Nonstationarities of regional climate model biases in European seasonal mean temperature and precipitation sums

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1 GEOPHYSICAL RESEARCH LETTERS, VOL. 39,, di: /2012gl051210, 2012 Nnstatinarities f reginal climate mdel biases in Eurpean seasnal mean temperature and precipitatin sums D. Maraun 1 Received 6 February 2012; revised 2 March 2012; accepted 2 March 2012; published 28 March [1] Bias crrecting climate mdels implicitly assumes statinarity f the crrectin functin. This assumptin is assessed fr reginal climate mdels in a pseud reality fr seasnal mean temperature and precipitatin sums. An ensemble f reginal climate mdels fr Eurpe is used, all driven with the same transient bundary cnditins. Althugh this mdel-dependent apprach des nt assess all pssible bias nn-statinarities, cnclusins can be drawn fr the real wrld. Generally, biases are relatively stable, and bias crrectin n average imprves climate scenaris. Fr winter temperature, bias changes ccur in the Alps and ice cvered ceans caused by a biased frcing sensitivity f surface albed; fr summer temperature, bias changes ccur due t a biased sensitivity f clud cver and sil misture. Precipitatin crrectin is generally successful, but affected by internal variability in arid climates. As mdel sensitivities vary cnsiderably in sme regins, multi mdel ensembles are needed even after bias crrectin. Citatin: Maraun, D. (2012), Nnstatinarities f reginal climate mdel biases in Eurpean seasnal mean temperature and precipitatin sums, Gephys. Res. Lett., 39,, di: /2012gl Intrductin [2] Reginal climate mdels (RCMs) prvide added value t glbal climate simulatins [Feser et al., 2011], but the actually simulated fields f climate variables are ften cnsiderably biased cmpared t gridded bservatinal data [Christensen et al., 2008]. End users f RCM simulatins therefre ften apply bias crrectin methds. Mst f these methds derive a crrectin functin that maps the empirical distributin f a simulated present day climate time series t the crrespnding bserved distributin. This functin is then applied t crrect a future climate simulatin (fr a review, see Maraun et al. [2010]). Appraches range frm simple additive crrectins f the mean r variance [e.g., Déqué, 2007; Lenderink et al., 2007], scaling f precipitatin [Widmann and Brethertn, 2000] t mre advanced quantile mapping methds [e.g., Piani et al., 2010;Li et al., 2010]. [3] A crucial assumptin f bias crrectin is statinarity f the bias, which is calculated fr present climate, under future climate change. This assumptin is, hwever, questinable [Christensen et al., 2008]. Just as mdel biases themselves are caused by an imperfect mdel representatin f the atmspheric physics, als the lcal mdelled respnse t external frcing, i.e., the lcal climate sensitivity is biased in general. Crrespnding bias changes might be called sensitivity related 1 GEOMAR, Helmhltz Centre fr Ocean Research Kiel, Kiel, Germany. Cpyright 2012 by the American Gephysical Unin /12/2012GL bias changes (SBC). In additin t such real bias changes, apparent changes might ccur. First, biases are estimated frm finite time series and afflicted with sampling uncertainty. Crrespnding bias changes merely caused by internal variability may be called variability related apparent bias changes (VABC). Secnd, mst bias crrectin methds are applied t uncnditinal climatlgical distributins and disregard that the derived verall bias may actually be a mixture f different underlying biases depending n weather types. Fr instance, biases fr cnvective and stratifrm precipitatin might be different. If the relative ccurrence f such weather types changes, als the verall bias might change. Such bias changes might be called mixture related apparent bias changes (MABC). [4] It is difficult t assess nn-statinarities f biases because the perid with a dense bservatinal netwrk shws a relatively small climate change signal and is hardly lng enugh fr rbust calibratin and validatin. Therefre, I use a pseud reality [Frías et al., 2006; Vrac et al., 2007; van der Linden and Mitchell, 2009] t assess the extent and type f RCM bias changes under future climate change. Fr the strngest changes, I als analyse ptential mechanisms causing the identified changes. T islate RCM biases I emply a perfect bundary setting, biases frm glbal climate mdels are explicitly nt cnsidered. As an example I investigate the crrectin f winter and summer mean temperature and precipitatin sums ver Eurpe. 2. Cncept and Data [5] As pseud reality, I chse ne glbal climate mdel / RCM cmbinatin, where the glbal climate mdel represents pseud bserved large scale bundary cnditins fr present and future climate, the reference RCM itself represents reginal pseud bservatins. An ensemble f ther RCMs is treated as mdels t be crrected. Using an ensemble and emplying each f the RCMs in turns as pseud reality reduces the RCM dependence f the results. The RCMs are frced with the same pseud bserved bundary cnditins as the reference RCM, i.e., the same glbal climate mdel. Fr present day climate simulatins, this crrespnds t a perfect bundary cnditin setting, i.e., RCMs driven with reanalysis data. Under the assumptin that GCM and RCM biases d nt interact, this setting islates RCM biases. Frcing with equal bundary cnditins als synchrnises variability n scales beynd a few days and allws fr relatively shrtcalibratin perids. I select the subset f RCMs frm the ENSEMBLES prject [van der Linden and Mitchell, 2009]whicharealldriven by the same bundary cnditins f ECHAM5 run three fr the SRES A1B scenari and perate n the same grid: HIRHAM5 (Danish Meterlgical Institute), RACMO2 (Ryal Dutch Meterlgical Institute), REMO (Max Planck 1f5

2 Institute fr Meterlgy) and RCA (Swedish Meterlgical and Hydrlgical Institute). The RCMs have a hrizntal reslutin f 25 km and cver the Eurpean dmain f the ENSEMBLES prject. As calibratin perid, I chse , as future perid [6] I cnsider seasnal mean temperature and precipitatin sums, separately fr each seasn. Pseud temperature bservatins f seasn i are dented as T,i, mdel simulatins as T m,i, precipitatin bservatins as P,i and mdel simulatins as P m,i ; temperature means ver the calibratin and scenari perid are dented as T cal and P fut and T fut, precipitatin sums as P cal, respectively. The temperature and precipitatin biases ver the calibratin perid are defined as BT cal ¼ T cal m BP cal P ¼ cal m P cal T cal ; Fr precipitatin relative changes are cnsidered, i.e., a value f 1 indicates n bias. Biases fr the future, BT fut and BP fut,are defined accrdingly. Mdel utput crrected relative t the calibratin perid is calculated as T crr m,i = T m,i BT cal and P crr m;i ¼ P m;i with crrespnding tempral means and sums. BP cal The change in temperature and precipitatin bias frm calibratin t future perid is given as DBT ¼ BT fut BT cal ; DBP ¼ BPfut BP cal ; The change in bias is equivalent t the future bias remaining after a crrectin based n the calibratin perid. When the uncrrected future bias is larger than the present day bias, bias crrectin imprves the results. Even when the uncrrected future temperature bias is smaller than the calibratin bias, the abslute remaining bias might still be smaller than withut crrectin, althugh the remaining bias changes sign. Only when the uncrrected future bias reduces t less than half the calibratin bias, bias crrectin deterirates the riginal future simulatin. A similar argument hlds in case f precipitatin, but psitive (negative) values have t be replaced by values larger (smaller) ne. T highlight the actual reductin in bias, I cnsider the imprvement in abslute bias as the difference (rati fr precipitatin) between the abslute future bias withut crrectin and with crrectin: IBT ¼ BT fut jdbtj; IBP ¼ RBPfut RDBP ð Þ : ð3þ Here R(x) isx fr x > = 1 and 1/x fr 0 < x < 1. The functin R(x) applied t ratis is the equivalent f taking abslute values f differences. In the fllwing, I will refer t bth peratins as taking abslute values. 3. Results [7] Of the fur selected RCMs, all six permutatins f ne mdel being the pseud bservatin and the ther three simulatins are cnsidered. As pseud bservatins and mdels are : ð1þ ð2þ interchangeable, nly abslute biases and abslute changes in biases are cnsidered (the abslute values f definitins (1) and (2)). [8] Clumns ne and tw f Figure 1 present the bias fr the calibratin perid (equatin (1)) and the remaining bias in the future (equatin (2)), averaged ver all permutatins. In general, the temperature bias (Figure 1, tp tw rws) as well as the precipitatin bias (Figure 1, bttm tw rws) are n average strngly reduced by the bias crrectin. The change in temperature bias is lwest ver the pen Atlantic and the Mediterranean (Figures 1b and 1f), where temperature is cntrlled by the prescribed SST bundary cnditins, and highest in the Barents Sea, White Sea and the Gulf f Bttnia during winter (Figure 1b) and spring (nt shwn). Over land, the change in winter temperature bias is strngest in the Alps (Figure 1b). In general a strnger temperature bias remains in summer, in particular in suthwestern Eurpe (Figure 1f). The change in precipitatin bias is in general lw. It is highest during summer arund the Mediterranean (Figure 1n). [9] The changes in bias are reflected in patterns f imprvement due t the bias crrectin (equatin (3)). Clumns three and fur f Figure 1 shw the mean (Figures 1c, 1g, 1k, and 1) and wrst case imprvement (Figures 1d, 1h, 1l, and 1p) after a bias crrectin fr the future based n the calibratin perid bias. The tp tw rws shw winter and summer temperature, the bttm tw rws the crrespnding results fr precipitatin. On average the temperature bias crrectin imprves the future simulatin despite changes in bias. Yet ver central Eurpe the imprvement is negligible and fr sme regins even deterirates the simulatin. The strngest deteriratin ccurs fr the Barents Sea, White Sea and the Gulf f Bttnia during winter (Figure 1c) and spring (nt shwn). The wrst case panels shw the lwest imprvement f all permutatins fr each grid bx. Fr winter (Figure 1d), biases in the Alps, the Barents Sea, White Sea and Gulf f Bttnia, and fr summer (Figure 1h), biases ver central Eurpe, Nrthern Italy and the Balkans stand ut. Only ver sme regins, temperature bias crrectin imprves the simulatins even in the wrst case. Precipitatin bias crrectin n average leads t an imprvement ver mst regins (Figures 1k and 1). Even fr the wrst case the deteriratin is weak, apart frm the Mediterranean and Nrthern Africa during summer (Figure 1p). 4. Discussin [10] T further investigate the causes leading t the described bias changes, I cnsider future changes in ptentially relevant climatic variables. Figure 2 shws the standard deviatin f changes between and fr winter surface albed (Figure 2a), summer clud cver (Figure 2b), summer sil misture (Figure 2c) and summer sea level pressure (Figure 2d). A strng mdel spread in winter albed can be bserved in the Alps (Figure 2a), whereas the spread in winter snw cver changes is negligible (nt shwn). This finding indicates a spread in temperature respnse due t different changes in the perennial snw fractin. Furthermre a strng mdel spread in winter albed is apparent in the Gulf f Bttnia, White Sea and Barents Sea (Figure 2a), which exceeds changes in sea ice cver (nt shwn). In these regins, the spread in temperature respnse might thus be explained by different sea ice/albed parameterisatins. Changes in clud 2f5

3 Figure 1. Biases and bias crrectin. (a d) DJF temperature [K], (e h) JJA temperature [K], (i l) DJF precipitatin [%], and (m p) JJA precipitatin [%]. Shwn are (left t right) bias, mean acrss all permutatins; change in bias vs ; mean imprvement acrss all permutatins; and minimum imprvement acrss all permutatins. cver exhibit the mst apparent spread in summer, in particular in central Eurpe (Figure 2b). The crrespnding respnses in radiative surface heating may partly explain changes in temperature biases. These might have been amplified in sme regins by sil misture feedbacks (Figure 2c). Figure 2d shws the spread in summer sea level pressure changes. The pattern is likely a respnse t the spread in diabatic heating f the atmsphere (Figure 1e). Yet the initial presence f such a respnse pattern causes a meridinal wind anmaly that might als cntribute t the bias change patterns. T cnclude, the described changes in temperature biases can be related t different respnses f the climate system t the prescribed greenhuse frcing and thus cnstitute SBC. [11] Figure 3 shws reginal mean changes in precipitatin biases fr precipitatin averaged t different space scales. Results fr central Eurpe (48N, 5E t 53N, 17E, the regins are aligned parallel t the rtated grid) are depicted in dark blue (circles), fr the Iberian peninsula (36N, 9W t 44N, 0E) in light blue (triangles) and fr the western Maghreb (30N, 5W t 35N, 10E) in range (crsses). Slid lines indicate winter changes, dashed lines summer changes. The fact that averaging precipitatin, in particular fr summer arid regins, strngly reduces the bias, indicates a key rle f VABC: where precipitatin ccurs as rather rare and lcalised cnvective events, internal variability may dminate the estimated seasnal biases n a lcal scale even when averaging ver 30 years. 5. Cnclusins [12] Nn-statinarities in RCM biases f Eurpean seasnal mean temperature and ttal precipitatin, and their ptential causes have been assessed in a pseud reality. T this end a multi RCM ensemble has been emplyed, driven by the same glbal climate mdel simulatin t islate RCM biases. Each RCM has in turns been taken as pseud reality, the thers as mdels t be crrected. I investigated the change in bias between a present day calibratin perid and future simulatins, as well as the imprvement f the future simulatins by a bias crrectin based n the calibratin perid. [13] Biases between the mdels are in general relatively stable, such that bias crrectin n average cnsiderably imprves future scenaris fr many regins and all seasns (results fr spring and autumn nt shwn). Biases, hwever, remain and fr sme regins and seasns bias crrectin may even deterirate future simulatins. Temperature bias crrectin n average imprves future simulatins, but sme SBC 3f5

$(a) DJF surface albed, (b) JJA fractinal clud cver, (c) JJA sil misture (relative t the 1970 1999 mean), and (d) JJA sea level pressure [hpa]. have been identified.$

4 Figure 2. Standard deviatin f changes in different variables, vs , acrss all permutatins. (a) DJF surface albed, (b) JJA fractinal clud cver, (c) JJA sil misture (relative t the mean), and (d) JJA sea level pressure [hpa]. have been identified. During winter, fr the Alps as well as the Barents Sea, White Sea and Gulf f Bttnia large biases remain; in these regins bias crrectin may even increase the future bias. These changes are likely linked t changes in surface albed, with biased respnses f perennial snw cver in the Alps and sea ice albed in the Nrthern seas (the latter is als relevant in spring). During summer, in Suthern France and the Iberian Peninsula large biases remain, and in Central Eurpe bias crrectin may even deterirate future simulatins. These changes can be explained by biased respnses f clud cver and sil misture. Precipitatin bias crrectin appears t be successful fr mst f Eurpe, but is affected by VABC in arid regins. Here, especially during the dry seasn (summer, and in the Maghreb als spring) precipitatin events are s rare that bias estimates even f seasnal sums are dminated by internal variability. Fr these regins it is advisable nt t derive precipitatin biases n a grid bx scale, but rather t cnsider larger regins r smthly varying bias mdels. As biases have nt been cnditned n weather types, this study culd nt identify MABCs. The fact that the strngest bias changes have been identified as SBC and VABC, hwever, indicates that in practice MABCs play nly a minr rle. [14] Althugh the results have been btained in a pseud reality, they als demnstrate the likely prblems ne might face using bias crrectin in real wrld applicatins; where different RCMs disagree, at least sme f them will als differ frm reality. As an agreement amng RCMs des nt prve an agreement with reality, a pseud reality apprach des nt unambiguusly identify where bias crrectin will be successful. Nevertheless, the results indicate ptential prblems as well as regins less prne t nn-statinary biases. As extreme events are gverned by different mechanisms than the mean climate, als biases fr high quantiles tend t be different frm biases in the mean [Christensen et al., 2008].Therefre,this analysis shuld be carried ut separately fr extreme events. The fact that the minimum imprvement shws strng nnstatinarities in biases between at least sme mdels highlights that even after bias crrectin multi mdel ensembles are still required t assess the range f uncertainties in lcal climate sensitivities. Figure 3. Precipitatin bias change as functin f spatial scale, average acrss all mdel permutatins. Orange crsses: nrthern Africa, light blue triangles: Iberian Peninsula, dark blue circles: central Eurpe. Slid lines: DJF, dashed lines: JJA. 4f5

5 [15] Acknwledgments. IthankP.Naveau,A.Schindler,M.Widmann, W. Park and J. Christensen fr helpful discussins. The analysis has been carried ut with R using the ncdf package. The editr thanks the three annymus reviewers. [16] The Editr thanks the three annymus reviewers fr their assistance in evaluating this paper. References Christensen, J., F. Bberg, O. Christensen, and P. Lucas-Picher (2008), On the need fr bias crrectin f reginal climate change prjectins f temperature and precipitatin, Gephys. Res. Lett., 35, L20709, di: /2008gl Déqué, M. (2007), Frequency f precipitatin and temperature extremes ver France in an anthrpgenic scenari: Mdel results and statistical crrectin accrding t bserved values, Glbal Planet. Change, 57, Feser, F., B. Rckel, H. vn Strch, J. Winterfeldt, and M. Zahn (2011), Reginal climate mdels add value t glbal mdel data A review and selected examples, Bull. Am. Meterl. Sc., 92(9), Frías, M., E. Zrita, J. Fernández, and C. Rdríguez-Puebla (2006), Testing statistical dwnscaling methds in simulated climates, Gephys. Res. Lett., 33, L19807, di: /2006gl Lenderink, G., A. Buishand, and W. van Deursen (2007), Estimates f future discharges f the river Rhine using tw scenari methdlgies: direct versus delta apprach, Hydrl. Earth Syst. Sci., 11(3), Li, H., J. Sheffield, and E. F. Wd (2010), Bias crrectin f mnthly precipitatin and temperature fields frm Intergvernmental Panel n Climate Change AR4 mdels using equidistant quantile matching, J. Gephys. Res., 115, D10101, di: /2009jd Maraun, D., et al. (2010), Precipitatin dwnscaling under climate change: Recent develpments t bridge the gap between dynamical mdels and the end user, Rev. Gephys., 48, RG3003, di: /2009rg Piani, C., J. O. Haerter, and E. Cppla (2010), Statistical bias crrectin fr daily precipitatin in reginal climate mdels ver Eurpe, Ther. Appl. Climatl., 99(1 2), van der Linden, P., and J. F. B. Mitchell (2009), ENSEMBLES: Climate change and its impacts: Summary f research and results frm the ENSEMBLES prject, technical reprt, Hadley Cent., Met Off., Exeter, U. K. Vrac, M., M. L. Stein, K. Hayhe, and X. Z. Liang (2007), A general methd fr validating statistical dwnscaling methds under future climate change, Gephys. Res. Lett., 34, L18701, di: /2007gl Widmann, M., and C. S. Brethertn (2000), Validatin f messcale precipitatin in the NCEP reanalysis using a new gridcell dataset fr the nrthwestern United States, J. Clim., 13(11), D. Maraun, GEOMAR, Helmhltz Centre fr Ocean Research Kiel, Düsternbrker Weg 20, D Kiel, Germany. (dmaraun@gemar.de) 5f5

Better definition of the objective, novelty and relevance of this study improving the structure, content and length of the publication accordingly:

Better definition of the objective, novelty and relevance of this study improving the structure, content and length of the publication accordingly: Answers t REVIEW2 Interactive cmment n An imprved perspective in the representatin f sil misture: ptential added value f SMOS disaggregated 1km reslutin prduct by Samir Khdayar et al. Answers t Reviewer