1 Introduction. Jean-Philippe Boulanger Æ Fernando Martinez Enrique C. Segura

Transcription

1 Climate Dynamics (26) DOI 1.17/s Jean-Philippe Bulanger Æ Fernand Martinez Enrique C. Segura Prjectin f future climate change cnditins using IPCC simulatins, neural netwrks and Bayesian statistics. Part 1: Temperature mean state and seasnal cycle in Suth America Received: 2 June 25 / Accepted: 2 February 26 Ó Springer-Verlag 26 Abstract Prjectins fr Suth America f future climate change cnditins in mean state and seasnal cycle fr temperature during the twenty-first century are discussed. Our analysis includes ne simulatin f seven Atmspheric-Ocean Glbal Circulatin Mdels, which participated in the Intergvernmental Panel n Climate Change Prject and prvided at least ne simulatin fr the twentieth century (2c3m) and ne simulatin fr each f three Special Reprt n Emissins Scenaris (SRES) A2, A1B, and B1. e develped a statistical methd based n neural netwrks and Bayesian statistics t evaluate the mdels skills in simulating late twentieth century temperature ver cntinental areas. Sme criteria [mdel weight indices (MIs)] are cmputed allwing cmparing ver such large regins hw each mdel captures the temperature large scale structures and cntributes t the multi-mdel cmbinatin. As the study demnstrates, the use f neural netwrks, ptimized by Bayesian statistics, leads t tw majr results. First, the MIs can be interpreted as ptimal weights fr a linear cmbinatin f the climate mdels. Secnd, the cmparisn between the neural netwrk prjectin f twenty-first century cnditins and a linear cmbinatin f such cnditins allws the identificatin f the regins, which will mst prbably change, accrding t mdel biases and mdel ensemble variance. Mdel simulatins in the suthern tip f Suth America and alng the Chilean and Peruvian casts r in the nrthern casts f Suth America (Venezuela, Guiana) J.-P. Bulanger (&) Tur 45-55/Etage 4/Case 1 UPMC, LODYC, UMR CNRS/IRD/UPMC, 4 Place Jussieu, Paris Cedex 5, France jpb@ldyc.jussieu.fr Tel.: F. Martinez Æ E. C. Segura Æ J.-P. Bulanger Departament de Ciencias de la Atmsfera y ls Oceans Facultad de Ciencias Exactas y Naturales, University f Buens, Aires, Argentina are particularly pr. Overall, ur results present an upper bund f ptential temperature warming fr each scenari. Spatially, in SRES A2, ur majr findings are that Trpical Suth America culd warm up by abut 4 C, while suthern Suth America (SSA) wuld als underg a near 2 3 C average warming. Interestingly, this annual mean temperature trend is mdulated by the seasnal cycle in a cntrasted way accrding t the regins. In SSA, the amplitude f the seasnal cycle tends t increase, while in nrthern Suth America, the amplitude f the seasnal cycle wuld be reduced leading t much milder winters. e shw that all the scenaris have similar patterns and nly differ in amplitude. SRES A1B differ frm SRES A2 mainly fr the late twenty-first century, reaching mre r less an 8 9% amplitude cmpared t SRES A2. SRES B1, hwever, diverges frm the ther scenaris as sn as 225. Fr the late twenty-first century, SRES B1 displays amplitudes, which are abut half thse f SRES A2. 1 Intrductin The Intergvernmental Panel n Climate Change (IPCC) published a Special Reprt n Emissins Scenaris (SRES) in 2. This reprt describes the new set f emissins scenaris used in the Third Assessment Reprt. The SRES scenaris have been cnstructed t explre future develpments in the glbal envirnment with special reference t the prductin f greenhuse gases and aersl precursr emissins. hile exhaustive descriptin f the scenaris can be fund elsewhere (Nakicenvic et al. 2), it is wrth recalling that they are based n a set f fur narrative strylines labeled A1, A2, B1, and B2. The strylines cmbine tw sets f divergent tendencies: ne set varying its emphasis between strng ecnmic develpment and strng envirnmental prtectin, the ther set between increasing

2 J.-P. Bulanger et al.: Prjectin f future climate change cnditins glbalizatin and increasing reginalizatin. Analyses f such scenaris in different regins f the glbe perfrmed fr the Third Assessment Reprt have shwn that, fr a given mdel, the large scale gegraphical pattern f the simulated respnse t varius frcing scenaris prved t be very similar, as nly the amplitude f the respnse varied (Rusteenja et al. 23). hile in its Third Assessment Reprt, the IPCC cncluded that the glbal average surface air temperature has increased by.6±.2 C during the twentieth century, it is als prjected t increase by C between 199 and 21. Hwever, the prjectins frm ne regin t anther may differ significantly. A majr challenge nw fr the scientific cmmunity is t take advantage f the large ensembles f multi-mdel simulatins prvided by IPCC in the Furth Assessment Reprt. Mrever, the imprtance f estimating the mst prbable climate change cnditins in the different regins f the glbe requires develping new statistical techniques, which will ptimally cmbine the multimdel simulatins based n their skills in simulating present climate cnditins. rks by Girgi et al. (21), Girgi and Mearns (22), and Tebaldi et al. (25) are based n Bayesian statistics and ffer an interesting methdlgy t ptimally cmbine mdels. A crucial step in the Bayesian apprach is t chse crrectly the prir distributins f the quantities f interest (igley and Raper 21; Reilly et al. 21; Allen et al. 21; Frest et al. 22). Cnsidering the errrs f CGCMs in simulating present-day climate, the mst usual assumptin is t give mre imprtance in a multi-mdel apprach t mdels with skill in simulating present climate cnditins. Hwever, the reader must keep in mind that a mdel may simulate well present-day climate and prly respnd t greenhuse gas frcing. Such a pssibility is a caveat f the methd. In the present study, we aim at evaluating the evlutin f large scale patterns rather than reginally averaged indices. Our strategy is therefre based n cmbining spatial maps f a multi-mdel ensemble. e decided t define a methd based n the ability f each mdel t represent the large scale cntinental temperature. A slutin t the present prblem is the use f a neural netwrk, whse parameters are ptimized by Bayesian statistics (see Appendix). The neural netwrk apprach shuld lead (1) t determining which mdel cntributes mst t the utput and (2) t extraplating the ptimal cmbinatin f mdels t twenty-first century cnditins: (a) The imprtance f an input t a trained variable is actually measured by the magnitude f the weights fanning ut frm the input (see Figs. 19, 2). If the weights are small, the input cntributes little; if the weights are large, the input cntributes mre. The remaining questin is t knw what mre means. In fact, the magnitude is relative t the ther input weights. Thus, an interesting index, the mdel weight index (MI), is the scaled inverse variance f the weights fanning ut frm each input. As a cnsequence, the MI is a measure f the relative imprtance f each input t the trained dataset. Fr this reasn, it can be als used as a weight fr a linear cmbinatin f all the mdels, which can be cmpared t the neural netwrk utput. (b) The neural netwrk parameters (like thse f any statistical methd), als called weights, are ptimized, based n a training dataset. If the distributin f the dataset changes dramatically, the methd (and its parameters) usually des nt prject, i.e., extraplate well. The neural netwrk apprach is usually cnsidered t have gd skills when the input data belng t a distributin similar r clse t the distributin f the training dataset. In the case f temperature climate, all mdels predict an increase f the mean temperature in Suth America f varius C by the end f the twenty-first century. Such a big change prduces a significant shift in the distributin and can impede the neural netwrk frm prperly prjecting twenty-first century cnditins. In a case like that, it is interesting t analyze the linear cmbinatin and prjectin f mdels based n the MIs (if shwn t have a certain skill), which, t a certain extent, is a simplified linear versin f the neural netwrk. The neural netwrk ptimized thrugh Bayesian prcedures then ffers tw alternatives in estimating future climate changes. One alternative is t use the netwrk directly as an extraplatr if it is prven t have an extraplatin skill. A secnd alternative is t cmbine the IPCC mdels linearly, using the MIs. Our wrk mainly fcuses n Suth America as a cntributin t the CLARIS Eurpean Prject ( but ur methd is universal and will sn be applied in different regins f the wrld. Data, mdels, and scenaris used in the present study are described in Sect. 2. In Sect. 3, we discuss the methd and intrduce the MI, which describes the weights f each mdel in the mdel cmbinatin. In Sect. 4, we fcus n the seasnal temperature cycle prjectins. In Sect. 5, we present the prjectin f temperature mean states. In Sect. 6, we cnclude and discuss the results and summarize the reginal impacts f mean state and seasnal cycle changes. 2 Data, mdels, and scenaris 2.1 Data The CRU TS 2. dataset cmprises 1,2 mnthly grids f bserved climate and cvering the glbal land surface at.5 reslutin. There are five climatic variables available: clud cver, DTR, precipitatin, temperature, and vapr pressure. The temperature and precipitatin data sets used are the.5 latitude/lngitude dataset f mnthly surface climate extending frm 191 t 22

3 J.-P. Bulanger et al.: Prjectin f future climate change cnditins ver glbal land areas, excluding Antarctica ( The authrs have already used a previus versin (New et al. 2) f this dataset (Bulanger et al. 25), and have shwn that, at least fr precipitatin, the cmparisn with satellite-based rainfall in Suth America was relatively gd. Cnsidering that we are mainly interested by large-scale patterns, the data are interplated nt a grid. Althugh this data set may present sme differences t the Jnes and Mberg (23) data sets since urban effects have nt been crrected in CRU TS 2., ur spatial average n a grid filters ut a large part f this effect and des nt affect the large scale pattern structures under study. 2.2 Mdels e fcused ur effrt n a multi-mdel analysis, cnsidering nly ne simulatin fr each Atmspheric- Ocean Glbal Circulatin Mdel (AOGCM). Mrever, we nly cnsidered mdels, which prvided mnthly precipitatin and temperature utputs fr twentieth century (2c3m), A2, A1B, and B1 scenaris. Overall, and althugh mre IPCC mdels are certainly available nw, ur analysis was limited t a list f seven AOGCMs presented in Table 1. All the mdel utputs are interplated ver the grid defined fr the bservatins. Sme mdels have finer reslutins, ther have carser reslutins, but verall the 2.5 reslutin grid is a gd cmprmise, which des nt affect the large-scale patterns, and which allws a reasnable level f reginal descriptin. 2.3 Scenaris The SRES scenaris are reference scenaris fr the twenty-first century that seek specifically t exclude the effects f climate change and climate plicies n sciety and the ecnmy ( nn-interventin ). They are based n a set f fur narrative strylines labeled A1, A2, B1, and B2. The strylines cmbine tw sets f divergent tendencies: ne set varying its emphasis between strng ecnmic develpment and strng envirnmental prtectin, the ther set between increasing glbalizatin and increasing reginalizatin (Nakicenvic et al. 2). Our analysis made use f nly three families briefly described as fllws: A1: A future wrld f very rapid ecnmic grwth, lw ppulatin grwth, and rapid intrductin f new and mre efficient technlgy. Majr underlying themes are ecnmic and cultural cnvergence and capacity building, with a substantial reductin in reginal differences in per capita incme. In this wrld, peple pursue persnal wealth rather than envirnmental quality. A2: A differentiated wrld. The underlying theme is that f strengthening reginal cultural identities, with an emphasis n family values and lcal traditins, high ppulatin grwth, and less cncern fr rapid ecnmic develpment. B1: A cnvergent wrld with rapid change in ecnmic structures, dematerializatin and intrductin f clean technlgies. The emphasis is n glbal slutins t achieving envirnmental and scial sustainability, including cncerted effrts fr rapid technlgy develpment, dematerializatin f the ecnmy, and imprving equity. The strylines were quantified t prvide families f scenaris fr each stryline. In all 4 scenaris were quantified, six f which are used as illustrative scenaris by the IPCC, and we nly cnsidered three f them: A1B (balanced acrss energy surces), A2 (with a high-rder radiative frcing), and B1 (mre mderate radiative frcing). Table 1 List f Atmspheric-Ocean Glbal Circulatin Mdels Mdel name and institute Ocean mdel Atmsphere mdel Land mdel Ice mdel References ipsl_cm4 IPSL cnrm_cm3 Me te -France mpi_echam5 MPI ukm_hadcm3 UKMO ncar_ccsm3_ NCAR gfdl_cm2_1 GFDL mirc3_2_medres MIROC OPA L31 LMDZ ORCHIDEE1.3 LIM OPA8.1 Arpege-Climat v3 TRIP Gelat 3.1 Salas-Melia et al. (24) 2 2L31 (T42L45, cy 22b+) (1 1L41) ECHAM5 (T63L32) ECHAM5 Reckner et al. (23) Marsland et al. (23) Haak et al. (23) MOSES1 Grdn et al. (2) Jhns et al. (1997) POP1.4.3, g 1v3 CAM3., T85L26 CLM3., CSIM5., Cllins et al. (25) g 1v3 T85 OM3.1 AM2.1 (am2p13fv, LM2 SIS Delwrth et al. (25) (mm4p1p7_m3p5, M45L24) Gnanadesikan et al. (25) triplar36 2L5) ittenberg et al. (25) COCO L44 AGCM5.7b, T42 L2 MATSIRO T42 COCO3.3, L44 Stuffer et al. (25)

4 J.-P. Bulanger et al.: Prjectin f future climate change cnditins 3 The neural netwrk apprach 3.1 General cncepts A detailed descriptin f the multi-layer perceptrn (MLP) and the prcedures used in the present study are presented in Appendix. A brief summary f the methd fllws. In the present study, we will nly fcus n a tw-layer netwrk architecture (Fig. 19). 3.2 Training f the MLP architecture The bjective is t cmpare spatial temperature maps simulated by a set f climate mdels t bservatins. Therefre, we define: In the input layer: ne neurn fr the lngitude grid pint, ne neurn fr the latitude grid pint and as many additinal neurns as mdels (in the present case 7). Giving tw neurns t the spatial lcatin f each grid pint makes it pssible t take int accunt the mdel and data spatial dependence and crrelatin. In the utput layer: ne neurn fr bservatins. In the hidden layer: a number f neurns t ptimize. The evidence prcedure (Bayesian methd) is used t train the MLP (see Appendix). Tw methds (Bayesian apprach and classical apprach) are used t select the MLP architecture. 3.3 Multi-layer perceptrn selectin prcedure hen the relatinship between inputs and utputs is cmplex r when the dimensin f the inputs is high, we fund that the MLP ptimizatin prcedure may actually cnverge tward a lcal minimum rather than an expected abslute minimum. T avid this prblem, we decided t run the ptimizatin prcedure up t 5 times (we fund this number t be large enugh t always cnverge t a cnsistent result) fr any given number f neurns in the hidden layer. Tw cases amng the 5 trials nly differ by their randmly initiated weights. In these 5 cases, we always ptimized the weights and hyperparameters using the evidence prcedure. Hwever, fr each given number f neurns in the hidden layer, we selected tw netwrks: (1) the ne with the minimum negative lg evidence value, called evidence index frm nw n (Bayesian apprach) and (2) the ne with the minimum errr during a test perid (classical apprach). In the classical apprach, a test perid (here ) different frm the training perid is selected and the MLP errr after cnvergence is evaluated. The MLP with the minimum test errr is then selected fr any given architecture. Fig. 1 Sensitivity f the evidence (upper panel), training errr variance (middle panel, in C 2 ) and test errr variance (lwer panel, in C 2 ) t the number f neurns in the hidden layer. The training errr variance is cmputed ver the training perid (1976 2). The test errr variance is cmputed ver the perid. Slid lines represent the values fr the netwrks selected using the classical apprach. The dashed lines represent the values fr the netwrks selected using the Bayesian apprach Evidence Training errr variance Sensitivity t architectures fr Temperaure Number f neurns in the hidden layer Number f neurns in the hidden layer Test errr variance Number f neurns in the hidden layer

5 J.-P. Bulanger et al.: Prjectin f future climate change cnditins In general, the netwrks selected either by the Bayesian r classical appraches give similar results (Fig. 1). In the present case, we fund the evidence index always increases with the architecture, in agreement with the fact that the increased number f neurns in the hidden layers penalizes the architecture. Mrever, we fund the evidence index t be relatively similar, whichever f the tw selected netwrks we study. Figure 1 shws the training and test errrs based n the mean annual temperature fields. The sensitivity t the architecture is similar whether we study the seasnal temperature fields r the mean annual field. In the case in Fig. 1, bth the training and test errrs decrease frm 1 t 3 neurns and then remain relatively stable as a cnsequence f using the evidence prcedure in the MLP parameter ptimizatin, which reduces the ver fitting risk. As ur results (twenty-first century temperature prjectins) were nt fund t be sensitive even if a maximum f 1r 15 neurns was cnsidered, nly the architectures between 3 and 1 neurns selected by the Bayesian r classical apprach are taken int accunt in the present study (this represents an ensemble f 16 netwrks, i.e., prjectins). Finally, each architecture was weighted accrding t the inverse f its errr during the test perid as fllws: (a) first, the test errr variance f the ensemble was linearly scaled between and 1; (b) secnd, the values are nrmalized. The weights are applied t the prjectin as well as t the MIs in any mean r standard deviatin calculatin. 3.4 Methd fr twenty-first century prjectin As stated in the intrductin, the use f a neural netwrk apprach t cmbine climate mdels actually ffers tw alternatives t prject twenty-first century climate cnditins. One alternative is t use the netwrk directly as an extraplatr if it is prven t have an extraplatin skill. A secnd alternative is t cmbine the IPCC mdels linearly with the MIs. In the ideal case (first alternative), the MLP culd be used as an extraplatr. Unfrtunately, in mst cases, the nn-linear nature f the netwrk makes it impssible t use it as such. Indeed, extraplatin is much mre reliable in linear mdels than in nnlinear mdels. In the present case, the majr prblem in using the MLP fr extraplatin is that all IPCC mdels simulate a strng increase in cntinental temperatures at the end f twenty-first century, s the values f the input space under twenty-first century climate cnditins d nt appear in the training values meaning that the netwrk has never learned such values. Therefre, the netwrk may underestimate r prly reprduce the ptential increase f temperature. This hypthesis will be tested in the next sectin. As t the secnd alternative, tw questins naturally arise. (1) hy wuld the indices assciated t a nnlinear netwrk ptimizatin have skill t cmbine mdels linearly?. (2) In what way is the result dependent n the mdels chsen in the cmbinatin? These tw questins cannt be answered a priri. The skill f the linear cmbinatin can nly be evaluated a psteriri. As fr any multi-mdel ensemble cmbinatin, ur mdel cmbinatin is, by definitin, dependent n the skills f the mdels taken int accunt. It is bvius that, if a mdel were fund t be better than all thers in simulating certain aspects f the climate variability, nt taking it int accunt wuld certainly affect the twentyfirst century climate prjectin negatively. It is therefre better t wrk with an ensemble f mdels as large as pssible. As stated earlier, the present wrk aims at demnstrating the feasibility f using a neural netwrk apprach with Bayesian statistics t cmbine IPCC mdels. e plan in extending the present wrk t as many mdels as will finally be available in the IPCC data server. 4 Calibratin t twentieth century bservatins 4.1 Temperature mean state Mdel-data cmparisn Figure 2 cmpares the temperature bservatins t the seven mdels. The mdels are mstly different with bservatins in the Amaznian basin and alng the Brazilian casts. It is likely that the different sil mdels used by the different AOGCMs explain the large differences f their respnse in the Amaznian basin. Other differences are als bserved between 15 and 3 S west f the Andes. Sme differences in the way the different mdels represent the suthward extensin f warm temperature east f the Andes and the meridinal and znal gradients are als wrth nting Temperature MI As previusly described, MLPs with three t ten neurns in the hidden layer were calibrated by cmparing the temperature mean state ver the perid simulated by the seven mdels t the ne bserved (maps displayed in Fig. 2). Figure 3 presents the temperature MI as well as its uncertainty. It can be shwn that, accrding t that index, the mdels, which cntribute mst t the utput, are (in decreasing rder) the Mete-France (cnrm_cm3) mdel, the MPI (mpi_echam5) and the IPSL (ipsl_cm4) mdel. It is likely that the majr weight fund fr the Mete-France mdel is due t its relatively gd amplitude ver mst f the Amaznian basin and the suthern regins. The weak MIROC index may be assciated t the large differences in the mdel amplitude and general patterns, while the weak GFDL index is mre likely t be assciated t the high warm temperatures ver the Amaznian basin and a relatively large znal gradient n the eastern part f the cntinent, differing frm the bserved weak znal

6 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 2 Annual mean temperature fr bservatins (CRU) and each f the seven mdels cmputed ver the perid. Cnturs are every 1 C CRU IPSL CNRM MPI S S S S 6 S 3 S 3 S 3 S UKMO NCAR GFDL MIROC S S S S 6 S 3 S 3 S 3 S gradient. The mst striking result is the pr index f the UKMO mdel. Althugh it is difficult t identify exactly the reasn fr this, we suggest that it may result frm: (1) a strng znal gradient in temperature east f the Andes between 15 and 3 S where the bservatins have a rather weak znal gradient; (2) cld temperatures in the suthern tip f Suth America. It is imprtant t clarify that the index is nt a quality index. It represents the mdel cntributin in the mixing f all mdels when cnsidering the entire cntinent. There is n dubt that mre reginal studies fcusing n either the trpical r the subtrpical regin (such studies are beynd the scpe f this paper) may give different results in the weighting f each mdel. 4.2 Temperature seasnal cycle Mdel-data cmparisns Figures 4, 5, 6, and 7 shw the shift f the fur seasns (December February, DJF; March May, MAM; June August, JJA; September Nvember, SON) frm the mean state fr CRU bservatins and the seven mdels.

7 J.-P. Bulanger et al.: Prjectin f future climate change cnditins IPSL CNRM MPI UKMO NCAR GFDL MIROC In austral summer (DJF; Fig. 4), the majr differences between mdels and bservatins are as fllws. First, the strng warm pattern centered near 35 S and between 7 and 65 is ften t strng (except fr MIROC and NCAR) and usually lcated t far nrth (such as in UKMO). Secnd, mst f the mdels verestimate the cld anmalies ver the Amaznian basin (except CNRM, UKMO, and MIROC) r display large warm anmalies near the equatr (IPSL, NCAR, GFDL). In austral fall (MAM; Fig. 5), relatively weak anmalies are bserved during that transitin seasn. All the mdels tend t verestimate the anmalies in the Amaznian basin with sme very large mdel-discrepancies in GFDL and NCAR. MIROC displays large cld anmalies near 3 S, while CNRM simulates cld anmalies in suthern tip f Suth America. In austral winter (JJA; Fig. 6), the bserved pattern is similar t the DJF pattern but has the ppsite sign. Sme differences are bserved in the abslute temperature amplitude as well as in the znal gradient between the Andes and the Atlantic cast. Mdels als shw an ppsite pattern t DJF cnditins althugh sme mdels have mre variability in their amplitude r gradients than the bservatins. Finally, in austral spring (SON; Fig. 7), the bserved and simulated patterns are nt anti-symmetric t the MAM patterns. It appears that the mdels have a very strng bias in simulating the temperature anmalies ver the Amaznian basin, and prly simulate the warm anmalies extending alng the Andes frm 15 S t the suthern tip f Suth America (except t a certain extent the MPI mdel) Temperature MI Temperature Mdel eight Index Fig. 3 Temperature mdel weight index cmputed fr each mdel. Mean values are in blue and the errr bar is in red As previusly, the MLP was calibrated ver the perid The temperature MI is displayed fr the fur seasns in Fig. 8. As previusly stated, this index measures the weight that the neural netwrk attributes t that specific mdel in the functin f transfer between IPCC mdels and bservatins. The majr pint bserved in Fig. 8 is that, cntrary t Fig. 4, errr bars are relatively large meaning that frm ne specific architecture t anther the weighting amplitude varies a lt s that it is much mre difficult t identify the reasns why the methd weights mre r less ne mdel r anther. Anyway, we can draw sme suggestins frm Fig. 8 and Figs. 4, 5, 6, 7. First, the NCAR and GFDL mdel indices are significantly weak during mst f the fur seasns as cmpared t the mdel with the largest index. e tend t believe that this behavir is assciated t their cmplex patterns ver the Amaznian basin. The relatively better results f the GFDL mdel in JJA may actually be assciated t a better simulatin f the lcatin and amplitude f the cldest anmalies in the subtrpical regin, which may have cmpensated the bias in the Amaznian basin. The relatively nn-significant differences between the varius mdel indices suggest that the methd takes advantage f the different mdel patterns in its fit t the bservatins, althugh the twenty-first century prjectin may actually display larger ensemble errrs (t be discussed later). 4.3 Neural netwrk versus linear cmbinatin Figure 9 shws the mean f ur ensemble and the difference t bservatins, and the ensemble errr (r standard deviatin) bth fr the training and test perids. It shws that the MLP Ensemble crrects fairly well the different mdel biases in rder t recver a largescale pattern in gd agreement with annual mean temperature bservatins. The differences with the bserved mean state shw a relatively patchy structure with values usually between ±1 C. Mrever, all the MLPs are cnsistent in their reprductin f the training perid cnditins displaying an ensemble errr lwer than.4 C. hen the MLPs are used t prject the test perid ( ), the pattern f differences is similar althugh slightly larger. It must be nted that the simulated differences between the tw perids are very different frm the bserved differences. In rder t test whether this result is an errr f the methd (verfitting) r an errr f the mdels used as inputs, we cmputed the linear ensemble mean fr the tw perids with the MIs. hen representing the perid, interestingly the linear ensemble mean reprduces fairly well the bserved features althugh it displays larger differences t bservatins than the MLP ensemble mean with structured patterns. These patterns represent mdel biases in the Amazns, ver the Nrdeste, in the La Plata Basin (LPB) as well as west f the Andes. Mrever, the linear ensemble mean errr is much larger than the MLP cnsistent with the large differences between the mdels in certain regins (Fig. 2), and the MIs display f large standard

8 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 4 Same as Fig. 2 but fr the DJF seasn. Cnturs are every.5 C CRU IPSL CNRM MPI S S S S 6 S 3 S 3 S 3 S UKMO NCAR GFDL MIROC S S S S 6 S 3 S 3 S 3 S deviatins fr certain mdels (Fig. 3). Interestingly, when the linear ensemble mean is cmputed ver the perid, it is seen that the differences between the tw perids are mre similar than the nes displayed by the MLP, althugh f larger amplitude. Hwever, the changes in the simulated patterns are very different than thse bserved. In fact, majr changes in the precipitatin regimes have been bserved since the 196s 197s. Such changes are nt simulated by the IPCC cupled GCMs. Mrever, the fact that bth the MLP and linear ensemble means are similar shws that the MLPs are nt verfitted. Finally, we fund the level f fit f the MLP fr each f the fur seasns during the training and test perids t be similar (nt shwn). Befre analyzing in detail the twenty-first century prjectins (Sect. 5), it must be seen whether the MLP has extraplatin skill. Figure 1 cmpares the respective behavir f the MLP and the linear ensemble, nly cnsidering as inputs the IPCC mdel mean temperature simulated under SRES A2 scenari fr the perid. There are big differences between the tw ensemble prjectins. The linear ensemble displays a strng warming with values ranging between 2 and 4 C,

9 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 5 Same as Fig. 4 but fr the MAM seasn CRU IPSL CNRM MPI S S S S 6 S 3 S 3 S 3 S UKMO NCAR GFDL MIROC 3 S S S S S 3 S 3 S 3 S while the MLP prjectin is much weaker and reaches a temperature increase f 4 C nly, in specific regins (Pacific cast and parts f the Amazns and Suthern Brazil). The agreement rati between the MLP and the linear prjectins (Fig. 1, Cnfidence Level ) shws that the regins where the tw methds cnverge (rati mre than.8) are the Pacific cast frm Clmbia t nrthern Chile (15 S), the Atlantic cast (frm 15 t 35 S) with intermediate values (between.6 and.8) cvering mst f Brazil. In all ther regins f Suth America, the rati is lw and can reach values clse t. In Tebaldi et al. (25), the psterir distributin f the parameters used in the climate change linear prjectin is sensitive t tw factrs: the bias criterin (hw the IPCC mdels represent present climate bservatins) and the cnvergence criterin (hw the IPCC mdels agree in their climate change respnse). Cnsidering that the MLP weights are built n present-day climate, we analyzed tw criteria: the bias criterin (hw the IPCC linear ensemble cmpares t bservatins; Fig. 1) and the divergence criterin r inter-mdel variance (hw the IPCC mdels differ frm each ther in simulating present-day climate; Fig. 1). The bias criterin presents significant errrs west f the Andes frm 1 t 35 S as well as in the suthern tip f Suth America. In bth cases, the cnfidence level is

10 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 6 Same as Fig. 4 but fr the JJA seasn CRU IPSL CNRM MPI S S S S 6 S 3 S 3 S 3 S UKMO NCAR GFDL MIROC S S S S 6 S 3 S 3 S 3 S clse t zer. The divergence criterin displays significant errrs alng the Pacific cast as well as ver part f the Amazns, in Guyana, Venezuela, and Clmbia. In these regins, the cnfidence level is lw r even clse t zer displaying similar cntur patterns. In cnclusin, and t a certain extent by analgy t the wrk by Celh et al. (24), the MLP penalizes the prjected warming when either the linear cmbinatin errr t bservatins r the IPCC inter-mdel variance are large. One culd linearize the MLP prjected change as fllws: MLPðx; yþ ¼Pðx; yþ PN MIðnÞIPCCðn; x; yþ; n¼1 where IPCC(n, x, y) represents the anmalus spatial map f the nth IPCC mdel cnsidered in the study (difference between twentieth and twenty-first century cnditins), MI(n) is the mdel weight index assciated t the nth IPCC mdel and P(x, y) is a penalizing functin, which culd be written as: P(x, y) = exp ( Ve(x, y)) exp ( Vm(x, y)), where Ve and Vm are respectively the nrmalized variance f the linear ensemble errr (bias criterin) and the nrmalized variance f the IPCC mdels (divergence criterin). herever Ve r Vm are different frm, the MLP will penalize the twenty-first century prjectin. Such

11 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 7 Same as Fig. 4 but fr the SON seasn CRU IPSL CNRM MPI S S S S 6 S 3 S 3 S 3 S UKMO NCAR GFDL MIROC 3 S S S S S 3 S 3 S 3 S behavir is bvius in the Suthern tip f Suth America, alng the Chilean and Peruvian casts as well as in the Guyana, Venezuela, and Clmbia regin (the shape f the weak warming there is strikingly similar t the shape f the divergence criterin). Finally, the MLP prjectins underestimate the ptential climate change prjectins simulated by the IPCC mdel, as the MLP penalizes the mdel prjectins accrding t the tw kinds f errrs described earlier. Hwever, such behavir is als an advantage as by cmparisn t linear prjectin, it makes it pssible t cmpute the spatially dependent cnfidence level f the changes in climate cnditins (Fig. 1). Therefre, bth the MLP and linear prjectins (based n MLP weights) shuld be analyzed jintly. The linear ensemble prjectin displays a pssible climate change pattern, while the MLP helps t cmpute the cnfidence level f such a change. Here belw, we will nly shw the linear cmbinatin f IPCC mdels based n the MIs. Hwever, the linearly prjected patterns are upper bunds f climate change amplitudes, and the cnfidence in these changes is limited t the regins where the cnfidence level in Fig. 1 is clse t 1.

12 J.-P. Bulanger et al.: Prjectin f future climate change cnditins.8 Temperature Mdel eight Index-DJF.8 Temperature Mdel eight Index-MAM IPSL CNRM MPI UKMO NCAR GFDL MIROC IPSL CNRM MPI UKMO NCAR GFDL MIROC.8 Temperature Mdel eight Index-JJA.8 Temperature Mdel eight Index-SON IPSL CNRM MPI UKMO NCAR GFDL MIROC IPSL CNRM MPI UKMO NCAR GFDL MIROC Fig. 8 Same as Fig. 3 but fr the fur seasns Finally, in Fig. 11, we present the linear cmbinatins f each seasn. It can be seen that the mdel linear cmbinatin presents varius biases. In austral summer (DJF), the general structures are fairly well reprduced, but the amplitudes f the large temperature anmalies bserved between 15 and 3 S are actually simulated t far t the nrth. Mrever, the decrease in temperature frm the interir f the cntinent t the Atlantic Ocean nrth f 3 S is t strng in the ensemble, leading t a strng negative bias. Similar patterns are still present in austral fall (MAM) but with a reduced amplitude. In austral winter (JJA), the majr bias is bserved in the Nrdeste and in the LPB with t cld an ensemble, and in the suthern tip with t warm temperatures. Finally, in austral spring (SON), the mdel linear cmbinatin is way t warm ver the Amazns and t cld in the suthern tip f the cntinent. The ensemble errr displays a pattern strngly related t the regins f larger differences. Overall, the ensemble errr is in the rder f r weaker than 1 C. In cnclusin, in decreasing rder f magnitude, the mst sensitive regins are the Amazn basin (with large anmalies except in winter), the LPB (during the extreme phases f the seasn), the suthern tip f the cntinent and the Clmbia Venezuela Guyana regin. 5 Twenty-first century prjectin 5.1 Temperature mean state Mdel-prjectin cmparisn First, we cmpare the mean temperature prjectin given by the methd when mixing the seven mdel utputs fr the three scenaris A2, A1B, and B1 and fr the fur

13 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Observatins Ensemble Difference Ensemble errr 3 S 3 S 3 S 3 S 6 S S S S Observatins Ensemble Difference Ensemble errr 3 S 3 S 3 S 3 S 6 S S S S Observatins Ensemble Difference Ensemble errr 3 S 3 S 3 S 3 S 6 S S S S Observatins Ensemble Difference Ensemble errr 3 S 3 S 3 S 3 S 6 S S S S year perids (21 225, , , and ). Fr the simplicity s sake, we will nly cmpare scenari A2 during (Fig. 12). First, we can bserve that all the mdels display a much warmer temperature mean state than during the perid ver the Amaznian basin. This warming is

14 J.-P. Bulanger et al.: Prjectin f future climate change cnditins b Fig. 9 Frm tp t bttm fr each rw f panels: (1) Frm left t right Observed annual mean temperature (cnturs are every 1 C), neural netwrk prjectin based n the perid (cnturs are every 1 C), differences between the prjectin and the bservatins (cnturs are every.5 C), ensemble variance (cnturs are every.1 C). (2) Frm left t right Observed differences between the and annual mean temperatures (cnturs are every.2 C), differences between the neural netwrk prjectin based n the perid and the perid (cnturs are every.2 C), ensemble variance fr the prjectin (cnturs are every.1 C). (3) Frm left t right Observed annual mean temperature (cnturs are every 1 C), linear prjectin based n the perid (cnturs are every 1 C), differences between the linear prjectin and the bservatins (cnturs are every.5 C), ensemble variance (cnturs are every.1 C). (4) Frm left t right Observed differences between the and annual mean temperatures (cnturs are every.2 C), differences between the linear prjectin based n the perid and the perid (cnturs are every.2 C), ensemble variance fr the linear prjectin (cnturs are every.1 C) actually relatively general ver mst f the cntinent. e fund that these patterns were mstly identical whatever the perid under study as nly the amplitude f the respnse varied. Mrever, when cmparing the different scenaris (A2, A1B, and B1), we als fund that the prjected patterns were similar and differed mainly in their amplitude. hile all the mdels suggest a warming f at least 2 C in the suthern tip f the cntinent and f 3 4 C in the nrthern regins, large differences are bserved between the mdels. NCAR displays the weakest warming amplitude, while UKMO exceeds the 5 C warming ver trpical Suth America. Mst f the mdels suggest a greater warming in the Clmbia Venezuela Guyana regin f 3 5 C. Then, depending n the mdel, strng warming patterns can be bserved ver the Amazns basin, the LPB, Nrdeste r Chilean casts. The ensemble prjected pattern is nw discussed Twenty-first century prjectin Figure 13 displays the twenty-first century SRES A2 prjected mean temperature fr the fur 25-year perids (21 225, , , and ), the difference t the pattern and the ensemble errr. e can see clearly a warming ver the cntinent after the perid. The majr patterns assciated t the warming are: 1. The trpical Pacific castal warming assciated t a warming in the IPCC mdels f the Pacific cean castal sea surface temperatures alng the casts f Equatr, Peru, nrthern Chile, and Clmbia, the warming reaches 4 C in certain regins; 2. A strng warming ver suthern Venezuela and nrthern Brazil; 3. On the eastern side f the Andes, a majr warming (arund 4 C), which cvers a large part f the Amazns, and, which extends ver mst f the cntinent, slightly decreasing eastward and mre strngly suthward. Overall, the warming is higher than 2 C at each grid pint. Hwever, as pinted ut earlier, the actual amplitude f the future warming is very uncertain given the differences between the mdels (Fig. 12) and the cnfidence level displayed in Fig. 1. The main cnclusins ne can actually make, given such levels f uncertainty, are that the entire cntinent is likely t warm with a strnger amplitude in the trpical regin than in the suthern part, that the warming shuld be clse t 3 4 C alng the trpical Pacific cast and 2 3 C alng the Atlantic cast where the cnfidence level is high (Fig. 1). In the Amazn basin, significant differences certainly result frm land surface mdel physics. The same prjectin fr scenaris A1B and B1 fr the last 25-year perid is displayed in Fig. 14. e find the methd t be relatively cnsistent as the warming patterns are very similar t the nes prjected fr scenari A2. The figures nly differ in amplitude. SRES A1B warming amplitude pattern is intermediate between the and SRES A2 patterns. SRES B1 warming amplitude pattern is intermediate between the and SRES A2 patterns. Overall, the prjected cntinental mean warming is clse t 4 C fr SRES A2, while the same prjectins fr the scenaris A1B and B1 are respectively 3.4 and 2.2 C. The ensemble errr bar n the cntinentally averaged annual mean temperature rise is actually relatively small (n the rder f.1 C), but it des nt take int accunt the bias and divergence criteria, nr the discrepancies between mdel prjectins. 5.2 Temperature seasnal cycle Fr the sake f clarity and brevity, we d nt present here the cmparisn between the ensemble and the evlutin f each mdel temperature patterns fr each 25-year perid and each f the fur seasns but. cncentrate n the descriptin f the late twenty-first century prjectin SRES A2 Figure 15 shws late twenty-first century SRES A2 prjectin fr each seasn. Sme striking large-scale patterns can be bserved: 1. First, in DJF, the largest warming is bserved alng the casts f Chile and Peru (4 C) and ver Venezuela and part f Clmbia (4.5 C). Mst f the Atlantic cast culd experience a near 3 C warming as far suth as 4 S. In the suthern tip f the cntinent, the warming may reach frm 1 t 2 C. Thus, the warming ver nrthern Suth America (NSA) culd get t 3.5 C (Fig. 16) and 3.7 and 3.1 C ver suthern Suth America (SSA) and the La Plata Basin (LPB).

15 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 1 Frm tp t bttm fr each rw f panels: (1) Frm left t right MLP ensemble prjectin fr late twenty-first century cnditins (SRES A2; cnturs are every 1 C), differences with present-day climate cnditins (cnturs are every.5 C) and ensemble variance f the prjectin (cnturs are every.1 C). (2) Frm left t right Linear ensemble prjectin fr late twenty-first century cnditins (SRES A2; cnturs are every 1 C), differences with presentday climate cnditins (cnturs are every.5 C) and ensemble variance f the prjectin (cnturs are every.1 C). (3) Frm left t right Spatial representatin f the bias criterin (squared errr between bservatins and the linear ensemble cmputed fr twentieth century cnditins; amplitudes are in C 2 ), f the divergence criterin (IPCC mdel dispersin r variance; amplitudes are in C 2 ), f the cnfidence level (rati between the MLP and linear prjectins; values are between and 1) 3 S 6 S 3 S 6 S (276-21)-(1976-2) 3 S 6 S (276-21)-(1976-2) 3 S 6 S S 6 S 3 S 6 S MLP ensemble errr Linear ensemble errr Bias Criterin Divergence Criterin Cnfidence Level 3 S 3 S 3 S 6 S S S In MAM (Fig. 15), the majr temperature increase wuld be the same as seen ver Clmbia and Venezuela and the casts f Chile and Peru. A warming f abut 4 C culd be lcated in suthern Brazil. The meridinal gradient f the warming trend may be weaker in MAM than in DJF. Thus, the suthern tip f the cntinent culd experience a warming f mre than 2 C. In the three selected regins, the averaged warming culd be 3 C inssa,3.9 C in NSA, and 3.7 in LPB. 3. In JJA (Fig. 15), the warming trend displays a strng meridinal gradient near 3 S. Nrth f 3 S, the warming culd be strng with higher values ver the Amazn and the nrthern casts f Suth America. It culd reach an average f abut 4.5 C. Suth f 3 S, the average warming culd be (it seems the place is missing here) arund 2.6 C, while in LPB lcated part nrth and part suth f 3 S, the warming culd reach 3.6 C. 4. Finally in SON (Fig. 15), the highest warming (arund 5.5 C) wuld be bserved ver the center f the Amazn and part f the Clmbia Venezuela regin. The meridinal gradient culd be weaker than

16 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Observatins Linear Ensemble Difference 15 N 15 N 15 N 15N 15 S 15 S 15 S 15S 3 S 3 S 3 S 3 S 45S 45S 45S 45S 6S S 6 4 6S Ensemble errr S N 15 S 3 S 45S 6 S 15 N 15S 3S 45S 6 S 15 N 15S 3S 45 S 6S Fig. 11 Frm tp t bttm, each rw represents, fr each seasn (DJF, MAM, JJA, SON), the bserved seasnal anmalies cmputed ver the perid (cnturs are every 1 C), the linear ensemble mean value (cnturs are every 1 C), the difference (cnturs are every.5 C), and the ensemble variance (cnturs are every.1 C)

17 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig SRES A2 annual mean temperature change prjected by the linear methd cmpared t the annual mean temperature change simulated by each mdel. Values are relative t the perid. Cnturs are every.5 C ENS IPSL CNRM MPI S S S S 6 S 3 S 3 S 3 S UKMO NCAR GFDL MIROC 3 S S S S S 3 S 3 S 3 S in DJF, but the warming culd remain much greater in NSA (4.7 C) than in SSA (2.9 C) r LPB (3.8 C). Befre cncluding this analysis, it is interesting t highlight that the mean temperature-warming trend bserved in each selected regin (3. C in SSA, 4.3 C in NSA and 3.7 C in the LPB) is actually mdulated alng the curse f the seasnal cycle. Fr instance, in SSA, the warming culd be strnger in austral summer and fall (3.4 and 3. C) and weaker in winter and spring (2.6 and 2.9 C) suggesting greater amplitude f the seasnal cycle. In NSA, the warming culd be weaker in austral summer and fall (4.1 and 3.9 C) and strnger in winter and spring (4.5 and 4.7 C) suggesting smaller amplitude f the seasnal cycle. Of curse, the result is a very largescale index and the mdulatin f the seasnal cycle may vary between sub regins. Finally, in the LPB, which is lcated n the edge f NSA and SSA, the trend is fund t be relatively unifrm ver the seasns. It is wrth pinting ut that, at latitudes brdering between the trpical and subtrpical climates, the prjected large warming and especially a much warmer winter may have

18 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 13 Frm tp t dwn, SRES A2 annual mean temperature prjectins fr each perid , , , and Frm left t right Linear prjectin f the annual mean temperature (cnturs are every 1 C); differences between the linear prjectin and the cnditins (cnturs are every.5 C); Ensemble variance (cnturs are every.2 C) 3 S 6 S (21-225)-(1976-2) 3 S 6 S S 6 S Ensemble errr (226-25)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S ( )-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S

19 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 14 Frm tp t dwn, prjectins respectively fr SRES A1B and SRES B1. Frm left t right: same as Fig SRES A1B (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S SRES B1 (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S significant cnsequences fr crps and health. In the last case, a milder winter may reinfrce the risk f endemic Dengue in the suthern part f the regin, which may affect nt nly Brazil (as it already des) but als Uruguay and Argentina SRES A1B Figure 17 displays late twenty-first century SRES A1B prjectin fr each seasn. As can be bserved, mst f the features described earlier fr SRES A2 wuld be valid fr SRES A1B, and nly differ in amplitude. Mrever, the reginal indices shw trends very similar t SRES A2 althugh f smaller amplitudes. On average, the warming trends cmputed as the difference between late twenty-first century and late twentieth century is abut 8 9% f the value f thse bserved in SRES A2. It is wrth pinting ut that the majr differences between SRES A2 and SRES A1B are bserved in late the twenty-first century. Befre that, the tw scenaris are similar SRES B1 Figure 18 displays late twenty-first century SRES B1 prjectin fr each seasn. As can be bserved, mst f the features described earlier fr SRES A2 r SRES A1B are valid fr SRES B1, and nly differ in amplitude. Mrever, the reginal indices shw trends very similar t SRES A2, althugh with much smaller amplitudes. SRES B1 diverges frm bth SRES A2 and SRES A1B as sn as 225. In the late twenty-first century, the trends suggested by SRES B1 are abut half (5 6%) thse bserved in SRES A2. Hwever, as pinted ut earlier, the large-scale patterns are relatively similar t thse bserved in SRES A2 and SRES A1B. 6 Cnclusin and discussin A majr challenge fr the scientific climate cmmunity at the beginning f twenty-first century is t prvide as accurate as pssible an estimate f future climate cnditins, accrding t ptential ecnmic scenaris f

20 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 15 Frm tp t dwn, same as Fig. 13 but fr each seasn (DJF, MAM, JJA, and SON) (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S evlutin. The great internatinal effrt made by numerus climate centers t prviding the entire cmmunity with ensembles f climate simulatins fr these scenaris is an imprtant step tward that gal. There is n dubt that each climate mdel has skills in capturing certain aspects f the climate system mechanisms. It is

21 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 16 Time evlutin f annual and seasnal mean temperature in three different regins f Suth America. NSA stands fr nrthern Suth America (nrth f 25 S). SSA stands fr suthern Suth America (suth f 25 S). LPB stands fr La Plata basin (simplified t a rectangular bx extending frm 15 t 35 S and frm 65 t the cast). SRES A2 prjectins are in red. SRES A1B prjectins are in blue. SRES B1 prjectins are in green Mean SSA DJF SSA Mean NSA DJF NSA Mean LPB DJF LPB MAM SSA 28 MAM NSA 25 MAM LPB JJA SSA 28 JJA NSA 21 JJA LPB SON SSA 31 SON NSA 27 SON LPB unlikely, hwever, that ne specific mdel will capture all f them better than all ther mdels. Therefre, multi-mdel/multi-ensemble analysis is a way fr the future t take advantage f what each mdel represents best in rder t ptimize the prjectins f future climate change cnditins. The present paper suggests a pssible strategy t reach that gal. e fcused n a small set f mdels (7) in rder t describe the methdlgy, and we hpe t be able t extend ur wrk t a larger set f mdels in the future. Our methdlgy is based n the use f neural netwrks, whse weights and hyperparameters are ptimized thrugh Bayesian statistics (see Appendix). As cmpared t ther methds using Bayesian methds t cmbine mdel prjectins (e.g., Girgi and Mearns 22; Tebaldi et al. 25), the use f neural netwrks prvides a nn-linear way t take int accunt mdel spatial biases in their simulatin f present climate cnditins. The majr difficulty in using such a methd is the ptimizatin f the architecture f the neural

22 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 17 Same as Fig. 15, but fr SRES A1B prjectins (276-21)-(1976-2) 15 N 15 N 15 N 15 S 15 S 15 S 3S 3S 3S 45S 45S 45S 6S S Ensemble errr S N 15S 3S 45S 6S 15N 15S 3S 45S 6 S 15 N 15S 3S 45S 6 S 2 netwrk, aviding cnvergence in lcal minima, which wuld bias the ptimal IPCC cmbinatin. Mrever, it is imprtant t take int accunt different architectures, which may nt be significantly different in representing present-day cnditins, but may differ when prjecting twenty-first century cnditins. e tk great care in

23 J.-P. Bulanger et al.: Prjectin f future climate change cnditins Fig. 18 Same as Fig. 15, but fr SRES B1 prjectins (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S (276-21)-(1976-2) Ensemble errr 3 S 3 S 3 S 6 S S S 8 6 4

24 J.-P. Bulanger et al.: Prjectin f future climate change cnditins ensuring that the methd fits present-day cnditins fr crrect reasns (i.e., that a mixture f mdels is actually able t cmpensate fr their bias, and avids an verfitting). One f the utputs f the methd is hyperparameter cmputatin, called in the paper, MI, which can be interpreted, by analgy t linear fitting methds, as nrmalized weights f a linear mixture f mdels. The MI is nt a quality criterin fr mdels; it indicates, which mdels will cntribute mre t the transfer functin represented by the neural netwrk when mixing the mdels. Since we analyzed the entire Suth American cntinent, a mdel may have a weak MI, but may have very gd skill in simulating temperature in a sub regin f Suth America. In rder t use the MI as a quality criterin ne wuld have t divide the glbe int climate-cherent regins, befre perfrming the analysis. This was beynd the scpe f the present study. A majr difficulty in using neural netwrks fr climate change determining the netwrk s skill t extraplate. A cmparisn between MLP prjectin and a linear ensemble prjectin based n the MIs allwed us t determine that the MLP penalizes future climate change prjectins (i.e., the MLP prjectins are f smaller amplitudes than any mdel r their linear cmbinatin). The rati between MLP and linear prjectins (als called cnfidence level) is sensitive t tw factrs: the bias and the divergence criteria.they represent respectively the errr between the linear cmbinatin and present-day climate cnditins and the variance between the mdels. The largest cnfidence levels are bserved n the Atlantic cast frm the trpics t 35 S and the Pacific cast frm Clmbia t 15 S. In the ther regins, the cnfidence level is lw and can drp t zer in Chile between 15 and 3 S. In cnclusin, when applied t temperature, the neural netwrk apprach, using a Bayesian statistics fr ptimizatin, makes it pssible t cmpute the ptimal set f weights fr a linear cmbinatin f the IPCC mdels, and a penalizing functin r prbability that such a change ccurred, based n the present-climate mdel biases and their prjectin dispersin. Therefre, we fcused n the linear ensemble prjectin, althugh the reliability f the results depends n the cnfidence level displayed in Fig. 1. hen prjecting future climate cnditins, we fund that the three scenaris (A2, A1B, and B1) shw similar patterns and differ nly in amplitude, cnfirming results btained by Rusteenja et al. (23). Hwever, SRES A1B differ frm SRES A2 mainly in the late twenty-first century reaching abut 8 9% amplitude (respective) cmpared t SRES A2. SRES B1, hwever, diverges frm the ther tw scenaris as sn as in 225. In the late twenty-first century, SRES B1 displays abut half the amplitude f SRES A2. Spatially, ur majr findings in SRES A2 fr the end f the twenty-first century are that trpical Suth America may warm up by abut 4 C with larger amplitudes ver the Chilean and Peruvian casts, the central Amazn and the Clmbia Venezuela Guyana regin. In the suthern part f the cntinent, the warming culd reach abut 2 3 C. Hwever, as pinted ut befre, the methd indicates a large uncertainty (the cnfidence level is clse t zer in the suthern tip f Suth America, see Fig. 1). Interestingly, this annual mean temperature trend is mdulated by the seasnal cycle in cntrasted ways in each sub regin. In SSA, the amplitude f the seasnal cycle wuld increase, while in NSA the amplitude f the seasnal cycle wuld be reduced. The reductin f the winter summer cntrasts tgether with a significant warming trend may induce strng impacts in these regins. In particular, diseases such as Dengue, which are vectr-brne (Degallier et al. 25), depend strngly n hw lng the msquites live and hw they survive cld winter cnditins. In a much warmer climate than the ne prjected, it is likely that changes in winter cnditins may increase the risk f Dengue develping t the suth f its actual psitin. The study f such impacts in Suth America is under analysis in the framewrk f the Eurpean CLARIS Prject. Acknwledgements e wish t thank the Institut de Recherche pur le De velppement (IRD), the Institut Pierre-Simn Laplace (IPSL), the Centre Natinal de la Recherche Scientifique (CNRS; Prgramme ATIP-22) fr their financial supprt crucial in the develpment f the authrs cllabratin. e are als grateful t the Eurpean Cmmissin fr funding the CLARIS Prject (Prject 1454) within whse framewrk the present study was undertaken. e are grateful t the University f Buens Aires and the Department f Atmsphere and Ocean Sciences fr welcming Jean-Philippe Bulanger. e thank Tim Mitchell and David Viner fr prviding the CRU TS2. datasets. Finally, we thank the Eurpean prject CLARIS ( fr facilitating the access t the IPCC simulatin utputs. e thank the internatinal mdeling grups fr prviding their data fr analysis, the Prgram fr Climate Mdel Diagnsis and Intercmparisn (PCMDI) fr cllecting and archiving the mdel data, the JSC/ CLIVAR rking Grup n Cupled Mdelling (GCM) and their Cupled Mdel Intercmparisn Prject (CMIP) and Climate Simulatin Panel fr rganizing the mdel data analysis activity, and the IPCC G1 TSU fr technical supprt. The IPCC Data Archive at Lawrence Livermre Natinal Labratry is supprted by the Office f Science, U.S. Department f Energy. Special thanks are addressed t Alfred Rlla fr his strng supprt in dwnlading all the IPCC mdel utputs. 7 Appendix: The multi-layer perceptrn (MLP) 7.1 General descriptin The MLP is prbably the mst widely used architecture fr practical applicatins f neural netwrks (Nabney 22). Frm a cmputatinal pint f view, the MLP can be described by a set f functins applied between different elements (neurns) using relatively simple arithmetic frmulae, and a set f methds t ptimize these functins based n a set f data. In the present study, we will nly fcus n a tw-layer netwrk architecture (Fig. 19). Its simplest element is called a neurn and is cnnected t all the neurns in the upper

25 J.-P. Bulanger et al.: Prjectin f future climate change cnditins layer (either the hidden layer if the neurn belngs t the input layer r the utput layer if the neurn belngs t the hidden layer). Each neurn has a value, and each cnnectin is assciated t a weight (Fig. 2). As shwn in Fig. 19, in the MLP case we cnsidered, the neurns are rganized in layers: an input layer (the values f all the input neurns except the bias are specified by the user), a hidden layer and an utput layer. Each neurn in ne layer is cnnected t all the neurns in the next layer. Mre specifically, defining the input vectr ðn i Þ i¼1; I ; the first layer f the netwrk frms H linear cmbinatins (H is the number f neurns in the hidden layer) f the input vectr t give the fllwing set f intermediate activatin variables: Fig. 19 Schematic representatin f a tw-layer MLP. n u is the set f input value and u is its crrespnding utput (here we represent a specific case with a three-value input vectr and a tw-value utput vectr). The units r neurns called bias are units nt cnnected t a lwer layer. Their values are always equal t 1. They actually represent the threshld value f the next upper layer h ð1þ j ¼ XI i¼1 w ð1þ ji n i þ b ð1þ j j ¼ 1;...; H; where b (1) j crrespnds t the bias f the input layer. Then, each activatin variable is transfrmed by a nnlinear activatin functin, which in mst cases (including urs), is the hyperblic tangent functin (tanh): v j =tanh (h j (1) ), j=1,..., H. Finally, the v j are transfrmed t give a secnd set f activatin variables assciated t the neurns in the utput layer: h ð2þ k ¼ XH j¼1 w ð2þ kj v j þ b ð2þ k k ¼ 1;...; O; where b (2) k crrespnds t the bias f the hidden layer. In mst cases (including urs), the activatin variables are assciated t each neurn f the utput layer thrugh the linear functin: y k =h (2) k. Other mre cmplex functins may be used accrding t the prblem under cnsideratin. The weights and biases are initialized by randm selectin frm a zer mean, istrpic Gaussian unit variance where the variance is scaled by the fan-in f the hidden r utput units as apprpriate. During the training phase, the neural netwrk cmpares its utputs t the crrect answers (a set f bservatins used as utput vectr), and it adjusts its weights in rder t minimize an errr functin. In ur case, the weights and biases are ptimized by back-prpagatin using the scaled cnjugate gradient methd. This architecture is capable f universal apprximatin and, given a sufficiently large number f data, the MLP can mdel any smth functin. Finally, the interested reader can find an exhaustive descriptin f the MLP netwrk, its architecture, initializatin and training methds in Nabney (22). Our study made use f the Netlab sftware (Nabney 22). 7.2 Bayesian apprach fr selecting the best MLP architecture Fig. 2 In ur case, each unit in a certain layer is cnnected t all the units in the lwer layer. Each cnnectin is assciated t a specific weight, which value is ptimized during the learning phase. h is the bias value hen ptimizing a mdel t the data, it is usual t cnsider the mdel as a functin such as: y = f(x, w) + e, where y are the bservatins, x the inputs, f the mdel, w the parameters t ptimize (r the weights in ur case) and e the remaining errr (mdel-data misfit). The mre cmplex the mdel t fit (i.e., the number f parameters), the smaller the errr, with the usual drawback f verfitting the data by fitting bth the true data and its nise. Such an verfit is usually detected due t a very pr perfrmance f the mdel n unseen data (data nt included in the training phase). Therefre, ptimizing the mdel parameters thrugh minimizing the residual e may actually lead t a pr mdel perfrmance. One way t avid such a prblem is t cnsider als the errrs in the mdel parameters. The use f a Bayesian apprach is very helpful t address such an issue.