Multimodel ensemble (MME) seasonal forecasts are analyzed to evaluate numerical model performance in predicting the leading forced atmospheric circulation pattern over the extratropical Northern Hemisphere (NH). Results show that the time evolution of the leading tropical Pacific sea surface temperature (SST)-coupled atmospheric pattern (MCA1), which is obtained by applying a maximum covariance analysis (MCA) between 500-hPa geopotential height (Z500) in the extratropical NH and SST in the tropical Pacific Ocean, can be predicted with a significant skill in March–May (MAM), June–August (JJA), and December–February (DJF) one month ahead. However, most models perform poorly in capturing the time variation of MCA1 in September–November (SON) with 1 August initial condition. Two possible reasons for the models’ low skill in SON are identified. First, the models have the most pronounced errors in the mean state of SST and precipitation along the central equatorial Pacific. Because of the link between the divergent circulation forced by tropical heating and the midlatitude atmospheric circulation, errors in the mean state of tropical SST and precipitation may lead to a degradation of midlatitude forecast skill. Second, examination of the potential predictability of the atmosphere, estimated by the ratio of the total variance to the variance of the model forecasts due to internal dynamics, shows that the atmospheric potential predictability over the North Pacific–North American (NPNA) region is the lowest in SON compared to the other three seasons. The low ratio in SON is due to a low variance associated with external forcing and a high variance related to atmospheric internal processes over this area.
It is well known that some teleconnection patterns, such as the Pacific–North American (PNA) pattern and the North Atlantic Oscillation (NAO), can significantly influence the seasonal atmospheric condition over the Northern Hemisphere (NH) extratropics (Trenberth et al. 1998; Hoerling et al. 2001). Thompson and Wallace (1998) suggested that, compared to the NAO, the Arctic Oscillation (AO) would more adequately represent the dominant mode of extratropical tropospheric atmospheric variability in the NH. Although there is still debate regarding the differences between the AO and NAO in the literature, many authors regard them as the same phenomenon. The PNA and NAO/AO together explain a significant part of the interannual variance of the extratropical NH atmospheric variability and are the two most important atmospheric patterns over the NH in wintertime (Wallace and Guztler 1981; Barnston and Livezey 1987).
However, the PNA and NAO/AO structures may be distorted or become quite weak in other seasons than wintertime and may not be the dominant atmospheric patterns that influence the weather and climate over the NH (Folland et al. 2009; Lee et al. 2011; Lee and Wang 2012). For example, using both observations and outputs from four atmospheric general circulation models (GCMs), Jia and Lin (2011) demonstrated that instead of the traditionally defined PNA and NAO/AO, the surface air temperature (SAT) over China in summer and fall are more significantly influenced by the leading forced atmospheric pattern, obtained by applying a maximum variance analysis (MCA) analysis between 500-hPa geopotential height (Z500) in the extratropical NH and SST in the tropical Pacific Ocean. It is further revealed that the relationship between the tropical Pacific SST and the extratropical atmospheric circulation could be potentially useful to improve the forecast skill of dynamical numerical models. For instance, a statistical postprocessing approach has been formulated by Lin et al. (2005a) based on the regression of the forecast models leading forced MCA patterns and the historical observations to correct the atmospheric response pattern to tropical Pacific SST anomalies. They found that this approach can significantly improve the seasonal forecasts of many variables such as the Z500 over the NH and the precipitation over Canada in wintertime and the SAT in fall over North America and China (Lin et al. 2005a, 2008; Jia et al. 2010; Jia and Lin 2011). It is therefore important for seasonal forecasting that the main features and time evolution of these tropical Pacific SST-forced large-scale atmospheric patterns in the observations are reasonably well predicted by numerical models.
Jia et al. (2010) showed that the forecast skill of numerical models in forecasting the climate over North America is quite seasonally dependent. Examination of the temporal correlation coefficients (TCCs) between the observations and the multimodel ensemble (MME) of SAT forecasts during the period from 1969 to 2001 reveals a significant predictive skill over many regions of North America in March–May (MAM), June–August (JJA), and December–February (DJF). However, only limited areas of predictive skill are found in September–November (SON) over the east coast and northern Canada and parts of the Midwest and south-central United States. Examination of the percentage of significant area shows that more than 75% of North America has forecast skill significant at the 0.05 level in MAM, JJA, and DJF, whereas only 32% of North America has a significant forecast skill in SON. However, the reasons behind the pronounced seasonal dependence of numerical-model forecast skill remain unclear. The purpose of this study is to further investigate the forecast skill of numerical models in different seasons using more comprehensive model forecast results. Here we focus on investigating model ability in forecasting the SST-forced large-scale atmospheric pattern considering its importance to midlatitude seasonal forecasting as we mentioned before. The possible causes of the seasonal dependence of numerical model predictability will be explored and discussed.
The paper is organized as follows. In section 2, the data and models used in this study are described. Section 3 presents the tropical Pacific SST-forced leading atmospheric pattern and the performance of numerical models in predicting this pattern in different seasons. It shows that the forecast skill of the leading tropical Pacific sea surface temperature–coupled atmospheric pattern (MCA1) is the lowest in SON among the four seasons, and this is a common characteristic of most numerical models under examination. The possible reasons accounting for the poor predictability in SON are investigated in section 4 and conclusions are given in section 5.
2. Data and models
The following two hindcast datasets are used in this study. The first dataset is the ensemble of forecasts produced under the second phase of the Canadian Historical Forecasting Project (HFP2) multimodel two-tier seasonal forecasting system conducted by Canadian Meteorological Centre (Kharin et al. 2009). The second dataset is from the Climate Prediction and its Application to Society (CliPAS) project sponsored by the Asian-Pacific Economic Cooperation (APEC) Climate Center (APCC) (Wang et al. 2009; Lee et al. 2010). It is of interest to compare one-tier and two-tier approaches in predicting the leading atmospheric circulation pattern over the extratropics.
One-tier seasonal forecasts use coupled GCMs (CGCMs) in which both atmosphere and ocean are initialized. Previous studies showed that one-tier seasonal forecasts had considerable systematic errors in simulating the tropical ocean and atmosphere. As the systematic forecast errors could potentially cause biases in the global teleconnections that are associated with equatorial SST anomalies (SSTA), the two-tier system, which uses persistent or preforecasted SSTA forcing, has been demonstrated to have an obvious advantage over the direct use of CGCMs for the extratropics. However, recently, some studies have showed that it is important to take into account local monsoon–warm pool ocean interactions in seasonal forecasts over tropics (Wang et al. 2003, 2004, 2008; Wu and Kirtman 2005; Kumar et al. 2005). With the development of coupled climate models in the past decades it might be possible for CGCMs to improve their ability in capturing characteristics of extratropical teleconnections.
In the HFP2 project, four global atmospheric models were involved, including the second and third generations of the general circulation models (GCM2 and GCM3) of the Canadian Centre for Climate Modeling and Analysis (CCCma) (Boer et al. 1984; McFarlane et al. 1992), the reduced-resolution version of the global spectral model (SEF) (Ritchie 1991), and the Global Environmental Multiscale model (GEM) of the Recherche en Prévision Numérique (RPN) (Côté et al. 1998a,b). The first tier of the HFP2 forecasting system is the sum of the SSTA of the month prior to the forecast period, persisted through the forecast period, and the monthly varying climatological SST. The SST and ice data were taken from the Seasonal Prediction Model Intercomparison Project-2 (SMIP-2) boundary data. For each model, 10 four-month forecasts were carried out starting from the first day of each month during the period from 1969 to 2001. The initial conditions were reanalyses from the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) Reanalysis 1 (Kalnay et al. 1996).
For the HFP2 forecasts we make use of the ensemble mean of the seasonal forecasts spanning the 33 years from 1969 to 2001. As we are interested in the forecast skill coming from anomalies in the boundary conditions, seasonal forecasts with a one-month lead time are analyzed to minimize the influence of the initial conditions. In other words, 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). The dominant external source of a skillful forecast is derived from the prescribed SST anomalies (Derome et al. 2001).
CliPAS is an international project aimed at doing multimodel intercomparison and synthesis. One of the objectives of the CliPAS project is to develop a well-validated MME prediction system and to study the forecast skill of climate variations (Wang et al. 2009; Lee et al. 2010). This project involves a large group of climate scientists from the United States, South Korea, Japan, China, and Australia. Ensemble retrospective forecasts were made by one-tier and two-tier climate models from 16 different institutions. A brief summary of these institutions and model specifications have been given in Wang et al. (2009). While each model has a different forecast length and ensemble size, they all have ensemble forecasts starting from 1 May to at least 30 September for the boreal summer season (JJA) and from 1 November to at least 31 March for the boreal winter season (DJF). The two-tier predictions are from Florida State University (FSU2), Geophysical Fluid Dynamics Laboratory (GFDL), Institute of Atmospheric Physics/Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (IAPL), National Centers for Environmental Prediction (NCT2), Seoul National University (SUT2), and University of Hawaii (UHC2 and UHT2). The one-tier predictions that we use in this study are from the Centre for Australia Weather and Climate Research (CAWC), GFDL (GFT1), National Aeronautics and Space Administration (NASA), NCEP, Seoul National University (SUT1), and University of Hawaii (UHT1). All one-tier models do not apply any flux correction. Eight of the above numerical models have forecasts for all four seasons, which include CAWC, UHT1, SUT1, NCEP, GFT1, IAPL, UHC2, and NCT2. All two-tier models except NCT2 were forced by the global SST field preforecasted by the Seoul National University (SNU) statistical–dynamical forecast model. A detailed description of this SST forecast method is given in Kug et al. (2007). The NCT2 was forced by the forecast SST from its coupled version CFS. All models used the same initial conditions from the NCEP–DOE Reanalysis II (Kanamitsu et al. 2002). For the CliPAS data, we make use of the seasonal forecasts during the common hindcast period of these numerical models, which is from 1982 to 2001.
In the present study, the multimodel ensemble forecast (MME) seasonal forecasts were simply made by averaging forecasts of different models. The model climatology is removed for each individual model and only anomalies are considered. The data used for the verification of the seasonal forecasts are the Climate Research Unit (CRU) time series (TS) 2.1 dataset, which is a set of monthly averaged observed SAT over the land surface from the CRU at the University of East Anglia, United Kingdom (Mitchell and Jones 2005).
3. Seasonal forecast skill of MCA1
a. MCA analysis
The tropical Pacific is known to be a major forcing area for some extratropical circulation patterns over the Pacific Ocean and surrounding land area on seasonal time scales. The SST anomalies of the tropical Pacific and its associated anomalous heating in the tropical atmosphere are of central importance for determining tropical–extratropical teleconnections. In this study, the atmospheric patterns that are associated with the tropical Pacific SST forcing are obtained by conducting a maximum variance analysis (Bretherton et al. 1992) between the Z500 north of 20°N and the tropical Pacific SST (20°N–20°S, 120°E–90°W) in the observations. The MCA calculation is performed on the Z500 and the simultaneous SST anomalies for the period from 1969 to 2001 for the four seasons separately. When the MCA is applied, the data on a regular latitude–longitude grid are weighted by the square root of the cosine of the latitude to ensure that equal areas are afforded equal weight in the analysis. Here we only concentrate on the leading MCA mode, MCA1. The MCA results are displayed in Fig. 1 where the magnitude corresponds to one standard deviation of the respective expansion coefficient. Areas of heterogeneous correlation with statistical significance passing the 0.01 level are shaded. It should be mentioned that there is some limit in physical interpretation using MCA pairs. As discussed in Newman and Sardeshmukh (1995), the MCA technique may not always be able to recover the relationship between two physically related fields.
It is found that MCA1 accounts for a dominant percentage of the total covariance between the Z500 and SST fields. The covariance between Z500 and SST explained by this MCA mode is 50%, 63%, and 79% for MAM, SON, and DJF, respectively, for this period based on a squared covariance fraction (SCF). In JJA, only 36% of the covariance between Z500 and SST fields is explained by MCA1. As the purpose of this study is to investigate the seasonal dependence of numerical model forecast skill for the leading atmospheric pattern coupled with the tropical Pacific SST, we present the results of all four seasons while keeping the difference of JJA to the other three seasons in mind. The temporal correlation coefficients between the expansion coefficients of Z500 and SST fields during this period for the four seasons are all statistically significant at the 0.05 level according to a Student’s t test. Figure 1 shows that MCA1 varies from season to season with DJF having a tropical–Northern Hemisphere (TNH)-like pattern (Barnston et al. 1991) and JJA having the weakest pattern among the four seasons. The corresponding SST field of MCA1 shows a clear El Niño signal with positive SST anomalies in the eastern tropical Pacific for SON and DJF. In MAM and JJA the positive SST anomalies become weak in magnitude and are distorted to some extent.
To associate the atmospheric condition over North America with MCA1, we calculate the TCC between the CRU surface air temperature and the atmospheric expansion coefficients of MCA1 for the four seasons, and the results are displayed in Fig. 2. The shaded areas represent correlations with a significance level of 0.05 according to a Student’s t test. It shows that areas with significant correlations account for 34%, 45%, 62%, and 65% of North America for MAM, JJA, SON, and DJF, respectively. The CRU SAT is over the land surface and is seasonally averaged from the period from 1969 to 2001 on a 2.5° × 2.5° grid. There are 484 grid points located over North America north of 20°N. According to Livezey and Chen (1983), if we suppose that the grid data over North America are statistically independent, which they are not, in order to reject a null hypothesis that the result presented in Fig. 2 was by accident at the 95% level, it requires that at least 7% of the area is significant (their Fig. 2), which is much less than the percentages showed above. To assess the field significance of the correlation maps considering the spatial dependence, a Monte Carlo approach is applied following Livezey and Chen (1983). One thousand correlation maps are calculated between the CRU SAT and randomized time series of MCA1, and the significance at each grid point is tested at the 95% level. Results show that in MAM only 2.1% of these trials have an area of significant correlation that is larger than the shaded area in Fig. 2a, indicating that the correlations shown in Fig. 2a are field significant at the 0.05 level. The other three seasons even pass the 0.01 field-significance test.
It is seen that the influence of MCA1 on the SAT over North America is quite season dependent. The distribution of TCCs shows a similar pattern for MAM and DJF with DJF having a larger significant TCC area than MAM. A dipole structure is seen for these two seasons with significant positive TCC appearing over northwestern North America and a negative area over southeast North America. The TCC in SON is an east–west dipole pattern with positive values over northwestern North America and negative values over the east half of North America. In JJA significant positive correlations are seen over northern and southern North America. The links between the North American SAT and MCA1 for the four seasons are thus clear, implying that a skillful forecast of MCA1 can benefit the seasonal forecast of SAT over North America.
To see whether or not the relationship between the tropical Pacific SST and the atmosphere, shown in Fig. 1, can be captured by the numerical models, we examine the MCA1 in the HFP2 model atmosphere associated with the tropical Pacific SST forcing and compare it to its observed counterpart. A maximum variance analysis is applied between the observed tropical Pacific SST and the multimodel ensemble mean Z500 over the NH, and the results are depicted in Fig. 3. As we mentioned before, the forecast data used for MAM, JJA, SON, and DJF are from the forecasts made for FMAM, MJJA, ASON, and NDJF. The SST forcing used in HFP2 is the sum of SSTAs from the month before the start of the forecasts and the monthly varying climatological SST. Therefore, in the MCA analysis, the tropical Pacific SST used is from October, January, April, and July, respectively. A comparison between Fig. 1 and Fig. 3 shows that, though model prediction tends to overestimate the ENSO impact on the atmospheric variability, the MCA1 pattern of the atmospheric component in the observations is reasonably well reproduced by the HFP2 models, except in JJA when the atmospheric pattern is quite weak in both the observations and the model forecasts. The similarity of MCA1 in the observations and in the HFP2 model forecasts is further examined by calculating the pattern correlation coefficients (PCC) of MCA1 for the four seasons (not shown). Results showed that the PCC of MCA1 are all significant at the 0.05 significance level for all four seasons with the highest and lowest PCC appearing in DJF and JJA, respectively.
b. Forecast skill of the time variation of MCA1
In seasonal forecasts, the signal coming from a forcing external to the atmosphere (i.e., an SST anomaly) is considered potentially predictable. The part of variability that is related to atmospheric internal dynamics is unpredictable. The MCA1 obtained above is the most pronounced atmospheric pattern that is coupled with the tropical Pacific SST, and it is reasonable to assume that MCA1 is likely the most predictable atmospheric pattern. Based on this premise, we strive to first determine to what extent the climate models and their MME mean forecast can capture the time evolution of this observed atmospheric pattern. To evaluate the performance of numerical models in predicting the time variation of MCA1 we project the one-month lead ensemble forecast of Z500 of each individual HFP2 model on to MCA1, as shown in Fig. 1. The TCCs between the atmospheric expansion coefficients of MCA1 in the observations and in the ensemble forecasts are shown in Table 1. A correlation coefficient larger than 0.33 is considered to be statistically significant at a 0.05 level, and is shown in boldface in Table 1. The MME mean forecasts of the four HFP2 models as well as the averaged skill of all individual models, represented as “Avg,” are also presented in Table 1.
Table 1 shows that the HFP2 ensemble forecasts capture the realistic time evolution of MCA1 in MAM, JJA, and DJF where the TCC values for the three seasons exceed 0.62 for all four models, significant at the 0.01 level according to a two-tailed Student’s t test. In SON, however, only the SEF model has some skill in predicting the variability of MCA1. The HFP2 MME mean forecast has a TCC skill of 0.72, 0.75, and 0.70 for MAM, JJA, and DJF, respectively, whereas it is only 0.32 and cannot pass the significance test in SON. It also needs to be pointed out that the total covariance between the Z500 and SST fields explained by MCA1 in JJA is much less than the other three seasons. Also noticed is that the forecast skill of the MME mean forecast is better than the averaged skill of all individual models for all four seasons, indicating that the MME method is superior in reducing forecast errors and quantifying forecast uncertainties due to model formulation, consistent with previous studies (e.g., Wang et al. 2009).
To see whether or not the results shown in Table 1 are robust, the ensemble-mean forecast from the CliPAS project was also examined. The one-month lead ensemble mean forecasts from 1982 to 2001 were projected onto the atmospheric component of MCA1, as shown in Fig. 1, and the obtained time series were compared to the atmospheric expansion coefficients of MCA1 in the observations (Table 2). It can be seen that most models have a significant skill in predicting the variability of MCA1 in MAM, JJA, and DJF, and the MME forecast has a TCC of 0.71, 0.74, and 0.64, respectively, significant at the 0.01 level. The lowest forecast skill also appears in SON where only two of the models (UHT1 and NCT2) can skillfully predict the time variability of MCA1 and the average forecast skill is only 0.28. Although different numerical models are examined, the results shown in Table 2 are consistent with those obtained from the HFP2 output, indicating the robustness of the results.
c. Seasonal forecast skill over the NPNA region
The TCC between observations and the one-month lead ensemble forecasts of Z500 over the North Pacific–North American (NPNA) region for four seasons are presented in Fig. 4. The super MME mean Z500 forecast (Comp) includes output from the four numerical models from HFP2 and eight numerical models from CliPAS that have one-month lead forecasts for all four seasons during the period from 1982 to 2001. As is seen, the super MME mean Z500 forecasts have statistically significant skill over a broad tropical band. In the extratropical regions significant TCCs can be seen over the North Pacific, eastern Canada, and around the Gulf of Mexico in MAM and DJF, likely reflecting the atmospheric response to the ENSO signal over the eastern tropical Pacific (Derome et al. 2001). The forecast skill is relatively weaker in MAM than that in DJF. In contrast to MAM and DJF, only a small significant correlation region is observed over northwestern and northern Canada in JJA over the extratropics while there is almost no skill over mid high-latitude North America in SON. Also, it can be seen from Fig. 4 that the forecast skill tends to increase from JJA to DJF, which may be related to the enhanced ENSO forcing from its developing (JJA) to its mature (DJF) phase, consistent with previous studies (Kumar and Hoerling 2003; Wang et al. 2009). In the midlatitude North Pacific, the forecast skill in JJA is quite high, which is—as pointed out by Wang et al. (2009), Lee et al. (2011), and Lee and Wang (2012)—mainly attributable to an ENSO–monsoon atmospheric teleconnection. Also noticed is that the area of significant forecast skill over the low-latitude Pacific Ocean shifts eastward from JJA to DJF, in agreement with the results of Wang et al. (2009).
The forecast skill of numerical models over the NPNA region (20°–80°N, 160°E–80°W) is also evaluated by computing the PCC between the observed and Comp model forecast Z500 anomalies (Fig. 5) and then making a time-mean pattern correlation ccoefficients (PCC) over the entire hindcast period in order to quantify the overall MME hindcast skill (Fig. 6). Figure 5 shows that the 5-yr running average PCC is the highest in DJF and the lowest in SON while MAM and JJA have a comparable PCC during the period. The PCC for DJF in 1997 is 0.93, which is the strongest El Niño winter during the period. In general, the forecast skill is relatively poor during the early 1990s for most seasons. The time average of PCC for the Comp model forecasts shows that there is almost no skill in predicting Z500 anomalies in SON over this region. Examination of individual models reveals that the time-averaged PCC is the lowest in SON for all models except CAWC and NCT2 where JJA has an even lower forecast skill during the period under examination (Fig. 6).
The above results indicate that numerical models can reasonably well predict the variability of MCA1 in MAM, JJA, and DJF, but most models have problems in forecasting the MCA1 in SON. Considering the significant influence of MCA1 on the SAT over North America, as shown in Fig. 2, it is very possible that the numerical model ability in predicting the SAT over the NPNA region is impacted by the above results. We confirmed this by examining the TCCs between the observations and the MME of SAT forecasts in HFP2 data for four seasons during the period from 1969 to 2001 (Fig. 7). Areas with a correlation score significant at the 0.05 level or better are shaded. Significant predictive skills are found over many regions of North America in MAM, JJA, and DJF. For example, skillful areas appear over central and southern North America in MAM and DJF. In JJA skills can be found over most of Canada and North America south of 35°N, while only limited areas of predictive skill are found in SON. The predictive skill of the SAT seasonal forecast is also measured by mean-square error (MSE) (not shown). Following Smith and Livezey (1999) and Lin et al. (2008), MSE is calculated using the observed and four model-averaged SAT anomalies that are normalized using their respective standard deviations. The distributions of MSE for four seasons are consistent with the correlation skill shown in Fig. 4. Overall the forecast skill of SAT for the one-month lead MME mean forecasts is the lowest over North America in SON among the four seasons.
4. Possible causes of the poor forecast skill in SON
a. The climatological mean state over the tropical Pacific region
In this section we investigate possible reasons why most numerical models tend to produce an erroneous forecast of the atmospheric circulation over the NPNA region in SON. The tropical Pacific is known to be an important forcing area for atmospheric variability over the Pacific Ocean and surrounding land area on a seasonal time scale, especially for boreal winter. The SST anomaly in the equatorial Pacific—for example, that related to El Niño—is closely related to changes in precipitation and diabatic heating that generate anomalous vertical motion and upper-level divergence, which leads to extratropical Rossby waves and global teleconnections (Wallace and Guztler 1981; Sardeshmukh and Hoskins 1988). The 500-hPa geopotential height and SAT changes can be caused by the SST-related teleconnections that account for most of the seasonal forecast skill in the NPNA region (Derome et al. 2001; Lin et al. 2005b; Jia et al. 2009). Thus it is critical for numerical models to have a realistic SST simulation over this region to have a skillful seasonal forecast. We start by examining the climatological mean state of SST in the observations and compare to that in the model forecasts. Figure 8 depicts the difference between model forecasts and the observed SST averaged over the period from 1982 to 2001. The climatology of the model forecast SST was computed using the MME of five one-tier CliPAS models that have forecasts for all four seasons (see Table 2).
It is clear that the forecast skill of the climatological SST vary by season. The forecast climatological SST errors for JJA and SON are more obvious than those in MAM and DJF. In JJA pronounced positive SST biases appear over the eastern tropical Pacific Ocean with negative SST biases over the subtropical western Pacific. For SON positive biases can also be found along the tropical eastern Pacific Ocean. However, if we focus on the central equatorial Pacific area where SST has a close relationship to MCA1, as shown above (Figs. 1 and 3), huge negative SST biases are noticed, indicating that the forecast SST climatology is cooler than the observations in this region for SON. Examination of individual numerical models shows that almost all models produce a cooler SST climatology than the observations around this region in SON, except UHT1, which has positive SST biases for all four seasons.
The bias of the tropical Pacific SST forecast could degrade the model’s capability in simulating the precipitation climatology over there (Lee et al. 2010). A correct representation of the divergent circulation associated with tropical heating is important for determining midlatitude atmospheric circulation patterns. Furthermore, the mean tropical SST and precipitation, through diabatic heating, have an important influence on the atmospheric mean flow that in turn affects the tropical forced Rossby wave propagation, which is related to seasonal forecast skill. Here the climatological mean state precipitation fields are also examined and displayed in Fig. 9. The spatial distributions of precipitation errors are somewhat similar to each other among the four seasons. They all have negative precipitation biases around the equatorial Pacific and positive precipitation biases to the north. The magnitudes of the precipitation errors in JJA and SON are larger than those in MAM and DJF. Again, if we focus on the central equatorial Pacific, it is obvious that the negative precipitation biases in SON, which indicate a weaker tropical forcing than the observations, are more significant than for other seasons. Further examination indicates that the negative precipitation biases in this region are quite consistent among the numerical models. All numerical models have pronounced negative precipitation biases around the central equatorial Pacific in SON.
To examine the current level of precipitation forecast skill we also compute the pattern correlation coefficient (PCC) between the observed and Comp model forecast precipitation anomaly fields. Figure 10 depicts the 5-yr running average PCC over the tropical Pacific region (30°S–30°N, 120°E–60°W) for four seasons. It reveals that there is clearly a seasonal dependence and interannual variability of the precipitation forecast skill. The forecast skill for SON is not always the worst during this period. However, the PCC curve of SON is generally lower than the other three seasons. The time-averaged PCC of the Comp (shown as MME) and 12 individual numerical models are compared to each other in order to further quantify the forecast precipitation skill (Fig. 11). It shows that the forecast skill of Comp is higher than any individual model. Also it can be seen that the time-averaged PCC for SON is the lowest among the four seasons for 9 of the 12 model forecasts under examination. The time-averaged pattern correlation coefficients of the 12 numerical models vary from 0.18 to 0.35 in SON while that for Comp is 0.42. It can be concluded from the above analysis that the poor forecast skill of numerical models in SON over the NPNA region is at least partly due to the fact that in SON numerical model forecasts have relatively bigger errors in the climatological SST over the tropical Pacific (Fig. 8). The cold biases of SST in the model causes weaker precipitation response around the equatorial Pacific (Fig. 9) and more pronounced erroneous precipitation pattern (Fig. 10 and Fig. 11) than in the other three seasons. These precipitation biases may cause errors in the extratropical mean flow and global teleconnection patterns and can therefore degrade the prediction skill in this season.
Wang et al. (2009) examined the ability of CliPAS MME one-month lead hindcast in predicting the spatiotemporal structures of the first two leading empirical orthogonal modes of the equatorial SST anomalies for JJA and DJF. Bias of a westward shift of the SST anomaly between the date line and 120°E was found. In this study, we found that the cold bias of the mean state of SST and its associated erroneous precipitation response over the equatorial Pacific in the models is more significant in SON than in the other three seasons. These biases of tropical SST and precipitation may cause errors in the extratropical mean flow that influences the forced Rossby wave propagation and the global teleconnections associated with equatorial SSTA forcing, degrading seasonal climate prediction skill in extratropical regions. As demonstrated in Lee et al. (2010), a correction of the inherent bias in the mean state is critical for improving the long-lead seasonal prediction.
In the HFP2 two-tier seasonal forecast, the SST forcing used is the sum of SSTAs, obtained from observations one month preceding the forecast period, and the monthly varying climatological SST. An examination of the precipitation response of the four HFP2 models over the tropical Pacific region reveals that the amplitude of the precipitation response is generally weaker than the observations especially over the equatorial Pacific where negative precipitation biases are observed. These precipitation biases are found larger than those shown in Fig. 9, indicating the superiority of one-tier numerical models in simulating the climatological tropical Pacific precipitation compared to the two-tier models (not shown). In the study of Wang et al. (2004), they showed that the seasonal-mean SST anomalies are negatively correlated to precipitation in the Asian–Pacific monsoon region, especially when the precipitation leads SST by one month, suggesting that SST anomalies are forced by the atmospheric circulations over this region. This relationship can be captured by coupled models realistically. However, the two-tier models were found unable to simulate properly the local SST–precipitation correlation caused by the lack of feedback from the atmosphere.
b. Potential predictability over the NPNA region
It is known that the skill of seasonal forecasts depends on the extent to which boundary forcing can generate strong enough signals recognizable from the chaotic internal variability of the atmosphere (Kumar and Hoerling 1995). To investigate why most numerical models have the lowest forecast skill over the NPNA region in SON among the four seasons, we examine the potential predictability of the atmosphere over this region.
Let Xsy represent the forecast seasonal mean Z500, where s = 1, 2, … , S identifies a particular simulation in an ensemble of S simulations, and y = 1, 2, … , Y identifies a particular year in the period from 1982 to 2001.
The total variance of the data can be expressed as
where is the anomaly that is defined as the deviation of the model forecast Z500 from its climatology.
The total variance in the model simulation can be divided into the external variance and internal variance . The external variance is the part associated with SST variability and can be obtained from the ensemble mean:
where represents the ensemble mean for year y that can be obtained through
The internal variance is due to member-to-member differences and can be estimated by the deviation of each member from the ensemble mean, expressed as
where is the deviation of member from the ensemble average.
The potential predictability of the atmosphere can be estimated by calculating the variance ratio of the total variance to the internal variance (Zwiers 1996):
The variance ratio is assessed using models from the CliPAS project that have seasonal forecasts for all four seasons and have seasonal forecasts available for individual members (CAWC, UHT1, NCEP, GFT1, UHC2, and NCT2). The spatial distributions of the ratio over the NPNA region for the four seasons are depicted in Fig. 12. Regions where the ratio is greater than 1 at the 0.05 significance level from an F test are shaded. For MAM and DJF, high ratios can be seen over the low latitudes, the eastern North Pacific, western Canada, and southeastern North America—reminiscent of a wave train pattern over the NPNA region suggesting that the potential predictability over this region is related to ENSO variability. The distribution of the variance ratio is similar for MAM and DJF with MAM having relatively higher values than DJF. In JJA, although the wave train signal is not as obvious as that in MAM and DJF, high variance ratios also appear over central North America. Obviously, the lowest potential predictable season is SON when areas with relative high variance ratio appear along the tropical band. The above results can, at least, partly explain our previous results that most numerical models have difficulty in forecasting the time variability of MCA1 and have the lowest predictive skill for Z500 over the NPNA region in SON.
To further understand seasonal dependence of the potential predictability of the atmosphere over the NPNA region, the variance due to atmospheric internal dynamics (noise) and the variance associated with the external forcing (signal) are examined and presented in Figs. 13 and 14. It can be seen from Fig. 13 that, while the magnitudes of the noise level change distinctly from season to season, the maximum of the variance lying over the mid North Pacific for the whole year. The largest (weakest) noise levels appear in DJF (JJA), as expected. The maximum value of noise in DJF is almost five times larger than that in JJA. The noise level in SON is seen to have a magnitude about two times that in JJA. The variances of the model forecasts due to external forcing show that the signal level is comparable in magnitude between DJF and MAM (Fig. 14). However, the noise level in DJF is obviously greater than that in MAM, making MAM more predictable than DJF, as can be seen from Fig. 12. The signal levels in JJA and SON are quite similar and much weaker compared to those in MAM and DJF. The maximum value of signal during DJF is about six times greater than that in JJA and SON. The obvious seasonality of the signal is more likely the result of the dynamics of tropical–extratropical interactions since the seasonal variation of tropical convective forcing is not obvious, as discussed in Kumar and Hoerling (1998). Although JJA and SON have a similar signal level over the NPNA region, the noise level in SON is much higher than that in JJA, making the potential predictability of the atmosphere in SON the lowest among the four seasons. From JJA to SON, the NH extratropical westerly jet is enhanced, as are transient activities and nonlinear interactions. These atmospheric internal processes lead to strong interannual variability, which is unpredictable. The results of the potential predictability is consistent with our previous results showing that most numerical models have problems in forecasting the temporal variability of MCA1 in SON. However, as discussed in Kumar et al. (2007), it should be kept in mind that the decomposition of external and internal components of seasonal-mean atmospheric variability may be sensitive to the GCMs employed in this study.
5. Summary and discussion
Equatorial Pacific SST forcing is of central importance for determining well-known tropical–extratropical teleconnections and is known as the primary source of atmospheric variability on the seasonal time scale. In this study, we start by gauging numerical model performance in predicting MCA1 over the NH, which is obtained by doing an MCA analysis on the seasonally averaged Z500 over the NH and the simultaneous tropical Pacific SST for four seasons separately. The percentage of total covariance between the Z500 and SST fields explained by MCA1 varies from 50% to 79% for MAM, SON, and DJF, while it is about 36% for JJA. It was found that MCA1 can significantly influence the surface air temperature over North America. The structure of the atmospheric component of MCA1 varies from season to season. Examination of the model forecast results shows that numerical models can capture, with a high fidelity, the temporal evolution of MCA1 in MAM, JJA, and DJF while most models fail to predict the variability of MCA1 in SON. The temporal correlation coefficients (TCC) and pattern correlation coefficient (PCC) results further confirm that the poor skill for the extratropical atmospheric circulation patterns over the NPNA region in SON is quite systematic among GCMs.
Further examination reveals two possible sources of the model low skill for SON atmospheric variability over the NPNA region. First, most models have the most pronounced errors in the mean states of SST and precipitation along the central equatorial Pacific in SON. As indicated by previous studies (e.g., Lee et al. 2010), corrections of the inherent errors in the mean state are critical for improving seasonal prediction. Second, the potential predictability of the atmosphere over the NPNA region is lowest in SON in terms of the ratio of the total variance to the internal variance. In SON, high potential predictability appears only over the low latitudes. The low potential predictability in the extratropical regions in SON is attributable to low variance associated with external forcings and high variance related to atmospheric internal processes.
Many previous studies analyzed the predictability of numerical models over the tropics. Building on these studies, we examined the difference of forecast skill between one-tier and two-tier seasonal forecasting systems over extratropical regions. We divided the numerical models of HFP2 and CliPAS into one-tier and two-tier two categories and examined their abilities in predicting the time evolution of MCA1. The TCCs of the MME mean seasonal forecasts of Z500 for the four seasons are also compared between the one-tier and two-tier seasonal forecasting systems in the NPNA region. Although not shown, we found that the forecast skills of one-tier models are generally better than two-tier models in predicting the time evolution of MCA1 in JJA, SON, and DJF, while having a comparable skill in MAM. Although not very pronounced, examination of the TCC of Z500 shows that the performances of one-tier numerical models are better than two-tier numerical models over subtropical regions and some areas over the extratropical NPNA area.
This research was jointly funded by the National Natural Sciences Foundation of China (Grant 41105037), the Fund Project of Zhejiang Provincial Department of Education (Grant Y200907077), and by the Fundamental Research Funds for the Central Universities (Grant 2012XZZX012). Lin is partly supported by the Natural Science and Engineering Research Council of Canada (NSERC). Lee and Wang were supported by APEC Climate Center (APCC) international research project (CliPAS) and by IPRC, which is in part supported by JAMSTEC, NOAA, and NASA. We acknowledge contributions from all CliPAS team members. We are grateful to the reviewers for their helpful suggestions on improving our paper.
International Pacific Research Center Publication Number 862 and School of Ocean and Earth Science and Technology Publication Number 8582.