer, and September–November (SON) for fall] are investigated. An SVD analysis is conducted between the 500-hPa geopotential height Z500 over the Northern Hemisphere and SST in the tropical Pacific Ocean for the four seasons separately. The influences of these large-scale atmospheric patterns on SAT over China are examined. Furthermore, a statistical postprocess approach, which is constructed based on the SVD results, is applied to the second phase of the Canadian Historical Forecasting Project (HFP) data, with the aim of improving the seasonal forecast skill of SAT over China.

The paper is organized as follows. In section 2 the data and model used in this study are described. The association between SAT over the Northern Hemisphere and the PNA and NAO indices are presented in section 3. Sections 4 and 5 give the tropical Pacific SST forced large-scale atmospheric patterns in the observations and in the HFP data, respectively. The postprocessing approach and the seasonal forecast skill of SAT over China before and after the postprocessing approach are presented in section 6. The possible mechanisms behind the improvement of the forecast are discussed in section 7, followed by our conclusions in section 8.

## 2. Data and model description

The data used in this study are the seasonal ensemble forecast output from four global general circulation models (GCMs) employed in the second phase of the HFP. Two models, namely, the second and the third generations of the general circulation models (GCM2 and GCM3), were developed at the Canadian Centre for Climate Modeling and Analysis (CCCma; Boer et al. 1984; McFarlane et al. 1992). The other two models are from Recherche en Prévision Numérique (RPN) in Montréal, Quebec, Canada. They are the reduced-resolution version of the global spectral model (SEF; Ritchie 1991) and the Global Environmental Multiscale model (GEM; Côté et al. 1998a,b).

For each model, ten 4-month forecasts were carried out starting from the first day of each month. These 10 integrations were conducted with each of the four models using the same SST boundary forcing but different atmospheric initial conditions, which are taken from the NCEP–National Center for Atmospheric Research (NCAR) reanalysis (Kalnay et al. 1996) from 10 days preceding the start of the forecast period. The SST used in the forecast experiments is from the Seasonal Prediction Model Intercomparison Project-2 (SMIP-2) boundary data. The SST anomaly from the previous month prior to the expected forecast period is added to the climatological annual cycle of the SST and is persisted through the forecast period. The ensemble mean of the 10 model integrations is used to represent the forced signal. The source of forecast skill in the GCMs, if any, comes from the prescribed SST anomalies. More details about the HFP project can be found in Derome et al. (2001). We make use of the ensemble mean seasonal forecasts starting from the first day of February, May, August, and November spanning 33 yr from 1969 to 2001. As we are mainly interested in the forced signal, 3-month forecasts of a 1-month lead are analyzed, that is, the first month of forecasts is not used. Two datasets are used for the verification of the forecasts. One is the version 2.1 of the Climate Research Unit’s Time Series (CRU TS 2.1) dataset, a set of monthly averaged observed SATs over the land surface obtained from the CRU at the University of East Anglia in the United Kingdom (Mitchell and Jones 2005; http://www.cru.uea.ac.uk/cru/data/hrg.htm). The other observed dataset is the surface temperature of 160 meteorological stations in China for the same period. The data were collected and edited by the China Meteorological Administration and were relatively homogeneously distributed, especially in eastern China (Wu et al. 2003). A comparison between these two observed datasets shows that they have quite similar structures over China according to the climatological mean and the standard deviation.

## 3. The association between SAT and the PNA and NAO

We start by examining the association between SAT over the Northern Hemisphere and the NAO for four seasons. The seasonal station-based NAO index is the difference in the normalized sea level pressure (SLP) between Ponta Delgada, Azores, and Stykkisholmur/Reykjavik, Iceland, available online (http://www.cgd.ucar.edu/cas/jhurrell/indices.data.html#naostatseas). The influence of the NAO on SAT over the Northern Hemisphere for four seasons is measured by the temporal correlations. Figure 1 depicts the correlations between the CRU SAT and the NAO index for the period from 1951 to 2001 for the four seasons. Areas with a correlation significant at the 5% level or better are shaded. It is seen from Fig. 1 that the influence of the NAO on SAT over the Northern Hemisphere is most significant in winter when significant negative correlations occur over Greenland, northeastern Canada, and northern Africa, while positive correlations are found over northern Europe, northeastern Asia, and central-southern North America. A similar SAT pattern associated with the NAO index in winter is reported by Hurrell (1995, 1996). The correlation pattern of the NAO in MAM and SON has many similarities to that in DJF although the magnitude is much weaker. The association of the NAO to SAT in JJA is seen to be weak and with different patterns than that in DJF. Also noted is that the NAO has little impact on SAT over China with the exception that a small significant correlation area is seen over east-central China in JJA.

The influence of the PNA on the SAT over China has also been examined (not shown). It is found that the PNA has a marked and persistent impact on SAT over the North American region for all four seasons. The general structure of the correlation over the region is a dipole pattern with positive values in the northwest region and negative values in the southeast area associated with a positive PNA. The influence of the PNA on SAT outside North America is, however, quite weak and seasonally dependent.

## 4. Large-scale atmospheric patterns associated with tropical Pacific SST anomalies in the observations

Recall that the PNA and NAO indices used above are calculated by using fixed grid points. These patterns, however, as discussed before, could be distorted or become quite weak in seasons other than wintertime. In this section, we calculate the leading atmospheric patterns of variability over the Northern Hemisphere that are associated with tropical Pacific SST anomalies by conducting an SVD analysis. The SVD analysis is performed between the observed Z500 over the Northern Hemisphere north of 20°N and the observed tropical Pacific SST (20°N–20°S, 120°E–90°W). Here, we focus on the SST over the tropical Pacific Ocean as this is assumed to be the major source area for the seasonal forecast skill. The SVD analysis is performed for the four seasons separately to identify the corresponding leading atmospheric patterns associated with the tropical Pacific SST forcing for each season.

One of the objectives of this study is to examine and compare the atmospheric response to the tropical Pacific SST forcing in the observations and in the HFP models. In the HFP data, the ensemble average of the seasonal mean of 1-month-lead 3-month forecasts is used to represent the forced interannual variability. Therefore, the forecast data used for MAM, JJA, SON, and DJF are from the forecasts made for February–May (FMAM), May–August (MJJA), August–November (ASON), and November–February (NDJF). As we mentioned earlier, the HFP ensemble forecasts are performed in an operational environment where the SST anomaly used is from the previous month prior to the forecast and is persistent throughout the whole forecast period. The SST anomaly used for the forecasts of FMAM, MJJA, ASON, and NDJF are therefore from January, April, July, and October, respectively. To be consistent with the HFP data, in the SVD analysis, the observed Z500 values used for the four seasons are for MAM, JJA, SON, and DJF and the corresponding observed SSTs are from January, April, July, and October, respectively.

The linear regressions of the observed Z500 and SST fields onto their corresponding time series for the first three SVDs are illustrated in Figs. 2 –4 for the four seasons, respectively. The magnitudes of the Z500 and SST correspond to one standard deviation of their respective expansion coefficients. The first three pairs of SVDs together explain from 76% to 91% of the total covariance between the Z500 and SST fields based on a squared covariance fraction (SCF) in each season. It needs to be mentioned that the arithmetic sign of the loadings is arbitrary in this analysis. One could have the opposite atmospheric response when the SST anomalies reverse sign. The correlations between the expansion coefficients of the Z500 and the SST fields of these three SVDs are all significantly correlated to each other according to a Student’s *t* test. As is seen, in winter, the atmospheric components of SVD1 have many similarities to the PNA pattern, (Fig. 2d, top). The temporal correlation between the time series of the atmospheric component of SVD1 and the PNA index used in section 3 in winter is 0.94, significant at the 99% confidence level. In MAM and SON, the SVD1 pattern in the atmosphere is much weaker in magnitude compared to that in DJF and the SST-forced pattern is obviously distorted to some extent (Figs. 2a and 2c, top). For example, the atmospheric pattern appears to be more annular in MAM while that in DJF is localized over the PNA region. In summer, the SVD1 pattern in the atmosphere becomes the weakest among the four seasons and the PNA signal almost disappears in this season. We can also see that the atmospheric distribution of the SVD1 pattern concentrates over the Pacific–North American area and the magnitudes of the patterns are much stronger than those over the Eurasian continent, except in summer when the magnitudes of a positive center over northern Russia are stronger than those over North America. The SST field associated with SVD1 represents an ENSO signal in the tropics and the seasonal dependence of the ENSO signal magnitudes is likely related to the strength of the covariance with the Z500 field.

The difference among four seasons for the second SVD mode is more dramatic than SVD1. In winter, the atmospheric component of SVD2 bears good similarity to the NAO pattern (Fig. 3d, top). The temporal correlation between the time series of the atmospheric component of SVD2 and the NAO index used in section 3 in winter is 0.75, again significant at the 99% confidence level. It can be seen that, in contrast to SVD1, values of the SVD2 pattern in the atmosphere over the Eurasian continent are comparable to those over North America. For example in SON, positive centers can be found over central Eurasia and western Europe with the maximum value of the center over the Eurasian continent being even larger than that over North America (Fig. 3c, top). The SST component in SVD2 is a narrow negative SST anomaly band along the equator for JJA, SON, and DJF, which is consistent with the SST distribution associated with the NAO as discussed in Jia et al. (2009). In MAM, the SST pattern is dominated by a dipole pattern with a positive SST anomaly center over the western tropical Pacific and a negative one over the eastern tropical Pacific. The atmospheric component in the third SVD appears to be even more seasonally dependent than the leading two SVDs. The associated SST pattern of the third SVD in MAM is similar to those of SVD2 in JJA, SON, and DJF. In the other three seasons the SST distributions of SVD3 bear many similarities to that of SVD2 in MAM. The above results indicate that SVD2 and SVD3 switch orders in MAM compared to the other three seasons.

To assess the association between SAT over China and the leading SST forced atmospheric patterns, we calculate the temporal correlations between the 160-station SAT and the time series of Z500 of the three SVDs, which are depicted in Figs. 5 –7. The influence of SVD1 on the SAT over China is found to be quite seasonally dependent. Little area of significance is found for DJF. In MAM, a small area of significance can be found around Yunnan Province. Significant correlations also appear over parts of western and southern China for JJA, as well as over northeastern China for SON. In contrast to SVD1, SATs over China are found to be significantly influenced by the SVD2 and the impacts are more consistent during the four seasons than the first SVD mode. The most significantly impacted season is found to be SON where, significant correlations cover most part of the country. In JJA and DJF, significant correlations appear over most parts of central and northern China. The season with the least impact is MAM, where only part of northwest China is found to have significant correlations. For SVD3, it can influence the SAT over northeastern China in MAM and central China in DJF. In SON, in addition to parts of northeastern China, significant correlations can be found over southwestern China while only little significant correlation can be seen over southern China in JJA. The above results imply that a better forecast of the leading SVD modes can benefit the seasonal forecast over China.

Temporal correlations between the time series of the atmospheric component of SVD1 and SVD2 and the PNA and NAO indices for each season are calculated. Results show that, in addition to the winter season, the correlation between SVD1 and the PNA index is statistically significant in MAM and SON (0.63 and 0.79, respectively) while the expansion coefficient of the atmospheric components of the SVD2 is not significantly correlated with the NAO index during the same period. This indicates that the large-scale atmospheric patterns obtained using the SVD analysis are different from those defined by the PNA and NAO indices, and it is possible for them to have a more close relationship to the weather and climate over China than the PNA and NAO.

## 5. Tropical Pacific SST-forced large-scale atmospheric patterns in GCMs

As can be seen from the last section, the SST-forced large-scale atmospheric patterns can significantly influence SAT over China; therefore, it is important for numerical models to capture the association between the atmosphere and the SST to have a skillful seasonal forecast. In this section, we examine the leading large-scale atmospheric modes in the model atmosphere associated with the same tropical Pacific SST forcing as we used in last section for the purpose of comparison. An SVD analysis is applied between the observed tropical Pacific SST and the ensemble-averaged Z500 over the Northern Hemisphere. When an ensemble average is performed, it is most likely only the forced component that is left. As the SVD analysis was performed with the ensemble mean Z500, then clearly these SVD modes are forced patterns that have a connection to the Pacific SST in the preceding month.

Shown in Figs. 8 –10 are the corresponding three SVD modes obtained by doing a similar SVD analysis as we performed for the observations but here using the ensemble forecast of Z500. As with the observations, the correlations between the expansion coefficients of the Z500 and the SST fields are all significantly correlated to each other. The Z500 used here for SVD analysis is the average of the four numerical models. A comparison between Figs. 8 and 2 shows that the SVD1 pattern of the atmospheric component in the observations is reasonably well reproduced by the numerical models, except in JJA, when the PNA signal almost disappears in the observations, though some disagreement can also be noticed. The magnitudes of this SVD mode in the forecasts are, however, weaker in SON and DJF while they are stronger in MAM than in the observations. The SVD2 and SVD3, however, are found to be far from the observations. The SVD2 in the model atmosphere, though varying from season to season, has a general structure with negative centers near the polar region and positive centers over the midlatitudes. It should be kept in mind that the Z500 values in the ensemble forecasts are the atmospheric response to external forcings, especially the SST forcing over the tropics, while those for the observations includes both external forcing and internal-process-generated variability. The SST field associated with SVD1 is also an ENSO signal over the tropics, as in the observations, while that with SVD2 has a narrow negative SST anomaly band along the equator for all four seasons. The SST patterns in SVD3 are quite consistent among the four seasons, which bears a positive SST anomaly over the western tropical Pacific and a negative one over the eastern tropical Pacific.

It needs to be mentioned that an SVD analysis was applied in our study to obtain the large-scale atmospheric patterns associated with the tropical Pacific SST. Factors other than SST variability are also likely involved in the formation of climate modes, as pointed by several previous studies (Newman and Sardeshmukh 1995; Cherry 1997). For example, it is possible that the tropical Pacific SST is correlated with some other forcing mechanism of the NAO that has possible downstream consequences for China (Li et al. 2008). However, to pinpoint the ultimate driver is not the purpose of this study.

To understand how the SAT over China can be linked to the forced leading SVD modes, we also examined the spatial correlation between the observed SAT over China and the expansion coefficients of the atmospheric component for the three SVD modes in the models (Figs. 11 –13). For SVD1, an area of significance can be found mainly over western and central China in SON while in MAM and JJA significant correlations appear over the south border area of China. As with the observations, the SAT over China is more correlated to SVD2 than SVD1. Also notice that the distributions of the correlations over China to SVD2 in the forecasts have many similarities to those in the observations for JJA, SON, and DJF though the area of significance of the HFP2 data is smaller than that of the observations in DJF. As in the observations, SON has the most pronounced significant correlations among the four seasons. Obvious discrepancies, however, can be found between the model and the observations for SVD3 where DJF is the only season that has significant correlation to the SAT in China. In general, the relationship between SAT over China and the atmospheric leading patterns are captured by the GCMs to a certain extent. The correlation patterns between observations and the HFP2 ensemble forecast are similar because although the structures of the model atmospheric response to the tropical Pacific SST are bias and model dependent, especially for high-order SVD modes, the time series associated with these patterns are found to be well correlated to those in the observations to a certain extent, as will be shown in section 7.

## 6. The seasonal forecast skill of GCMs

A statistical postprocessing approach has been formulated by Lin et al. (2005a, hereafter LDB) to reduce the systematic forecast errors of GCMs. This approach was applied to Z500 over the Northern Hemisphere and precipitation over Canada in winter. Significant improvements in seasonal forecast skill were achieved (LDB; Lin et al. 2008). This statistical postprocessing approach is constructed based on the fact that the GCMs can reasonably predict the variability of the large-scale atmospheric patterns over the Northern Hemisphere while the forecast spatial patterns are biased and model dependent. In essence, this approach uses the forecast time series of the atmospheric components of the SVD analysis and the observed relationship between the tropical Pacific SST and the midlatitude flow to adjust the forecasts. The above studies mainly focused on the North American continent where the PNA and NAO play important roles in the weather and climate. Inspired by the above analysis that the large-scale atmospheric patterns associated with the tropical Pacific Ocean can also significantly influence the SAT over China, we extend their studies by applying this statistical postprocessing technique to the SAT forecasts over China, which is located upstream of the PNA area. We apply this statistical technique to the SAT over China for all four seasons to examine whether it also works for the seasonal forecast of SAT there and we examine the seasonality of its performance.

### a. The postprocessing approach

The postprocessing approach has been described in detail in LDB and is only briefly summarized here. First, an SVD analysis was performed between the HFP2 ensemble mean Z500 north of 20°N and the SST in the tropical Pacific Ocean, as described in section 5. After the SVD analysis we can get the atmospheric components of the expansion coefficients of the ensemble forecasts for the first three leading SVDs, which could be denoted by *C*_{1}(*t*), *C*_{2}(*t*), and *C*_{3}(*t*) (*t* = 1, 2, …, 33), respectively, where *t* represents the year in the period 1969–2001. We only make use of the first three SVD modes in this study.

*T*(

_{o}*t*)] for a specific grid point can be written as

*a*

_{1},

*a*

_{2}, and

*a*

_{3}are the regression coefficients and

*ϵ*is the residual. The three regression coefficients

*a*

_{1},

*a*

_{2}, and

*a*

_{3}are calculated using the historically observed SAT by the least squares method. A cross-validation method is applied in calculating these regression coefficients to mimic an operational environment meaning that when Eq. (1) is used to predict the SAT of year

*n*, the coefficients of the regression equation are computed with data from all years other than year

*n*.

*t*, we can project the ensemble mean forecasts of year

_{f}*t*onto

_{f}*a*

_{1},

*a*

_{2}, and

*a*

_{3}to get

*C*

_{1}(

*t*),

_{f}*C*

_{2}(

*t*), and

_{f}*C*

_{3}(

*t*). Then, the corrected forecast can be obtained as

_{f}### b. The seasonal forecast skill before and after the postprocessing

We first look at the seasonal forecast skill of the SAT over China for the original ensemble forecasts. The temporal correlation scores between the four HFP model-averaged ensemble forecasts before applying the postprocessing and the station SAT are first examined (Fig. 14). Correlation scores significant at the 5% level are shaded. It can be seen that the distributions of the predictive skill are quite seasonally dependent. JJA is the season having the best forecast skill with an area of significance over most of the northern half of China and around Yunnan Province. In SON, the skillful area is mainly over northwestern China while in MAM and DJF only small area of significance can be found.

The correlation scores of SAT after applying Eq. (2) for four seasons are illustrated in Fig. 15. It appears that MAM and DJF have gained skill in some areas through the postprocessing approach while losing skill in other areas. For example, improvement of skill can be seen over parts of eastern and central China in MAM and part of northeastern China in DJF. In JJA, the forecast skills of the original and postprocessed forecasts are comparative. Some of the skillful area of postprocessed forecasts is diminished over east China but there is some improvement seen over the south border regions. The season that has the largest improvement is SON when the area of significance of the postprocessed forecast skill is much larger than that of the original forecasts. Improvement in forecast skill is achieved over a large area in central China and parts of northeastern China. The skill over northwestern China is also strengthened. The forecast skill is also examined by the mean-square error (MSE) (not shown), which is calculated using the observed and four model-averaged SAT anomalies that are normalized using their respective standard deviations following Smith and Livezey (1999). Similar conclusions as for the correlation score can be drawn.

In real-time operational seasonal forecasts, it is also useful to create categorized forecasts. For example, the observed SAT can be categorized into three groups: below, near, and above normal. The threshold used to define the category is 0.43 times the standard deviation of the historical SAT variability. The choice of this threshold makes the three categories equiprobable (same probability) on average. The seasonal forecasts before and after the postprocessing are also categorized using the above criterion and are verified against the observations. A forecast is correct if both the forecast SAT and the observed SAT belong to the same category. The skill levels of the categorized SAT forecast before and after the postprocessing are measured by the Heidke skill score (HSS). The Heidke skill score indicates whether a prediction result is better than could be expected by chance, and its value measures how much better the prediction is compared to chance. A perfect model predictor has an HSS of one, a predictor that does no better than chance has a HSS of zero, and predictors that do worse than chance have negative HSSs. It is seen from Fig. 16 that the skill of the categorized SAT forecasts is significantly improved for both warm and cold events after the postprocessing especially over central-southern China, as can be seen from Fig. 16.

## 7. Reasons behind the improvement of the skill

As discussed in Lin et al. (2008) and Jia et al. (2009), although the model atmospheric response to the tropical Pacific SST are biased, the time series associated with these patterns are significantly correlated to those in the observations for SON and DJF. This is actually the key point of the postprocessing approach. As can be seen from Eq. (2), the postprocessed seasonal forecasts are calculated using the observed SAT and the atmospheric expansion coefficients of the leading SVDs obtained from the model forecasts. The correlations of the atmospheric expansion coefficients between the HPF2 data and the observations for SON and DJF were presented in Lin et al. (2008) and Jia et al. (2010), respectively. Here, we present the results for MAM and JJA to give a comprehensive picture of the performance of the GCMs for the whole year.

The correlations of the atmospheric expansion coefficients between the HFP2 data and the observations for MAM and JJA are displayed in Tables 1 and 2, respectively. It can be seen that the time evolution of SVD1 in the observations and in the HFP data are significantly correlated to each other for all HFP models for both MAM and JJA. In MAM, the time series associated with SVD2 in the HFP models are all significantly correlated to that of SVD3 in the observations while the time series associated with SVD3 in the forecasts are well correlated to that of SVD2 in the observations consistent with Fig. 3, where we found that in the observations SVD2 and SVD3 switch orders in MAM compared to the other three seasons. We can also see from Table 2 that the PC2s of the forecasts are significantly correlated with both the PC1 and PC2 of the observations for all the GCMs. The good correlations of the time series between the observations and the HFP models and the significant influence of the leading atmospheric patterns to SAT over China provide the possibility of improving the seasonal forecast skill with this postprocessing method.

As discussed in Lin et al. (2008) and Jia et al. (2009), the postprocessing approach can help reduce the model-dependent component of errors. To examine if this is also the case here, we examine the climatological mean and standard deviation of SAT in SON for the observations (Fig. 17) and the standard deviation of the original seasonal forecasts of the four GCMs (Fig. 18). In the observations, the values of the standard deviation decrease from north to south with the maximum values appearing over the northwest and northeast regions. The climatology of SAT can be reasonably well reproduced by the GCMs (not shown). However, the distribution of the standard deviation in the forecasts is far from the observations. The distribution of the standard deviation is quite model dependent and the magnitudes of the SAT standard deviations in the models are generally smaller than those in the observations with SEF having the lowest values among the GCMs. The corresponding standard deviations of the postprocessed forecasts for each model are illustrated in Fig. 19. Results show that the distributions of the standard deviation in the postprocessed forecasts are now consistent among the models and are much closer to those in the observations than the original forecasts, indicating that the postprocessing approach is effective in reducing the model-dependent part of the systematic errors.

It is known that a model forecast with an amplitude bias can still be skillful when the skill is measured by correlation scores or categorized forecast, as the forecast anomalies are computed relative to the model’s own variance, not the observations. It is our expectation that the variance of the model forecast can be enhanced after the postprocessing, as the observational fields are included in Eq. (2). The improvement of the forecast skill could come from correcting systematic dynamical model errors, such as improper stationary wave patterns, as we showed before, or by capturing some other factor(s) that covary with the SAT, stationary waves, etc.

## 8. Conclusions

Instead of using the traditionally defined PNA and NAO, which are the two of the most important atmospheric patterns in winter over the Northern Hemisphere, in this study, the influence of the tropical Pacific SST-forced leading atmospheric patterns on the seasonal forecast of SAT over China is investigated. These large-scale atmospheric patterns were obtained using an SVD analysis conducted between both the observed and the forecast Z500 values over the Northern Hemisphere and the observed SSTs in the tropical Pacific Ocean for four seasons separately. The SAT over China is found to have the closest relationship to the second SVD mode of tropical Pacific SST-forced atmospheric pattern. The relationship between the atmosphere and the tropical Pacific SST was also examined using the HFP data. The structure of the observed SVD1 is found to be reasonably well reproduced by the HFP models while that of the second SVD in the models is far from the observations. The relationship between the SVD modes and SAT over China is captured by the GCMs to a good extent. Examination of the correlations of the atmospheric expansion coefficients between the the HPF2 data and observations showed that the time series in the observations are significantly correlated to at least one of the PCs in the HFP data for all four seasons.

Previous studies showed that a statistical SVD-based postprocessing approach is very effective in reducing the model-dependent part of the systematic error and can significantly improve the seasonal forecast skill of Canadian winter precipitation and SAT over North America in fall. Inspired by the fact that there is a close relationship between the tropical Pacific SST-forced large-scale atmospheric patterns and SAT over China and that the time series of the leading SVD modes are reasonably well predicted by the HFP models, we extend previous studies by applying this postprocessing approach to the seasonal forecasts of SAT over China. The anomaly correlation score and the categorized forecast results show that the postprocessed seasonal forecasts of SAT over China are improved for all seasons to a certain extent. SON was taken as an example when the postprocessing approach works best to further understand where the sources of the improved seasonal forecast come from. We also found that the distributions of the standard deviation of the SAT over China were more consistent among the four GCMs after the postprocessing, indicating that the model-dependent part of the systematic errors was largely reduced.

Also, as discussed in previous studies (Lin et al. 2005b; Jia et al. 2009), it is should be kept in mind that this postprocessing approach has been developed using only the first three SVD modes that are mainly associated with tropical Pacific SST forcing. Other external forcings, for example, the SST anomalies in other ocean basins or the snow cover over the Eurasian continent, can also play a role and may not be well represented by these modes.

## Acknowledgments

This research was jointly funded by Fundamental Research Funds for the Central Universities and by the foundation from Chinese Academy of Meteorological Sciences under Grant 2008LASW-A03. Lin is partly supported by the Canadian Foundation for Climate and Atmospheric Sciences (CFCAS) and by the Natural Science and Engineering Research Council of Canada (NSERC). We are grateful to the reviewers for their helpful suggestions on improving our paper.

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Linear regressions of the observed (top) Z500 and (bottom) SST onto their corresponding time series of the first SVD for (a) MAM, (b) JJA, (c) SON, and (d) DJF. The contour interval is 5 m in the top panels and 0.2°C in the bottom panels. The magnitude corresponds to one standard deviation of each time coefficient.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Linear regressions of the observed (top) Z500 and (bottom) SST onto their corresponding time series of the first SVD for (a) MAM, (b) JJA, (c) SON, and (d) DJF. The contour interval is 5 m in the top panels and 0.2°C in the bottom panels. The magnitude corresponds to one standard deviation of each time coefficient.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Linear regressions of the observed (top) Z500 and (bottom) SST onto their corresponding time series of the first SVD for (a) MAM, (b) JJA, (c) SON, and (d) DJF. The contour interval is 5 m in the top panels and 0.2°C in the bottom panels. The magnitude corresponds to one standard deviation of each time coefficient.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 2, but for the second SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 2, but for the second SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 2, but for the second SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 2, but for the third SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 2, but for the third SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 2, but for the third SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Temporal correlation between the observed SAT and the time series of the atmospheric component of SVD1 for (a) MAM, (b) JJA, (c) SON, and (d) DJF. Those stations with correlations statistically significant at the 0.05 level according to a Student‘s *t* test are marked. The contour interval is 0.3. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s *t* test.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Temporal correlation between the observed SAT and the time series of the atmospheric component of SVD1 for (a) MAM, (b) JJA, (c) SON, and (d) DJF. Those stations with correlations statistically significant at the 0.05 level according to a Student‘s *t* test are marked. The contour interval is 0.3. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s *t* test.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Temporal correlation between the observed SAT and the time series of the atmospheric component of SVD1 for (a) MAM, (b) JJA, (c) SON, and (d) DJF. Those stations with correlations statistically significant at the 0.05 level according to a Student‘s *t* test are marked. The contour interval is 0.3. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s *t* test.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 5, but for the second SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 5, but for the second SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 5, but for the second SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 5, but for the third SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 5, but for the third SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 5, but for the third SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Linear regressions of the (top) ensemble forecast Z500 and (bottom) corresponding SST onto their corresponding time series of the first SVD modes for (a) MAM, (b) JJA, (c) SON, and (d) DJF. The contour interval is 3 m in the top panels and 0.2°C in the bottom panels. The magnitude corresponds to one standard deviation of each time coefficient.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Linear regressions of the (top) ensemble forecast Z500 and (bottom) corresponding SST onto their corresponding time series of the first SVD modes for (a) MAM, (b) JJA, (c) SON, and (d) DJF. The contour interval is 3 m in the top panels and 0.2°C in the bottom panels. The magnitude corresponds to one standard deviation of each time coefficient.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Linear regressions of the (top) ensemble forecast Z500 and (bottom) corresponding SST onto their corresponding time series of the first SVD modes for (a) MAM, (b) JJA, (c) SON, and (d) DJF. The contour interval is 3 m in the top panels and 0.2°C in the bottom panels. The magnitude corresponds to one standard deviation of each time coefficient.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 8, but for the second SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 8, but for the second SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 8, but for the second SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 8, but for the third SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 8, but for the third SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 8, but for the third SVD mode.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Temporal correlation between the model-forecast SAT and the time series of the atmospheric component of SVD1 for (a) MAM, (b) JJA, (c) SON, and (d) DJF. Those stations with correlations statistically significant at the 0.05 level according to a Student‘s *t* test are marked. The contour interval is 0.3. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s *t* test.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Temporal correlation between the model-forecast SAT and the time series of the atmospheric component of SVD1 for (a) MAM, (b) JJA, (c) SON, and (d) DJF. Those stations with correlations statistically significant at the 0.05 level according to a Student‘s *t* test are marked. The contour interval is 0.3. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s *t* test.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Temporal correlation between the model-forecast SAT and the time series of the atmospheric component of SVD1 for (a) MAM, (b) JJA, (c) SON, and (d) DJF. Those stations with correlations statistically significant at the 0.05 level according to a Student‘s *t* test are marked. The contour interval is 0.3. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s *t* test.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 11, but for the SVD2.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 11, but for the SVD2.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 11, but for the SVD2.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 11, but for the SVD3.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 11, but for the SVD3.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 11, but for the SVD3.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

The correlation scores for the original forecast of SAT for (a) MAM, (b) JJA, (c) SON, and (d) DJF. Those stations with correlations statistically significant at the 0.05 level according to a Student‘s *t* test are marked. The contour interval is 0.3. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s *t* test.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

The correlation scores for the original forecast of SAT for (a) MAM, (b) JJA, (c) SON, and (d) DJF. Those stations with correlations statistically significant at the 0.05 level according to a Student‘s *t* test are marked. The contour interval is 0.3. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s *t* test.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

The correlation scores for the original forecast of SAT for (a) MAM, (b) JJA, (c) SON, and (d) DJF. Those stations with correlations statistically significant at the 0.05 level according to a Student‘s *t* test are marked. The contour interval is 0.3. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s *t* test.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 14, but for the postprocessed SAT.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 14, but for the postprocessed SAT.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 14, but for the postprocessed SAT.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

The Heidke skill score for the (top) original and (bottom) postprocessed categorized forecasts of SAT for SON for (a),(b) above and (c),(d) below normal categories (see the text for details). The contour interval is 0.2. Areas with a value greater than 0.1 are shaded.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

The Heidke skill score for the (top) original and (bottom) postprocessed categorized forecasts of SAT for SON for (a),(b) above and (c),(d) below normal categories (see the text for details). The contour interval is 0.2. Areas with a value greater than 0.1 are shaded.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

The Heidke skill score for the (top) original and (bottom) postprocessed categorized forecasts of SAT for SON for (a),(b) above and (c),(d) below normal categories (see the text for details). The contour interval is 0.2. Areas with a value greater than 0.1 are shaded.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

(a) The climatological mean and (b) the standard deviation for the observed SAT in SON. The contour intervals are 4°C and 0.2 in (a) and (b), respectively.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

(a) The climatological mean and (b) the standard deviation for the observed SAT in SON. The contour intervals are 4°C and 0.2 in (a) and (b), respectively.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

(a) The climatological mean and (b) the standard deviation for the observed SAT in SON. The contour intervals are 4°C and 0.2 in (a) and (b), respectively.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

The standard deviations of the original ensemble forecasts of SAT in SON for (a) GCM3, (b) GCM2, (c) GEM, and (d) SEF.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

The standard deviations of the original ensemble forecasts of SAT in SON for (a) GCM3, (b) GCM2, (c) GEM, and (d) SEF.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

The standard deviations of the original ensemble forecasts of SAT in SON for (a) GCM3, (b) GCM2, (c) GEM, and (d) SEF.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 18, but for the postprocessed SAT.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 18, but for the postprocessed SAT.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

As in Fig. 18, but for the postprocessed SAT.

Citation: Monthly Weather Review 139, 3; 10.1175/2010MWR3348.1

Correlations between the atmospheric expansion coefficients of the first three SVDs in the observations and in the HFP2 data for MAM. PCO1, PCO2, and PCO3 are the atmospheric components of the observations. PCM1, PCM2, and PCM3 are the atmospheric components of the HFP2 data. The correlations with statistical significance passing the 0.05 level are set in boldface.