# Seasonal prediction and predictability of the Asian winter temperature variability

## Abstract

Efforts have been made to appreciate the extent to which we can predict the dominant modes of December–January–February (DJF) 2 m air temperature (TS) variability over the Asian winter monsoon region with dynamical models and a physically based statistical model. Dynamical prediction was made on the basis of multi-model ensemble (MME) of 13 coupled models with the November 1 initial condition for 21 boreal winters of 1981/1982–2001/2002. Statistical prediction was performed for 21 winters of 1981/1982–2001/2002 in a cross-validated way and for 11 winters of 1999/2000–2009/2010 in an independent verification. The first four observed modes of empirical orthogonal function analysis of DJF TS variability explain 69 % of the total variability and are statistically separated from other higher modes. We identify these as predictable modes, because they have clear physical meaning and the MME reproduces them with acceptable criteria. The MME skill basically originates from the models’ ability to capture the predictable modes. The MME shows better skill for the first mode, represented by a basin-wide warming trend, and for second mode related to the Arctic Oscillation. However, the statistical model better captures the third and fourth modes, which are strongly related to El Niño and Southern Oscillation (ENSO) variability on interannual and interdecadal timescales, respectively. Independent statistical forecasting for the recent 11-year period further reveals that the first and fourth modes are highly predictable. The second and third modes are less predictable due to lower persistence of boundary forcing and reduced potential predictability during the recent years. In particular, the notable decadal change in the monsoon–ENSO relationship makes the statistical forecast difficult.

### Keywords

Asian winter monsoon Seasonal climate prediction DJF 2 m air temperature variability Monsoon-ENSO relationship Statistical model Multi-model ensemble (MME)## 1 Introduction

During the 2009/2010 winter season, many parts of Asia experienced conspicuous climate anomalies concurrent with the Central Pacific El Niño and strong negative phase of the Arctic Oscillation (AO) in which frequent severe cold surges (outbreaks of cold air) and record-breaking heavy snowfall were observed. During the first few days of January 2010, North China and Korea dropped to 50- and 70-year record low temperature and snowfall, respectively. These events resulted in heavy losses from the viewpoint of agriculture, transportation, and other socioeconomic activities. The cold winter over the most parts of Asia seems against the global warming trend projected by the contemporary climate models (e.g. Lee and Wang 2012b). Although economic and social influences are equally affected by salient variability in the Asian winter monsoon (AWM) and that in the summer, prediction of the AWM (Wang et al. 2010; Wu et al. 2011; Sohn et al. 2011) has received less attention than that of the summer counterpart which has turned out to be the most challengeable in current climate models and observation shown by numerous studies (e.g. Kang et al. 2002; Ha et al. 2005; Kang and Shukla 2006; Yang et al. 2008; Wang et al. 2004, 2008, 2009; Lee et al. 2010, 2011a, b; Lee and Wang 2012a and many others). The extent to which we can predict dominant modes of the AWM variability with dynamical and with physically based empirical models is still unclear.

The identification of the dominant modes of AWM variability is a crucial step in understanding its predictability. Wang et al. (2010) identified two dominant modes of air temperature variability over the East Asian winter monsoon (EAWM) region, which were called the northern and southern mode respectively. The former represents a cold winter in northern East Asia due to cold air intrusion from northeastern Siberia, and the latter is characterized by deepening of the East Asian trough and strengthening of the Mongolian High. They showed that nine of ten existing EAWM circulation indices (Ji et al. 1997; Cui and Sun 1999; Lu and Chan 1999; Chen et al. 2000; Li and Zeng 2002; Jhun and Lee 2004; Wu et al. 2006) basically describe the southern modes and one index (Guo 1983) describes both modes equally. It was further demonstrated that the two dominant modes can explain a significant amount of temperature variability over the entire Asian region.

Several factors have been determined to influence interannual and interdecadal variability of the AWM. Many observational and modeling studies have shown that the decrease of snow cover over the Eurasian continent during the previous fall season results in weakening of the EAWM (Walland and Simmonds 1997; Watanabe and Nitta 1999; Clark and Serreze 2000; Jhun and Lee 2004). The importance of autumn Arctic sea ice to abnormal AWM climate was suggested (Wu et al. 2011; Li and Wu 2012). It is found that the joint action of western Pacific Subtropical High and Siberian High affects cold wave frequency in China (Ma et al. 2012). Moreover, El Niño-Southern Oscillation (ENSO) plays an important role in regulating the interannual variability of the AWM (Zhang et al. 1996; Wang et al. 2000; Chan and Li 2004; Chang et al. 2004; Wang et al. 2010). On the other hand, several studies have shown that AO and North Atlantic Oscillation (NAO) are related to the AWM on a decadal time scale (Gong et al. 2001; Jhun and Lee 2004; Wu et al. 2006; Li and Bates 2007). Wu et al. (2009) indicated that the Southern Hemisphere annular mode is also linked to the AWM variability.

Despite of the aforementioned studies, how to determine predictability of AWM variability on a seasonal time scale is still elusive. Better understanding of the origins and predictability sources of the AWM may contribute to the improvement of its seasonal prediction capability. Wang et al. (2007) and Lee et al. (2011a) suggested the concept of predictable mode analysis (PMA) because the multi-model ensemble (MME) seasonal prediction skill is based essentially on the major modes. With this method, attainable potential climate predictability can be quantified using the fractional variance of the “predictable” leading modes determined by examination of observation and hindcast results of the models. The purpose of this study is to explore the attained prediction skill and achievable potential predictability of the AWM variability by using the PMA approach and to understand the range for potential improvement of dynamical and statistical model predictions. The specific questions to be addressed include (1) how to determine the current level of dynamic prediction skill for the AWM seasonal mean 2 m air temperature (hereafter, TS) anomaly and identify the source of the dynamical forecast skill; (2) how to empirically estimate the potential predictability of the AWM; and (3) how to optimally construct a statistical model with physically based predictors for the AWM TS prediction. These points will be respectively addressed in Sects. 3, 4 and 5, respectively, following a brief discussion of the datasets, models, and methodology used in this study. Section 6 summarizes our major findings.

## 2 Models, data, and methodology

### 2.1 Coupled models’ hindcast data

Description of 13 coupled atmosphere–ocean models. Model index used in figures is also shown

Institute (model index) | Model name | AGCM | OGCM | Ensemble member | References |
---|---|---|---|---|---|

NCEP (M1) | CFS | GFS T62 L64 | MOM3 1/3°lat × 5/8°lon L27 | 15 | Saha et al. (2006) |

FRCGC (M2) | SINTEX-F | ECHAM4 T106L19 | OPA 8.2 2° cos(lat) × 2° lon L31 | 9 | Luo et al. (2005) |

SNU (M3) | SNU | SNU T42L21 | MOM2.2 1/3°lat × 1°lon L40 | 6 | Kug et al. (2008) |

UH (M4) | UH | ECHAM4 T31L19 | UH Ocean 1°lat × 2°lon L2 | 10 | Fu and Wang (2001) |

GFDL (M5) | CM2.1 | AM2.1 2°lat × 2.5°lon L24 | MOM4 1/3°lat × 1°lon L50 | 10 | Delworth et al. (2006) |

BMRC (M6) | POAMA1.5 | BAM 3.0d T47 L17 | ACOM3 0.5°–1.5° lat × 2.0° lon L31 | 10 | Zhong et al. (2005) |

CERFACE (M7) | CERFACE | ARPEGE T63 L31 | OPA 8.2 2.0° × 2.0° L31 | 9 | Déqué (2001) Delecluse and Madec (1999) |

ECMWF (M8) | ECMWF | IFS T95 L40 | HOPE-E 1.4° × 0.3°–1.4° L29 | 9 | Gregory et al. (2000) Wolff et al. (1997) |

INGV (M9) | INGV | ECHAM4 T42 L19 | OPA 8.2 2.0° lat × 2.0° lon L31 | 9 | Roeckner et al. (1996) Madec et al. (1998) |

LODYC (M10) | LODYC | IFS T95 L40 | OPA 8.0 182GP × 152GP L31 | 9 | Gregory et al. (2000) Delecluse and Madec (1999) |

MPI (M11) | MPI | ECHAM5 T42 L19 | MPI-OM1 2.5° lat × 0.5°–2.5° lon L23 | 9 | Roeckner et al. (1996) Marsland et al. (2003) |

METFR (M12) | Meteo- France | ARPEGE T63 L31 | OPA 8.0 182GP × 152GP L31 | 9 | Déqué (2001) Madec et al. (1997) |

UKMO (M13) | UKMO | HadAM3 2.5 × 3.75L19 | GloSea OGCM 1.25° × 0.3°–1.25°L40 | 9 |

### 2.2 Observed data

The observed TS data were obtained from the National Centers for Environmental Prediction (NCEP) reanalysis version 2 (NCEP R2; Kanamitsu et al. 2002). The monthly Niño 3.4 SST index was calculated using improved Extended Reconstructed SST Version 3 (ERSST V3) data (Smith et al. 2008). All data used in this study were normalized by their own standard deviations.

### 2.3 Predictable mode analysis

Wang et al. (2007) and Lee et al. (2011a) suggested a method for determining predictable modes from empirical orthogonal function (EOF) modes of observation and state-of-the-art climate model prediction. The correlation matrix is used for EOF analysis because dynamical models more effectively capture observed dominant modes with this approach than with that of the covariance matrix for the AWM TS anomalies. Two basic criteria were considered for the determination: (1) In observation, predictable modes should explain a large part of the total variability with physical interpretations and should be statistically separated from other higher modes; and (2) the climate prediction models should be capable of predicting these major modes.

*i*). The skill score for each mode is calculated by

The skill score ranges from 0 to 1, respectively indicating no skill at all and perfect forecast. It should be noted that we reordered the EOF modes of the MME prediction according to the skill score because the order of the predicted EOF mode is not necessarily the same as its observed counterpart. To reorder the predicted EOF modes, the skill score for the first observed mode was first calculated against all of the predicted modes, and the predicted mode with the best skill score in the first observed mode was taken as the first predicted mode. Other predicted modes were determined by repeating this process.

*TS*) is decomposed into the predictable and unpredictable parts. The predictable part (

*TS*

_{pred}), as a function of longitude (

*lon*), latitude (

*lat*), and time (

*t*), is reconstructed by the linear combination of the predictable EOF modes defined by

*λ*

_{i}is the eigenvalue of

*ith*mode, and

*N*is the total number of predictable modes. The unpredictable part (

*TS*

_{unpred}) is then calculated by subtracting the predictable part from the total field. We consider the correlation coefficient between the original

*TS*and

*TS*

_{pred}as a measure of attainable potential predictability assuming that predictable PCs are accurately predicted (Lee et al. 2011a; Lee and Wang 2012a).

### 2.4 Statistical model

We attempted to determine the extent to which we can predict the predictable dominant modes of AWM variability with a physically based statistical model. In this study, the statistical model, named predictable mode forecast model (PMFM), has two steps: (1) prediction of the predictable EOF PCs of DJF TS over the AWM region using physically based and optimally selected predictors; and (2) reconstruction of the TS field over the entire AWM region from predicted PCs with determined EV and eigenvalues during the training period.

*STM_PC*

_{i}is the predicted PC for the

*i*th EOF mode;

*t*, the time for forecast target;

*M*, the total number of predictors for each PC;

*Pred*

_{ij}, the

*j*th predictor for the

*i*th PC normalized by its own standard deviation with time lag τ (1 month in this study); and

*α*

_{ij}, the coefficient of the

*j*th predictor for the

*i*th PC. The most important factor for accurate prediction of PCs in the PMFM is the determination of optimal predictors for each predictand. The details of predictors for each PC will be addressed in Sect. 4.

*STM_TS*

_{training}indicates reconstructed DJF TS as a function of longitude and latitude at time

*t*, which is similar to Eq. (2). Two different statistical forecasts were made. In the first, we performed a cross-validated statistical forecast for the 21 years of 1981/1982–2001/2002 in order to compare with the MME prediction. In the second, an independent forecast was made for the period of 1999/2000–2009/2010 DJF with the latest 20-year training period for validation of the current statistical approach because cross-validated forecasts are not free from common overfitting problems. For example, the 1999/2000 (2009/2010) DJF forecast was made using the empirical relationship determined for the 20 years of 1979/1980–1998/1999 (1989/1990–2008/2009) DJF. The predicted DJF TS was determined by the following equation:

We considered the correlation coefficient between the original *TS* and *STM_TS*_{training} as a measure of attained fitting skill and that between the original *TS* and *STM_TS*_{forecast} as a measure of attained forecast skill for the PMFM.

## 3 Dynamical prediction

### 3.1 Evaluation of AWM TS prediction

### 3.2 Prediction of major EOF modes

The observed first mode represents a domain-wide warming trend across the period examined and accounts for 32.1 % of the total observed variability. This mode is the same as the second EOF mode of the EAWM (southern mode) shown in Wang et al. (2010). The MME captures its spatial pattern and temporal variation 1 month in advance with high fidelity. The PCC skill for EV_{1} is 0.95, and the TCC skill for PC_{1} is 0.83.

The second observed EOF mode features a north–south seesaw pattern with an interannual timescale, accounting for 16.6 % of the total observed variability. This mode resembles the first mode of the EAWM (northern mode) shown in Wang et al. (2010). The MME accurately captures the spatial and temporal characteristics of the second observed mode but underestimates its variance. The PCC skill for EV_{2} is 0.72, and the TCC skill for PC_{2} is 0.50.

The observed third mode displays a sandwich pattern characterized by a cold TS anomaly over the mid-latitude Asian continent with a warm TS anomaly over the high-latitude Asian continent and the Tropics and vice versa. This mode has mainly interannual variability and accounts for 11.2 % of the total observed variability. The MME reasonably predicts the spatial and temporal characteristics, although its accuracy is less than that of the first two observed modes. The percentage variance is significantly underestimated, and spatial errors are exhibited over most of the oceanic region. In addition, the strong positive phase of the observed PC in DJF 1982/1983 and 1997/1998 is not well captured.

The fourth observed mode exhibits prominent decadal variability and three variability centers over the WNP (negative anomaly), northwestern China (positive), and Kazakhstan (negative). Interestingly, the second predicted mode most resembles the fourth observed mode. However, the MME significantly overestimates its percentage variance and had remarkable spatial errors over most of mid-latitude Asia. Nonetheless, the MME offers some skill in predicting the fourth observed mode with a PCC skill of 0.36 and a TCC skill of 0.39.

## 4 Predictable mode analysis

### 4.1 Identification of predictable modes

*we defined the first four modes as predictable modes for DJF TS over the AWM region*. These modes account for approximately 69 % (83 %) of the total variance of DJF TS in observation (MME prediction).

### 4.2 Prediction skill and attainable potential predictability

_{pred}) and unpredictable (TS

_{unpred}) parts as described in Sect. 2.3. Reconstruction from PCs was achieved using Eq. (2). Figure 4a, b compare TCC skills for the DJF TS obtained from TS

_{pred}and TS

_{unpred}components, respectively, of the MME prediction. For the calculation, the observed total field was used for both predictable and unpredictable cases. The skills of the dynamical model predictions made by the four predictable modes are essentially comparable to the original prediction using all empirical modes (Fig. 1a). On the contrary, the contribution of all residual modes to seasonal prediction skill is minimal, except for those over the Indochina peninsula. This result clearly indicates that the current coupled model prediction skill for the DJF AWM TS essentially originates from the skill for prediction of the first four modes.

To improve the 1-month-lead MME prediction, we applied statistical postprocessing to the prediction. Since the MME prediction exhibited errors in capturing the spatial pattern of the observed EVs, the predicted EVs were replaced by the observed values during the reconstruction procedure for the predictable modes of the MME prediction. The statistical postprocessing potentially improved the dynamical prediction over most of the AWM region shown in Fig. 4c. However, if the statistical postprocessing was applied to the MME prediction with a cross-validated approach, no significant improvement was observed (not shown).

From the conventional perspective, potential predictability can be defined by the fractional variance of the predictable part. In this case, 69 % of the total observed variability was potentially predictable over the AWM region. In present study, however, the realizable potential predictability was estimated by the TCC between the observed total field and the observed TS_{pred} to facilitate comparison with the MME prediction skill, as mentioned in Sect. 2.3. Figure 4d indicates that the variability of the DJF TS is highly predictable, particularly over the EAWM region, the tropical oceans, and a large region of northern Asia. The predictability is relatively low over northern India. The area-averaged TCC skill is 0.82, which corresponds to 69 % of the total observed variability in the linear regression.

### 4.3 Sources of predictability

The second observed mode shows strong positive correlation with the DJF TS over most of northern Asia and Europe (Fig. 5b). This mode exhibits no relationship with the simultaneous Niño 3.4 SST anomaly but may be slightly related to the developing ENSO during following June–July–August (JJA), shown in Fig. 6. It is noted that this mode has significant correlation with the simultaneous AO with a TCC of 0.66 for the 21-year period of DJF 1981/1982–2001/2002. A significant positive correlation (0.68) remains for the recent 20-years period of DJF 1990/1991–2009/2010.

ENSO regulates the third observed EOF mode (Fig. 5c) on the interannual time scale. The lead–lag relationship between the seasonal Niño 3.4 SST anomaly and the third observed PC clearly indicates that the third mode is observed during the mature phase of ENSO (Fig. 6). During the mature phase of El Niño, the cold TS anomaly tends to occur over most of mid-latitude Eurasia, and the warm anomaly occurs over most of northern Eurasia and the Equatorial and South Indian Ocean.

The fourth observed mode is related to the decadal variability of the North Pacific Ocean variability (Fig. 5d) and has a prolonged relationship with the Niño 3.4 SST anomaly from the previous JJA to the following DJF (Fig. 6), indicating that the decadal component of ENSO and the North Pacific Ocean variability regulate the mode. The fourth observed PC is closely related to the long-term TS variability over the eastern Tibetan Plateau and northwest China, where the TS variability shows a weaker correlation with the observed PC_{1} than that over the other Asian region indicated in Fig. 5a. It is further noted that PC_{4} has no relationship (nearly zero) with the AO for the 21-year period of DJF 1981/1982–2001/2002; however, a significant negative correlation of −0.4 is evident for the recent 20-year period of DJF 1990/1991–2009/2010. Interestingly, the second predicted PC, which resembles the fourth observed PC, has a significant relationship with the predicted ENSO on both interannual and interdecadal time scales (not shown).

## 5 Statistical prediction

This section demonstrates the achievable prediction skill of the AWM using the physically based statistical model (predictable modes forecast model; PMFM) introduced in Sect. 2.4. In this approach, the first four predictable PCs are first predicted with optimally selected predictors, and the prediction of the DJF TS over the entire AWM is achieved from TS reconstruction using the observed EVs and statistically predicted PCs from Eq. (5). The selection of predictors plays a crucial role on improving the forecast skill of the PMFM.

### 5.1 Sources of predictability

*i.e.*basin-wide warming of the TS), pronounced warming is observed in the north Indian Ocean and in the subtropical-mid-latitude North Atlantic Ocean (Fig. 7a) that persists through the following DJF (Fig. 5a). In accordance with the noteworthy relationship, the predictors for the PC

_{1}(

*Pred*

_{1j}) are defined by

*COR*is the correlation coefficient between SO TS and the first PC as a function of longitude and latitude, σ is the standard deviation of

*CTS*time series, square brackets indicate area averaging over region R1 (Eq–25°N, 60°E–130°E) and region R2 (Eq–60°N, 80°W–10°W) shown in Fig. 7a. The SO TS anomaly, which has a correlation coefficient larger than +0.38 or smaller than −0.38 (95 % confidence level), is averaged over the selected region. For the forecast purpose, the correlation coefficient was obtained during training period.

_{1}, outstanding precursors were not observed for PC

_{2}(Fig. 7b) over the Northern Hemisphere. In the simultaneous relationship, the positive AO is strongly concurrent with the warm (cold) TS anomaly over the northern (subtropical) AWM. Because of the chaotic nature of the AO, however, no significant relationship of PC

_{2}with the SO AO was observed. However, useful precursors were detected over the Barents and Kara seas, some parts of the northern AWM, and the extratropical North Pacific. The predictors for the PC

_{2}(

*Pred*

_{2j}) are defined by

_{2}are not optimal; therefore, further study is needed to find more effective predictors.

_{3}tends to occur during the mature phase of El Niño, its correlation field with SO TS exhibits a clear progressing El Niño pattern over the tropical Indo–Pacific Ocean (Fig. 7c). In addition, a positive correlation is observed over Russia and Kazakhstan that may be related to SO snow cover over the region. The predictors for PC

_{3}(

*Pred*

_{3j}) are defined by

_{4}is strongly related to the cold SST anomaly over the WNP and the warm SST anomaly over the central and eastern Pacific (Fig. 7d) that persist through the following DJF. The predictors for PC

_{4}(

*Pred*

_{4j}) are defined by

### 5.2 Cross-validated statistical forecast

*r*indicates the correlation coefficient between the observed and predicted PCs. Because of the overfitting problem of the statistical model, the cross-validated skill dropped in comparison to the fitted skill. However, the first and fourth PCs that exhibit trend and interdecadal variability, respectively, are highly predictable with the current empirical approach. The empirical model is also able to predict the third PC with less fidelity than the first and fourth PCs. It is noted that current dynamical MME has better skill for the first and second PCs than the PMFM whereas the PMFM relatively better captures the third and fourth PCs, which are strongly related to ENSO variability on interannual and interdecadal timescales, respectively, than the MME.

*STM_TS*

_{training}) and cross-validated prediction (

*STM_TS*

_{forecast}) for the 21-year period. The fitted skill is as good as the dynamical prediction skill with spatial bias correction (Fig. 4c), and the cross-validated prediction skill is comparable to the 1-month-lead MME prediction reconstructed from the first four PCs (Fig. 4a). While the dynamical model has better skill in predicting the TS over the subtropical AWM, the statistical model more effectively predicts the TS over the mid-latitude EAWM region. In addition, the spatial distribution of the statistically fitted skill is similar as that of the attainable potential predictability shown in Fig. 4d, indicating that the selected predictors for each PC are capable of capturing most of interannual-to-interdecadal variability of the AWM TS. The persistent forecast skill was also compared with the statistical and dynamical forecast (Fig. 9c). The persistent forecast was obtained with the assumption that the October mean TS persists through the following DJF season. A comparison of Fig. 9b, c indicates that the PMFM exhibits significantly better skill than the persistent forecast except over some parts of Central Asia and the Arabian Sea, where large persistence was observed.

The spatial distributions of the dynamical (Fig. 4a) and statistical forecast skills (Fig. 9b) are demonstrated to be, to some degree, independent and complementary to each other. The dynamical forecast has significant skill over most of the oceanic region, while the statistical forecast has skill over the mid-latitude EAWM region. From these results, we simply averaged the dynamical and statistical forecasts and investigated their resultant forecast skill. Figure 9d shows that a simple average of two forecasts can improve the DJF TS forecast over most of the AWM region. The area-averaged forecast skill for the combined forecast was 0.59, which is larger than that of the dynamical (0.53) and statistical (0.51) skills.

### 5.3 Independent forecast

Although the statistical forecast utilized the cross-validated approach, overfitting problems remain inevitable. Thus, we performed independent forecasting for the 11-year period of DJF 1999/2000–2009/2010 to confirm whether the suggested methodology is actually useful. The independent forecast procedure is detailed in Sect. 2.4.

_{1}) and interdecadal mode (PC

_{4}) are highly predictable with TCC skills of 0.76 and 0.65, respectively, for the recent 11 years. However, two interannual modes of PC

_{2}and PC

_{3}are not well predicted. For the AO-related second PC (northern mode in Wang et al. 2010), the remarkable positive phases in 2001/2002, 2003/2004, and 2006/2007 are totally missed in the PMFM, while negative phases are relatively well predicted. The low performance of the ENSO-related third PC may be attributed to the interdecadal change in the ENSO–monsoon relationship. The correlation between the third PC and DJF Niño 3.4 SST index is 0.56 for 1979/1980–1999/2000 and 0.37 for 1989/1990–2009/2010, which indicates a weakening of the relationship during the recent decade. This notable decadal change in the monsoon–ENSO relationship likely causes difficulties in statistical forecasting.

## 6 Summary

The 1-month-lead seasonal forecast skills of current dynamical and statistical models were investigated on the DJF TS anomaly over the AWM region and were compared with attainable potential predictability obtained from the “predictable” leading modes for the 21-year period of 1981/1982–2001/2002.

The 1-month-lead dynamical prediction for the DJF AWM TS was achieved by the MME of thirteen coupled models with the November 1 initial condition that were included in DEMETER and CliPAS projects. The MME is capable of predicting the AWM TS 1 month in advance with the domain-averaged TCC skill of 0.51 for the 21-year period, which is significantly higher than the 0.33 averaged skill of all individual models and better than individual model skills, which ranged from 0.16 to 0.46.

The first four observed modes are identified as predictable modes because they explains 69 % of the total observed variability with physical interpretations and are statistically separated from other higher modes. Moreover, they are also well predicted by the current climate prediction models, to some extent. The MME effectively captures the first and second observed EOF modes with high fidelity, which are characterized by a domain-wide warming trend and by AO-related interannual variability, respectively. The observed third and the fourth modes are respectively associated with interannual and interdecadal components of ENSO and are reasonably captured by the MME, although less faithfully than the first two modes. The MME highly overestimates percentage variance of the fourth observed mode but far underestimates that of the second observed mode.

The observed total field of the DJF AWM TS was decomposed into predictable and unpredictable components. Considering the assumption that the first four predictable modes are perfectly predicted, attainable potential predictability can be quantified by the TCC between total TS and reconstructed TS from the predictable modes. The area-averaged attainable TCC skill is 0.82, and this corresponds to 69 % of the total observed variability in linear regression. The MME tends to more accurately predict areas of high potential predictability except over that above 50°N of the AWM region. It is important to note that the MME forecast skill essentially originates from the ability of dynamical models to capture the first four predictable modes.

A statistical prediction with the PMFM was achieved using predictors obtained from the SO mean TS that significantly correlated with the predictable modes of the DJF AWM TS. During 1981/1982–2001/2002, the cross-validated statistical forecast shows significantly high skills for the first and fourth observed modes, which exhibits trend and interdecadal variability, respectively. It is noted that the current dynamical MME shows better skills for the first and second PCs whereas the PMFM more effectively captures the third and fourth PCs, which are strongly related with ENSO variability on interannual and interdecadal timescales, respectively, compared to the MME. Since the dynamical and statistical predictions are complementary, a simple composite of two predictions is capable of improving the forecast skill of the DJF TS over most of the AWM region. The area-averaged forecast skill for the combined forecast is 0.59 which is larger than that of 0.53 dynamical and 0.51 statistical skills.

Independent statistical forecasting for the DJF AWM TS was achieved for the 11-year period of 1999/2000–2009/2010 to validate the statistical model’s usefulness for real-time forecasting during recent years. The area-averaged TCC skill of the statistical forecast is 0.43 for the recent 11 years, which is less than that of 0.51 for the 21-year period of 1981/1982–2001/2002. It is important to note that the attainable potential predictability is 0.71 over the AWM, which is less than that of 0.81 for the 21-year period, and this result indicates that the TS during the recent decade was potentially less predictable. In addition, the persistent skill of the TS from October to DJF of the 21-year period is also reduced from 0.24 to 0.12 in the recent 11 years. Considering the lower persistence and potential predictability during the recent decade, the independent statistical forecast skill appears to be valid and useful.

The interannual variability is less predicted than the interdecadal variability and warming trend by the current statistical forecast. The statistical forecast shows difficulty in capturing the positive phase (warming over the northern AWM region) but well predicts the negative phase of the second observed PC. The low performance of the ENSO-related third PC may be attributed to the interdecadal change in the monsoon–ENSO relationship. The correlation coefficient between the third PC and the Niño 3.4 SST index dropped to 0.37 for the recent 21 years from 0.56 for 1979/1980–1999/2000. This notable decadal change in the monsoon–ENSO relationship likely makes difficulty in statistical forecast.

It should be emphasized that the forecast skill demonstrated here for the AWM TS is a baseline and attained skill for both dynamical and statistical models. During the recent two decades, climate models have been improved remarkably; extensive effort will be devoted to further improvement. The statistical forecast can be further improved with the incorporation of better predictors than only the SO mean TS.

## Notes

### Acknowledgments

This work was supported by GRL grant of the National Research Foundation (NRF) funded by the Korean Government (MEST 2011-0021927). Lee and Wang acknowledge support from APEC Climate Center and IPRC, which is in part supported by JAMSTEC, NOAA, and NASA. This is the SOEST publication number 8777 and IPRC publication number 926.

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