1 Introduction

Early in 2008, extraordinarily frequent and long-lasting heavy snowstorms affected China in four major periods of January 10–16, 18–22, 25–29, and January 30–February 2, 2008 (Gao 2009; Wen et al. 2009; Zhou et al. 2009), which brought above normal precipitation, below normal temperatures and severe icing conditions, thus causing serious damages over southern China (Ding et al. 2008; Wang et al. 2008a, b, c; Liao and Zhang 2013). More than 20 provinces in China suffered power outages, suspension of air services and closures of most highways (Tao and Wei 2008; Li et al. 2008, 2009; Ma et al. 2011; Huang et al. 2013). The number of people affected by this event exceeded 100 million, and the direct economic losses amounted to more than 15 billion Chinese Yuan (Wang et al. 2008a, b, c; Zheng et al. 2008). The potential predictability of such extreme events have always been an important issue in the meteorological community.

Numerous studies have been conducted on the heavy snowstorms in early 2008 over southern China (Fu et al. 2008; Yang et al. 2008; Gao et al. 2008; Wen et al. 2009; Ma et al. 2011). Ding et al. (2008) have provided an overview of the atmospheric circulation anomalies and the role of corresponding signals at regional scales during the entire January–February event. It has been concluded that the event is caused by the combined effects of the Ural blocking high, the low trough over Central Asia and the southern branch trough of the Bay of Bengal. Under the favorable large-scale circulation conditions, a stationary front forms due to the confluence of the cold and warm air in southern China, leading to the extreme January–February snowstorm event (Yang et al. 2008). The strengthening and eastward movement of the Middle East jet stream is favorable for the southeastward shifts of the ridge and trough over Europe and the western Asia and also favorable for the strengthening of the southern branch trough in the subtropical westerlies over the southern Tibetan Plateau (Wen et al. 2009). The concurrent variation between the subtropical jet and the polar-front jet acts as an important bridge that links the snowstorms to the anomalous atmospheric signals associated with the cold- and warm-air activities (Liao and Zhang 2013). In particular, the intra-seasonal characteristics in this extreme events have been emphasized (He et al. 2008; Yang et al. 2008; Liang and Lin 2018). Huang et al. (2013) also simulated the extreme event in early 2008 using the Beijing Climate Center (BCC) model and revealed the influence of the real-time sea surface temperature on atmospheric circulation. It can be seen that this extreme event in early 2008 has been investigated from different aspects, including large-scale circulation features (Yang et al. 2008), regional abnormal signals (Wen et al. 2009), intra-seasonal oscillations (Ma et al. 2011), etc. However, the prediction ability of BCC model for these factors affecting the extreme event and that how these factors affect the skill in precipitation forecasting have not yet been analyzed.

The subseasonal-to-seasonal (S2S) forecasts play an important role in helping the development of weather business and service for social economy (Hudson et al. 2011; Lemos et al. 2012; Robertson et al. 2014; Vitart 2014a; MacLeod et al. 2015). To improve the forecasting ability on the S2S timescale, the World Weather Research Programme (WWRP) and World Climate Research Programme (WCRP) established a S2S Project in November 2013 (Vitart et al. 2012; Vitart 2014a, b), which has been issued an extensive database, including S2S reforecasts and near-real-time forecasts from 11 operational forecasting centers. This dataset has provided a unique opportunity for its application in verifying the prediction accuracy of extreme events on the S2S timescale. In recent years, some studies have been conducted on the subseasonal prediction of extreme events, such as the winter low temperature weather in Asia (June et al. 2013), the Asian summer monsoon (Jie et al. 2017) and the heat wave in South America (Marisol and Mariano 2018). Several important potential sources of predictability on the S2S timescale have been identified in latest researches, with a special emphasis on the low-frequency signals such as the Madden–Julian Oscillation (MJO) (Zhang 2013) and the Arctic Oscillation (AO) (Baldwin et al. 2003; Li and Wang 2003). According to Ding et al. (2008), the eastward propagation of MJO strengthens the southwest airflow, leading to the increase of the precipitation over southern China during the latter two snowstorms in early 2008. On the other hand, several studies have shown that the AO is related to the Asian winter monsoon on the seasonal timescale (Gong and Wang 2003; June et al. 2013), and the positive AO contributes to the maintenance of the planetary-scale waves during the extreme snowstorm event in early 2008 (Wang et al. 2008a, b, c). Therefore, as the low-frequency signals are one of the main sources for the S2S predictability of the East Asian climate, it is of vital significance to get a thorough understanding on the prediction ability of the model for the AO and MJO (Cavanaugh et al. 2015).

This extreme snowstorm event over southern China in early 2008 provides a good case to evaluate the sub-seasonal predictability of the Beijing Climate Center Climate System Model (BCC_CSM). As a participant in the WMO S2S project, the model was developed by the China Meteorological Administration (CMA). Based on the hindcast results from the BCC_CSM model, the predictability of precipitation and atmospheric circulation is evaluated with a special emphasis on the prediction ability with the lead time of longer than 10 days.

The rest of this paper is organized as follows. The model, data and methods are introduced in Sect. 2. The assessment on the sub-seasonal forecasting accuracy of the model for the extreme snowstorms over southern China in early 2008 is presented in Sect. 3. And the influence of the model’s initial conditions, including persistent atmospheric circulation systems, sea surface temperature (SST), MJO and AO signals, on the sub-seasonal prediction during the snowstorm event is analyzed in Sect. 4. Finally, conclusions and discussion are provided in Sect. 5.

2 Model, data, and methods

2.1 Model description

The BCC S2S model is based on BCC_CSM1.1, an atmosphere–ocean-ice-land coupled climate model (Wu et al. 2014).The atmospheric component of BCC CSM1.1 is the BCC Atmospheric General Model, version 2.1 (Wu et al. 2010), with a horizontal resolution of T106 and 40 layers in the vertical direction. The land component is the BCC Atmosphere and Vegetation Interaction Model, version 1 (Ji 1995). The oceanic component is the GFDL Modular Ocean Model, version 4 (Griffies et al. 2005), with gradually increased resolutions (1° to 1/3°) from 30°S or 30°N to the equator and 40 levels in the vertical direction. The sea-ice component is the GFDL Sea Ice Simulator (Winton 2000), which has the same resolution as that in the oceanic component.

For the prediction in the S2S hindcast experiments designed by the S2S project, with the initialization on each day from January 1, 1994 to December 31, 2013, the model is integrated for 60 days. To reduce the uncertainty from initial conditions, for each initial date, four-member ensembles are created using the initial conditions at 0000, 0600, 1200 and 1800 Coordinated Universal Time (UTC). For evaluating model prediction skill, the outputs of the ensemble mean from these four members are used in this study.

2.2 Data

The dataset used in this work include: (a) the S2S daily hindcast performed by the BCC_CSM from December of 2007 to February of 2008; (b) the 6-h interval reanalysis data (Kalnay et al. 1996) in 1982–2008 from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR), including wind components and geopotential height fields. Atmospheric model initial fields are from the NCEP Reanalysis with 2.5° × 2.5° horizontal resolution; (c) the observed daily precipitation data during the period of the extreme snowstorm from January 10 to February 2, 2008 over southern China obtained from 756 meteorological stations provided by the CMA; and (d) the AO index from the NOAA/Climate Prediction Center (CPC; see on-line website at https://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/ao.html).

2.3 Methods

The assessment in this study has been conducted for the entire snowstorm event (January 10 to February 2, 2008) and the four major periods (January 10–16, 18–22, 25–29, and January 30 to February 2, respectively). The evaluation period for the entire event starts on January 10, and that for each of the four periods starts on the first day of each period. The hindcasts of 0–30 day before the start dates are used. To analyze the influence of the initial conditions on the prediction ability of the model, the band-pass filtering (10–20 days) with the Butterworth filter (Murakami 1979) is conducted on both the wind and geopotential height fields. Moreover, the spatial correlation coefficient (SCC), root-mean-squared error (RMSE) and bias between the predictions and the observations are also computed to evaluate the prediction accuracy of the model for the extreme snowstorm event. In this study, the SCC and RMSE of accumulated precipitation are calculated over southern China (100°–122°E, 20°–35°N), which is the main precipitation area during the extreme event.

3 Results

3.1 Events accumulated precipitation

Studies have shown that the BCC_CSM has a certain prediction ability for the winter temperature and precipitation over most parts of the eastern China (Wu et al. 2016; Zhang et al. 2011), which has increased the confidence in predicting the extreme snowstorm event over southern China in early 2008 on the sub-seasonal timescale. The accumulated precipitation during the entire event has been evaluated in this study. Figure 1 shows the spatial distributions of observed and predicted precipitation at different lead times over southern China. Observed precipitation almost covers the entire southern China, and a northeast- southwest oriented rainbelt with a rainfall center larger than 100 mm is located in the southeastern coastal region (Fig. 1a). The spatial distribution of predicted precipitation at the 5-d lead time is consistent with observations, except that the spatial distribution of heavy precipitation (precipitation amount 30 mm) is slightly wider (Fig. 1b). Compared with the observation, the negative biases lower than − 30 mm are located in the coastal regions near the Yangtze estuary and in southern China. The pattern of forecasts at 10- and 15-d lead times are similar to observations, but the range of heavy precipitation shrinks, with the maximum precipitation being only 50 mm, the negative biases lower than − 30 mm are mostly located in the main rainbelt area (Fig. 1c, d). The forecasts at 20- and 25-d lead times show that the spatial range of heavy precipitation reduces to less than one fifth of the observation, and the maximum precipitation decreases to 30 mm, indicating a decline in the prediction ability of the model (Fig. 1e, f).

Fig. 1
figure 1

Spatial distributions of accumulated precipitation (mm) in southern China for January 10 to February 2, 2008, from observations a and predictions b–f at different lead times

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The correlation and RMSE between predictions and observations are also calculated to quantify the prediction accuracy of the BCC_CSM for the precipitation in this severe snowstorm event (Fig. 2). A skillful prediction is defined as that with a correlation coefficient greater than 0.5 (above the 95% confidence level). The predictability of precipitation during the entire snowstorm period can reach the lead time of 15 days (Fig. 2a). Meanwhile, the RMSE, which gradually decreases as the lead time shortens, is in the range of 20–37 mm at the lead time of 15 days (Fig. 2b).

Fig. 2
figure 2

Correlation (a) and root-mean-squared error (RMSE) (b) of the Beijing Climate Center Climate System Model (BCC_CSM) in snowstorm period with 1–25 d lead time

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3.2 Individual snowstorm episodes

The extreme snowstorm event in early 2008 is comprised of four major periods. To further investigate the model’s prediction ability on the sub-seasonal timescale, the spatial distributions of the accumulated precipitation for each period over southern China from both observations and predictions are given in Fig. 3. The first snowstorm occurred during January 10–16, 2008. It can be seen that a west–east main rainbelt is located in the middle and lower reaches of the Yangtze River, with a rainfall center larger than 30 mm (Fig. 3a). It has been revealed that the model can predict this rainbelt up to 15 days ahead, except that its position gradually moves southward with time and finally reaches the southeastern coastal area, and the negative biases are mainly located in the main rainbelt area, whereas the positive biases are along the coast of southern China (Fig. 3b–e). The precipitation pattern in the second period (January 18–22) is similar to that in the first one, but the rainfall center (maximum precipitation more than 50 mm) shifts southward (Fig. 3f). The location of the predicted rainbelt 10 days in advance is close to the observation, but the predicted precipitation is obviously weaker, and the negative biases are located in the main rainbelt area (Fig. 3g–j). In the third snowstorm period (January 25–29), the precipitation amount dramatically increases compared with that in the previous two periods, and the northeast-southwest oriented rainbelt moves from the Yangtze River Valley to southern China with a maximum precipitation center over 100 mm (Fig. 3k). The ability of the model to predict the main rainbelt is significantly better than that in the second period. The rainbelt predicted at the 5-d lead time is similar to the observation, except for the larger range. The regions with negative biases are in the southeastern coastal areas, whereas positive biases are distributed in most of other areas. The model can predict the rainbelts 10–20 days in advance, but the range of the rainbelts gradually reduces with the increasing lead time, and negative biases are mostly located in the main rainbelts (Fig. 3l–o). In the fourth snowstorm (January 30 to February 2), the observed rainfall pattern is similar to that in the third period but with a relatively smaller rainfall area, and the rainbelt shifts slightly northward (Fig. 3p). The model can predict the rainbelt with a lead time of nearly 10 days, but the range of the rainbelt is significantly smaller than that of the observation, and mostly negative biases in the main rain belts (Fig. 3q–t). Thus, there are obvious differences in the precipitation reproducibility for the four major periods, and the performance of the model in the first and third periods is significantly better than that in the second and fourth periods.

Fig. 3
figure 3

Spatial distributions of accumulated precipitation over southern China in four periods from observations (OBS) and predictions at different lead times

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Evaluation has also been carried out on the regional average precipitation over southern China (100°–122°E, 20°–35°N) in the four snowstorm periods (Fig. 4). The observed amounts of the regional average precipitation in the first and second periods are about 8 mm and 9 mm, respectively. The prediction results of the model present a regional average of about 6 mm in the first period 15 days in advance, while that is obviously weaker at the 20-d lead time with the regional average of only 3 mm. In the second period, the regional average precipitation predicted at the 5-d lead time is similar to the observation, however, it gradually reduces at longer lead times. In the third period, the regional average precipitation predicted at the 5-d lead time reaches 37 mm, which is more than the observation, however, it becomes obviously weaker with the increasing lead time. In the fourth period, the regional average precipitation predicted at the 10-d lead time is similar to that observed, with the value of about 7 mm, however, the predictions at 15- and 20-d lead times are significantly weaker, with a regional average of only 3 mm.

Fig. 4
figure 4

Regional average (100°–122°E, 20°–35°N) precipitation observed and predicted in four main snowstorm periods

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The correlation and RMSE between the prediction and the observation during the four snowstorm periods are also calculated (Fig. 5). Figure 5a shows that the prediction abilities in the four periods are 14, 10, 16, and 8 days in advance, respectively. Apparently, the model exhibits the higher prediction ability in the first and third periods, which is consistent with the conclusion from spatial distributions of the accumulated precipitation in the four periods (Fig. 3). The RMSE values in the four periods are all higher at longer lead times (Fig. 5b). Specifically, the RMSE values in the first and third periods are in the range of 7–16 mm, while those in the second and fourth periods are within 13–30 mm. The prediction error is obviously smaller during the periods with higher prediction skill.

Fig. 5
figure 5

Correlation (a) and RMSE (b) of the BCC_CSM model during four periods for 1–25 d lead time. Dashed horizontal line represents correlation equal to 0.5

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3.3 Evaluation of the atmospheric circulation for the extreme event

Large-scale circulations during this extreme event in early 2008 can be characterized by the persistent blocking situation over mid-high latitudes and the strong southwest airflow from the Bay of Bengal to southern China at low latitudes (Fig. 6). Under this circulation pattern, a stationary front forms due to the confluence of both the cold and warm air, thereby resulting in this extreme snowstorm event (Ding et al. 2008; Wen et al. 2009; Liao and Zhang 2013).

Fig. 6
figure 6

Observed (OBS) and predicted (at various lead times) 500 hPa height fields (contour lines, in gpm) and anomalies (shaded), 700 hPa wind vectors (in ms−1) and wind speed anomalies (shaded), during the whole snowstorm

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Figure 6a shows that the most evident characteristics of the large-scale circulations at 500 hPa are the Ural blocking high and the trough over Central Asia during the whole snowstorm, which is consistent with the conclusions of previous studies (Ding et al. 2008; Wen et al. 2009). The model can reproduce the blocking situation and the geopotential height anomaly at 500 hPa 10 days in advance, except that the ridge of the Ural blocking high shifts slightly westward (Fig. 6b, c). The predicted the blocking high and the trough over Central Asia are weaker than the observed ones at the 15-d lead time, whereas the blocking situation can not be predicted at the 20-d lead time (Fig. 6d, e). At 700 hPa, the wind speed anomalies at mid-high latitudes can be predicted up to 15 days ahead, however, the values of the anomaly centers are less than the observed ones, and the positive wind-speed anomaly in southern China cannot be predicted (Fig. 6f–i). The southwesterly over southern China can be predicted 10 days ahead, however, the forecasts at 15- and 20-d lead times show that the wind speed is weaker than the observation, which is obviously unfavorable for the precipitation (Fig. 6h–j). This can help explain why the prediction ability of the model for precipitation in southern China decreases gradually with the increasing lead time.

The atmospheric circulation patterns from observation and prediction in the four snowstorm periods are compared for more precise evaluation on the corresponding prediction ability of the model (Fig. 7). It is shown that the Ural blocking high and the trough over Central Asia over mid-high latitudes and the southwest airflow at low latitudes have persisted throughout the four periods, especially in the latter two periods, and the southwesterly east of 90°E at 700 hPa is particularly strong (Fig. 7a, d, g, j). In the four periods, the atmospheric circulation patterns predicted 5 days in advance are close to the observations (not shown). However, the blocking high cannot be predicted at 10- and 15-d lead times in the first period, meanwhile, the predicted the trough over Central Asia is weaker and its location shifts eastward with the increasing leading time (Fig. 7b, c), compared with the observation. The southwesterly over southern China can be predicted 15 days in advance, but the wind speed is weakened. In the second period, the atmospheric circulation patterns at the 10-d lead time are similar to the observation, however, at the lead times of 15 days, the blocking situation cannot be predicted, while the predicted wind speed over southern China at 700 hPa becomes rather small with the lead time increasing (Fig. 7e, f). During the third snowstorm, the geopotential height fields and wind fields can be predicted 15 days in advance, except that the wind speed over southern China gradually decreases with time (Fig. 7h, i). In the fourth snowstorm, the geopotential height fields and wind fields at the 10-d lead time are similar to the observation, except that the simulated the Ural blocking high intensity is stronger while the simulated southwesterly over southern China is weaker (Fig. 7k). For 15-d lead times, the geopotential height fields are quite different from the observation, and the wind speed over southern China is obviously lower (Fig. 7l). The fact that the predictions of the atmospheric circulation in the first and third snowstorms are significantly better than those in the second and fourth snowstorms, further confirms the better predictability of the precipitation in the first and third periods.

Fig. 7
figure 7

Observed (OBS) and predicted 500 hPa geopotential height (contour lines, in gpm) and 700 hPa wind fields (in ms−1) at different lead times during the four periods

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The large-scale atmospheric circulation has provided a favorable background, under which the convergence of the cold and warm air over southern China is closely related to this extreme event. The northerly wind is strong in the lower and middle troposphere and reaches about 10°N before the occurrence of snowstorms. However, the intensity of cold air gradually weakens and withdraws back to nearly 30°N during the snowstorm period. Meanwhile, abundant water vapor has been transported by the strong southwesterly low-level jet stream from the Bay of Bengal to southern China (Ding et al. 2008; Wen et al. 2009). This situation is favorable for the formation and maintenance of the stationary front. Following Liao and Zhang (2013), the regional averaged values [(100°–120°E, 30°–60°N) and (100°–120°E, 10°–30°N)] of V700 are defined as the index of cold-air (I-CD) and warm-air (I-WM), respectively. The variations of I-CD and I-WM during the snowstorm period are displayed in Fig. 8. The I-CD value is 3.2 ms−1 during the period of the severe snow storms from 10 January to 2 February 2008. The predicted I-CD values at different lead times are higher than the observation (Fig. 8a). On the other hand, the I-WM value is 3.57 ms−1 during the extreme event, the predicted intensity of the warm-air becomes weaker with the longer leading time (Fig. 8b), which leads to a weak precipitation prediction in southern China.

Fig. 8
figure 8

Variation of index of cold-air activity (I-CD) a and index of warm-air activity (I-WM) b during snowstorm period

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The forecasts of the cold- and warm-air activities during each sub-period at different lead times are also compared with the observation (Fig. 9). The I-CD value during the first snowstorm is 4.03 ms−1, the predicted cold air intensity at 10- and 15-d lead times is weaker than observation, and stronger than that at 5- and 20-d lead times. In the last three snowstorms, the I-CD values predicted are stronger than the observation, except for that at the 10-d lead time in the fourth period (Fig. 9a). However, the predicted warm air intensity for all lead times is weaker than the observed value (Fig. 9b), which is the main reason for less precipitation predicted by the model. In addition, it is found that the predicted warm air intensity in the first period is closer to the observation than that in the second period. The model also captures the sudden increase of the warm air intensity at the 5–15 d lead times in the third period, but the predicted value is relatively weaker. In the fourth period, the biases of the predicted warm air intensity increase significantly at 15- and 20-d lead times. The difference of the model’s ability to predict the cold- and warm-air activity is one reason for the better performance of the precipitation prediction in the first and third periods of this extreme event. It is found that no matter how the predictability of cold air is, as long as there is a significant difference in the predictability of the warm air, it will definitely lead to the difference in precipitation prediction skill of the model. This may be attributed to the fact that the cold air conditions are easy to meet in winter, and the precipitation would occur under suitable warm air conditions. Therefore, it is very important to improve the prediction skill of the warm air activity.

Fig. 9
figure 9

Variation of index of cold-air activity (I-CD) a and index of warm-air activity (I-WM) b in the four sub-periods

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4 Influence of the initial conditions on the sub-seasonal prediction of the extreme event

The memory of the model to the initial conditions is the primary source of the predictability for medium-range weather forecasts (2 weeks; Lorenz 1975). Recently, researches have revealed that the low-frequency processes in the climate system are extremely valuable in providing useful information that strongly influences the lead times of the S2S forecast (Fu et al. 2011; Zhang et al. 2014). To explain the decline of the prediction skill with time in this extreme event, analyses have been conducted on the influences of initial conditions on the sub-seasonal prediction from four aspects: persistent atmospheric circulation systems, SST, MJO and the AO signals. Since the evolution of these four signals with time is almost the same in the whole snowstorm event and sub-periods, the following analysis takes the whole event as an example.

4.1 Analysis of persistent atmospheric circulation systems

The persistent atmospheric circulation systems that affect the extreme event are obtained by the band-pass filtering. The most obvious atmospheric circulation systems of 500 hPa at the initial time (10 January 2008) are the Ural blocking high and the trough over Central Asia (Fig. 10a), this configuration persists throughout the snowstorm event. The anomaly center of the Ural blocking high (about 16 gpm) is stronger than that of the trough over Central Asia (about 14 gpm). It is found that these two systems persist in forecast period and the persistent circulation anomalies could also be accurately predicted by the model, except for the fact that the intensities of the predicted systems vary slightly with the forecast time (Fig. 10b–f). Meanwhile, the most obvious feature of the wind field at 700 hPa under the initial condition is the strong southwest airflow from the Bay of Bengal to southern China at low latitudes (Fig. 11a). This airflow is one of the key factors for the occurrence of the extreme snowstorms in early 2008, which is produced in the model, however, the predicted wind speed is weaker than the observation (Fig. 11b–f).

Fig. 10
figure 10

The height fields (contour) and abnormal fields (shadow) at 500 hPa by band-pass filtering at initial time (10 January 2008, OBS) and prediction periods during the extreme snowstorm

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Fig. 11
figure 11

The wind fields (arrows) and abnormal fields (shadow) at 700 hPa by band-pass filtering at initial time (10 January 2008, OBS) and prediction periods during the extreme snowstorm

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To quantitatively assess the prediction ability of the model for these persistent atmospheric circulation systems during this extreme event, the spatial correlation between the prediction and the observation is calculated, and the selected regions for the three systems are as follows: the 500 hPa Urals high (60°–90°E, 50°–80°N), the trough over Central Asia (40°–70°E, 30°–50°N) and the 700 hPa southwest airflow (80°–100°E, 10°–30°E) (Fig. 12). It is shown that the prediction ability of the model for the Ural blocking high and the trough over Central Asia can reach 24 and 22 days, respectively. The prediction skill of the 700 hPa southwesterly is relatively low, but the correlation is within the range of 0.3–0.5 for the 15-d lead time (significant at the confidence level of 95%).

Fig. 12
figure 12

Correlation skill between prediction and observation of three persistent atmospheric circulation systems during the extreme event within 24-d forecast period. (SW southwest airflow, TCA trough over Central Asia, UH Urals high)

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4.2 Analysis of the MJO

MJO is a well-known phenomenon prevailing in the tropics with significant intra-seasonal variability, and it is thought to be a major source of sub-seasonal predictability of tropical and extratropical climate (Waliser et al. 2003). Using the hindcast experiments outputs from 1994 to 2013, the capability of BCC_CSM model in forecasting MJO is evaluated, MJO forecast skill is about 16 days (Liu et al. 2017). Compared to the observations, the forecasts reproduce MJO’s main characteristics such as intensity, structure and propagation, however, the errors in these features become pronounced gradually as the lead time increases. During the extreme snowstorm in early 2008, the center of MJO activity is mainly in phase 7 during the first two periods of this extreme event, in phase 2 during the third period and in phase 3 during the fourth period. Wen et al. (2009) found that the winter precipitation over southeastern China increased significantly when the MJO was in phase 2–3. According to the analysis, there is no systematically eastward propagation of the convective activity at the initial condition in the first two periods (January 10–22). However, the eastward propagating signal becomes obvious after January 20 and reaches 120°E in early February (Fig. 13a). The result is consistent with Zhang et al. (2008). The eastward propagation of MJO convection can deepen the low trough of the Bay of Bengal, strengthen the southwest airflow in front of the trough, and thus leads to the increase of precipitation in the east of China (Ding et al. 2008; He et al. 2019). The model shows a good performance in predicting the convective activity in the range of 40°–60°E, but fails in predicting the corresponding systematically eastward propagation of this convective activity in the latter two periods (Fig. 13b). This may be related to the ability of model to predict MJO. Eastward propagation occurs after January 20, which is 10 days earlier from the initial date (January 10) and close to the upper limit of the MJO forecast skill.

Fig. 13
figure 13

Longitude-time section of geopotential height anomalies (in gpm) at 700 hPa along 25°N averaged from January 10 to February 4, 2008. a Observation. b Forecast

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4.3 Analysis of the arctic oscillation

The Arctic Oscillation (AO) is an annular atmospheric circulation pattern and the most dominant atmospheric fluctuation in the Northern Hemisphere in boreal winter. The AO has been abnormally active since January of 2008, and its index changes from negative to positive phase on January 15 and maintain this phase until the early February (Fig. 14c). Wang et al. (2008a, b, c) found that the positive AO is conducive to the maintenance of the blocking situation in this extreme snowstorm event. The positive AO strengthens the anomaly of polar-low, resulting in the southerly wind anomaly at low latitudes, which can enhance the warm and humid airflow over southern China. Following the previous studies (Wang et al. 2008a, b, c; Ding et al. 2008), the regional averaged (65°–90°N, 0–180°E) values of the normalized geopotential height anomalies can approximately represent the evolution of AO index. Using this method, we draw Fig. 14. Figure 14a shows that the anomaly of the geopotential height between 500 and 100 hPa changes from positive to negative on January 15 in the polar region, which corresponds to the phase transition of the AO index from negative to positive. The geopotential height anomaly maintains negative till January 30, then changes into positive anomaly in early February. This change is basically consistent with the variation of AO index, except for the difference in early February. The model made a successful performance in predicting the geopotential height anomaly in the polar region (Fig. 14b), which means that the model can well predict the change of the AO index, thus reproduce the circulation situation at mid-high latitudes in this extreme event.

Fig. 14
figure 14

Normalized geopotential-height (GPH) anomalies within range 65°–90°N at different constant-pressure levels from January 10 to February 2, 2008. (a) OBS. (b) Forecast. (c) Normalized Arctic Oscillation (AO) index (https://www.cpc.noaa.gov)

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4.4 Analysis of SST

Huang et al. (2013) indicated that the BCC model forced by real SST well reproduced the snowstorm event over southern China in early 2008, including the distribution of precipitation and the atmospheric circulations. When the SST bias is more than 0.5 °C, the simulated atmospheric circulation is quite different from the actual one, especially in the south westerly airflow over southern China. Although it is not known whether the SST bias is a cause or effect of the bias in south westerly airflow, the correct SST simulation is an important condition for successful prediction of extreme event in early 2008. Figure 15 shows the mean SST biases over the whole period (10th January–2nd February) predicted by the model at different lead times. It is found that the areas with the SST bias over 0.5 °C cover most of the Pacific region north of the equator, while those with more than 1.5 °C are mainly located in the northwestern Pacific and north American coast (Fig. 15a). Moreover, the positive and negative biases in the tropical central eastern Pacific exist simultaneously at the 5–15 days leadtime (Fig. 15b–d). The range of SST biases expands with the increasing lead time, indicating the decline of the model’s ability to predict the sea temperature. Following Huang et al. (2013), SST bias can lead to a decline in the ability of the model to predict atmospheric circulation, and finally affects the predictability to this extreme event.

Fig. 15
figure 15

Sea surface temperature (in k) bias at different lead times during the extreme snowstorm

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5 Conclusions and discussion

In this study, investigations were conducted on the ability of BCC_CSM for sub-seasonal predictions of the precipitation and the atmospheric circulation in the extreme snowstorm event over southern China in early 2008. It reveals that the model can predict the spatial distribution of precipitation in this extreme event 15 days in advance. For the four periods of the snowstorm event, the prediction ability of the model is 14, 10, 16 and 8 days in advance, respectively. By comparisons, the prediction skills are slightly higher in the first and third periods. Moreover, the analyses of correlation, bias, and RMSE all quantitatively support the above conclusions. However, the predicted precipitation is less than the observation, especially in the main rainbelt regions, resulting in smaller ranges of the main rainbelts.

The prediction accuracy is further analyzed in forecasting the atmospheric circulation and associated cold- and warm-air activities during this extreme snowstorm event. The results show that the blocking situation at 500 hPa over mid-high latitudes and the southwesterly in front of the Bay of Bengal trough at 700 hPa at low latitudes can be predicted 15 days in advance. In each period, the predictability of the atmospheric circulation is basically consistent with that of the precipitation. The atmospheric circulation provides a large-scale background for the extreme event, under which the direct factor leading to the generation of this snowstorm event is the convergence of the cold and warm air over southern China. Therefore, the cold- and warm-air indexes are identified for comparing the predictions with observations. It is found that the predicted cold air is stronger while the warm air is weaker compared with the observation. The forecast biases of the cold and warm air increase gradually with the lead time, especially for the warm air, which lead to decline in the prediction ability and underestimation of precipitation. The bias of warm air flow mainly comes from two aspects: one is that the model prediction skill for warm air is low, the other is that the prediction ability of some regional anomalous signals that affect the intensity of warm air is weak, such as MJO and SST. The predictability of the atmospheric circulation and the prediction accuracy of precipitation in the first and third periods are relatively higher than those in the second and fourth periods. In addition, the predictability of the cold air has little influence on the prediction skill of precipitation, but the warm air is a key factor for precipitation. Therefore, the prediction skill of warm air is important for improving the ability of the model to predict the precipitation in winter to a certain extent.

Finally, the influences of the persistent circulation systems on the sub-seasonal prediction for this extreme snowstorm event are analyzed. It is found that the Ural blocking high, the trough over Central Asia and the southwest airflow at low latitudes are the most obvious persistent circulation systems in the initial conditions. These systems persist during the forecast period. The model can retain signals of the Ural blocking high and the trough over Central Asia for more than 20 days while the southwesterly signal for about 15 days in the forecast period. As the BCC_CSM exhibited a good performance in the prediction ability for the persistent circulation systems, it is able to predict the precipitation of this extreme event 15 days in advance. It is also found that the low-frequency signals, such as AO and MJO, can cause atmospheric circulation anomalies in this extreme snowstorm event. The AO index changes from the negative to positive phase on January 15, and its intensity continue to increase thereafter, which is conducive to maintaining the blocking situation during the extreme snowstorm event in early 2008. The phase change of the AO index can be predicted very well in the model, so the evolution of the atmospheric circulation at mid-high latitudes can also be accurately predicted. The eastward propagation of MJO convection in the tropics is evident during the last two snowstorms of this extreme event, but the model fails in predicting this eastward propagating signal, therefore the predicted southwest airflow is weakened, eventually affecting the prediction ability of the model for this event.

In this study, we have mainly evaluated the sub-seasonal prediction ability for an extreme snowstorm event over China. The results have revealed that the BCC_CSM can predict the extreme snowstorm events up to two weeks in advance, which indicates that the model has a certain prediction ability for the extreme event. It is found that the model has high prediction ability for the atmospheric circulation systems over mid-high latitudes but poor prediction ability for southwest airflow at low latitudes. The variation of the AO index can be reproduced very well, but the eastward propagating signal of MJO cannot be produced. The MJO has global impacts that depend on its amplitude and phase, including modulation of tropical cyclone activity (Lee et al. 2018; Zhao et al. 2019) and extratropical phenomena such as the East Asian summer monsoon (Li et al. 2018). Therefore, it is necessary to improve the prediction skill of the model for MJO. These conclusions can provide some valuable information for the further development of sub-seasonal forecasting systems. However, it should also be noted that there are many factors affecting this extreme event, which cannot be covered in this study. For example, the Middle East jet stream, which intensifies and shifts southeastward, also plays a role in maintaining the atmospheric circulation anomaly during this extreme event (Wen et al. 2009). Another example is that the concurrent variation between the subtropical jet stream and the polar-front jet stream acts as an important bridge between the snowstorm and the anomalous atmospheric signals associated with the cold- and warm-air activities (Liao and Zhang 2013). Recent studies have shown that the SST anomalies in the tropical central eastern Pacific force the negative upper-level geopotential height anomalies over the Middle East, which push the subtropical jet stream southward during La Nina year (Kang et al. 2015; Ehsan et al. 2017). Variations in the subtropical jet stream during the period of the extreme event in early 2008, which occurred in La Nina year, also need further discussion. In terms of the prediction ability of BCC_CSM for other impact factors, further analyses are required. Furthermore, to evaluate the ability of the model for sub-seasonal prediction with only one case is insufficient, but more cases are required in the future work.