Interannual changes of the ocean wave variability in the North Atlantic and in the North Sea

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1 CLIMATE RESEARCH Vol. : 3 9, Pulishe Otoer Clim Res Internnul hnges of the oen wve vriility in the North Atlnti n in the North Se E. Buer* Potsm Institute for Climte Impt Reserh, PO Box 3, Potsm, Germny ABSTRACT: A high-resolution oen wve hinst for 9 to 993 with the WAM wve moel is use to stuy the men se stte n its ominnt moes of vriility in the North Atlnti n in the North Se. The win n wve t shre high orreltion oeffiients with the North Atlnti Osilltion (NAO) inex of the winter seson n rther low orreltion oeffiients with the monthly NAO inex. The low orreltions re inue y the ifferent moes of vriility. The NAO inex vries t seminnul n shorter perios n the win n wve t vry with the sesonl yle. In ition, onsierly unstey vriility is pprent t synopti sles. The ominnt moes of tht vriility, retrieve y wvelet nlysis, re similr for win n wve t of the sme yer ut my hnge onsierly from yer to yer. From 97 to 99, when the NAO inex inreses, the ominnt perio of vriility lso inreses. The sme tren is inferre from win n wve mesurements t Oen Wether Sttion M. In ontrst, the ominnt perios inferre from t of the southern North Se show reverse tren. This inites tht the wve vriility in the North Se is reue when the westerlies re more zonl, n is intensifie when the westerlies re less zonl through more meriionl ontriutions initite y the Northest Atlnti win n wve vriility. KEY WORDS: NAO inex Win fiels Signifint wve height Wvelet power spetrum Synopti-sle vriility Resle or repulition not permitte without written onsent of the pulisher. INTRODUCTION Surfe win fiels n win-riven oen wves exhiit lrge vriility on wie rnge of time sles. The vriility we oserve is ompose of flututions on the wether sle n the sesonl sle, n of flututions on internnul to el sles ssoite with lrge-sle limte vritions. The 9s to 99s time series of signifint wve height (H s ) from the Northest Atlnti show signifint upwr tren (Bon & Crter 99, Bouws et l. 99). Bon & Crter (993) inite tht the upwr tren of nnul men H s is onnete to the inrese of the lrge-sle grient of se level pressure etween the Azores High n the Ieln Low represente y the North Atlnti Osilltion (NAO) inex (Hurrell 99). The high orreltion etween the NAO inex n the *E-mil: uer@pik-potsm.e H s t for winter months in prtiulr suggests tht the NAO inex might e useful prmeter to preit future hnges in wve height from lrge-sle limte hnge simultions. Speifilly, n inrese in H s n e inue y stronger men westerly wins in the mi-ltitues s onsequene of lrger NAO inies. This oupling mehnism hs een emonstrte to e effetive from ynmil wve moeling stuies (Kushnir et l. 997, WASA Group 99). However, ler eviene for n upwr tren in the mesure men win spees to explin the tren in the men wve height is missing (Bon & Crter 993). Furthermore, the orreltion of the NAO inex with the men win t is foun to e smller thn with the H s t. This my hve severl resons. Firstly, historil time series of win t show inhomogeneities ue to hnging prties in prouing the t (Crone et l. 99), while wve height t re onsiere to e more homogeneous. Seonly, win fiels ontin reltively lrge nturl vriility, Inter-Reserh

2 Clim Res : 3 9, whih iminishes the sttistil orreltion. Furthermore, the upwr tren of the men wve height might not e inue solely y n inrese in men win spee ut lso y hnge in win vriility. However, the effet on the men wve height from hnging the win vriility is rther smll, s inferre from hnging the storm frequeny in the North Atlnti (Buer et l. ) or from inresing the high-frequeny gustiness (Buer & Weisse ). The experiment on hnge storm frequeny revele tht fster (slower) moving wether strem proue lower (higher) men H s through shortening (lengthening) of the storm urtion. The win vriility on the synopti sle is most relevnt for the evolution of high se sttes. In previous investigtions the t se ws insuffiient to nlyze the oserve growth of the men wve height with respet to win vriility on the synopti sle. In prtiulr, resolving tren on el time sles in the frequeny, urtion, size n intensity of storms, is iffiult exerise. However, limte simultions with inrese CO senrios provie initions tht the ttriutes of the North Atlnti ylones in the storm trk my hnge in future (e.g., Shuert et l. 99). In the following, the win n wve vriility on the synopti sle is nlyze for the North Atlnti, uring the 3 yr perio from 9 to 993. The investigtion is se on the h win nlyses from the tmosphere moel of the Europen Centre for Meium Rnge Wether Forest (ECMWF), the win-riven wve t from the WAM wve moel n the mesure t from the Oen Wether Sttion Mike (OWS M). The ominnt moes of vriility re etermine y wvelet nlysis n their internnul hnges re ompre with NAO hnges. The struture of the stuy is s follows. In Setion, the win n wve height t otine from ynmil moeling re esrie. Setion 3 shows the orreltions of the moele win n wve height t with the NAO inex. In Setion, the ominnt moes of vriility on the synopti sle re erive from the nlysis of wvelet spetr. Emphsis is put on interprettion of the 97 t, with low NAO inex, n of the 99 t, with high NAO inex. The results re isusse in Setion.. DESCRIPTION OF MODEL DATA The tmospheri win fiels re provie y the ECMWF Re-Anlysis (ERA) Projet (Gison ltitue 7 et l. 99). The signifint wve height fiels re otine with the WAM spetrl wve moel (Komen et l. 99), riven y the h ERA win fiels. The ltitue-longitue resolution of wve moel is. The moel re omprises the entire Atlnti Oen n the North Se. The wve spetrum is resolve y frequenies spe logrithmilly etween. Hz n. Hz, n y iretions in steps of. Signifint wve height n wve perio re integrl hrteristis etermine from the oen wve spetrum. The zonl n meriionl omponents of signifint wve height re erive from the men wve propgtion iretion of the iretionlly resolve spetrum. The renlysis of the wve t is performe for the 3 yr perio from 9 to 993, with -hourly output. 3. CORRELATION OF WIND AND WAVE DATA WITH NAO INDEX The men lrge-sle istriutions of the wins n of the win-riven wves resemle the istriution of the horizontl grients of se level pressure, oring to the geostrophi reltionship. Consequently, the.. orreltion U x Uy U x y T 3 3 longitue Fig.. Distriution of orreltion oeffiient etween winter (Deemer to Mrh) NAO inex n win n wve t, verge long 3 setions in the NE Atlnti n setion in the North Se, mrke y symols. Correltion oeffiients re given for: zonl win U x (lue), meriionl win U y (light lue), win spee U (green), zonl signifint wve height H sx (yellow), meriionl signifint wve height H sy (ornge), signifint wve height H s (re), n wve perio T (lk). Winter NAO inex from se level pressure mesurements t Pont Delg, Azores n Stykkisholmur/Reykjvik, Ieln; win t from ECMWF moel; wve t from WAM moel hinst for

3 Buer: Chnges in oen wve vriility zonl omponents of the win n the signifint wve height long the setion etween the Azores n Ieln re highly orrelte with the NAO inex, wheres the meriionl win n wve height omponents re poorly orrelte with the NAO inex (Fig. ). The NAO inex is inferre from the meriionl ifferene etween se level pressure mesurements t Pont Delg, Azores n t Stykkisholmur/ Reykjvik, Ieln. During the winter months the win n wve t in the northestern prt of the North Atlnti, in the Sotln/Norwy region, re more highly orrelte with the NAO inex thn the win n wve t from the entrl North Atlnti (Fig. ). This suggests tht the win fiels with zonl motions from west to est exten fr estwr of the Azores High n the Ieln Low. The zonlity of the west win n involves lrge feth n long urtion of win foring n thus uses estwr enhne orreltions of the NAO inex with wve height n perio. The winter NAO inex is seen to e onsierly more orrelte with the win n wve height t thn the monthly men t (Fig. ). The time series of the monthly NAO inex show flututions on seminnul n shorter perios wheres the win spees (m) (m) Yer Fig.. WAM signifint wve heights n NAO inex time series from 9 to 993. () Winter t (Deemer Mrh), () monthly t. Moel t verge long the setion etween Sotln n Norwy (see Fig. ). The orreltion oeffiient for the winter t is high (.9) n for the monthly t is low (.7) s well s the wve heights vry minly with the sesonl yle. The reue zonlity of the westerlies in the monthly t implies more frequent meriionlly irete wins in the estern North Atlnti n the North Se. This is inferre from the signifintly inrese orreltion etween the monthly NAO inex n the meriionl win n wve omponents in the estern North Atlnti ompre to the winter t. For the meriionl wve heights the orreltion inreses up to. for the monthly t, ompre to orreltion of. for the winter t (Fig. ). In the North Se, however, the orreltion oeffiient of the NAO inex with H s n the wve perio is reue through the sheltering effet of the British Isles. The lrgest orreltions with the NAO inex re otine for the zonl win n the zonl wve height omponent uring winter (Fig. ). This gin inites wie extension of the zonl motions over the Northest Atlnti n the North Se uring winter.. WAVELET ANALYSIS High-resolution time series of the win n wve t show, esies the sesonl vriility, lrge ontriutions from nonstey n turulent motions on the smller sles. The ominnt moes of the synopti-sle vriility re estimte using wvelet spetrum nlysis. Wvelet nlysis is useful metho to estimte ominnt sles of vriility s funtion of time, from time series ontining trnsient or temporlly lolize events. The wvelet spetrum nlysis yiels power istriution s funtion of time n sle. This metho ws pplie to oen win wves for the first time y Liu (99), who stuie wve growth with wins from mesure uoy time series of s resolution. In this stuy moele n mesure time series of win n signifint wve height with h resolution re nlyze. For prtil resons, the 3 yr time series from 9 to 993 is ivie into yr setions. From eh setion the sesonl yle ws filtere out y sutrting the monthly mens. Thus, in the nomly time series, it is minly the vriility on the synopti sle tht is retine. The wvelet power spetr re ompute with the so-lle Mexin ht wvelet whih is equivlent to the seon erivtive of the Gussin (DOG). DOG wvelets re ontinuous, non-orthogonl n relvlue wvelet funtions whih re preferle for signl nlysis (Frge 99). In omprison to other ontinuous wvelet funtions, suh s the Morlet or the Pul wvelet, the Mexin ht wvelet yiele smoother wvelet power spetr. Results re presente from the moel time series t lotion lose to the sttion of OWS M. Fig. 3 isplys

4 Clim Res : 3 9, Perio () Glo. Wvelet Power (m ) ver. Power (m ) - - the wvelet power spetrum of the moele signifint wve height t ( N, E) from the nomly time series of 97 (Fig. 3). The wvelet power spetrum E is efine, in nlogy to the Fourier power spetrum, s the squre of the solute vlue of the wvelet trnsform W of the nomly time series: E(t,s) = W(t,s) () where t enotes the time n s the sle. The wvelet trnsform W here is etermine from the inverse Fourier trnsform of the omplex onjugte prout etween the Fourier-trnsforme Mexin ht wvelet n the Fourier-trnsforme time series. From the wvelet power spetrum E(t,s) follows the glol wvelet spetrum E g from verging over time (here yr): E g N () s = Et ( i,) s N i= [N, E] 3 3 Time (ys of 97) Time (ys of 97) 3 Perio (ys) 3 3 Time (ys of 97) () In this wy the glol wvelet spetrum (Fig. 3) eomes omprle to the Fourier power spetrum. For iret omprison, the sle s is onverte to the orresponing Fourier perio in Fig. 3. An lterntive wy of smoothing the wvelet power spetrum is y verging over n of sles s j to s j : E () t = where C is normliztion ftor n s j enotes isrete sle. The sle-verge wvelet power E, whih n e expresse y the orresponing perioverge wvelet power, is useful to emonstrte the ifferent temporl vrition of wvelet power for ifferent ns of perios. The perio-verge wvelet power my e signifint in lolize time intervl, even if the glol wvelet power is not signifint in tht n of perios. This is evient from ompring Fig. 3 n 3. Further etils on wvelet spetrum nlysis n e foun in Torrene & Compo (99). The wvelet spetr of the win spee n wve height t from moeling n mesurements of the sme yer re seen to resemle eh other very losely. Their ominnt moes of vriility, expresse y the Fourier perio, lie in the rnge of to. Some of the wvelet spetr lso show seonry moe, n in 9 even thir moe is visile (not shown). The ourrene of seonry moes within yr inites tht the - - wins n the wves re ompose of vrying lolize ontriutions, whih ompli- - tes the esription of the ttriutes of synopti-sle win vriility. C j j= j Ets (, j ) s j (3) Fig. 3. () Anomly time series of H s from WAM moel with h resolution ( N, E) for 97, when NAO inex ws low. Anomly time series is without sesonl yle n normlize with stnr evition. () Contour plot of wvelet power spetrum using DOG wvelet s funtion of Fourier perio in ys n time in ys. Color shing isplys log(wvelet power) in units of vrine (m ). Blk ontour lines inite signifintly enhne wvelet power t 9% onfiene with respet to fitte re noise. Dshe line (one of influene) mrks the perios eyon whih the wvelet power is ffete y ege effets. () Glol wvelet spetrum, epening on perio from time-verge of wvelet power spetrum in (). Dshe line mrks men kgroun spetrum inferre from re noise. () Perio-verge wvelet power (lue) in 9. n n (re) in 9. 3 n s funtion of time. Dshe lines: 9% onfiene levels

5 Buer: Chnges in oen wve vriility 7 In omprison to the wvelet spetrum nlysis for the 97 t (Fig. 3) the wvelet spetrum for 99 t from the sme lotion is shown in Fig.. The t for 97 n 99 re hosen from the 3 yr perio euse the nnul men vlues of signifint wve height in the Northest Atlnti re foun to e very low in 97 n high in 99. At the sme time, the NAO inies were low in 97 n high in 99. The omprison of wvelet spetr shows tht the pek wvelet power n the pek perio in the moele win n wve height t lso inrese with growing NAO inex. This is more lerly evient from the wvelet nlysis of mesure win spees n H s t OWS M (Tle ). However, the shift in the pek vlues of the wvelet spetr shoul e onsiere only qulittively, euse the estimtes of wvelet power re signifint only t the shorter perios. At the longer perios, pek vlues re elow the 9% onfiene level, erive from the kgroun re noise spetrum s shown in Figs 3 &. In the North Se, the wvelet spetr of win spees n wve heights re lso very similr, ut the shift of the ominnt prmeters of the North Se wvelet spetr from 97 to 99 is reverse ompre to the Northest Atlnti t (Tle ). In the North Se, the pek vlue of the wvelet power spetrum n the pek perio re lrger in 97 (Fig. ) thn in 99 (Fig. ). This inites tht in times of high (low) NAO inex, when the lrge-sle tmospheri irultion hs stronger (weker) zonl omponents n weker (stronger) meriionl omponents, the synopti-sle vriility in the North Se experienes less (more) influene from the North Atlnti storm trk.. CONCLUSIONS The lrge-sle istriution of winriven oen wves in the North Atlnti is relte on the one hn to the lrgesle istriution of the grient of se level pressure, oring to the geostrophi reltionship, n on the other hn to the integrl proess of wve genertion. This explins the high orreltion Perio () Glo. Wvelet Power (m ) ver. Power (m ) - - [N, E] 3 3 Time (ys of 99) Time (ys of 99) 3 Perio (ys) 3 3 Time (ys of 99) Fig.. Sme s Fig. 3 ut for 99 time series of H s, when NAO inex ws high Tle. Pek vlues of glol wvelet power E p n pek perio p p () otine from h time series for 97 n 99, with low n high NAO inex respetively. Time series of win spee u n signifint wve height H s tken from mesurements of OWS M in Northest Atlnti, from ECMWF moel n WAM moel t the sme lotion ( N, E), n from the ECMWF moel n the WAM moel in southern North Se ( N, 7 E) Lotion Time series E p p p E p p p NE Atlnti OWS M u 7. m s 7.9. m s 3. ECMWF u 79. m s m s. OWS M H s 7.3 m 7.9. m 3. WAM H s.3 m.9. m 37. North Se ECMWF u. m s 37.. m s.9 WAM H s. m m.9 Glol wvelet spetrum hs signifint seonry pek t -

6 Clim Res : 3 9, [N, 7E] Time (ys of 99) 3 Perio () 3 3 Time (ys of 99) Perio (ys) ver. Power (m ) Glo. Wvelet Power (m ) [N, 7E] Time (ys of 97) 3 3 Time (ys of 99) Fig.. Sme s Fig. 3 ut for 99 time series of H s from southern North Se ( N, 7 E), when NAO inex ws high Perio () Time (ys of 97) 3 Perio (ys) Glo. Wvelet Power (m ) 3 3 Time (ys of 97) ver. Power (m ) Fig.. Sme s Fig. 3 ut for 97 time series of H s from southern North Se ( N, 7 E), when NAO inex ws low

7 Buer: Chnges in oen wve vriility 9 etween signifint wve height in the North Atlnti n the NAO inex, in prtiulr uring winter. In the estern North Atlnti the umultive wve growth, onnete with longer win urtion n feth, results in lrger orreltion of the NAO inex with the wve t (wve height n perio) thn with win spee. In ition to lrge-sle hrteristis, the h time series of win n wve height t revel onsierle ontriutions of ifferent strength from synoptisle vriility, whih re lolize minly in winter. An ttempt to esrie the ominnt perios of the synopti-sle vriility is me using renlyze s well s mesure t of win spee n signifint wve height from 9 to 993. The wvelet power spetr etermine for yr setions representing nomlies from the sesonl yle show reltively lrge internnul hnges. The ominnt perio of vriility erive from the 3 time series vries etween n. The inrese of the NAO inex from 97 to 99 ppers to e ompnie y signifint growth of the nnul men signifint wve height, the ominnt wvelet power n the ominnt perio of the wvelet power. This inites tht the high se sttes in the Northest Atlnti in 99 my result prtly from the inrese strength of the westerlies n prtly from n intensifition of the synoptisle vriility. But from the present nlysis no generl onlusion n e rwn on systemti reltionship etween the zonlity of the westerly wins n storminess in mi-ltitues. To otin etter sttistil esription, longer time series re require. The lose resemlne etween the wvelet power spetr otine from the moele win n wve height t n those from mesure time series t OWS M provies onfiene in the usefulness of the tmosphere n wve moel simultions. As wve heights in the Northest Atlnti re losely orrelte with the winter NAO inex, the winter NAO inex ppers to e useful preitor. This implies tht preitions of the future evelopment of the winter NAO inex my e use to estimte future hnges in wve height for the North Atlnti. But the intertion etween lrge-sle hnges n synopti-sle vriility is seen to e highly nonliner. In ition, regionl ifferenes ply role s internnul hnges on the synoptil sle in the North Atlnti re seen to e quite ifferent to those in the North Se. Nevertheless, ynmil moels of the tmosphere n of oen wves pper to e vlule tools to infer informtion on lrge-sle n synopti-sle vriility, whih is neee for tking preutions in the routing of ships n for the inhitnts of the zone. Aknowlegements. This stuy ws fune y the Bunesminister für Bilung un Forshung, Bonn, uner projet KLINO (Climtology of spetrl wve t in the North Se n the Blti Se, 3FA). LITERATURE CITED Bon S, Crter DJT (99) Wve limte hnges in the North Atlnti n North Se. Int J Climtol : Bon S, Crter DJT (993) A onnetion etween men wve height n tmospheri pressure grient in the North Atlnti. Int J Climtol 3:3 3 Buer E, Weisse R () Determintion of high-frequeny win vriility from oservtions n pplition to North Atlnti wve moeling. J Geophys Res (C): 79 9 Buer E, von Storh H, Stolley M () Sensitivity of oen wves to spee hnges of the wether strem. Glo Atmos Oen Syst 7:9 Bouws E, Jnnink D, Komen GJ (99) The inresing wve height in the North Atlnti Oen. Bull Am Met So 77:7 77 Crone VJ, Greenwoo JG, Cne MC (99) On trens in historil mrine win t. J Climte 3:3 7 Frge M (99) Wvelet trnsforms n their pplition to turulene. Annu Rev Flui Meh :39 7 Gison R, Kllerg P, Uppl S (99) The ECMWF Re- Anlysis (ERA) projet. ECMWF Newsletter 73:7 7 Hurrell JW (99) Del trens in the North Atlnti Osilltion: regionl tempertures n preipittion. Siene 9:7 79 Komen GJ, Cvleri L, Doneln M, selmnn K, selmnn S, Jnssen PAEM (99) Dynmis n moelling of oen wves. Cmrige University Press, Cmrige Kushnir Y, Crone VJ, Greenwoo JG, Cne MA (997) The reent inrese in North Atlnti wve heights. J Climte :7 3 Liu PC (99) Wvelet spetrum nlysis n oen win wves. In: Foufoul-Georgiou E, Kumr P (es) Wvelets in geophysis. Aemi Press, Sn Diego, p Shuert M, Perlwitz J, Blener R, Frerih K, Lunkheit F (99) North Atlnti ylones in CO -inue wrm limte simultions; frequeny, intensity, n trks. Clim Dyn :7 37 Torrene C, Compo GP (99) A prtil guie to wvelet nlysis. Bull Am Met So 79: 7 WASA Group (99) Chnging wves n storms in the Northest Atlnti? Bull Am Met So 79:7 7 Sumitte: July, ; Aepte: Mrh, Proofs reeive from uthor(s): July 3,