Impact of tropical SST variations on the linear predictability of the atmospheric circulation. in the Atlantic/European region, and

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1 ANNALS OF GEOPHYSICS, VOL. 46, N. 1, Ferury 2003 Impct of tropicl SST vritions on the liner predictility of the tmospheric circultion in the Atlntic/Europen region Henrik Feddersen Climte Reserch Division, Dnish Meteorologicl Institute, Copenhgen, Denmrk Astrct Sesonl men vlues of tropicl Se Surfce Temperture (SST) nd Atlntic/Europen Men Se Level Pressure (MSLP) from 301-yer coupled ocen/tmosphere model run re nlysed sttisticlly. Reltions etween the two fields re identified on oth internnul nd interdecdl timescles. It is shown tht tropicl SST vriility ffects Atlntic/Europen MSLP in winter. In prticulr, there ppers to e sttisticlly significnt reltion etween the leding modes of vriility, the El Niño/Southern Oscilltion (ENSO) nd the North Atlntic Oscilltion (NAO). During cold ENSO (L Niñ) yers the NAO tends to e in its positive phse, while the opposite is the cse during wrm ENSO (El Niño) yers, lthough to lesser extent. Similr nlyses tht re presented for gridded oservtionl dt, confirm this result, lthough here tropicl Atlntic SST ppers to e stronger relted to the NAO thn tropicl Pcific SST. The liner predictility of model simulted NAO index is estimted y mking sttisticl predictions tht re sed on model simulted tropicl SST. It is shown tht the predictive skill is rther insensitive to the length of the trining period. On the other hnd, the skill score estimte cn vry significntly s result of interdecdl vriility in the climte system. These results re importnt to er in mind when mking sttisticl sesonl forecsts tht re sed on oserved SST. Key words sesonl predictility sttisticl nlysis ENSO NAO 1. Introduction Miling ddress: Dr. Henrik Feddersen, Climte Reserch Division, Dnish Meteorologicl Institute, Lyngyvej 100, DK-2100 Copenhgen Ø, Denmrk e-mil: hf@dmi.dk Internnul vriility of the lrge-scle tmospheric circultion in the Atlntic/Europen region is dominted y vriility tht is internl to the tmosphere. The internl vriility is lrgely result of the chotic dynmics of the tmosphere in the Atlntic/Europen region, nd thus the potentil would seem limited for sesonl to internnul prediction of Europen climte (Rowell, 1998). However, oth oservtionl nd model studies suggest tht smll frction of the Atlntic/Europen internnul climte vriility is ffected y the tropicl oscilltions through tmospheric teleconnections. Severl nlyses of internnul vriility in generl circultion models (Brnkovic nd Plmer, 1997; Dvies et l., 1997; My nd Bengtsson, 1998; Feddersen, 2000) s well s nlyses of oservtionl dt (Fredrich nd Müller, 1992; Pozo-Vzquez et l., 2001) hve demonstrted link etween the El Niño/ Southern Oscilltion (ENSO) nd the winter climte in Europe, including the sesonl men 109

2 Henrik Feddersen phse of the North Atlntic Oscilltion (NAO). In summry, these ppers find tht cold ENSO events re ssocited with the positive phse of the NAO, while wrm ENSO events (to lesser extent) re ssocited with the negtive phse of the NAO. The identified sttisticl links etween ENSO events nd the phse of the NAO hold some potentil for Atlntic/Europen sesonl to internnul predictility, prticulrly in yers with lrge tropicl Se Surfce Temperture (SST) nomlies, lthough study y Johnsson et l. (1998) found no significnt predictility of surfce ir temperture in Northern Europe ssocited with ENSO. It is possile tht in this study no predictility ws detected ecuse the region tht ws considered, is rther smll, nd the study ws sed on reltively short period (39 yers) which my not e long enough to identify teleconnection signl tht is hidden in the chotic internl vriility. Thus, there is need for longer time series of dt. Given the lck of oservtionl dt ck in time, we focus our nlysis in the present study on dt time series from 301-yer integrtion of the ECHO-G coupled ocen/tmosphere generl circultion model. Such long time series llow us not only to etter identify tropicl/ extrtropicl teleconnection signls, ut lso to study the roustness over mny decdes of the teleconnection reltions. Comprisons with nlyses of oservtionl dt re mde when the oservtionl dt series re sufficiently long to do so. Teleconnections on interdecdl timescles re lso identified etween tropicl SST nd tmospheric vriility in the Atlntic/Europen region in the model time series. Teleconnections on these longer timescles will show up in internnul climtic time series s pprent trends, nd they lso contriute (positively or negtively) to the internnul predictility. The pper is orgnised s follows. The nlysed oservtionl dt nd the 301-yer model run re riefly descried in Section 2. Section 3 descries teleconnections etween tropicl SST nd Atlntic/Europen Men Se Level Pressure (MSLP), oth for oservtions (for the period ) nd for the 301-yer model run. Here nd in the following we consider only the Jnury-Mrch (JFM) seson. The teleconnection ptterns re identified y pplying Singulr Vlue Decomposition (SVD) nlysis to cross-covrinces of tropicl SST nd Atlntic/ Europen MSLP in JFM. In Section 4 similr SVD nlysis is pplied to JFM time series tht re verged over severl yers in order to study teleconnections tht relte to interdecdl vriility. Section 5 discusses implictions for the internnul predictility of Atlntic/ Europen MSLP. In prticulr, dt from the model run is used s synthetic dt for sttisticl predictions of NAO index nd Europen surfce tempertures in winter. The reltively long model run llows us to discuss spects of the roustness of sttisticl predictions which is not possile for the much shorter oservtionl dt series. Finlly, conclusions re presented in Section Dt 2.1. Oservtionl dt Glolly gridded oservtions of tropicl SST hve een tken from the GISST2.2 dtset which includes monthly men vlues for the period on 1 1 grid (Ryner et l., 1996). However, here we include only every third grid ox in oth directions in order to otin resolution comprle to the model s T30 resolution. The MSLP dt ws tken from 5 10 gridded dtset from the Climtic Reserch Unit. This dtset covers the Northern Hemisphere from 15 N-85 N nd includes monthly men vlues for the period (Jones, 1987; Bsnett nd Prker, 1997) Model dt We use sesonlly verged dt from 301- yer simultion of the present-dy climte from the ECHO-G coupled ocen/tmosphere generl circultion model. The model consists of the ECHAM4 tmospheric model (e.g., Roeckner et l., 1996; Stendel nd Roeckner, 1998) nd the HOPE-G ocen model, including dynmic/ 110

3 Impct of tropicl SST vritions on the liner predictility of the tmospheric circultion in the Atlntic/Europen region thermodynmic se ice model (e.g., Legutke nd MierReimer, 1999). ECHAM4 hs horizontl resolution of T30 (corresponding to grid points on the corresponding Gussin grid) nd 19 verticl levels (e.g., Stendel nd Roeckner, 1998). In the extrtropics HOPE-G hs horizontl resolution of , corresponding to tringulr trunction of T42. In nd from 30 to 10 off the equtor the distnce etween ltitudes decreses to 0.5 in order to etter resolve the equtoril dynmics. The verticl resolution of HOPE-G is 20 lyers. 3. Internnul covriility 3.1. Oservtionl dt An SVD nlysis (Bretherton et l., 1992; Wllce et l., 1992) ws pplied to JFM sesonl mens of 92 yers ( ) of gridded oservtions of tropicl SST nd Atlntic/Europen MSLP. Both the SST nd MSLP fields were stndrdised prior to the SVD nlysis so tht ll grid oxes contriute the sme mount to the nlysis. The SVD nlysis cn in mny respects e regrded s n extension of the well-known principl component (or EOF) nlysis. In the ltter, one or more ptterns re derived tht mximise the frction of «explined» vrince for prticulr field, wheres the SVD nlysis provides one or more pirs of ptterns tht mximise the frction of «explined» covrince etween two fields. It is common prctice to give the Squred Covrince Frction (SCF) tht is ssocited with pir of SVD ptterns, just like it is common prctice to lwys give the frction of explined vrince tht is ssocited with n EOF pttern. Both the SCF nd the correltion etween the ssocited SVD time series re often found to e very high for the leding SVD mode. However, this does not necessrily imply strong sttisticl connection etween the two fields (Wllce et l., 1992; Cherry, 1996). Therefore, dditionl tests of sttisticl significnce re required. Here we use Monte Crlo resmpling to test sttisticl significnce (Wrd nd Nvrr, 1997). The Atlntic/Europen MSLP time series re rndomly resmpled 200 times, nd ech time n SVD nlysis is pplied to tropicl SST nd the resmpled MSLP. An estimte of the significnce level (i.e. the proility tht n eqully strong coupled mode would pper y chnce for independent SST nd MSLP fields) is then given y the numer of times tht the rndomly generted SCF exceeds the ctul SCF divided y the totl numer of times the SVD nlysis ws pplied to the resmpled MSLP fields nd tropicl SST. In order for the resmpled time series to pper rndom, the originl MSLP time series must not e serilly correlted. It ws checked tht seril correltion is not prolem. Figure 1, shows the leding pir of heterogeneous correltion ptterns, i.e. the temporl correltion in ech grid ox etween the stndrdised time series of one field (MSLP in fig. 1; SST in fig. 1) nd the first SVD time series of the opposite field (Bretherton et l., 1992). Thus, the heterogeneous correltion pttern for MSLP shows how well MSLP nomlies cn e specified from the first SVD time series of tropicl SST, i.e. the heterogeneous correltion pttern yields n estimte of the skill of SVD predictions of Atlntic/Europen MSLP if the predictions were sed on the sttisticl link etween tropicl SST nd Atlntic/Europen MSLP. The totl internnul MSLP vrince tht is «explined» y tropicl SST is simply given y the re verge of the squred correltions in fig. 1. The first pir of SVD time series for Atlntic/Europen MSLP nd tropicl SST, respectively, re shown in fig. 2,. The MSLP pttern shows north/south dipole which is lso found in the first EOF of JFM MSLP (fig. 3, the NAO pttern in its negtive phse), ut in the EOF pttern the dipole is much more pronounced over the Europen continent thn wht is seen in fig. 1. Likewise, the tropicl SST pttern ers some resemlnce to the first EOF of tropicl JFM SST (not shown). But the SST pttern in fig. 1 hs reltively more weight in the tropicl Atlntic, while the first EOF looks more like the generic ENSO pttern of Hrrison nd Lrkin (1998). The SVD ptterns re found to e sttisticlly significnt t 3.5% level, using the Monte Crlo resmpling test, so the SVD nlysis supports the notion tht wrm (cold) tropicl SST is ssocited with n tmospheric 111

4 Henrik Feddersen Fig. 1,. Leding pir of heterogeneous correltion ptterns from n SVD nlysis of 92 yers ( ) of gridded oservtions of JFM sesonl men tropicl SST nd JFM sesonl men Atlntic/Europen MSLP. ) MSLP correltions (in %); ) SST correltions (in %). Squred covrince frction = 73%. Totl explined MSLP vrince frction in Atlntic/Europen region = 7%. Sttisticl significnce level = 3.5%. Fig. 2,. Stndrdised time series for the ptterns in fig. 1,. ) For Atlntic/Europen MSLP; ) for tropicl SST. Correltion coefficient etween time series is

5 Impct of tropicl SST vritions on the liner predictility of the tmospheric circultion in the Atlntic/Europen region Fig. 3. First EOF pttern (explining 43% of the totl vrince) of gridded oservtions of JFM sesonl men Atlntic/Europen MSLP. SST is likely to e felt in the Atlntic/Europen region only in yers of extreme tropicl SST nomlies. If the SVD time series for tropicl SST is correlted with the MSLP time series in ech grid ox in the Northern Hemisphere then the pttern in fig. 4 is otined. This pttern shows tht the Atlntic/Europen MSLP pttern is just wek prt of n hemispheric pttern which hs strong centre of ction over the tropicl Atlntic nd secondry centre over the western prt of the tropicl Pcific Model dt Fig. 4. Correltions (in %) etween the tropicl SST time series (fig. 2) nd gridded oservtions of MSLP on the Northern Hemisphere north of 15 N. lrge-scle circultion in winter over the Atlntic/ Europen region tht more or less corresponds to the negtive (positive) phse of the NAO. The MSLP pttern, however, only explins out 7% of the totl vrince, so the impct of tropicl A similr SVD nlysis ws pplied to the 301-yer of model simulted JFM sesonl men tropicl SST nd JFM sesonl men Atlntic/ Europen MSLP. The first pir of heterogeneous correltion ptterns re shown in fig. 5,. The Pcific prt of the SST pttern is dominting the pttern nd is similr to the model s ENSO pttern (clculted s the first EOF of tropicl Pcific SST; not shown). Likewise, the MSLP pttern in the Atlntic/Europen region ers some resemlnce to the first model EOF pttern (fig. 6, NAO pttern in its negtive phse). However, the model s first EOF pttern is locted 113

6 Henrik Feddersen Fig. 5,. Leding pir of heterogeneous correltion ptterns from n SVD nlysis of 301 yers of model simulted JFM sesonl men tropicl SST nd JFM sesonl men Atlntic/Europen MSLP. ) MSLP correltions (in %); ) SST correltions (in %). Squred covrince frction = 84%. Totl explined MSLP vrince frction in Atlntic/Europen region = 7%. Sttisticl significnce level < 0.5%. Fig. 6. First EOF pttern (explining 38% of the totl vrince) of model simulted JFM sesonl men Atlntic/ Europen MSLP. 114

7 Impct of tropicl SST vritions on the liner predictility of the tmospheric circultion in the Atlntic/Europen region slightly north of the SVD pttern, nd over the Ierin peninsul the EOF pttern hs centre which is sent in the SVD pttern, while the EOF pttern does not show the centre north of Scotlnd. Nevertheless, the SVD nlysis of the model run supports the oservtionl finding tht tropicl SST modultes the NAO so tht negtively phsed NAO is more likely in winters with wrm tropicl SST nomlies, wheres positively phsed NAO is more likely in winters with cold tropicl SST nomlies. The first SVD pttern is found to e highly sttisticlly significnt (with n estimted significnce level < 0.5%), lthough the Atlntic/Europen MSLP pttern explins only 7% of the totl internnul vrince for the JFM seson. If we consider only the yers when the tropicl SST is most extreme, then the frction of MSLP vrince explined y tropicl SST is considerly higher. For exmple, for the yers of the 25 most positive vlues nd Fig. 7,. Stndrdised time series for the ptterns in fig. 5,. ) For Atlntic/Europen MSLP; ) for tropicl SST. Correltion coefficient etween time series is

8 Henrik Feddersen the 25 most negtive vlues of the SVD time series for SST we find tht tropicl SST explins out 16% of the corresponding MSLP vrince. The ssocited stndrdised time series re shown in fig. 7,. The SST time series hs very strong iennil component which is not seen in the oservtions (cf. fig. 2,). This iennil component reflects the model s tendency to switch ck nd forth etween El Niño nd L Niñ sttes lmost every yer. This tendency is not seen in the MSLP time series. In fct, the utocorreltion function for the MSLP time series is similr to tht of white noise (not shown), ut lthough the MSLP vritions pper s those of rndom process, the correltion coefficient etween the MSLP nd the SST time series is 0.45, so the MSLP is not sttisticlly independent of the tropicl SST vritions. The pttern of correltions etween the SVD time series for tropicl SST nd the time series for MSLP in ech grid ox in the Northern Hemisphere is shown in fig. 8. The strongest correltions re found over the tropicl Pcific, indicting tht ENSO is the dominnt source of the vriility in the tropicl Pcific tht influences Atlntic/Europen MSLP vriility. Notice tht north of the direct influence of the southern oscilltion, the pttern hs some resemlnce with the surfce prt of the Arctic oscilltion pttern (Thompson nd Wllce, 1998). It ppers tht in the model s climte tropicl Pcific SST is the most importnt prt of the tropicl SST in reltion to the Atlntic/Europen MSLP vriility, nd, indeed, if the SVD nlysis is repeted with tropicl Pcific SST only, then n lmost identicl MSLP pttern nd lmost identicl SVD time series re recovered (not shown). But, interestingly, this is lso the cse if the SVD nlysis is repeted with tropicl Atlntic SST only. So the notion of one dominnt tropicl oscilltion (which itself is dominted y ENSO) seems resonle in this coupled ocen/ tmosphere model. The SVD nlysis gives no indiction of cuse nd effect, ut it seems most likely tht the tropicl SST hs (smll) influence on Atlntic/Europen internnul MSLP vriility nd not vice vers. This ssumption is confirmed y pplying n SVD nlysis to tropicl SST in the OND seson nd Atlntic/Europen MSLP in the following JFM seson. The resulting leding pir of heterogeneous correltion ptterns (not shown) re very similr to the pir of no-lg ptterns in fig. 5,, except tht the correltions generlly re lower in the lgged ptterns. 4. Interdecdl covriility Fig. 8. Correltions (in %) etween the tropicl SST time series (fig. 7) nd model simulted MSLP on the Northern Hemisphere. In order to study teleconnections tht relte to interdecdl vriility loosely defined s vritions with periods etween 10 nd 100 yers new time series re constructed y dividing the originl long model time series into 5-yer chunks, ech one of which is represented y n verge vlue. Note tht we re not using running mens; there is no overlp etween two 5-yer chunks. Thus, for the 301-yer model simultion the new «decdl» time series cn hve length of 60 t most. The period of five yers is chosen ecuse it represents the miniml smpling frequency tht is needed in order to resolve 10- yer periods, nd lso ecuse 5-yer verges re long enough to eliminte effects of the strong iennil ENSO vrition. 116

9 Impct of tropicl SST vritions on the liner predictility of the tmospheric circultion in the Atlntic/Europen region An SVD nlysis similr to the ones descried in the previous section ws pplied to the decdl time series of model simulted tropicl SST nd model simulted Atlntic/ Europen MSLP, ut the Monte Crlo resmpling test for sttisticl significnce gve significnce level > 20%, i.e. no sttisticl significnce. However, if SST leds MSLP y one yer (i.e. Fig. 9,. Leding pir of heterogeneous correltion ptterns from n SVD nlysis of 60 5-yer verges of model simulted JFM sesonl men Atlntic SST nd JFM sesonl men Atlntic/Europen MSLP. SST leds MSLP y one yer s descried in text. ) MSLP correltions (in %); ) SST correltion (in %). Squred covrince frction = 68%. Sttisticl significnce level = 1.5%. 117

10 Henrik Feddersen the decdl SST time series re sed on verges of yers 1-5, 6-10, 11-15, etc. nd the decdl MSLP time series re sed on verges of yers 2-6, 7-11, 12-16, etc.), then the sttisticl significnce level drops to 7.5%. And if the SST domin is extended to lso include the extrtropicl North Atlntic, then the sttisticl significnce level drops further to 1.5%. The SVD heterogeneous correltion ptterns nd ssocited time series re shown in fig. 9, nd fig. 10,, respectively. The SST pttern shows tripole in the tropicl Atlntic. This tripole is lso seen in the second mode (not shown) of the SVD nlysis of internnully vrying SST nd MSLP. As the time series nd the MSLP correltion pttern for the first interdecdl SVD mode lso pper to correspond to those of the second internnul SVD mode (not shown), it seems resonle to ssume tht they re in fct the sme mode of vriility. The interdecdl SST time series ppers to hve n oscilltion period of round 45 yers. Further nlysis, including nlysis of dditionl ocenic dtsets, is required in order to ttempt n explntion of the driving mechnism for this oscilltory ehviour. However, vriility in the thermohline circultion is possile cndidte (Tourre et l., 1999). A similr nlysis of interdecdl covriility for the oservtionl dt mkes little sense s the ville 92 yers of dt is simply not enough to study vriility with expected periods of nerly 50 yers. 5. Internnul predictility Sesonl forecsts for surfce ir temperture nd precipittion tht re sed on sttisticl reltions with tropicl SST (e.g., Brnston, 1994) Fig. 10,. Stndrdised time series for the ptterns in fig. 9,. ) For Atlntic/Europen MSLP; ) for Atlntic SST. Correltion coefficient etween time series is

11 Impct of tropicl SST vritions on the liner predictility of the tmospheric circultion in the Atlntic/Europen region re issued routinely round the world (see e.g., The Experimentl Long-Led Forecst Bulletin t Such sttisticl forecsts re typiclly sed on records of out 50 yers of oservtionl dt. In order to estimte forecst skill the sttisticl predictions re cross-vlidted, i.e. for ech yer in the oservtionl record hindcst is mde tht is sed on trining period tht does not include the prticulr hindcst yer (Michelsen, 1987). Here the 301-yer long model run is used s synthetic dt for sttisticl predictions of n NAO index tht descries the lrge-scle circultion over the Atlntic/Europen region. The purpose of this exercise is twofold: 1) to quntify predictility of the NAO tht cn e linerly relted to tropicl SST; 2) to investigte to wht extent the predictive skill depends on c d e f Fig. 11-f. Leding MSLP heterogeneous correltion ptterns from SVD nlyses of six different 50-yer periods of model simulted JFM sesonl men tropicl SST nd JFM sesonl men Atlntic/Europen MSLP. ) Yers 1-50; ) yers ; c) yers ; d) yers ; e) yers ; f) yers Totl explined MSLP vrince frctions in the Atlntic/Europen region vry etween 6.6% nd 13.1%. Cf. fig. 5 which is sed on n SVD nlysis of ll 301 model yers. 119

12 Henrik Feddersen the length of the sttisticl trining period, nd how well the predictive skill is estimted y the cross-vlidtion technique. The nswers to the ltter questions require long dt series, such s those of the present 301- yer model run, tht re not ville for the reltively short record of oservtionl dt. The leding heterogeneous MSLP correltion ptterns from SVD nlyses of model simulted tropicl SST nd Atlntic/Europen MSLP for six non-overlpping 50-yer periods show notle differences, lthough north/south dipole structure is evident in ll six ptterns (fig. 11-f). The frction of explined internnul MSLP vrince in JFM vries etween 6.6% nd 13.1%, i.e. y more thn fctor 2. SVD nlyses of oservtionl dt lso show differences etween the two ptterns tht re sed on the first nd the lst 46-yer period, respectively, of the period (fig. 12,). These results show tht the sttisticl reltionship etween tropicl SST nd Atlntic/Europen MSLP vries on inter- Fig. 12,. Leding MSLP heterogeneous correltion ptterns from SVD nlyses of two different 46-yer periods of gridded oservtions of JFM sesonl men tropicl SST nd JFM sesonl men Atlntic/Europen MSLP. ) For ; ) for Cf. fig. 1 which is sed on n SVD nlysis of ll 92 yers. 120

13 Impct of tropicl SST vritions on the liner predictility of the tmospheric circultion in the Atlntic/Europen region decdl timescles. Therefore it is likely tht internnul predictility of Atlntic/Europen MSLP will lso vry on interdecdl timescles. Predictions of n NAO index re mde y sttisticl specifiction of the index (clculted s the difference etween MSLP nomlies in the model grid oxes centred pproximtely t (39 N, 30 W) nd (65 N, 19 W)) from the first three SST time series from n SVD nlysis etween tropicl SST in JFM (or OND) nd Atlntic/Europen MSLP in JFM (tht is, for led time of zero or one seson). The sttisticl specifiction is simply mde y multiple liner regression of the NAO index on the three SST time series. The choice of including three time series is sed on the oservtion tht the squred covrinces ccounted for y susequent SVD modes re smll, nd generlly the SCF is tending to zero very slowly for these modes, which would indicte tht these modes re close to the «noise level» of the vriility (O Lenic nd Livezey, 1988). Moreover, repetition of few of the predictility clcultions descried elow indictes tht including more SST time series in the regression does not led to n increse of the predictive skill. First, the predictive skill is clculted s function of trining period length. The vlidtion period is the 150-yer period from yer 151 until yer 300. A prediction for yer n is lwys sed on trining period tht ends in yer n-1, i.e. the trining period is sliding through the vlidtion period, just s one would like to lwys use the ltest dt for rel sttisticl forecst. As mesure of predictive skill we use the nomly correltion. Figure 13 summrises the dependence on trining period length for led times of zero nd one seson. For short trining periods the predictive skill increses with incresing trining period length, ut seems to sturte lredy t trining period lengths of out 30 yers. This is n encourging result for sttisticl sesonl forecsting ecuse it suggests tht there is no need for very long trining dt sets in order to mke forecsts for lrge-scle fetures such s the NAO index. The predicted phse of the NAO depends on the phse of ENSO. Figure 14 shows sctterplot of predicted (t zero led time nd for 50-yer trining period) versus ctul NAO index in the Fig. 13. Predictive skill s function of length of trining period for sttisticl predictions of model simulted NAO index (see text) for JFM, yers Top curve: predictions sed on tropicl SST from the sme seson (JFM). Bottom curve: predictions sed on tropicl SST from the previous seson (OND). Fig. 14. Actul model NAO index versus sttisticlly predicted NAO index for 25 wrm ENSO yers (circles) nd 25 cold ENSO yers (crosses). Led time = 0, length of trining period = 50 yers. See text for further explntion. model run for 25 wrm nd 25 cold ENSO yers. Generlly, cold ENSO yers led to positive NAO index, nd wrm ENSO yers led to negtive NAO index, ut the vriility of the NAO index is much lrger in wrm ENSO yers thn it is in cold ENSO yers. Also, positive NAO index is more likely in cold ENSO yer thn negtive NAO index is in wrm ENSO 121

14 Henrik Feddersen yer. For exmple, the NAO index is more thn +1 (indicted in fig. 14) in 84% of the cold ENSO yers, wheres the NAO index is less thn 1 (indicted in fig. 14) in only 60% of the wrm ENSO yers. Thus, it seems tht cold ENSO events ffect the NAO more thn wrm ENSO events, s lso found in previous studies (Dong et l., 2000; Pozo-Vzquez et l., 2001). The dt from the long model run llows us to compre cross-vlidted skill scores nd skill scores tht re estimted from truly independent dt. The dt is divided into six non-overlpping 50-yer periods. Using ech 50-yer period s trining period the skill score for prediction of the NAO index is estimted s nomly correltions for: 1) predictions of the NAO index in the trining period itself (i.e. the predicted NAO index is lso prt of the trining dt set); 2) crossvlidted predictions in the trining period (i.e. for ech prediction the predicted NAO index is excluded from the trining dt set), nd 3) predictions of the NAO index in the remining five 50-yer periods. The estimted skill scores re shown in fig. 15,. The skill scores tht re estimted from dependent dt re higher thn the cross-vlidted skill scores in every cse, nd they re lmost lwys higher thn the «true» skill scores for independent dt. Overll (i.e. for the verge over ll cses), the cross-vlidted skill score mtches the «true» skill score very well, ut there re individul cses when the cross-vlidted skill score ppers to overestimte the «true» skill score, s well s cses when it ppers to under-estimte it. For oth led times, we find in one of the six cses tht one skill score for the independent dt flls outside 95% confidence intervl for the cross-vlidted skill score. Although the confidence intervl is estimted under the ssumption tht the NAO index follows norml distriution, the result indictes tht sttisticlly significnt differences etween cross-vlidted nd true skill scores cn occur. It is likely tht these differences re cused y the interdecdl vriility tht ws illustrted in fig. 11-f. Cross-vlidted nd «true» skill scores were lso clculted for the oservtionl dt. For two non overlpping 46-yer periods (nd zero led time) we find skill scores tht re comprle to those of the model run s shown fig. 15. Fig. 15,. Predictive skill for sttisticl predictions of model simulted NAO index in JFM s estimted from six non-overlpping 50-yer trining periods for the model run (cse 1-6). Top curve: vlidtion period identicl to trining period. Bottom curve: s top curve, ut using cross-vlidtion (see text). Error rs: estimted 95% confidence intervl for cross vlidted skill scores. Circles: vlidtion periods not overlpping with trining period. ) Predictions sed on tropicl SST from JFM, i.e. led time = 0. Predictive skill scores re lso included for two non-overlpping 46- yer trining periods for gridded oservtions. ) Predictions sed on tropicl SST from OND, i.e. led time = 1 seson. 6. Conclusions It hs een demonstrted tht the lrge-scle sesonl men tmospheric circultion in winter (JFM) in the Atlntic/Europen region is sttisticlly relted to tropicl SST. This hs een shown for oth 92 yers of gridded oservtions of Atlntic/Europen MSLP nd for 301 yers 122

15 Impct of tropicl SST vritions on the liner predictility of the tmospheric circultion in the Atlntic/Europen region of coupled ocen/tmosphere model simultions. Although the verge effect is smll (only out 7% of the totl internnul vrince of Atlntic/ Europen MSLP is explined y the leding mode of internnul vriility in tropicl SST), it mkes sense to tke dvntge of the existence of this tropicl/extrtropicl teleconnection in sesonl predictions of Atlntic/Europen climte, prticulrly in yers when there is strong forcing from tropicl SST. A sttisticlly significnt reltion etween interdecdl vritions of Atlntic SST nd Atlntic/Europen MSLP hs een found for the 301 yers of model simultions. A corresponding pir of ptterns hve not een identified for the oservtionl dt, s only 92 yers of oservtionl dt were ville, which is insufficient to identify n interdecdl mode with dominnt oscilltion period of round 45 yers. The sttisticl reltion etween tropicl SST nd Atlntic/Europen MSLP in winter is sufficiently strong to llow us to mke skilful sttisticl sesonl forecsts of n NAO index, using liner sttisticl techniques, such s multiple liner regression on the leding SVD modes. The trining period for the sttisticl forecsts of the NAO index need not e very long in order to otin good skill scores. Incresing the length of the trining period eyond 30 yers does not seem to dd more skill to the predictions. Estimtion of the expected predictive skill is n importnt prt of sesonl forecsting. Skill estimtion is typiclly done y hindcsting, preferly cross-vlidted, ut it hs een demonstrted here tht internnul predictility is ffected y interdecdl vriility. Thus, skill score estimtes otined y cross-vlidtion of sttisticl hindcsts cn e misleding in the presence of interdecdl vriility. Acknowledgements This work ws supported y the Commission of the Europen Union through the «Environment nd Climte Progrmme» under contrct ENV4- CT , «Internnul to decdl climte vriility: scle interction experiments». REFERENCES BARNSTON, A.G. (1994): Liner sttisticl short-term climte predictive skill in the Northern Hemisphere, J. Climte, 7, BASNETT, T.A. nd D.E. PARKER (1997): Development of the glol men se level pressure dt set GMSLP2, Climtic Reserch Technicl Note n. 7, Hdley Centre, Meteorologicl Office, Brcknell, pp. 16 plus ppendices. BRANKOVIC, C. nd T.N. PALMER (1997): Atmospheric sesonl predictility nd estimtes of ensemle size, Mon. Wether Rev., 125, BRETHERTON, C.S., C. SMITH nd J.M. WALLACE (1992): An intercomprison of methods for finding coupled ptterns in climte dt, J. Climte, 5, CHERRY, S. (1996): Singulr vlue decomposition nlysis nd cnonicl correltion nlysis, J. Climte, 9, DAVIES, J.R., D.P. ROWELL nd C.K. FOLLAND (1997): North Atlntic nd Europen sesonl predictility using n ensemle of multidecdl tmospheric GCM simultions, Int. J. Climtology, 17, DONG, B.W., R.T. SUTTON, S.P. JEWSON, A. O NEILL nd J.M. SLINGO (2000): Predictle winter climte in the North Atlntic sector during the ENSO cycle, Geophys. Res. Lett., 27, FEDDERSEN, H. (2000): Impct of glol se surfce temperture on summer nd winter tempertures in Europe in set of sesonl ensemle simultions, Q. J. R. Meteorol. Soc., 126, FRAEDRICH, K. nd K. MÜLLER(1992): Climte nomlies in Europe ssocited with ENSO extremes, Int. J. Climtol., 12, HARRISON, D.E. nd N.K. LARKIN (1998): El Niño Southern Oscilltion se surfce temperture nd wind nomlies, , Rev. Geophys., 36, JOHANSSON, Å., A. BARNSTON, S. SAHA nd H. VAN DEN DOOL (1998): On the level nd origin of sesonl forecst skill in Northern Europe, J. Atmos. Sci., 55, JONES, P.D. (1987): The erly twentieth century Arctic Highfct or fiction?, Clim. Dyn., 1, LEGUTKE, S. nd E. MAIER-REIMER (1999): Climtology of the HOPE-G glol ocen generl circultion model, DKRZ Technicl Report n. 21 (Deutsches Klimrechenzentrum, Hmurg), pp. 50. MAY, W. nd L. BENGTSSON (1998): The signture of ENSO in the Northern Hemisphere midltitude sesonl men flow nd high-frequency intrsesonl vriility, Meteorol. Atmos. Phys., 69, MICHAELSEN, J. (1987): Cross-vlidtion in sttisticl climte forecst models, J. Climte Appl. Meteor., 26, O LENIC, E.A. nd R.E. LIVEZEY (1988): Prcticl considertions in the use of Rotted Principl Component Anlysis (RPCA) in dignostic studies of upper-ir height fields, Mon. Wether Rev., 116, POZO-VAZQUES, D., M.J. ESTEBAN-PARRA, F.S. RODRIGO nd Y. CASTRO-DIEZ (2001): The ssocition etween ENSO nd winter tmospheric circultion nd temperture in the North Atlntic region, J. Climte, 14,

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