Jian RAO,Rongcai REN,Haishan CHEN,Xiangwen LIU,Yueyue YU,and Yang YANG

1Key Laboratory of Meteorological Disaster,Ministry of Education/Joint International Research Laboratory of Climate and Environment Change/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters,Nanjing University of Information Science and Technology,Nanjing 210044,China

2State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,China

3Climate Model Division,National Climate Center,China Meteorological Administration,Beijing 100081,China

4Institute of Urban Meteorology,China Meteorological Administration,Beijing 100089,China

5Fredy and Nadine Herrmann Institute of Earth Sciences,The Hebrew University of Jerusalem,Edmond J.Safra Campus,Givat Ram Jerusalem 91904,Israel

ABSTRACT This study focuses on model predictive skill with respect to stratospheric sudden warming(SSW)events by comparing the hindcast results of BCC CSM1.1(m)with those of the ECMWF’s model under the sub-seasonal to seasonal prediction project of the World Weather Research Program and World Climate Research Program.When the hindcasts are initiated less than two weeks before SSW onset,BCC CSM and ECMWF show comparable predictive skill in terms of the temporal evolution of the stratospheric circumpolar westerlies and polar temperature up to 30 days after SSW onset.However,with earlier hindcast initialization,the predictive skill of BCC CSM gradually decreases,and the reproduced maximum circulation anomalies in the hindcasts initiated four weeks before SSW onset replicate only 10%of the circulation anomaly intensities in observations.The earliest successful prediction of the breakdown of the stratospheric polar vortex accompanying SSW onset for BCC CSM(ECMWF)is the hindcast initiated two(three)weeks earlier.The predictive skills of both models during SSW winters are always higher than that during non-SSW winters,in relation to the successfully captured tropospheric precursors and the associated upward propagation of planetary waves by the model initializations.To narrow the gap in SSW predictive skill between BCC CSM and ECMWF,ensemble forecasts and error corrections are performed with BCC CSM.The SSW predictive skill in the ensemble hindcasts and the error corrections are improved compared with the previous control forecasts.

Key words:sub-seasonal to seasonal(S2S)hindcast,stratospheric sudden warming,BCC CSM,ensemble forecast,error correction

1.Introduction

Weather forecasting mainly focuses on synoptic weather conditions within two weeks,whereas climate prediction is mainly concerned with climate conditions beyond one or two months.A time gap exists in the prediction of circulation betweenthesetwotimescales(Hurrelletal.,2009;Brunetetal.,2010),which is the so-called sub-seasonal to seasonal(S2S)time scale.S2S time-scale prediction is still a great challenge for both the research and the operational communities,because it is beyond the extended range of weather forecasting that can be realized mainly based on the atmospheric“memory”of initial conditions and is also out of the time range of climate prediction in which the influence of boundary conditions can be included.The influence of both the initial conditions and the boundary forcing needs to be considered in S2S predictions(Vitart et al.,2017).Sub-seasonal forecasts are of particular importance for society and economies because of their critically determinative value for proactive disaster mitigation.In recent years,with improvements in the description of boundary conditions(e.g.,resolutions and parameterized processes)and their interactions with the atmosphere,as well as that of initial conditions in numerical models,the skill of seasonal forecasts has improved significantly(Kug et al.,2008;Kim et al.,2012;Jiang et al.,2013a,b;Zhu and Shukla,2013;Yang and Jiang,2014).

In 2013,the World Climate Research Program and the World Weather Research Program initiated an S2S prediction project to bridge the gap between weather forecasts and climate predictions(Hurrell et al.,2009;Brunet et al.,2010;Liu et al.,2017).There are 11 operational centers or research institutes providing S2S hindcast products,which are collected by the European Centre for Medium-Range Weather Forecasts(ECMWF;http://apps.ecmwf.int/datasets/data/s2s/)and China Meteorological Administration(CMA;http://s2s.cma.cn/dataset/)(Vitart et al.,2017).

The latest research has identified several important potential sources of S2S time-scale predictability,with a special emphasis on stratosphere–troposphere interactions(Vitart et al.,2017).There seems to be a consensus that the stratospheric variability contributes largely to the tropospheric predictability in the extratropics and that stratosphere-resolving numeral weather forecast systems might improve weather forecasts(Smith et al.,2012;Tripathi et al.,2015,2016).Ample evidence already indicates the possible application prospects of the stratosphere,because stratospheric processes evolve much slower than those in the troposphere(Ren and Cai,2007;Rao et al.,2015;Yu et al.,2015;Hu et al.,2017).Perturbations in the troposphere can act as a potential source for stratospheric changes by modulating planetary wave activity,the circumpolar westerly,and the polar vortex in the stratosphere(e.g.,Rao and Ren,2016c,2017;Ren et al.,2017).However,the signals of the stratospheric change related to the stratospheric northern annular mode(Baldwin and Dunkerton,1999),the polar vortex oscillation(Cai and Ren,2006;Ren and Cai,2007),or stratospheric sudden warming(SSW)events(Charlton and Polvani,2007;Hu et al.,2014),can propagate downward and influence tropospheric circulation.The occurrence of SSW events is one of the most distinct and radical troposphere–stratosphere coupling phenomena,and the effects of SSW events on tropospheric circulation usually persist for several weeks(Baldwin and Dunkerton,2001;Polvani and Waugh,2004;Ren and Cai,2007;Rao et al.,2015).

Understanding and producing reliable predictions of extreme stratospheric events is of vital importance,since the signal from the middle atmosphere is one of the main sources for the S2S predictability of the extratropical climate(Yu et al.,2015;Cai et al.,2016).Fortunately,the variability of the northern winter stratospheric polar vortex,the stratosphere–troposphere interaction,and even the stratospheric Quasi-Biennial Oscillation–like circulation variation,can be represented or reproduced by an increasing number of state-of-theart climate models(Wu et al.,2014;Rao et al.,2015;Ren et al.,2017).

After participating in phase 5 of the Coupled Model Intercomparison Project(Taylor et al.,2012;Rao et al.,2015;Liu et al.,2017),the Beijing Climate Center Climate System Model(BCC CSM;Wu et al.,2014;Liu et al.,2017)has changed from 26 levels to 40 levels in the atmosphere and has been used to conduct comprehensive S2S hindcast experiments.Based on the fact that the stratosphere is a vitally important source for S2S prediction in the troposphere,the present study focuses on the prediction skill of the BCC model in the stratosphere—in particular,the model’s skill in forecasting stratospheric extreme events,such as SSW events.Using parallel comparisons of its S2S products with those of the ECMWF’s model(hereafter referred to simply as ECMWF),we also propose possible approaches to improving the prediction skill of BCC CSM.

Following this introduction,the remainder of the paper is designed as follows:Section 2 introduces the data,model and methods employed in the study.Section 3 presents a parallel comparison of SSW events in the BCC CSM and ECMWF S2S hindcast systems.Section 4 provides ensemble prediction and error correction results for SSW events.A summary and discussion are provided in section 5.

2.Model,data and methods

2.1.Model description and S2S experimental design

The moderate-resolution version of BCC CSM[BCC CSM1.1(m)]has been used in seasonal prediction,exhibiting reliable performance(Liu et al.,2017).This moderateresolution version of BCC CSM is used to conduct the S2S prediction in this study.The atmospheric component of this model is BCC AGCM,version 2,which uses the T106 horizontal resolution and has 40 levels in the vertical direction(Wu et al.,2010,2014).The land component of BCC CSM is the Atmosphere and Vegetation Interaction Model,version 1.0,with the T106 horizontal resolution(Ji et al.,2008).The ocean component uses the Modular Ocean Model,version 4(Griffies et al.,2005),and the sea-ice component is the GFDL Sea Ice Simulator(Winton,2000).The ocean and seaice components have a tripolar horizontal grid,with the resolution changing from 1°×1°at the poles to 1°×1/3°at the equator.The length of the BCC CSM sub-seasonal forecast is 60 days.For a comparison with BCC CSM,the ECMWF sub-seasonalintegrationsarealsoused.Thelengthofthesubseasonal forecast for this model has increased from 32 to 46 days since May 2015.More details about the ECMWF model can be found in Vitart(2014)and references therein.

The S2S hindcast is performed by BCC CSM every day from January 1994 to December 2014.Every hindcast experiment is continuously integrated for 60 days.The atmospheric initialfields are from the six-hourly(four times daily)data of NCEP-1(Kalnay et al.,1996).The atmospheric initialization uses a fast nudging strategy(Jie et al.,2014;Liu et al.,2017).The BCC Global Ocean Data Assimilation System assimilates multi-source observational data(Zhou et al.,2016)and provides oceanic initialfields for the S2S experiments.No land and sea-ice initializations are performed.

To reduce the uncertainty in the initialfields,every hindcast experiment also uses an ensemble running scheme with a six-hour interval of atmospheric initial conditions ahead.Taking the forecast on 1 August as an example,the initial conditions at 0000 UTC 1 August,1800 UTC 31 July,1200 UTC 31 July,and 0600 UTC 31 July,are used for each of the four ensemble members,respectively.Thefirst hindcast member initiated at 0000 UTC on the hindcast day is denoted as the control hindcast,and the other three initiated at 1800,1200,and 0600 UTC on the previous day are denoted as the perturbed hindcast.Unless stated otherwise,this study mainly assesses the control hindcast.

2.2.Reanalysis and model data

Because the atmospheric initializations use NCEP-1(Kalnay et al.,1996),this reanalysis dataset is used to represent the real atmosphere in the observations.The prediction skill of the stratospheric circulation in BCC CSM is calculated using this reanalysis.ERA-Interim(Dee et al.,2011)is also used,and wefind that the results are insensitive to the choice of data criteria.To compare the prediction skill in different models,the control hindcast from ECMWFisalsoassessed.Becauseahindcastfromthismodel is performed twice a week in the last 20 years relative to 2015,2016 and 2017—for example,in 2015/2016/2017,the model version was updated and the hindcast was performed twice a week from 1 January 1995/1996/1997 to 31 December 2014/2015/2016—we mainly focus on the common period(1995–2014).We have assumed that the effect of the ECMWF model version update can be negligible.All hindcasts considered,the ECMWF model has an equivalent frequencyof six(6=2 times weekly in 2015,2016,and 2017×3 years)times weekly.This study mainly assesses the hindcasts initialized 0–4 weeks before the SSW onset dates,which are all available from BCC CSM.Three SSW events(February 2007,January 2009,and January 2013)did not onset on the hindcast initialization dates,so hindcasts initialized one day earlier are considered as the D-0,D-7,D-14,D-21,and D-28 forecasts.The ECMWF initialization time for the 11 SSW events is listed in Table S1 in electronic supplementary material.

2.3.Methods

An SSW is defined when the westerly winds at 60°N and 10 hPa reverse direction and become easterly,and the meridional temperature gradients at 10 hPa change sign from 60°N to the North Pole(Charlton and Polvani,2007;Hu et al.,2014).When an SSW occurs in the polar stratosphere,the polar vortex is completely disrupted:the vortex is either split into two separate vortices or displaced from the North Pole.We mainly focus on major SSW events with a more radical circulation change.

It has been reported that extratropical stratospheric warming is preceded by the western Pacific(WP)Oscillation(Dai and Tan,2016)and the Pacific–North America(PNA)teleconnection(Hu et al.,2017;Ren et al.,2017;Rao and Ren,2018).Large zonal mean circulation anomalies associated with SSW descend from the stratosphere to the upper troposphere and are followed by a negative tropospheric North Atlantic Oscillation(NAO;Baldwin and Dunkerton,1999;2001).To analyze the tropospheric precursor and “follower”,we calculate several teleconnection indices,including for the WP,the PNA,and the NAO.Their definitions(Wallace and Gutzler,1981)are as follows:

In in Eqs.(1)–(3),Z is the height anomaly and the subscript is the latitude(°N)and longitude(°E,°W).We also use the two-dimensional Eliassen–Palm(EP)flux and its divergence in spherical coordinates to diagnose the propagation of planetary waves(Andrews et al.,1987).

To improve the prediction skill from the forecast outputs,adirecterrorcorrectionmethodisappliedforwinter(December,January,February,and March)hindcasts in this study.The mean squared error between model predictions and observations can be expressed as

where i is the prediction index sorted by hindcast dates chronologically,Oiis the observation,Siis the model prediction,andis the corrected prediction.Namely,both Oiand Siare the same variable,but the former is taken from observations and the latter from model predictions.Thefirst term on the right-hand-side of Eq.(4),,is the systematic error determined by the model performance.The second term,,is the random error.For simplicity,the least squares method is adopted to construct the relationship between the corrected prediction()and the observation(Oi)on a linear assumption(a is the slope and b is the intercept).

3.Parallelcomparison ofS2S hindcasts of SSW events between BCC CSM and ECMWF

3.1.Observations

There are 11 SSW events during 1995–2014 in the NCEP-1 reanalysis:15 December 1998,25 February 1999,16 February 2001,7 January 2004,21 January 2006,24 February 2007,22 February 2008,24 January 2009,9 February 2010,24 March 2010,and 6 January 2013.Based on the composite result of 11 major SSWs relative to the onset day(i.e.,day 0)during 1995–2014(e.g.,Charlton and Polvani,2007;Hu et al.,2014),the circumpolar westerlies in the upper stratosphere reverse to easterlies(Fig.1a),and the westerlies in the lower stratosphere are also greatly decelerated after SSW onsets.Based on the evolution of the circumpolar wind anomalies,the easterly anomalies form on day-12,and reach maxima on day 3(-30 m s-1;Fig.1a).In contrast,stronger circumpolar westerly anomalies are observed before day-15(8 m s-1).According to the principle of the thermal wind balance,the stratospheric polar cap warms suddenly after day-5(212 K)and reaches its warmest temperature(232 K)on day 2,with an abrupt increase of 20 K in one week(Fig.1b).Accordingly,positive anomalies of the polar cap temperature begin to form on day-12 and reach maxima on day 3(18 K).

After SSW onset,the stratospheric circulation and temperature signals show remarkable downward propagation.For example,the 8 m s-1isotach in Fig.1a and the 220 K isotherm in Fig.1b are located in the upper stratosphere(10 hPa)on day-4 and gradually descend,reaching 200 hPa on day 10.The downward-propagating signals can be more clearly verified by the circulation and temperature anomalies(contours in Fig.1).

Fig.1.(a)Composite pressure–time evolution of the zonal mean zonal wind(uwnd,shadings;units:m s-1)at 60°N and its anomaly(contours;units:m s-1;interval:2)from day-30 to day 30 relative to the SSW onset date in NCEP-1.(b)As in(a)but for the polar cap temperature(shading;units:K)areaaveraged over 60°–90°N and its anomaly(contours;units:K;interval:2).

Figure 2 displays the composite evolution of the 10-day running mean temperature(shading)and its anomalies(contours)at 50-hPa during SSW onset in the observations.The stratospheric polar vortex is anomalously cold on day-25 to-15(-6 K),and southern Alaska and western Canada are covered by an initiation of warm anomalies(1 K;Fig.2a).As the polar cold center deviates from the pole to Eurasia on day-15 to-5(Fig.2b),a wavenumber-1 pattern of temperature forms in the mid-to-high latitudes,with a cold center(-4 K)over Arctic Eurasia and a warm center(4 K)over Arctic Canada.The strengthened warm anomaly(12 K)arrives over the North Pole(Fig.2c),with the stratospheric polar vortex collapsing and largely deviating from the North Pole on day-5 to 5.As warm anomalies intensify(16 K)and expand over the Arctic(Fig.2d),the cold center disappears,indicating a complete breakdown of the stratospheric polar vortex on day 5 to 15.In addition to the stratospheric warming over the Arctic,the midlatitude stratosphere is anomalously cold following SSW onset(-2 K).The positive temperature anomalies in the extratropical stratosphere can last for several weeks(14 K;Fig.2e),accompanied by persistent reversed meridional temperature gradients.Next,we assess the prediction skill of the two models based on the evolution of circulation and temperature during SSW events in the observations.

3.2.SSW hindcasts from BCC CSM and ECMWF

The hindcasts initialized at different lead times relative to SSW onset dates from the two models are compared.In Figs.3 and 4,the circulation and temperaturefields before the initialization time are shown as blank.Comparing BCC CSM and ECMWF in Figs.3 and 4(shading),we can see that the evolutionofthecircumpolarwesterliesandthepolarcaptemperatures are fairly realistically predicted by both BCC CSM and ECMWF when the initialization time is set on the SSW onset day(labeled as D-0;Figs.3a and 4a)or one week earlier(labeled as D-7;Figs.3b and 4b).Specifically,as in the observations(Fig.1),the maximum easterly anomalies occur at 10 hPa on day 3 in the D-0 and D-7 hindcasts.Furthermore,the observed easterlies in the upper stratosphere during days 0–12 only persist for approximately 8(10)days in BCC CSM(ECMWF).In other words,the predicted westerlies are biased to recover more rapidly in the D-0 hindcasts(Fig.3a).If the initialization time is set earlier,i.e.,one to four weeks before SSW onset(labeled as D-7,D-14,D-21,and D-28;Figs.3b–3e),the circumpolar easterly anomalies are not predicted to be large enough to reverse the polar night jet(Figs.3b–e).

In the D-0 and D-7 hindcasts,the evolution of the circumpolar wind anomaly(contours)after SSW onset is successfully reproduced by both BCC CSM and ECMWF(Figs.3a and b).Although the polar jet does not reverse to easterlyflow in the D-7 hindcast by BCC CSM,the westerlies are fairly close to zero on days 0–5(Fig.3b1).In the D-14 hindcast,the prediction skill of BCC CSM becomes lower than that of ECMWF(Fig.3c).The maximum easterly anomaly in the observations can be as large as-30 m s-1,while that in the D-14 hindcast is-4 m s-1(Fig.3c1)and-22 m s-1(Fig.3c2;Tripathi et al.,2016).As a result,BCC CSM only repro-duces 13%of the maximum anomalies in the D-14 hindcast,while ECMWF reproduces 73%of the observational anomalies.

Fig.2.Composite 50-hPa temperature(shading;units:K)and its anomaly(contours;units:K;interval:2)during(a)day-25 to-15,(b)day-15 to-5,(c)day-5 to 5,(d)day 5 to 15,and(e)day 15 to 25,relative to the onset of SSW events in NCEP-1.

The prediction skill decreases rapidly once the initialization time isfixed more than two weeks before SSW onset(Figs.3d and e).The circumpolar westerlies are still fairly strong on days 0–10 in both BCC CSM(Figs.3d1 and e1)and ECMWF(Figs.3d2 and e2).However,the sign of the anomalous wind in both BCC CSM and ECMWF is successfully predicted(Figs.3d and e).The maximum easterly anomalies on days 0–10 can be as large as-4 m s-1(-10 m s-1)in BCC CSM(ECMWF),reproducing only 13%(33%)of the total easterly anomalies in the observations.

An SSW is always characterized by rapid warming of the stratospheric polar cap.Similar to that of circumpolar wind,the evolution of polar cap temperature is most accuratelypredictedin theD-0,D-7 andD-14 hindcasts(Figs.4a–c).Specifically,as in the observations,the predicted Arctic stratosphere warms up to 228–232 K(shading)at 10 hPa on day 2 in the D-0 and D-7 hindcasts(Figs.4a and b).The polar cap temperature anomalies(contours)reach maxima(12–16 K)at 10 hPa on day 2,and then the warm center gradually descends as the central value(e.g.,8–16 K isotherms)gradually diminishes.The warm anomalies develop fairly deep(e.g.,500–200 hPa)into the Arctic troposphere,exhibiting downward propagation.In the D-14 hindcast,the maximum temperature anomaly predicted by BCC CSM is only 4 K(Fig.4c1),whereas that reproduced by ECMWF is as high as 12 K(Fig.4c2).Compared with the warm anomalies that can reach as high as 18 K in the observations(Fig.2),22%(67%)of the total anomalies are reproduced by BCC CSM(ECMWF).

In the D-21 and D-28 hindcasts,the polar warm center occurring on day 2 is also not realistically reproduced by BCC CSM and ECMWF(Figs.4d and e).Compared with ECMWF,the initial information in the Arctic stratosphere is excessively “memorized”by BCC CSM.For example,the anomalously stronger polar vortex on days-30 to-20 in the observations is seldom disturbed in the D-21 and D-28 hindcasts,and the polar warming on day-5 is barely predicted.Fortunately,the sign of the warm anomalies in the Arctic stratosphere is reproduced well by both models.The maximum warm anomalies are only 2 K(8 K)in the Arctic upper stratosphere on day 2 in BCC CSM(ECMWF),which is about 11%(44%)of that in the observations.

Figures 5 and 6 present the evolutions of the 50-hPa temperature distribution in different hindcasts to clearly demonstratethepredictionofstratospherictemperatureduringSSW.The earlier the initialization time is,the stronger the Arctic stratospheric cold center on days-5 to 5 is predicted by BCC CSM(Fig.5c)and ECMWF(Fig.6c).The cold and strong stratospheric polar vortex is hardly disturbed in both models,and the prediction biases are gradually amplified.In contrast,the weakened cold center and its deviation from the North Pole are almost realistically reproduced in the D-0 and D-7 hindcasts by both BCC CSM and ECMWF(first and second rows in Figs.5 and 6).The warming anomaly(contours)begins earliest in the Pacific sector as the stratospheric polar cold center(shading)deviates to the Atlantic sector and Scandinavia on days-15 to-5(Figs.5c1 and c2;Figs.6c1 and c2).The cold center disappears on days 5–15,indicating the reversal of the meridional temperature gradient from middle to high latitudes,as well as the collapse of the stratosphere polar vortex.The warm center over Northeast Asia is fairly well predicted in the D-0 and D-7 hindcasts on days-5 to 5(226 K)and on days 5–15(224 K).The collapse of the shifted vortex cold center is successfully predicted on days 5–15 and 15–25.Comparing BCC CSM and ECMWF,it is apparent that ECMWF still has a relatively higher prediction skill level than BCC CSM in the D-14 hindcast(cf.Figs.5a3–e3 and 6a3–e3).The cold center of the stratospheric polar vortex is stable and remains nearly stationary after days-15 to-5(Figs.5b3–e3)in BCC CSM,although the cold center over Scandinavia warms up gradually from 200 K(Fig.5b3)to 208 K(Fig.5e3).In contrast,ECMWF predicts that the cold center develops equatorward as the warm center over the Pacific sector moves poleward,extending its coverage area(Figs.6b3–e3).It denotes that the heat exchange between the midlatitudes and the Arctic region in the D-14 hindcast is better reproduced by ECMWF than by BCC CSM.

Fig.3.Composite pressure–time evolution of the zonal mean zonal wind at 60°N(shading;units:m s-1)and its anomaly(contours;units:m s-1;interval:2)in the(left column)BCC CSM and(right column)ECMWF hindcast initiated(a)on the SSW onset day,and(b)one week before,(c)two weeks before,(d)three weeks before,and(e)four weeks before the SSW onset date.

Fig.4.As in Fig.3,but for the composite pressure–time evolution of the polar cap temperature area-averaged over 60°–90°N(shading;units:K)and its anomaly(contours;units:K;interval:2).

Fig.5.Composite 50-hPa temperature distribution(shading;units:K)and its anomaly(contours;units:K;interval:2)during day(a)-25 to-15,(b)-15 to-5,(c)-5 to 5,(d)5 to 15,and(e)15 to 25,relative to the onset of SSW events in BCC CSM hindcasts initiated(a1–e1)on the SSW onset day,and(a2–e2)one week before,(a3–e3)two weeks before,(a4–e4)three weeks before,and(a5–e5)four weeks before the SSW onset date.

In the D-21 and D-28 hindcasts,the predicted polar vortex by BCC CSM evolves fairly slowly,centered over the North Pole(Figs.5a4–e4;Figs.5a5–e5).Unlike in the observations,the predicted cold center over the Arctic and a relatively warm band in the midlatitude stratosphere never reverse the meridional temperature gradient,which indicates an unrealistic warming event.BCC CSM and ECMWF still possess limited prediction skill for SSW events up to three to four weeks in advance.Given that the polar vortex cold center weakens continuously from 198 K(Figs.5a4 and a5;Figs.6a4 and a5)to 206 K(Figs.5e4 and e5;Figs.6e4 and e5),the central temperature is predicted to be 10 K smaller than that in the observations.

3.3.Year-by-year prediction skill of BCC CSM and ECMWF with respect to the stratospheric circumpolar polar jet

From the above analysis,it is clear that the closer the initialization time is to SSW onset,the more realistically the stratospheric evolution is forecast.In fact,the prediction skill of the models for the stratospheric circumpolar westerly varies from year to year for a prediction lead time ranging from 1 to 30 days(Fig.7).Specifically,the anomaly correlation coefficients(ACCs)are larger during some winters,such as 1998 and 2004,even at lead times that exceed three weeks(Figs.7aandc).Furthermore,theACCsbetweenhindcasts and observations also differ for different lead times,and even from model to model.In general,the prediction skill of BCC CSM for the circumpolar westerly is a little lower than that of ECMWF,and the ACC in BCC CSM decreases much faster with lead time than that in ECMWF(Figs.7b and d).

As shown in Figs.7b and d,the circumpolar westerly ACC during SSW winters(thin solid line)and during non-SSW winters(thick solid line)are also calculated,separately.The prediction skill during SSW winters is clearly higher than that during non-SSW winters when the lead time of the BCC CSM hindcasts ranges from 1–18 days(Fig.7b).The ACC decreases slowly from 1.0 to 0.6 with the lead time increasing from 1–17 days in BCC CSM.However,with the leadtimeincreasingfrom17–30daysinBCC CSM,theACC for non-SSW winters remains nearly constant,while that for the SSW winters decreases gradually to below 0.4.In contrast,ECMWF has a relatively stable prediction skill:the ACCfluctuates above 0.9 with the lead time increasing from 1–10 days,and then decreases gradually.The prediction skill also depends on the occurrence of SSWs in ECMWF:the ACC in SSW winter is generally higher than that in non-SSW winter when the lead time falls between one week and four weeks(cf.Figs.7b and d).

Fig.7.Prediction skill of the daily circumpolar westerly at 60°N and 10 hPa in each winter(November–March)during 1995–2014,denoted as the anomaly correlation coefficient between the observation and hindcast,with a lead time ranging from 1 to 30 days relativeto the hindcast initialization time in(a)BCC CSM and(c)ECMWF.(b,d)Prediction skill in all winters(dashed line),in SSW winters(thin solid line),and in non-SSW winters(thick solid line).

3.4.Hindcast for teleconnections and upward planetary waves in the extratropical troposphere

Theweakening andshifting ofthe stratosphericpolar vortexiscloselyassociatedwithplanetarywaveactivityoriginating from the extratropical troposphere(Garfinkel and Hartmann,2007;Rao and Ren,2016a,b;Hu et al.,2017).On different time scales,the tropospheric precursor for the variability of the stratospheric polar vortex also changes.On the interannual timescale,the tropospheric PNA pattern in its positive phase is an important teleconnection bridging El Ni?no–Southern Oscillation(ENSO)and the extratropical stratosphere,which modulates the upward propagation of planetary waves(Ren et al.,2012,2017;Xie et al.,2012;Hu et al.,2017;Rao and Ren,2018).However,on the S2S time scale,the extratropical stratospheric warming is preceded by the WP Oscillation(Dai and Tan,2016),which is projected to an enhanced wavenumber-1.The day-to-day evolution of the three tropospheric teleconnection indices that are closely related with stratospheric variability is shown in Fig.8.Based on the observations,the PNA teleconnection is fairly weak and generally in its negative phase before SSW onset(Fig.8a),which is contrary to the well-established relationship between the PNA teleconnection and stratospheric polar vortex on the interannual time scale(Garfinkel and Hartmann,2007;Rao and Ren,2016c).However,WP persists in its negative phase on day-25 to 2 and reaches its climax on day-10,indicating the persistent deepening of the North Pacific low before SSW onset(Fig.8b).Following SSW onset,the zonal meanheightandwesterlysignalspropagatedownward(Baldwin and Dunkerton,1999;Cai and Ren,2006;Ren and Cai,2007),favoring a long-lasting NAO in its negative phase(Fig.8c).

The evolution of the tropospheric teleconnection(especially the WP)in the D-0,D-7 and D-14 hindcasts is reproduced well in both models.Specifically,the persistent negative WP before SSW onset is realistically forecast by both models(Fig.8b).In the observations,the WP begins to develop toward its positive phase on day 3,indicating a successful upward propagation of the extratropical waves.The phase transition of WP is also predicted by ECMWF,but fairly limitedly reproduced by BCC CSM.The negative WP persists too long in BCC CSM(Fig.8b1),and the potential of the up-ward propagation of the strengthened planetary waves to perturb the stratosphere is limited.The negative NAO is inaccurately and limitedly predicted,indicating weak stratosphere–troposphere coupling in BCC CSM(Fig.8c).

Fig.8.Day-to-day evolution of the(a)PNA,(b)WP and(c)NAO indices on day-30 to 30 in(left column)BCC CSM and(right column)ECMWF hindcasts.Black(colored)curves represent evolutions from observations(hindcasts).

Next,we show the evolution of the upward-propagating waves in the circumpolar region in Fig.9 to verify the critical importance of tropospheric variations for the stratospheric prediction.In the observations,the upward propagation of planetary waves is anomalously large from day-20 when the polar vortex is still fairly strong(Fig.9a).It is then gradually strengthened until SSW onset on day 0.Accompanying the increase of planetary waves penetrating into the stratosphere,persistent convergence of anomalous EPflux occurs in the circumpolar region during day-20 to 0 between 200 and 10 hPa,accounting for the reversal in the direction of the westerlies and the negative zonal wind anomalies.

Because the anomalous upward propagation of planetary waves begins on day-20,the D-0,D-7 and D-14 hindcasts can still incorporate the tropospheric precursor fairly well(Figs.9b–d).However,there is a time shift for the EPflux convergence center,especially in the D-7 hindcast(Fig.9c),where the maximum convergence is biased to appear on day 8(4)in BCC CSM(ECMWF).In the D-21 and D-28 hindcasts,the absence of significant upward propagating waves largely restricts a realistic SSW onset(Figs.9e and f),indicating the critical importance of upward propagating waves in predicting SSW onset.

4.Ensemble hindcasts and error corrections for BCC CSM

4.1.SSW evolution in ensemble hindcasts

Figure 10 displays the evolution of the predicted circumpolar westerlies in BCC CSM by ensemble forecasts(one control hindcast and three perturbed hindcasts).The predicted zonal wind evolution,especially by the D-14 hindcasts is greatly improved when compared with that in the control hindcasts(cf.Figs.10c1 and 3c1).The maximum easterly anomaly in Fig.10c1 is below-8 m s-1,reproducing nearly 27%of the observationalanomalies.Improvementin the D-0,D-7,D-21 and D-28 hindcasts is relatively small(Figs.10a–e).As in the control hindcasts,the wind anomaly sign in the stratospheric circumpolar region is correctly predicted by the ensemble hindcasts,although the anomaly value is weaker than that in the observations.

The evolution of polar cap temperature is displayed in Fig.S1 in electronic supplementary material.The temperature evolution—in particular in the D-14 hindcast—is also slightly improved when compared with the control hindcast set(cf.Figs.S1c1 and 4c1).In addition,the cold bias over the Arctic after days 5–15 in Fig.S2 is also reduced.

Fig.9.Spatiotemporal evolution of EPflux anomalies(vectors;m3s-2;normalized by local air density)and their divergence(shading;m s-1d-1)in the subpolar regions(60°–80°N)on day-30 to 30 from(a)observations and hindcasts initiated(b)on the SSW onset day,and(c)one week before,(d)two weeks before,(e)three weeks before,and(f)four weeks before the SSW onset date,in(b1–f1)BCC CSM and(b2–f2)ECMWF.The contours are the circumpolar westerly anomalies.

Fig.10.As in Fig.3,but in(left column)BCC CSM ensemble hindcasts and(right column)BCC CSM hindcasts with error corrections.

4.2.SSW evolution in hindcasts with error corrections

Because the ensemble hindcasts initiated more than two weeks before SSW onset still have very limited prediction skill,we apply an error correction to the control hindcasts.Figure 10 displays the evolution of the circumpolar zonal wind in the control hindcasts by BCC CSM with error correction.Comparing Figs.3 and 10,the hindcasts with error corrections have the highest skill in predicting the zonal wind evolution.For example,the maximum easterly anomaly on day 30 in the right-hand column of Fig.10 is 12,12,10,10 and 10 m s-1in thefive hindcasts,accounting for 75%,75%,62.5%,50%and 50%of the observed anomaly(16 s-1;Fig.1a),respectively.With the improvement in the circumpolar wind anomalies,a deceleration of the polar night jet is observed in Figs.10a2–e2,although the westerly fails to reverse to an easterly.Similarly,the predicted polar cap temperature anomalies also evolve in a more reasonable way if the system errors are corrected(refer to Figs.S1 and S3),compared with those in the one-member(Fig.4)and the ensemble(Fig.S1)hindcasts.

5.Summary and discussion

5.1.Summary

Thisstudy explorestheSSW prediction skillof BCC CSM in reference to S2S hindcast results.Composite analysis of the evolution of the 11 SSW events during 1995–2014 shows that all the hindcasts initialized 0–4 weeks before SSW onset have certain prediction skill to forecast the circumpolar westerly and polar cap temperature during days 0–30 after SSW onset.From D-0 to D-28,as the hindcasts are initialized increasingly earlier,the prediction skill of SSW evolution slowly decreases for both BCC CSM and ECMWF.In general,the evolution of the stratospheric polar night jet and polar cap temperature are relatively realistically predicted by BCC CSM in the D-0 and D-7 hindcasts.ECMWFstillhasfairlyhighpredictionskillintheD-14hindcast,and it can reproduce more than 50%(-16 m s-1,12 K)of the observed circumpolar easterly anomalies(-30 m s-1)and the polar cap temperature anomalies(16 K).For the D-21 and D-28 hindcasts,the circumpolar westerly(polar cap temperature)anomalies reproduced by ECMWF reduce to about-8 m s-1(8 K),at 27%(50%)of those in the observations.In contrast,the reproduced anomalies in the D-28 hindcasts by BCC CSM reduce to only 10%of that in the observations,although the signs of the easterly anomalies and the polar cap temperature anomalies are correctly forecast in the hindcasts within 2–4 weeks before SSW onset.

The breakdown of the stratospheric cold polar vortex after SSW onset is predicted successfully in the D-0 and D-7 hindcasts by BCC CSM and in the D-0,D-7,and D-14 hindcasts by ECMWF.If the initialization time is set any earlier than SSW onset,a cold bias in the Arctic stratosphere is observed in both hindcast systems.Further diagnosis of the prediction skill of the two hindcast systems in the northern winter stratosphere indicates that their prediction skills are both relatively higher during SSW winters than during non-SSW winters when the lead time is less than 18(28)days for BCC CSM(ECMWF).This can be attributed to the tropospheric precursors captured by the model initial conditions.Specifically,the negative WP teleconnection during day-25 to 2 is captured well by BCC CSM(ECMWF)in the D-0 and D-7(D-0,D-7 and D-14)hindcasts,which is related to an enhancement of the upward propagation of planetary waves in the hindcasts.

To narrow the gap in SSW prediction between BCC CSM and ECMWF,ensemble forecasts and error corrections are applied to BCC CSM.Compared with the control forecasts,the prediction skill of SSW is indeed improved,with the predicted maximum wind(temperature)anomalies increasing from-4 m s-1(4 K)by the one-member hindcast to-8 m s-1(6 K)by the ensemble hindcasts and in the error corrections in D-21 and D-28.

5.2.Discussion

Because the stratosphere has a longer“memory”than the troposphere,effort has been devoted to performing extendedrange forecasts based on the long-lasting signals related to stratospheric variability.Such statistical models can successfully predict tropospheric cold-air outbreaks more than a week in advance if the preceding meridional mass circulation associated with the changes in the stratospheric polar vortex is correctly observed(Yu et al.,2015;Cai et al.,2016).To extend weather prediction to more than two weeks,additional work is still needed to construct a robust troposphere–stratosphere relationship at a longer lead time.BCC CSM has reliable prediction skill for stratospheric extreme events when the lead time does not exceed two weeks.A combination of model predictions and a robust statistical relationship between the stratosphere and tropospheric cold-air outbreaks may further extend the effective time span of weather prediction on the S2S timescale.

Error corrections performed on the control forecasts and ensemble forecasts can improve the SSW prediction skill,especially in experiments initiated more than two weeks in advance.However,improvement in the prediction skill from a one-member control forecast to multiple control and perturbed members is still fairly limited.The error correction method also has limited prediction skill,especially for hindcasts initiated more than two weeks before warmingevent onset.The prediction skill in the stratosphere-resolving ECMWF model is relatively higher,indicating the vital importance of stratospheric processes in SSW forecasts.It is expected that the next version of BCC CSM,which will have a higher horizontal resolution and higher model top that includes the mesosphere and will incorporate more complex physical parameterizations,will perform better in predicting SSW onset more than two weeks in advance.Because 11 models have participated in the S2S project,a comprehensive assessment and comparison is also required to explore the predictability in theory,and the maximum effective predictive time span in practice.

Acknowledgements.This work was jointly supported by the National Key R&D Program of China(Grant Nos.2016YFA0602104 and 2016YFA0602102),the National Natural Science Foundation of China(Grant Nos.41705024,41575041,41705039 and 41705076),the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA17010105),the Startup Foundation for Introducing Talent of NUIST(Grant No.2016r060),and the Priority Academic Program Development of Jiangsu Higher Education Institutions.We acknowledge the CMA BCC,NCAR–NCEP and ECMWF for providing their hindcast and/or reanalysis data.

Electronic supplementary material: Supplementary material is available in the online version of this article at https://doi.org/10.1007/s00376-018-8165-8.