A study of non-local effects on the Budyko Sellers infrared parametrization using atmospheric general circulation models

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1 Tellus (2005), 57A, Copyright C Blkwell Munksgrd, 2005 Printed in Singpore. All rights reserved TELLUS A study of non-lol effets on the Budyko Sellers infrred prmetriztion using tmospheri generl irultion models By PETER L. LANGEN 1 nd VLADIMIR A. ALEXEEV 2, 1 Niels Bohr Institute, University of Copenhgen, Juline Mries Vej 30, 2100 Copenhgen O, Denmrk; 2 Interntionl Arti Reserh Center, University of Alsk Firnks, 930 Koyukuk Dr., PO Box , Firnks, AK , USA (Mnusript reeived 2 Novemer 2004; in finl form 31 Jnury 2005) ABSTRACT We perform series of simplified tmospheri GCM runs with fixed zonlly symmetri spheril hrmoni se surfe temperture (SST) perturtions to study the response of the outgoing long-wve rdition (OLR) to SST nomlies of different horizontl sles nd strutures. The lssil liner reltionship used in energy lne models etween the OLR nd the SST holds quite well t high ltitudes. This is not the se in the tropis; even for lrge-sle perturtions, espeilly ntisymmetri out the equtor, the orreltion is poor. This is explined y the ft tht the struture of the Hdley ell ontrols most of the properties of the tropil tmosphere, using lol reltionship etween the surfe nd the top of the tmosphere to rek down. This onlusion is supported y our nlyses of the reltionship etween OLR nd SST in the wvenumer domin. For very lrge-sle SST perturtions (wvenumers 0 2) the greement is resonle the OLR response hs most of the energy in the sme wvenumer. For higher wvenumers, however, the orreltion deteriortes nd the OLR response hs signifint energy in other hrmonis. 1. Introdution Energy lne limte models (EBMs) hve een used with gret suess in idelized studies of limte stility nd sensitivity (e.g. Budyko, 1969; Sellers, 1969; North, 1975) nd hve provided us with tool to reognize the potentil rihness of the solution struture of the limte system (North, 1990). After the initil introdution in their simple form, EBMs hve een used more widely in two-dimensionl versions (e.g. Rook, 1983) nd s upper oundry onditions in hierrhy of oen modeling experiments (e.g. Nkmur et l., 1994; Mrotzke nd Stone, 1995; Lohmnn et l., 1996). In this mnner, EBMs re still used for oth reserh nd tehing purposes. The prinipl strengths of EBMs re their low omputtionl ost nd their trtility to nlytil solutions (North, 1975), oth fetures tht rely on simple prmetriztions of the energy fluxes in the limte system. One suh prmetriztion is the ommonly used liner reltionship F I = A + BT S, (1) Corresponding uthor. e-mil: plngen@gfy.ku.dk etween the outgoing long-wve rdition (OLR), F I, nd the se surfe temperture, T S. This is n empiril reltionship linking the top of the tmosphere OLR to the lol temperture t the surfe; in this pper, we fous on the non-lol effets tht the tmospheri irultion hs on this reltionship nd on the prolems they pose. By negleting vritions in the frtionl loud overge Budyko (1969) ws first to employ eq. (1). Sellers (1969) used more omplited form of the dependene, whih, however, is liner to within 1% in the interesting rnge of tempertures (North, 1975). The vlue of the prmeter A is of rther little importne for the stility nd sensitivity of given limte model. In ft, A is often used to tune the temperture to mth ertin trget profile (e.g. Wrren nd Shneider, 1979). Conversely, the prmeter B hs mjor influene on the ehvior of EBMs, nd numerous studies hve foused on determining the optimum vlue (e.g. Wrren nd Shneider, 1979; Grves et l., 1993). Despite the mny efforts, there still exists quite wide rnge of possile vlues: Mrni (1999) sums up previous estimtes to lie etween out 1.5 nd 2.3 W m 2 K 1. The simple vlue of 2.0 W m 2 K 1 is often hosen when EBMs re used for qulittive rther thn quntittive purposes. One reson for the miguities in the determintion of B is the inility of eq. (1) to del suffiiently with the effets of tropil 654

2 NON-LOCAL EFFECTS ON THE BUDYKO SELLERS IR PARAMETRIZATION 655 onvetion. While the rnge of tropil temperture vritions is rther limited, oservtions show lrge vritions in OLR from one tropil region to nother (Bess et l., 1989). Low vlues of OLR re seen in regions with high-level loudiness nd old loud tops ssoited with onvetive tivity, while high vlues re found minly over deserts hrterized y susidene nd ler skies. Suh differene in regimes hs led reserhers to onstrut prmetriztions for ler nd loudy skies seprtely, oth in modeling studies (Thompson nd Wrren, 1982; Gutzler nd Stone, 1986) nd in oservtionl studies (Grves et l., 1993; Rvl et l., 1994). Thompson nd Wrren inluded the vertil men reltive humidity long with surfe temperture s preditor of OLR nd devised prmetriztion from urve fitting the output of detiled rditive model. These preditors were oservtionlly onfirmed y Rvl et l. to yield good results. They rgue tht the moisture field, whih hs lrge influene on the OLR, is most diretly represented y the olumnintegrted preipitle wter; however, euse this field is so tightly oupled to the temperture field, use of reltive humidity provides more independent informtion. In GCM study, Gutzler nd Stone onlude tht inlusion of mesure of the tmospheri lpse rte s o-preditor with surfe temperture is useful when onsidering results from limte hnge experiments. Both reltive humidity nd lpse rte re influened y the lrge-sle irultion (suh s the Hdley ell) nd thus provide informtion out the non-lol onditions, whih in the present pper will e rgued to hve dominnt influene t low ltitudes. This ws lso found y Alln et l. (1999), who explined the ourrene of low-ltitude regions with OLR nd surfe temperture eing ntiorrelted in terms of sesonl shifts of the Hdley ell nd internnul vritions in the Wlker irultion. As will e done in the following, Short et l. (1984) worked in terms of spheril hrmonis in their pprisl of eq. (1). Using 1 yr of Nimus-6 dt they performed spheril hrmoni expnsion of the time-vrying temperture nd OLR fields. Vrines nd ovrines lulted in terms of these expnsions were onluded to e dominted y the lrgest spe nd timesles. Higher-order ontriutions to the OLR vriility, whih re not nerly s pronouned in the temperture vriility, were ttriuted lrgely to loud vriility in tropil onvetion regions. Eqution (1) ws found to hold quite well in mid to high ltitudes nd this explins its suess in modeling even the sesonl yle in EBMs; it works where it hs to (i.e. in the lrge low het pity ontinentl interiors t mid nd high ltitudes). The error mde when negleting the very old loud tops in the liner reltionship of eq. (1) is, y Short et l. (1984), rgued to e ountered y similr error in the ledo (where the effet of the high tropil louds is lso negleted), suh tht the net effet is resonle representtion. Aording to Pierrehumert (2004), however, the tmosphere (humidity, vertil strtifition, et.) hnges drstilly in old extremes suh s Snowll Erth senrios. This my use rekdown of the ove fortuitous nelltion of errors nd exemplifies the potentil hzrds of extending liner reltionships tuned to present-dy onditions into vstly different limte regimes. On the sme note, Wrren nd Shneider (1979) speulte tht the high vlue of B 3W m 2 K 1 found over Antrti my imply tht glil world is sujet to stility onditions unlike those of tody. As proposed y Short et l., it my lso simply e due to omintion of high ltitudes nd low surfe tempertures. Due to the nture of the ville oservtions, the presentdy ltitudinl vritions nd sesonl yle re ommonly used to determine prmetriztions of the OLR (e.g. Short et l., 1984; Rvl et l., 1994). However, y ompring their vrile-loudtop-temperture nd fixed-loud-top-ltitude prmetriztions of the OLR, Neemn et l. (1987) demonstrted tht suessfully reproduing the present-dy sesonl yle is not suffiient for limte hnge studies. The two prmetriztions yield similr sesonl yles ut imply ftor of 2 different sensitivities to solr onstnt hnges. Similrly, the improvement in the prmetriztion tht Gutzler nd Stone (1986) gined from inlusion of lpse rte s o-preditor ws present only in limte hnge senrios, nd not in present-dy runs. We speulte tht the reorgniztions of the lrge-sle irultion tht render the lpse rte useful s preditor re not ptured y present-dy vritions. The perturtions introdued in the present study onsist of zonlly symmetri spheril hrmonis nd thus spn the zonlly symmetri prts of oth present-dy limte vritions nd limte hnge senrios. In Setion 2 we desrie the experiments nd the two different GCMs employed therein. The results re presented nd disussed in Setion 3, nd summry nd onlusion re offered in Setion Experimentl onfigurtion Two different models hve een used in the experiments: the Goddrd Spe Flight Center GEOS model nd the Ntionl Center for Atmospheri Reserh CCM3. Both models re run with quplnet oundry onditions nd without the sesonl yle. Insted, modified equinox onditions s desried y Alexeev (2003) re employed. The GEOS model is run t 4 5 horizontl resolution with 20 lyers in the vertil nd the louds zeroed out in the rdition ode (s desried y Alexeev, 2003). The CCM3 (desried y Kiehl et l., 1996) is run t T21 horizontl resolution with 18 levels in the vertil nd the full physis pkge inluded. Our modifitions to the stndrd distriution of the model re desried y Lngen nd Alexeev (2004) with the extr modifition here tht we exlude ll effets of se ie, i.e. the surfe ledo is uniform nd fixed nd sufreezing grid points re treted s open wter. The solr onstnt nd CO 2 onentrtion re set to 1367 W m 2 nd 355 ppm, respetively. Before the experiments were strted, oth models were run with 50 m mixed lyer oens, suh tht the se surfe tempertures (SSTs) were llowed to settle into equilirium. The

3 656 P. L. LANGEN AND V. A. ALEXEEV The first five perturtions re illustrted in Fig. 1. Note tht the order of the polynomils orresponds to the numer of roots, nd tht the prity of the order determines the symmetry of the polynomil. Even-ordered polynomils re symmetri out the equtor, nd odd ones ntisymmetri. While our trunted series nturlly omits the smllest-sle fetures, the zonlly symmetri spheril hrmonis spn ll possile zonlly symmetri perturtions. Aprt from this mthemtil property (whih ny sis possesses) the spheril hrmonis re ppeling euse they re redily envisged nd n prtilly e relted to physil proesses nd fields. The lowest even-order hrmonis desrie the typil lrge-sle ptterns in limte hnge experiments, suh s glol wrming nd polr mplifition. The first symmetri hrmonis desrie oth the sesonl yle nd possile hemispheri symmetries in limte hnges. Intermedite sles (of either prity) re needed when the effets of ontinents re to e ddressed nd the highest wvenumers n e relted to more lolized fetures suh s, for exmple, gliers or oeni upwelling res. All plots in the following re verged zonlly nd over 20 yr of fixed SST perturtion runs. 3. Results Fig. 1. () Referene SST profiles for the CCM3 (open irles) nd the GEOS model (shded irles). () The five first Legendre polynomil perturtions: long-dshed line, zeroth order; dotted line, first order; dsh-dotted line, seond order; solid line, third order; short-dshed line, fourth order. surfe ledo ws tuned in oth models to yield SST profiles similr to tht of the present dy. The models were then run for 20 yr in their respetive equiliri nd the SSTs were verged over this period nd symmetrized zonlly nd out the equtor. The resulting SST profiles re termed the referene profiles nd re plotted in Fig. 1. The tul experiment onsists of set of 17 fixed SST runs with oth models: referene run, where the temperture is fixed t the referene profile, nd 16 perturtion runs, where the SST profiles re pertured with the 16 first zonlly symmetri spheril hrmonis, i.e. zonlly symmetri perturtions where the meridionl struture is given y the 16 first Legendre polynomils in sin φ: In Fig. 2 we hve plotted the result of the first-order nd seondorder perturtion experiments. The solid lines show the temperture inreses multiplied y 1.9 W m 2 K 1 nd thus represent (the shpe of) the hnges in OLR one should see if eq. (1) holds. The vlue B = 1.9 W m 2 K 1 ws hosen simply to filitte the omprison, nd tully grees quite well with the optimum vlue of 1.93 W m 2 K 1 rrived t y Short et l. (1984). The dotted lines show the hnges in ll-sky OLR while the dshed lines show hnges in ler-sky OLR, oth for the CCM3 model. The former is the tul hnge while the ltter is dignosti lulted internlly in the ode using the rel temperture nd moisture field ut negleting effets of louds. The dsh-dotted lines show OLR hnges in the GEOS model, whih hs louds zeroed out in the ode, implying tht the hnges orrespond most diretly to the CCM3 ler-sky hnges. In generl, there is firly good orrespondene etween the tul nd expeted hnge in OLR. This is espeilly true t high ltitudes in the ler-sky ses (dshed nd dsh-dotted lines), while with louds P 0 (φ) = 1, P 1 (φ) = sin φ, P 2 (φ) = 1 2 (3 sin2 φ 1),... Fig. 2. OLR hnges in the first-order () nd seond-order () perturtion experiments: solid line, SST hnge multiplied y 1.9 W m 2 K 1 ; dshed line, CCM3 ler-sky; dotted line, CCM3 ll-sky; dsh-dotted line, GEOS model.

4 NON-LOCAL EFFECTS ON THE BUDYKO SELLERS IR PARAMETRIZATION 657 Fig. 3. Zonl men meridionl stremfuntion (kg s 1 ): () stremfuntion in referene limte; () hnge when going to first-order perturtion; () hnge when going to seond-order perturtion. All plots for CCM3 model. there is generlly n underestimtion of the mplitude of the hnge polewrd of 50. This hs to do with the very lrge loud over in the referene se (not shown), whih, in ft, tends to shield the OLR hnge. Muh of the OLR omes from the loud tops suh tht when the surfe temperture hnges without the louds hnging signifintly the OLR effet from the surfe is dmped. In oth the ler-sky nd ll-sky ses, the symmetri perturtion yields hnge in the OLR of the wrong sign in the off-equtoril region. In the symmetri se, this region shows n overestimtion of the hnge while the equtoril region shows n underestimtion of the hnge. These re fetures tht lerly demonstrte the filure of eq. (1) in low ltitudes. The prolem is tht lol reltionship suh s eq. (1) nnot dequtely model the hnges in dynmis tht follow from the perturtions. Figure 3 demonstrtes these hnges in the CCM3. Figure 3 shows the zonlly verged meridionl stremfuntion in the referene se where the Hdley ells lerly stnd out. Figures 3 nd show the hnges in the stremfuntion in the first- nd seondorder perturtions, respetively. The former is hrterized y lrge negtive region entered over the equtor; this is the footprint of shift of the Intertropil Convergene Zone (ITCZ) nd the whole Hdley ell struture into the Northern (wrm) Hemisphere. Figure 3 shows wekening of the irultion due to the derese in meridionl temperture grdient ompnying the perturtion. The importne of these hnges for the OLR is due to the ft tht the tropil moisture field is ontrolled minly y the dynmis rther thn the lol temperture struture. Figure 4 shows the zonlly verged reltive humidity field where the sending rnh of the tropil irultion is seen to e hrterized y high vlues nd the desending rnh y low vlues. In Fig. 4, whih shows the hnges ssoited with the symmetri perturtion, we see northwrd shift of the RH field, while in Fig. 4, orresponding to the symmetri perturtion, moistening of the desending rnh nd drying of the sending rnh re seen. The smll line-plots tthed to the two-dimensionl plots show the height-men reltive humidity H RH = 1 RH(z)dz, (2) H 0 whih, s mentioned in the introdution, ws shown y Thompson nd Wrren (1982) nd Rvl et l. (1994) to e n effetive o-preditor of OLR. The vlue of H = 12 km ws found y Thompson nd Wrren to work well, nd is employed here. Rvl et l. put forth tht the suess of this definition of RH, rther thn the more intuitive pressure-weighted verge, my stem from its preferentil weighting of the upper-tropospheri moisture field. The referene profile (Fig. 4) of this numer reitertes the influene of the irultion on the moisture field. The hnges ompre very well with the disrepnies in Fig. 2. In Fig. 2, the downwrd spikes in the OLR in the Northern Hemisphere re positioned extly in the sme ple s the upwrd (moist) spike in Fig. 4, nd vie vers for the Southern Hemisphere. In Fig. 2, the overestimtion of the off-equtoril OLR derese oinides with the moistening seen in Fig. 4 due to the deresed strength of the Hdley ell. Likewise, the underestimtion of the derese over the equtor oinides with the drying Determining the liner sensitivity prmeter A vlue of the sensitivity prmeter, B, hs een determined for eh of the perturtion experiments y performing reweighted liner regressions of the hnges in OLR with the hnges in SST. In the zero-order se, of ourse, the regression fils euse ll points hve the sme SST hnge, nd here we hve simply tken the re-weighted rtio of the OLR hnge to the SST hnge. For ll perturtions, in oth the ler-sky nd ll-sky ses, the ove regression ws performed using the whole gloe, the tropis (30 S 30 N) nd the extrtropis (polewrd of 30 S nd 30 N), respetively. The result is shown in Fig. 5 where Fig. 5 displys the ll-sky se, Fig. 5 the lersky se nd Fig. 5 the results from the GEOS model. The solid lines re for the whole gloe, the dshed lines re for the tropis nd the dotted lines re for the extrtropis. In the ll-sky se (Fig. 5) we see lrge vritions in the estimte for B, espeilly t low ltitudes result tht seems rther disourging for the ility of EBMs to model the ll-sky tropis. The high-ltitude estimte is resonle for lrge-sle perturtions, ut s higher wvenumers re pprohed the

5 658 P. L. LANGEN AND V. A. ALEXEEV Fig. 5. Estimtes of the sensitivity prmeter, B. () CCM3 ll-sky: solid line, sed on whole gloe; dshed line, tropis; dotted line, extrtropis. (), () As in () ut for CCM3 ler-sky nd GEOS models, respetively. Fig. 4. Reltive humidity (%): () referene limte with height-men tthed; () hnge when going to first-order perturtion; () hnge when going to seond-order perturtion. All plots for CCM3 model. ove-mentioned high-ltitude loud shielding effet tends to dominte nd the sensitivity tends to zero. At higher wvenumers, the symmetri perturtions yield highly negtive estimtes for B. This is onsequene of the effet tht ws disussed ove for the first symmetri perturtion. The entire meridionl irultion hnges position nd the resulting hnges in the reltive humidity field nd espeilly the loud field yield OLR hnges with no onnetion to the lol temperture hnge. Considering still the CCM3, the high-ltitude estimte of the sensitivity is rther onsistent in the ler-sky se (Fig. 5). It does not vry muh with wvenumer nd its vlue is lose to the nonil vlue of 2 Wm 2 K 1. This is not the se t low ltitudes where, t wvenumer 2, we lredy see tht the lrge underestimtion of the OLR hnge in the ITCZ (Fig. 2) uses the slope of the regression line to eome negtive. It is importnt to stress tht this negtive vlue does not imply tht lol rule holds in the tropis sying tht the OLR dereses with inresing SST. It simply reflets the omplete rekdown of ny lol reltionship in the tropil region. Going towrds higher wvenumers, the odd-order perturtions tend to use more prolems for the low-ltitude estimte thn do the evenorder perturtions. This seems to imply tht when onsidering smll-sle perturtions in the CCM3, the strength of the meridionl irultion is less vulnerle thn its position the effet of shifting the Hdley ell is more pronouned thn the effet of hnging its strength. The glol estimte of B remins positive throughout the rnge of wvenumers, ut, influened y the tropil filure of the prmetriztion, the vlue tends wy from 2Wm 2 K 1 t higher wvenumers. An interesting exeption is the vlue t wvenumers 6 nd 8 where ll three regions (gloe, tropis, nd extrtropis) yield lmost perfet results. The reson for this is illustrted in Fig. 6 where results from wvenumers 4, 8, nd 12 re shown. As in Fig. 2, the solid lines re the temperture inreses multiplied y 1.9 W m 2 K 1 nd the dshed lines re the tul ler-sky OLR hnges. The rtoon displyed y the three pnels demonstrtes how the intermedite wvenumer 8 (pplies lso to 6, not shown) mthes the horizontl sle of the tropil irultion suh tht hnge in the strength nd the ompnying hnges in the moisture field hs the sme meridionl struture s the pplied perturtion. At smller nd lrger sles, the overturning strength hnges without the resulting OLR hnges resemling the perturtion. In the GEOS model (Fig. 5) the estimtes look, s expeted, more like the CCM3 ler-sky estimtes thn the ll-sky estimtes. The high-ltitude vlue remins resonly lose to 2 W m 2 K 1 throughout the onsidered rnge of experiments. For lrge sles, the low-ltitude estimte lterntes etween positive vlues for even perturtions nd negtive vlues for odd

6 NON-LOCAL EFFECTS ON THE BUDYKO SELLERS IR PARAMETRIZATION 659 Fig. 6. As in Fig. 2 ut for fourth-order (), eighth-order () nd twelfth-order () perturtions: solid line, SST hnge multiplied y 1.9 Wm 2 K 1 ; dshed line, CCM3 ler-sky. perturtions, inditing gin tht shifting the Hdley ell hs more impt on the OLR thn hnging its strength. At intermedite wvenumers (4 nd 6) we gin see the low-ltitude estimte eing lose to 2Wm 2 K 1.Asopposed to the lersky CCM3 se, where it ws due to the perturtion hving the sme struture s the hnge in the irultion, the result is now simply fortuitous nelltion of errors. Both struture nd mplitude of the OLR hnge re quite different from the perturtion. At higher wvenumers there is reversl of the ehvior with even orders giving more negtive estimtes thn odd orders, suh tht for smller-sle perturtions the strength hnge effet seems to dominte over the shifting effet. In neither se, however, does the low-ltitude OLR hnge hve ny resonle orrespondene to the perturtion Results in wvenumer spe A different wy of displying our results is to mke plots orresponding to Fig. 2 in the sis of Legendre polynomils. Figure 7 shows the results of the first-, seond- nd third-order perturtions. The solid lines re gin the temperture inreses multiplied y 1.9 W m 2 K 1 while the dshed lines nd dotted lines re the hnges in OLR for the CCM3 ler-sky nd ll-sky ses, respetively. The dsh-dotted lines re the GEOS model OLR hnges. In Fig. 7, showing the first symmetri perturtion, the dshed line flls quite losely on top of the solid line, refleting the good mth etween the lulted hnge nd the CCM3 ler-sky OLR hnge in Fig. 2. The dsh-dotted line (GEOS) reflets how the lrger error in the tropis ples more power on the higher wvenumers. The dotted line (CCM3 llsky) shows how the loud shielding effet redues the power in wvenumer 1 nd how the shifts in the low-ltitude loud field Fig. 7. As in Fig. 2 ut in wvenumer spe: () first-order, () seond-order nd () third-order perturtions. ple signifint mounts of power on higher wvenumers. A similr piture emerges in Fig. 7 (wvenumer 2) where the loud shielding effet, however, works in the sme diretion in oth hemispheres nd ples power on the zeroth wvenumer. The irultion hnges ssoited with the lrge-sle symmetri perturtion led to no signifint error in the GEOS model nd the dsh-dotted line is even etter thn the dshed line orresponding to the CCM3 ler-sky se. In Fig. 7 the CCM3 ll-sky OLR hnge is seen to hve prtilly no resemlne with the temperture perturtion. There is no power on the pertured wvenumer while it is distriuted mong ll the higher odd-order wvenumers. The CCM3 ler-sky nd GEOS urves re more well ehved, lthough the fits hve deteriorted s ompred to the two previous perturtions. The root-men-squre (rms) distne etween the solid urve nd the dshed, dotted, nd dsh-dotted urves, respetively, n e used s mesure of how well eq. (1) performs t given wvenumer. In Fig. 8 we hve plotted this differene for the CCM3 ler-sky (solid) nd ll-sky (dshed) ses nd for the GEOS model (dotted) s funtion of wvenumer. A feture ommon to ll three ses is the deteriortion of the reltionship with deresing horizontl sle. An exeption to this is the good fit in the CCM3 t intermedite even wvenumers where the horizontl struture of the perturtion, s mentioned, mthes the hnges indued in the irultion. It is lso pprent how the symmetri perturtions in generl yield etter results thn the symmetri perturtions, whih, s we hve seen, indue shift in the position of the ITCZ. There re two exeptions to this. (i) In the CCM3 ler-sky se, the first symmetri perturtion gives s good fit s the two first symmetri perturtions. The hnges in strength re, t the lrgest sles, s importnt s the shift of the irultion. As intermedite sles re pprohed, the symmetri shifts in the ITCZ

7 660 P. L. LANGEN AND V. A. ALEXEEV Fig. 8. The rms distne etween tul nd expeted wvenumer spe representtions of OLR hnge: solid line, CCM3 ler-sky; dshed line, CCM3 ll-sky; dotted line, GEOS model. tend to derese the projetion of the OLR hnge onto the perturtion, giving worse fits, while the symmetri perturtions tend to give even etter fits. At the smllest sles, the symmetri fits no longer deteriorte, ut the symmetri perturtions no longer mth the irultion hnges nd the errors eome nerly s lrge s those for the symmetri perturtions. (ii) For the GEOS model, we see tht t the smllest sles the symmetri perturtions tend to give smller errors thn the symmetri perturtions. Here the hnges in the strength of the irultion ssoited with the symmetri perturtions re reltively lrge, tending to reverse the sign of the OLR hnge nd pling most of the power on the neighoring even-order wvenumers. 4. Conlusions In two different GCMs, we hve performed series of Legendre polynomil perturtions of the surfe temperture nd nlyzed the response in the OLR. For ler skies, the OLR response follows rther losely liner reltionship s eq. (1) t high ltitudes. Due to lrge high-ltitude loudiness in the CCM3 referene limte, the ll-sky OLR response is dmped, leding to worse greement with eq. (1) t high ltitudes. At low ltitudes, the higher moisture ontent of the tmosphere eomes importnt, s does the meridionl irultion whih, to lrge extent, sets the struture of the low-ltitude moisture field. As disussed y, for exmple, Alln et l. (1999), the sesonl shifts in onvetive regimes led to off-equtoril res displying negtive orreltions etween SST nd OLR. This is lso oserved in our study where the symmetri perturtions yield shift in the Hdley ell nd ssoited shifts in the reltive humidity field, whih, in turn, led to spikes in the OLR direted in the opposite diretion of the lol temperture hnge. Assoited with symmetri perturtions is nother effet on the meridionl irultion, whih is not ptured y the sesonl yle. Chnges in the meridionl temperture grdient led to strengthening (or wekening) of the Hdley ell, whih leds to moistening (drying) in the sending rnh nd drying (moistening) in the desending rnh. These moisture hnges were lso seen to hve lrge impt on the OLR. An interesting effet ws seen in the CCM3 where symmetri perturtions of intermedite wvenumers (6 nd 8) led to irultion hnges of omprle meridionl strutures suh tht the OLR hnges were very well represented y eq. (1). The role of loud rditive feedks in limte sensitivity nd stility is still muh deted, espeilly when it omes to tropil dynmis. In terms of the OLR prmetriztion, it hs een proposed (e.g. Short et l., 1984; Grves et l., 1993) tht due to the nelltion of the long-wve nd short-wve effets of louds (s mentioned in Setion 1) we should e on sfe ground if we ignore the louds in the prmetriztions of oth fluxes. Thus, we hve in this pper presented oth ll-sky nd lersky results from the CCM3. A lrge prt of the disgreement in the ll-sky se is, s mentioned, due to the rther exessive loudiness in the CCM3 referene limte. We speulte tht, with deresed referene loudiness, the ll-sky se would ehve more like the ler-sky se, nd thus, t lest t mid nd high ltitudes, yield etter greement with eq. (1). The CCM3 ll-sky OLR is not very well represented y eq. (1) while its ler-sky OLR is resonly represented (Fig. 8). The results for the GEOS model, whih, in ft, is ler-sky model, lie etween these two. With lrge, symmetri perturtions the GEOS model nd the CCM3 ler-sky results re eqully good, ut t intermedite nd smll sles the CCM3 s ler-sky response is loser to the liner reltionship. In generl, lrge-sle, symmetri perturtions produe OLR responses etter in ordne with eq. (1) thn do smll-sle, symmetri perturtions. This seems to imply tht the Budyko Sellers prmetriztion is est suited for the simplest nnully verged EBM experiments nd tht disrepnies re more lile to our in experiments inluding the sesonl yle (symmetries), two dimensions, nd ontinents (smller sles). However, feture ommon to ll perturtions is tht they yield good ler-sky results t high ltitudes where the fous of EBM studies (of, for exmple, the ie-ledo feedk) typilly lies. Hd we inluded ontinents, sesons, nd longitudinlly vrying perturtions, hnges in strength nd position of monsoonl nd other irultions would hve led to prolems similr to those enountered in the simplified setup. However, ording to Short et l. (1984), the symmetri prt of the fields only ounts for smll prt of the vrine in the nnul men, nd we my expet the results of our zonlly symmetri experiments to ount for the dominnt prt of nnul men quntities in limte hnge experiments. In onlusion, tropil irultion nd dynmis re so importnt for even the ler-sky OLR tht lol reltion with SST is insuffiient. One ould, of ourse, inlude some representtion of the moisture field, ut one would then e left with the tsk of determining tht in n EBM. The solution tht we propose is to use the mtrix tht is otined when omining the full set of 16 plots orresponding to the three shown in Fig. 7. The i th

8 NON-LOCAL EFFECTS ON THE BUDYKO SELLERS IR PARAMETRIZATION 661 plot gives the OLR response in ll wvenumers rising from temperture perturtion in the i th wvenumer. The OLR field n thus e lulted s F I = [B 1 B 2... B i... B N ]T S, where the olumns of the B mtrix re the vetors represented y the plots in Fig. 7. F I is the OLR perturtion nd T S is the SST perturtion, oth given in the N-dimensionl sis of Legendre polynomils. A requirement for this prmetriztion to hold is tht the OLR response is liner with respet to the different omintions of the Legendre polynomil SST perturtions. We hve not yet heked this systemtilly, ut in ll our preliminry runs it hs, in ft, een the se. This is enourging for the possiility of running EBMs in Legendre spe (s hs often een done; North, e.g. 1975) nd in this mnner inluding the non-lol effets seen in the present study while still using liner nd inexpensive prmetriztion. 5. Aknowledgments This work ws supported y IARC/NSF Coopertive Agreement nd the University of Copenhgen. Severl points of the pper hve een shrpened onsiderly due to the suggestions of our nonymous reviewers. Referenes Alexeev, V. A Sensitivity to CO 2 douling of n tmospheri GCM oupled to n oeni mixed lyer: liner nlysis. Climte Dyn. 20, Alln, R. P., Shine, K. P., Slingo, A. nd Pmment, J. A The dependene of ler-sky outgoing long-wve rdition on surfe temperture nd reltive humidity. Q. J. R. Meteorol. So. 125, Bess, T. D., Smith, G. L. nd Chrlok, T. P A ten-yer monthly dt set of outgoing longwve rdition from nimus-6 nd nimus-7 stellites. Bull. Am. Meteorol. So. 70, Budyko, M The effet of solr rdition vritions on the limte of the Erth. Tellus 21, Grves, C. E., Lee, W-H. nd North, G. R New prmetriztions nd sensitivities for simple limte models. J. Geophys. Res. 98(D3), Gutzler, D. S. nd Stone, P. H Infrred flux prmetriztions derived from limte hnges in three-dimensionl limte model. J. Geophys. Res. 91(D7), Kiehl, J. T., Hk, J. J., Bonn, G. B., Boville, B. A., Briegle, B. P. nd o-uthors Desription of the NCAR Community Climte Model (CCM3). Tehnil Report TN-420, CGD, Ntionl Center for Atmospheri Reserh, Boulder, CO, USA. Lngen, P. L. nd Alexeev, V. A Multiple equiliri nd symmetri limtes in the CCM3 oupled to n oeni mixed lyer with thermodynmi se ie. Geophys. Res. Lett. 31 (doi: /2003gl019039). Lohmnn, G., Gerdes, R. nd Chen, D Sensitivity of the thermohline irultion in oupled oeni GCM tmospheri EBM experiments. Climte Dyn. 12, Mrni, M Prmetriztions of glol therml emissions for simple limte models. Climte Dyn. 15, Mrotzke, J. nd Stone, P. H Atmospheri trnsports, the thermohline irultion, nd flux djustments in simple oupled model. J. Phys. Oenogr. 25, Nkmur, M., Stone, P. H. nd Mrotzke, J Destiliztion of the thermohline irultion y tmospheri eddy trnsport. J. Climte 7, Neemn, B. U., Joseph, J. H. nd Ohring, G The sensitivity of the outgoing longwve rdition to surfe temperture: modeling the opity feedk nd experiments with vrile loud-top temperture provision. J. Atmos. Si. 44, North, G. R Anlytil solution to simple limte model with diffusive het trnsport. J. Atmos. Si. 32, North, G. R Theory of energy-lne limte models. J. Atmos. Si. 32, North, G. R Multiple solutions in energy lne limte models. Pleogeogr., Pleolim., Pleoeol. 82, Pierrehumert, R. T High levels of tmospheri ron dioxide neessry for the termintion of glol glition. Nture 429, Rvl, A., Oort, A. H. nd Rmswmy, V Oserved dependene of outgoing longwve rdition on se surfe temperture nd moisture. J. Climte 7, Rook, A Ie nd snow feedks nd the ltitudinl nd sesonl distriution of limte sensitivity. J. Atmos. Si. 40, Sellers, W. D A glol limti model sed on the energy lne of the Erth-tmosphere system. J. Appl. Meteorol. 8, Short, D. A., North, G. R., Bess, T. D. nd Smith, G. L Infrred prmetriztions nd simple limte models. J. Climte Appl. Meteorol. 23, Thompson, S. L. nd Wrren, S. G Prmteriztion of outgoing infrred rdition derived from detiled rditive lultions. J. Atmos. Si. 39, Wrren, S. G. nd Shneider, S. H Sesonl simultion s test for unertinties in the prmetriztions of Budyko Sellers zonl limte model. J. Atmos. Si 36,