Interactions between the tropical ISO and midlatitude low-frequency flow

Transcription

1 Clim Dyn (2008) 31: DOI /s Interctions between the tropicl ISO nd midltitude low-frequency flow Lin-Lin Pn Æ Tim Li Received: 3 October 2006 / Accepted: 2 My 2007 / Published online: 12 June 2007 Ó Springer-Verlg 2007 Abstrct In this study, we investigte the interction between the tropicl Intrsesonl Oscilltion (ISO) nd midltitude tmospheric low-frequency vribility, using observtionl dt nd numericl models, with specil emphsis on the role of the synoptic eddy feedbck. A sttisticl closure for the synoptic eddy-to-low frequency flow feedbck is constructed, bsed on singulr vlue decomposition (SVD) method with observtionl dt. Applying this sttisticl closure to brotropic model nd broclinic 2½-lyer model, we study the role of the synoptic eddy feedbck in the midltitude response to the tropicl ISO forcing. Both observtionl nd modeling studies show tht the strongest synoptic eddy forcing ppers t the Pcific nd Atlntic storm-trck regions, nd the synoptic eddy exerts positive feedbck to the midltitude low-frequency flow induced by tropicl ISO forcing. Our numericl experiments demonstrte the possible role of midltitude disturbnce forcing in the ISO initition t the equtor. The signl of the midltitude perturbtions propgtes southestwrd in the form of Rossby wve pckge. It my rech the equtor within severl dys under either esterly or westerly bsic flow regimes. The response t the equtor hs observed ISO-like structure nd estwrd propgtion chrcteristics. This pper is contribution to the AMIP-CMIP Dignostic Sub-project on Generl Circultion Model Simultion of the Est Asin Climte, coordinted by W.-C. Wng. L.-L. Pn T. Li Interntionl Pcific Reserch Center, University of Hwii t Mno, Honolulu, HI, USA L.-L. Pn (&) Deprtment of Lnd, Air nd Wter Resources, University of Cliforni, Dvis, CA 95616, USA e-mil: llpn@ucdvis.edu; lpn@hwii.edu 1 Introduction Tropicl intrsesonl oscilltion (ISO), especilly its dominnt component t the equtor Mdden Julin oscilltion (MJO), hs been extensively studied over the pst decdes (Mdden nd Julin 1971, 1972; Wng nd Rui 1990). ISO (or MJO) consists of lrge-scle coupled ptterns in tmospheric circultion nd deep convection, nd is chrcterized by estwrd propgtion cross the equtoril Indin nd western/centrl Pcific ocens t timescle of dys (Weickmnn 1983; Knutson nd Weickmnn 1987; Kildis nd Weickmnn 1992; Mdden nd Julin 1994; Wng nd Li 1994; Hendon nd Slby 1994; Zhng 2005). The ISO (or MJO) is often explined on the bsis of equtoril Kelvin wve dynmics due to its estwrd movement nd lrge mplitude t the equtor. However, the slow estwrd propgtion t n verged speed of 5 m/s (e.g., Weickmnn et l. 1985; Knutson et l. 1986) distinguishes the MJO from the pure dry nd wet Kelvin wves, which propgte estwrd t greter speeds of 50 m/s nd m/s (e.g., Wheeler nd Kildis 1999; Wheeler et l. 2000), respectively. The lrge-scle wind structure of MJO is often described in terms of convectively coupled Kelvin Rossby wve pckge (e.g., Wng nd Li 1994). Est of the convective center, the low-level esterlies nd upper level westerlies resemble the equtoril Kelvin wve. To the west, low-level westerlies (upper level esterlies) nd the ssocited pir of cyclonic (nticyclonic) gyres strddling on the both sides of the equtor re the chrcteristics of the equtoril Rossby wve (Mdden 1986; Nogues-Pegle et l. 1989). Both Kelvin nd Rossby wve structures hve been considered dynmiclly essentil to the MJO (Hendon nd Slby 1994; Wng nd Li 1994; Zhng 2005).

2 376 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow Mny studies show tht the influence of MJO cn extend to the subtropics nd midltitudes (Liebmnn nd Hrtmnn 1984; Weickmnn et l. 1985; Lu nd Phillips 1986; Knutson nd Weickmnn 1987; Ferrnti et l. 1990; Hsu 1996; Higgins nd Mo 1997; Jones 2000; Bond nd Vecchi 2003; Nogues-Pegle et l. 2000; Mtthews 2004). Associted with enhnced (reduced) tropicl convection, the upper-level divergence (convergence) is often ccompnied by subtropicl upper-level convergence (divergence) counterprt. As the convective region of ISO moves estwrd long the equtor from the Indin Ocen to the western Pcific, the divergent circultion connecting the tropics nd subtropics lso moves estwrd. The subsesonl wind fluctutions ssocited with ISO re often observed ner the exit region of the Asin-Pcific jet. In prticulr, north south dipole in the stremfunction field ppers over the north western Pcific in the upper troposphere when ISO convection is locted in the Indin Ocen (Knutson nd Weickmnn 1987; Hsu 1996; Kim et l 2006). Tropicl convection my lso influence midltitude low-frequency vribility indirectly vi zonl wind chnges (Schubert nd Prk 1991). Frederiksen nd Frederiksen (1993, 1997) found tht the MJO is coupled tropiclextrtropicl mode in broclinic model with convective prmeteriztion. Without convective prmeteriztion, the internl tropicl mode structure disppers but the extrtropicl structure is lrgely unchnged s is the period. This implies tht tropicl nd extrtropicl ISO modes my be determined by different processes/fctors. There is no generlly ccepted view on tht. The dynmicl processes responsible for the ISO-midltitude connection hve been intensively studied. The extrtropicl response to nomlous tropicl heting is essentilly tht of Rossby wve propgtion nd dispersion (Hoskins nd Kroly 1981). The brotropiclly nd brocliniclly unstble bckground flows cn serve potentilly s n energy source for midltitude response (Simmons et l. 1983; Frederiksen 1983; Schubert 1985; Strus nd Lindzen 2000). Synoptic eddy feedbck, on the other hnd, my lso ply n importnt role (Schubert nd Prk 1991). Plumb (1985) suggests tht trnsient eddies my ct s source of sttionry wve ctivities over the ocens. Modeling studies of the role of the trnsient eddies ssocited with the midltitude response to the El Nino forcing by Held nd Kng (1987) nd Held et l. (1989) showed tht the trnsient eddies, which re modified by chnges in the sttionry flow (due to the chnge of tropicl heting), my strongly feed bck to the sttionry wves. This synoptic eddy feedbck plys n importnt role in the Pcific-North Americn (PNA) pttern-like response in the midltitude to the tropicl forcing (Jin et l. 2006b; Pn et l. 2006). Previous studies bsed on observtionl nlyses hve suggested the potentil role of subtropicl Rossby wve trins, midltitude broclinic systems, nd cold surges over the South Chin Se in the initition nd intensifiction of MJO (e.g., Lim nd Chng 1981; Hsu et l. 1990; Kildis nd Weickmnn 1992; Meehl et l. 1996; Compo et l. 1999; Hoskins nd Yng 2000; Lin et l. 2000). However, so fr not much modeling simultion hs been done to clerly demonstrte the sole initition effect by midltitude perturbtions. In this study we will explore both the impct of the tropicl ISO on the midltitude low-frequency tmospheric vribility (with prticulr focus on the role of the synoptic eddy feedbck) nd the effect of midltitude perturbtions on equtoril ISO initition. A simple brotropic model nd 2½-lyer broclinic model with sttisticl closure describing the synoptic eddy feedbck to low-frequency flows will be constructed. The rest of the pper is orgnized s follows. In Sect. 2 we describe the two models to be used in this study, nd in Sect. 3 we construct sttisticl closure for the synoptic eddy nd low-frequency flow interction. Sections 4 nd 5 present the observtionl nd modeling results ssocited with the impct of tropicl ISO on midltitude circultion. In Sect. 6 we further investigte the effect of midltitude disturbnces in ISO initition. A conclusion is given in Sect The models Both brotropic model nd 2½-lyer broclinic model with prmeterized synoptic eddy feedbck to low-frequency flows re used in this pper, to explore the role of high-frequency trnsients (synoptic eddy) in the tropiclmidltitude teleconnection. 2.1 A brotropic model with synoptic eddy feedbck The brotropic model used here is similr to tht used in Pn nd Jin (2005; see lso Pn 2003; Jin et l. 2006, b) except tht we use sttisticl closure to relte the synoptic eddy forcing to the low-frequency flow. The brotropic vorticity eqution for the low-frequency vribility cn be written s odw þ Jðw ot ; Dw c þ f ÞþJðw c ; Dw Þ ¼ Jðw 0 ; Dw 0 Þj þ F n ð1þ where stremfunction w is seprted into three prts: climtologicl bsic stte w c ; low-frequency nomly component w ; nd high-frequency synoptic eddy component w. The D nd J re Lplcin nd Jcobin opertors, respectively; f indictes the Coriolis prmeter, nd F n represents dissiptions nd externl forcing (e.g., f*diver-

3 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow 377 gence). The dissiption terms included here re bihrmonic horizontl diffusion with the dmping timescle of one dy for the smllest wve, nd the Newtonin dmping nd Ryleigh friction. The ltter is represented by liner drg tht hs n e-folding timescle of 10 dys. The forcing is derived bsed on regressed 250 hp divergence fields. The climtologicl bsic stte is obtined by time verge t 250 hp for the northern hemisphere cold seson (November Mrch) between 1979 nd The brotropic model is spectrl model with tringulr trunction t T42. The time stepping is implicit, with time increment of 30 minutes. Without the trnsient eddy forcing term Jðw 0 ; Dw 0 Þj ; Eq. (1) is reduced to trditionl linerized brotropic model. By constructing sttisticl reltionship between the observed trnsient forcing Jðw 0 ; Dw 0 Þj nd low-frequency nomly w fields, we obtined sttisticl closure for the trnsient eddy forcing, this is, Jðw 0 ; Dw 0 Þj ¼ L sw : where L s is feedbck mtrix. The detiled description of this sttisticl closure method cn be found in the next section. After this sttisticl closure is derived, the system is closed. Then we use this model to investigte the role of synoptic eddy feedbck in the midltitude tmospheric response to the tropicl ISO forcing. 2.2 A 2½-lyer broclinic model We extend the originl 2½-lyer model (Wng nd Li 1993; Li nd Wng 1994; Wng nd Xie 1996) to include the synoptic eddy feedbck. The governing equtions for zonl wind (u), meridionl wind (v) nd temperture (T) re (Wng nd Li 1993): Du ou ¼ fv Dt ox þ F u; Dv ou ¼ fu Dt oy þ F v; DT Dt C p x ¼ Q C p þ F T ; ð2þ ð3þ ð4þ where F, Q, C p, x, nd denote geopotentil height, dibtic heting, specific het, verticl velocity, nd specific volume, respectively. In the first prt tht investigtes the midltitude synoptic eddy feedbck, fixed heting pttern (regression bsed on the OLR index) is specified. In the second prt tht exmines the effect of midltitude perturbtions on the equtoril ISO initition, circultiondependent heting scheme is used, in which the condenstionl heting rte due to deep convection is prmeterized on the bsis of moisture nd het budget, following Kuo (1974). The bsic-stte specific humidity is specified from the observed sesonl men climtology vlues. F u, F v, nd F T represent both dissiption nd externl forcing similr to F n : The Newtonin dmping nd Ryleigh friction hve n e-folding timescle of 15 dys (2 dys) in the free tmosphere (boundry lyer), nd wek verticl diffusion with dmping timescle of 1,000 dys is lso included. Similr to the brotropic model, we seprte ll vribles into climtologicl men, low-frequency (intrsesonl) nomly, nd high-frequency trnsient (i.e., synoptic eddy with timescle between 2 nd 8 dys) components, i.e., u ¼ u c þ u þ u 0 ; ð5þ where subscripts nd c stnd for the intrsesonl (or low-frequency) nomly nd climtology, respectively, nd prime indictes high-frequency vribility. The linerized low-frequency nomly equtions for zonl wind ðu Þ; meridionl wind ðv Þ nd temperture ð T Þ re ou ot þ u ou c ox þ u þ v 0 ou0 oy ¼ f v o U ox þ F u ; ov ot þ u ov c ox þ u þ v 0 ov0 oy o T ot oy þ ou c ox þ v ou c oy þ v ou c ou þx c op þ x ou c op þ ov c ox þ v ov c oy þ v ov c ov þx c op þ x ¼ f u o U oy þ F v ; o T þ u c ox þ u o T c ox þ v c!! þ u 0 ot0 þ v ox 0 ot0 oy! o T c þ x op þ ot0 x0 op ov c op þ ou0 x0 op oy þ ov0 x0 op ou0 u0 ox ov0 u0 ox o T oy þ v o T c oy x C p þx c o T op Q ¼ þ F T C p ð6þ ð7þ ð8þ We further relte the synoptic eddy forcing terms to the low-frequency nomly terms, A ¼ L s B; where 0 A ¼ u 0 ou0 ox þ ou0 v0 oy þ ou0 x0 op u 0 ov0 ox þ ov0 v0 oy þ ov0 x0 op u 0 ot0 ox þ ot0 v0 oy þ ot0 x0 op ð9þ 1! u C A ; B ¼ v ; T ð10þ

4 378 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow L s is feedbck mtrix, describing the interction between the synoptic eddy nd low-frequency flow. It cn be sttisticlly determined bsed on the observed synoptic eddy forcing terms A nd low-frequency nomlies B. With this sttisticl reltionship, the 2½-lyer model is closed. In the next section we describe in detil how this sttisticl closure for the synoptic eddy feedbck is derived. The broclinic model is grid-point model, with finitedifference schemes pplied in both spce nd time; the time increment is 30 min. In ddition to lepfrog timeintegrtion scheme, Euler nd Euler-bckwrd schemes re used every 12 h to reduce numericl noises. Sptil resolution in stndrd runs is 5 longitude by 2 ltitude. A finer resolution of 2.5 longitude by 2 ltitude ws tested, nd the results re not sensitive to the chnge in resolution. The climtologicl sesonl men bsic stte is derived from the NCEP NCAR (Ntionl Centers for Environmentl Prediction Ntionl Center for Atmospheric Reserch) renlysis t 200 nd 850 hp, respectively. 0 1 Y B X B 1 A ¼ X A Y A ¼ X A 2 Y B 1 2 C A ¼ 2 X B XA 2 B. A B; N Y B N N X B N therefore, 0 1 X B 1 2 L s ¼ X A 2 X B 2 B. A : N X B N ð14þ ð15þ Thus we get closure for the 2½-lyer model if A nd B re defined ccording to Eq. (10). A similr closure cn lso be obtined for the brotropic model if we chnge the trnsient forcing A to Jðw 0 ; Dw 0 Þj nd the low-frequency nomly B to w ; i.e., Jðw 0 ; Dw 0 Þj ¼ L s w : Using the observed Jðw 0 ; Dw 0 Þj nd w ; one my obtin L s through the SVD nlysis of the covrince mtrix for the brotropic model. 3 A sttisticl closure for synoptic eddy feedbck We derived sttisticl closure for synoptic eddy feedbck bsed on NCEP NCAR renlysis dt (Klny et l. 1996) by using singulr vlue decomposition (SVD) method. Through the singulr vlue decomposition (Nvrr 1993; Bretherton et l. 1992) of the covrince mtrix C of the synoptic eddy forcing nomly A nd the low-frequency flow nomly B, we hve C ¼ X A RðX B Þ T ; ð11þ where X A nd X B re orthonorml mtrices, which give the covring ptterns of A nd B. The (X B ) T denotes the trnspose of X B, nd R is digonl mtrix of rel singulr vlues. The time series Y A nd Y B corresponding to the sptil ptterns X A nd X B cn be obtined by projecting them onto A nd B, Y A ¼ðX A Þ T A; Y B ¼ðX B Þ T B: ð12þ Conducting liner regression between the two time series Y A nd Y B for ech mode i, Y A i ¼ i Y B i ði ¼ 1; 2;...; NÞ ð13þ one my relte the eddy-forcing nomly A to the lowfrequency flow nomly B, 4 Observtionl nlysis of tropicl ISO influence on midltitude low-frequency nomlies The min dtsets used here re dily globl gridded fields (zonl wind, meridionl wind, nd stremfunction) from the NCEP-NCAR renlysis from 1 Jnury 1979 to 31 December Dily verges of the Ntionl Ocenic nd Atmospheric Administrtion (NOAA) stellite outgoing longwve rdition (OLR) for the sme period re used to represent tropicl convection. The OLR dt re filtered t dy bnd to keep the intrsesonl signl. Three OLR indices re defined t box centered t (100 E, 0 ), (120 E, 0 ), nd (140 E, 0 ), respectively, to represent the tropicl convection ssocited with ISO t different loctions. The stremfunction fields t 250 hp nd 1,000 hp re further regressed onto these indices to revel lrge-scle flow ptterns ssocited with ISO. Figure 1 shows the sptil pttern of the regressed stremfunction nomly t 250 hp for the OLR index t (100 E, 0 ) during November to Mrch. Here the regression is clculted bsed on unfiltered originl stremfunction dily dt nd the OLR index hs been normlized. The regressed pttern hs positive centers in the north Indin nd Atlntic Ocens nd over Austrli, nd negtive centers in the south Atlntic nd Indin Ocens. A mrked north south dipole structure ppers in the north Pcific, consistent with previous results (e.g., Knutson nd Weickmnn 1987; Hsu 1996; Kim et l. 2006).

5 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow 379 () () Fig. 1 Sptil pttern nd b time-ltitude cross section t 180 longitude of the 250 hp stremfunction nomlies regressed on the OLR index centered t (100 E, 0 ) during the cold seson (November Mrch). The contour intervl is 10 6 m 2 s 1. The verticl xis in b represents the leding time (unit: dy) by which the OLR index leds the stremfunction field The temporl vrition of this dipole cn be clerly seen from lg regression nlysis shown in Fig. 1b. It hs n oscilltion period of 40 dys. The result implies tht the forcing ssocited with tropicl ISO heting my produce significnt tmospheric low-frequency vribility in midltitudes on the intrsesonl timescle. The vrition of the dipole cn be further seen from time-longitude cross section long 20 N nd 45 N (Fig. 2), corresponding to its south nd north centers. Along 20 N, the estwrd propgtion of the stremfunction signl is clerly evident (Fig. 2), closely following the estwrd propgtion of equtoril convection from the Indin Ocen to the western Pcific. At 45 N, the estwrd propgtion is only evident between 180 nd 60 W, while it is uncler over other longitudes. Figure 3 illustrtes the regressed stremfunction pttern t 1,000 hp. Compred to the upper tropospheric field (Fig. 1), the low-level stremfunction hs monopole structure in the north Pcific, with its center locted t Fig. 2 As in Fig. 1b except for the time-longitude cross section t 20 N nd b 45 N (180, 40 N). The verticl structure of the regressed rottionl flow in generl exhibits broclinic structure in the tropics (30 S to 30 N). In the midltitude it exhibits n equivlent brotropic structure. The time-ltitude cross section t 180 (Fig. 3b) shows dominnt oscilltive period of round 40 dys, consistent with the results t 250 hp. The dominnt feture for the time-longitude cross section t 1,000 hp is similr to tht t 250 hp. The midltitude flow ptterns chnge ccordingly when the forcing ssocited with tropicl ISO moves estwrd. This cn be inferred from the regressed ptterns ssocited with the OLR indices t (120 E, 0 ) nd (140 E, 0 ) (not shown). In the tropicl region, the dominnt pttern does not chnge much except tht the positive nd negtive centers shift estwrd following the equtoril convection center (see lso Fig. 2, similr results were lso obtined by Frederiksen 2002), nd it still hs broclinic structure in the verticl. In the midltitude, there re wve trin ptterns, nd their verticl structure remins equivlent brotropic.

6 380 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow () () Fig. 4 Eddy forcing of the stremfunction nomly regressed on the OLR index centered t (100 E, 0 ), clculted bsed on sttisticl closure () nd from the observtions. The contour intervl is 1m 2 s 2 Fig. 3 As in Fig. 1 except for 1,000 hp 5 Role of synoptic eddy feedbck in the midltitude response to the tropicl ISO In this section, we investigte the role of synoptic eddy feedbck in the midltitude tmospheric response to the tropicl ISO forcing in both the brotropic nd broclinic models. 5.1 Brotropic model results The extrtropicl response to nomlous tropicl heting is often explined in terms of Rossby wve propgtion nd dispersion (Hoskins nd Kroly 1981). Here using brotropic model with the synoptic eddy nd low-frequency flow interction, we investigte the role of synoptic eddy feedbck in the response of midltitude low-frequency flows to the forcing ssocited with tropicl ISO heting. In the following, we first vlidte the sttisticl closure for the synoptic eddy feedbck in the brotropic model Jðw 0 ; Dw 0 Þj ¼ L s w : nd then investigte the difference in the response fields with nd without the synoptic eddy feedbck. Figure 4 illustrtes the model simulted eddy forcing ½D 1 ðl s w ÞŠ nd observed eddy forcing ½ D 1 Jðw 0 ; Dw 0 Þj Š regressed on the OLR index t (100 E, 0 ). The observed results re well reproduced by the sttisticl closure nd the pttern correltion between observed eddy forcing nd model simulted one is round 0.8. The eddy forcing minly is locted t midltitude storm trck regions, nd it hs positive center round 40 N nd negtive center to its south in the Pcific, consistent with the dipole structure in the stremfunction field (Fig. 1). The positive correltion between the synoptic eddy forcing nd low-frequency flow in the region implies tht there is positive feedbck between them, which cn be further confirmed by subsequent numericl experiments. Similr results re obtined for the OLR indices centered t (120 E, 0 ) nd (140 E, 0 ) (not shown). Next we exmine the midltitude response to tropicl ISO forcing t (100 E, 0 ), (120 E, 0 ) nd (140 E, 0 ) in the brotropic model. The forcing ptterns re obtined ccording to the OLR ptterns (not shown) regressed on the OLR indices centered t (100 E, 0 ), (120 E, 0 ), nd (140 E, 0 ), nd re confined mostly in the equtoril region (15 S 15 N) (Fig. 5). The mgnitude of forcing is determined by regressed 250 mb divergence field (which hs n mplitude round s 1 ). The Rossby wve source used here is just f* Divergence. Our focus is on the difference in the response fields between cses with nd without the synoptic eddy feedbck. Figure 6 shows the observed nd the model simulted response fields (The

7 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow 381 Fig. 5 Regressed pttern of OLR nomlies on the OLR index centered t (100 E, 0 ). The contour intervl is 6 W m 2 observed field is the sme s tht in Fig. 1 except tht only the northern hemispheric portion is plotted here.) Compring the results with nd without the eddy feedbck (Fig. 6b vs. Fig. 6c), it is cler tht the response is significntly enhnced when the synoptic eddy feedbck is included, implying positive feedbck between the synoptic trnsients nd low-frequency flows in the midltitudes. The difference field in Fig. 6d shows tht two mximum centers re locted long the Pcific nd Atlntic storm trcks. The north south dipole structure in the north Pcific does exist in both simultions with nd without the synoptic eddy feedbck. However, the strength is weker thn tht of the observed when the synoptic eddy feedbck is not included. To illustrte the role of the zonlly symmetric men flow in the genertion of the north south dipole, we conducted n dditionl experiment in which we delibertely suppress the zonlly symmetric prt of the climtologicl men stte (i.e., sttionry wves) in the model. Figure 7 shows the model simultion results in this cse. Without the sttionry wves in the bsic flow, the model filed to reproduce the observed strength of the response, s clerly shown in the difference field (Fig. 7b). This illustrtes the importnt role of the sttionry wve lowfrequency flow interction in the formtion of the north south dipole structure. Consistent with previous studies by Simmons et l. (1983) nd others, who pointed out the importnce of the zonlly symmetric bsic flow in the midltitude response to tropicl heting, here we demonstrte tht both the sttionry wves nd trnsient eddies re crucil for the tropicl-midltitude teleconnection. When the ISO forcing shifts to (120 E, 0 ) or (140 E, 0 ), the model simultes weker midltitude response, in greement with the observtions. The positive synoptic eddy feedbck still exists except the strength of the feedbck decreses correspondingly. To exmine the sensitivity of the model solution to nonstedy forcing, we conducted sensitivity experiment in which we llow the ISO forcing to propgte slowly estwrd long the equtor. The dominnt feture of the response filed is similr to tht of the stedy forcing except the mgnitude is slightly smller compring with the stedy response (not shown). 5.2 Results from the 2½-lyer model We further investigte the role of the synoptic eddy feedbck in the midltitude response to tropicl ISO heting by using 2½-lyer model. Similr to wht we did in the brotropic model, we first vlidte the sttisticl closure for Fig. 6 Stremfunction nomly ptterns in ssocition with the ISO forcing centered t (100 E, 0 ): observtionl results, b brotropic model simultions without the synoptic eddy feedbck, c brotropic model simultions with the synoptic eddy feedbck, nd d difference between the cses with nd without the synoptic eddy feedbck. The contour intervl is m 2 s 1 for, b nd c, nd 10 6 m 2 s 1 for d () (c) (d)

8 382 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow () () Fig. 7 Stremfunction nomly ptterns ssocited with the ISOlike forcing centered t (100 E, 0 ) in brotropic model under the zonl symmetric bsic stte (i.e., without the sttionry wve), nd b difference of the stremfunction fields between the cses with nd without the sttionry wve in the bsic stte. The contour intervl is 10 6 m 2 s 1 the synoptic eddy feedbck in the 2½-lyer model, nd then investigte the difference in the response field in cses with nd without the synoptic eddy feedbck. Figure 8 compres the observed nd simulted eddy forcing terms in the zonl wind eqution, regressed on the OLR index centered t (100 E, 0 ). The correltion between the observed nd simulted ptterns is round 0.75, indicting tht the sttisticl closure is vlid. Similr to the brotropic model results, the eddy forcing minly loctes t the Pcific nd Atlntic storm trck regions nd it positively feeds bck to the low-frequency flow. The forcing field hs n equivlent brotropic structure in the middle nd high ltitudes (not shown). Similr results re obtined for the forcing centered t (120 E, 0 ) nd (140 E, 0 ). Therefore, the observed eddy forcing effect is well represented by the sttisticl closure. After the vlidtion of the sttisticl closure for the synoptic eddy feedbck, we further investigte the role of the feedbck in the midltitude response to tropicl forcing in the 2½-lyer model. Similr to the previous brotropic Fig. 8 As in Fig. 4 except for the zonl wind nomly t 200 hp in the 2½-lyer model. The contour intervl is ms 2 nd the zero line is omitted study, we put the tropicl ISO forcing t (100 E, 0 ), (120 E, 0 ), nd (140 E, 0 ), respectively, nd investigte the difference in the response field between cses with nd without the synoptic eddy forcing. The horizontl pttern of the forcing (heting) is bsed on the regressed OLR pttern while its verticl profile hs mximum in the middle troposphere. Since the model is liner, chnging in mgnitude of the forcing field will linerly chnge the response field. Figure 9 presents comprison between the observtionl result (Fig. 9) nd the model simultions (Fig. 9b c) to the ISO forcing centered t (100 E, 0 ). The observtionl result is obtined by regressing the zonl wind field onto the OLR index centered t (100 E, 0 ). Figure 9b nd c shows simultions with nd without the eddy feedbck, while their difference is presented in Fig. 9d. Similr to the brotropic model results, the difference minly ppers in the Pcific nd Atlntic storm trck regions. The response field is enhnced when the

9 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow 383 Fig. 9 As in Fig. 6 except for the zonl wind nomly t 200 hp in the 2½-lyer model. The contour intervl is 1 m s 1 for, b nd c, nd 0.5 m s 1 for d () (c) (d) synoptic eddy feedbck is included, which gin implies positive feedbck between the synoptic eddy nd the lowfrequency flow nomly. Similr experiments re conducted for the forcing centered t (120 E, 0 ) nd (140, 0 ) nd the results re in generl similr. A sensitivity experiment with the specifiction of zonl symmetric men flow verifies the effect of the sttionry wves in midltitude response. By converting the stremfunction field (Fig. 6) to the zonl wind field (not shown), we cn see tht the brotropic nd broclinic model responses re consistent. Thus both the brotropic model nd the 2½lyer model experiments demonstrte the role of the synoptic eddy feedbck nd the sttionry wves in the midltitude response to the tropicl ISO forcing. Before conducting the model simultion, we investigte the observed reltionship between the southwrd propgtion of extrtropicl disturbnces nd the equtoril ISO convection, s reveled from the composite nlysis bsed on dily stremfunction nomlies. Using the OLR index centered t (0, 100 E) defined in the pper, we get the composite of the stremfunction nomlies when the OLR index is lower thn one stndrd devition nd the box-verged (10 10 ) stremfunction nomly centered t (45 N, 20 E) is lso lower thn one stndrd 6 ISO initition by midltitude disturbnces While the tropicl ISO my force low-frequency tmospheric response in the midltitude, the disturbnces in the midltitude, on the other hnd, my initite ISO convection t the equtor, possibly through the southwrd propgtion of subtropicl Rossby wve trins (e.g., Lim nd Chng 1981; Hsu et l. 1990; Compo et l. 1999; Lin et l. 2000). In this section we intend to simulte nd investigte this subtropicl triggering process in the 2½-lyer model. Fig. 10 Composite of stremfunction nomly ssocited with convection in the Indin Ocen. The contour intervl is m 2 s 1

10 384 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow devition (Fig. 10). The stremfunction field is obtined from NCEP NCAR renlysis nd the dt period is from 1979 to Figure 10 illustrtes cler equtorwrd wve propgtion chrcteristics. Next we exmine the influence of extrtropicl disturbnces on equtoril ISO initition in the 2½-lyer model. A Jnury monthly men climtology verged between 1979 nd 2002 is specified s the model bsic stte. Initilly, midltitude vorticity perturbtion is introduced, with center locted t (20 E, 45 N). We integrte the model forwrd to exmine how this perturbtion evolves with time nd whether or not it cn initite the tropicl ISO. Figure 11 shows the evolution of simulted zonl wind nomlies t 850 hp. As time dvnces, the midltitude disturbnce propgtes estwrd nd equtorwrd in both the lower level (Fig. 11 d) nd the upper troposphere (Fig. 12 d). Greter signls pper to the est of the initil perturbtion, owing to the effect of the men flow. An ISOlike pttern ppers in the low-level zonl wind field on the equtor t t = dy 4 (Fig. 11e), when coupled Kelvin Rossby wve structure is more evident in the upper troposphere (Fig. 12e). The verticl structure of the equtoril response t dy 4 ppers to be broclinic structure with the low-level convergence nd upper-level divergence round 60 E, coinciding well with strong mid-tropospheric scending motion nd positive rinfll nomlies. The equtoril wve perturbtions grow slowly with time while propgting estwrd long the equtor, resembling typicl ISO event. The enhnced equtoril convection my further excite polewrd propgtion of Rossby wve trins in the upper troposphere, s seen in Fig. 12f. The ISO initition on the equtor my be further reveled by the time-longitude cross section of the zonl wind t the equtor (Fig. 13). During the initition stge, the lower-level winds grow t much fster rte thn their upper-level counterprts. For exmple, the low-level esterly is enhnced from 0.2 to 1 m s 1 during dy 2 6, while the upper-level westerly increses only 0.2 m s 1. The ISO-like signl, once initited, propgtes estwrd long the equtor, nd completes one cycle t period of bout 40 dys. It is noted tht the midltitude triggering process is ssocited with the southestwrd Rossby wve energy dispersion. This cn be seen from time-longitude cross section long 45 N nd time-ltitude cross section t 25 E of perturbtion kinetic energy [(u 2 + v 2 )/2] (Fig. 14). Figure 14 shows tht during the initil four dys there is cler southwrd nd estwrd energy propgtion t 850 nd 200 hp. Both the upper- nd lower-level energy propgtions show tht the signl cn rech the equtor within severl dys. The propgtion speed is bout 10 ltitude per dy, within the rnge of observed Rossby wve southwrd propgtion speeds (Compo et l. 1999). To test the sensitivity of the equtoril ISO response to the longitude loction of the midltitude disturbnce, we shift the initil disturbnce from (20 E, 45 N) to (180, 45 N) (Fig. 15). While n equtoril ISO cn still be initited, the mplitude of the equtoril response ppers Fig. 11 Evolution of the model zonl wind nomlies t 850 hp t t = dy 0, b t = dy 1, c t = dy 2, d t = dy 3, e t = dy 4, nd f t = dy 6. An initil disturbnce is locted t (20 E, 45 N). The contour intervl is 1 ms 1 for nd 0.1 m s 1 for b, c, d, e, nd f () (c) (d) (e) (f)

11 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow 385 Fig. 12 As in Fig. 11 except for the zonl wind field t 200 hp. The contour intervl is 1ms 1 for nd 0.2 m s 1 for b, c, d, e, nd f () (c) (d) (e) (f) Fig. 13 Time-longitude cross section of the zonl wind field t the equtor t lower level nd b upper level. The contour intervl is 0.2 m s 1 () weker nd the initition loction is shifted further to the est compred to the previous cse. Given tht the bsicstte upper-level zonl wind in the tropics is esterly (westerly) to the west (est) of round 180, the experiments bove demonstrte tht the midltitude wve perturbtion cn penetrte into the tropics nd initite n ISO under both the esterly nd westerly flow regimes. To further exmine the sensitivity of the equtoril response to upper or lower-level perturbtions, we conducted two prllel experiments in which n initil disturbnce is plced only t the lower or upper level. The sensitivity experiments show tht the equtoril response is not sensitive to the initil perturbtion positions. An initil upper- (or lower-) tropospheric perturbtion my quickly excite lower- (or upper-) level counterprt during short djustment period (within 1 2 dys), nd s result, the southestwrd Rossby wve propgtion feture remins similr (not shown). The effect of the zonlly symmetric men flow (i.e., sttionry wves) in the southestwrd Rossby wve propgtion is exmined by conducting n dditionl experiment in which we specify zonl symmetric bsic stte. Figure 16 shows the model simultion t t = dy 6. Compring it to Fig. 11f, the equtoril wind response is slightly weker, nd ppers more symmetric bout the equtor. A further sensitivity experiment points out tht the condenstionl heting is primry energy source for the mintennce nd growth of the ISO; without this process, no ISO-like response cn be excited t the equtor even though there is southwrd energy propgtion from midltitudes. 7 Conclusion In this study, the interction between tropicl ISO nd midltitude low-frequency flow is investigted with focus

12 386 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow Fig. 14 Time-longitude section t 45 N nd time-ltitude section t 25 E of the model simulted kinetic energy t 850 hp (, b) nd 200 hp (c, d). The initil disturbnce is locted t (20 E, 45 N). The kinetic energy field hs been normlized by its mximum mgnitude t ech time level () (c) (d) Fig. 15 Simulted 850 hp zonl wind field t t = dy 6 for the cse with n initil disturbnce locted t (180, 45 N) Fig. 16 As in Fig. 11f except for the specifiction of zonl symmetric bsic stte on the effect of the synoptic eddy feedbck. A sttisticl closure tht reltes the synoptic eddy forcing to the midltitude low-frequency flow is constructed, which leds to new estimtion of the role of the synoptic eddy feedbck on the response of midltitude low-frequency circultion to the forcing ssocited with tropicl ISO. By pplying the newly constructed sttisticl closure, the observed eddy feedbck cn be well represented in both simple brotropic model nd 2½-lyer broclinic model. Our observtionl nlysis nd modeling study show tht the heting ssocited with tropicl ISO cn excite significnt midltitude response. In prticulr, the ISO heting in the equtoril Indin Ocen my produce north south dipole structure t the upper lyer in the North Pcific, with n oscilltion period of bout 40 dys. The midltitude response hs n equivlent brotropic structure while broclinic structure ppers in the tropics. When the heting moves estwrd in ssocition with the estwrd propgtion of the ISO, the response pttern in the midltitude lso shifts estwrd. Both the brotropic model nd the 2½-lyer model show tht the strong synoptic eddy feedbck ppers t the Pcific nd Atlntic storm trck regions, in greement with the observtion. The synoptic eddy forcing hs positive feedbck to the midltitude low-frequency nomly forced by the tropicl ISO. Our 2½-lyer model experiments demonstrte, for the first time, the pure effect of the midltitude disturbnce forcing in the ISO initition, given tht the model does not contin the cloud-rdition nd ocen feedbcks nd preexisting globl-encirculting MJOs. Given midltitude disturbnce initilly, the signl my propgte southestwrd, rech the equtor within severl dys, nd trigger ISO convection t the equtor. This midltitude triggering scenrio is consistent with previous (e.g., Compo et l. 1999) nd current observtionl nlysis results. The pen-

13 L.-L. Pn nd T. Li: Interctions between the tropicl ISO nd midltitude low-frequency flow 387 etrtion of the disturbnce from the midltitude to the tropics is in the form of Rossby wve pckets. Unlike sttionry Rossby wve, the southwrd propgtion of the trnsient Rossby wve pckets does not require the presence of westerly winds in the bsic stte (Hoskins nd Yng 2000). Thus the midltitude forcing my trigger significnt equtoril ISO response in both the esterly nd westerly regimes. The dynmics of the tropicl midltitude teleconnection require full interction mong the sttionry wve, zonl men flow, low-frequency vribility, nd trnsient wve (synoptic eddy). In the current study, we linerize the model bout time-independent bsic stte, so tht the nonliner feedbck to the men flow is neglected. 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