Impact of Climate Change on Hydrometeorological Variables in a River Basin in India for IPCC SRES Scenarios

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2 CHAPTER 2 Impact of Clmate Change on Hydrometeorologcal Varables n a Rver Basn n Inda for IPCC SRES Scenaros Aavuda Anandh, V. V. Srnvas, and D. Nagesh Kumar 2. Introducton In the recent years, the new paradgm of abrupt clmate change has been well establshed, and a major global concern s to assess mplcatons of clmate change on hydrology of rver basns and avalablty of water, whch s consdered to be a vulnerable resource. The future clmate s unknown and uncertan. Hence to evaluate plausble mpacts of clmate change on the hydrology of a rver basn, t s necessary to develop plausble future projectons of hydrometerologcal processes n the rver basn for varous clmate scenaros. For ths purpose, a varety of methods are avalable. The classcal methods use clmate varables smulated by General Crculaton Models (GCMs) for projected changes n GCM boundary condtons based on emssons scenaros. Among the scenaros avalable n lterature, those that were publshed n the Specal Report on Emssons Scenaros (SRES) (Nakcenovc et al. 2000) are wdely used, and are known as SRES scenaros. The GCMs are among the most advanced tools, whch use transent clmate smulatons to smulate the clmatc condtons on earth, several decades nto the future. For quanttatve clmate mpact studes n hydrologcal processes, the varous projectons of varables output from the GCM smulatons are studed. Snce GCMs are run at coarse resolutons, the output clmate varables from these models cannot be used drectly for mpact assessment on a local scale. Hence n the past two decades, several downscalng methodologes have been developed to transfer nformaton from the GCM smulated clmate varables to local scale. The remander of ths chapter s structured as follows. Frst, a bref descrpton of SRES scenaros, downscalng methods and Support Vector Machne (SVM) s provded n secton 2.2. The descrpton of Malaprabha rver basn n Inda, whch s consdered for case study, s provded n secton 2.3. Subsequently, the SVM based methodology suggested for downscalng precptaton and temperature n the rver basn s presented n secton 2.4. Followng ths, results of downscalng models are 327

3 presented n secton 2.5, and possble consequences on hydrology of the rver basn are dscussed. Fnally, summary and conclusons drawn based on the study and some of the conceptual and phlosophcal ssues concernng the use of downscalng models are provded n secton Background In ths secton a general descrpton on the varous SRES scenaros, downscalng methods and SVM s provded SRES The SRES scenaros are constructed based on the major drvng forces or factors (e.g., human development ncludng economc, demographc, socal and technologcal changes) that are suted for clmate mpact assessment. These factors play sgnfcant role n energy consumpton, land use changes and emssons, and represent a dverse range of dfferent development pathways of the world for mpact assessment. Hence they are useful for research on sustanable development and mpact assessment, servng as nputs for evaluatng clmatc and envronmental consequences of future greenhouse gas emssons and for assessng alternatve mtgaton strateges. These SRES scenaros were constructed wth dfferent ranges for each projecton called storylne. There are four storylnes (A, A2, B and B2), descrbng the way the world populaton, land use changes, new technologes, energy resources, economes and poltcal structure may evolve over the next few decades. Thus dfferent world futures are represented n two dmensons, wth one dmenson representng economc or envronmental concerns, and the other representng global or regonal development patterns. For each storylne several emsson scenaros were constructed, producng four scenaro famles. Ultmately, sx SRES marker scenaros were defned: A has three marker scenaros (AB, AFI and AT) and the others have one each. A Story-lne. Ths scenaro represents very rapd economc growth wth ncreasng globalzaton, an ncrease n general wealth, wth convergence between regons and reduced dfferences n regonal per capta ncomes. Materalst consumerst values wll be predomnant, wth rapd technologcal change and low populaton growth when compared to A2 scenaro. Three varants wthn ths famly make dfferent assumptons about sources of energy for ths rapd growth: fossl ntensve (AFI), non-fossl fuels (AT), and a balance across all sources (AB). A2 Story-lne. A2 scenaro s represented as a heterogeneous, market-led world, wth rapd populaton growth but less rapd economc growth than A. The underlyng theme s self relance and preservaton of local denttes. Economc growth s regonally orented, and hence both ncome growth and technologcal change are regonally dverse. Fertlty patterns across regons converge slowly, resultng n hgh populaton growth. 328

4 B Story-lne. Ths scenaro represents low populaton growth as A, but development takes a much more envronmentally sustanable pathway wth globalscale cooperaton and regulaton. Clean and effcent technologes are ntroduced. The emphass s on global solutons to achevng economc, socal and envronmental sustanablty. B2 Story-lne. B2 scenaro represents populaton ncrease at a lower rate than A2, but at a hgher rate than A, wth development followng envronmentally, economcally and socally sustanable local orented pathways. In SRES, none of the presented scenaros explctly assumes mplementaton of the Unted Natons Framework Conventon on Clmate Change or the emssons target of the Kyoto Protocol. They exclude even the outlyng surprse or dsaster scenaros. It s preferable to consder a range of scenaros for clmate mpact studes as such an approach better reflects the uncertantes of the possble future clmate change. For the case study presented n ths chapter, AB, A2, B and COMMIT scenaros were consdered. In the COMMIT scenaro, the atmospherc carbon-doxde concentratons are mantaned ( Commtted ) at the same level as n the year Methods of Downscalng The varous downscalng methods avalable n lterature can be broadly classfed as dynamc downscalng and statstcal downscalng (Fgure 2.). Fgure 2.. Methods of downscalng In the dynamc downscalng method, a Regonal Clmate Model (RCM) s embedded nto GCM. There are two types of dynamc downscalng based on the types of nestng: one-way nestng and two-way nestng (Wang et al. 2004). One-way nestng conssts of drvng a lmted-area hgh-resoluton RCM wth low-resoluton data obtaned prevously by a GCM or by analyses of atmospherc observatons. The 329

5 one-way nestng technque does not allow feedback from the RCM to the drvng data. In two-way nestng, the RCM s run smultaneously wth the host GCM, and t regularly updates the host GCM n the RCM regon. Models of ths type are typcally developed usng dfferent numerc and physcal parameterzatons. They are not presently n use as they are cumbersome. Benefts smlar to two-way nestng can be derved from the use of a varable-resoluton GCM. Statstcal downscalng nvolves developng quanttatve relatonshps between large-scale atmospherc varables (predctors) and local surface varables (predctands). There are three types of statstcal downscalng namely- weather types, weather generators and transfer functons. Weather types or weather classfcaton methods group the days nto a fnte number of dscrete weather types or states accordng to ther synoptc smlarty. These methods n turn are classfed as subjectve, objectve, or hybrd. In subjectve classfcaton methods, the classfcatons were carred out manually usng emprcal rules. Some of the most wdely known subjectve classfcatons are Grosswetterlagen (Hess and Brezowsky 969) and Brtsh Isles Weather Types (Lamb 972). In objectve classfcaton methods, a varety of automated technques developed usng computers are used to group the weather types. The most popular objectve classfcaton methods are based on correlaton based algorthms (Brnkmann 999), clusterng technques (Huth et al. 993; Kdson 994) and Fuzzy rules based approaches (Wetterhall et al. 2005). The hybrd technques combne elements of emprcal/manual and automated procedures for groupng weather types, thereby avodng tme delay and enablng the producton of easly reproducble and nterpretable results (Frakes and Yarnal 997; Anandh 200). Some of the hybrd technques are screenng dscrmnant analyss (Enke and Spekat 997) and Classfcaton and Regresson Trees (CART) (Breman et al. 984). Weather generators are statstcal models of observed sequences of weather varables. They can also be regarded as complex random number generators, the output of whch resembles daly weather data at a partcular locaton. There are three fundamental types of daly weather generators, based on the approach to modelng the daly precptaton occurrence: the Markov chan approach (Hughes et al. 999), the spell-length approach (Wlks 999) and weather types (Conway and Jones 998). In the Markov chan approach, a random process s constructed whch determnes a day at a staton as rany or dry, condtonal upon the state of the prevous day, followng gven probabltes. If a day s determned as rany, then the ranfall amount s drawn from yet another probablty dstrbuton. In case of the spell-length approach, nstead of smulatng ranfall occurrences day by day, the models operate 330

6 by fttng probablty dstrbuton to observed relatve frequences of wet and dry spell lengths. Transfer functons are a conceptually smple means for representng lnear and nonlnear relatonshps between the predctors and predctands. Therefore, a dverse range of statstcal downscalng methods usng transfer functons have been developed n the recent past. Examples nclude transfer functons based on lnear and nonlnear regresson, artfcal neural networks, canoncal correlaton analyss, prncpal component analyss, Support vector machne (Trpath et al. 2006; Anandh et al. 2008; Anandh et al. 2009) and Relevant vector machne (Ghosh and Mujumdar 2008). Transfer functon based downscalng methods are senstve to the subjectve choces made n ther desgn, vz., the type of transfer functon used, choce of predctors and how well they are smulated by GCM, type of predctand, calbraton perod, tmescale of downscalng (e.g., annual, seasonal, monthly, or daly), and temporal varaton of the relatonshp between the predctors and predctand. However, transfer functon methods have generally not been subjected to careful evaluaton as the other downscalng technques (Wnkler et al. 997; Anandh et al. 2008; Anandh et al. 2009). In spte of ths, transfer functons are most commonly used for downscalng due to relatve ease of ther applcaton. Indvdual downscalng schemes dffer accordng to the choce of mathematcal transfer functon, predctor varables or statstcal fttng procedure (Conway et al. 996; Schubert and Henderson-Sellers, 997). Regresson-based downscalng methods rely on the drect quanttatve relatonshp between the local scale clmate varable (predctand) and the varables contanng the larger scale clmate nformaton (predctors) through some form of regresson functon (Karl et al. 990; Wgley et al. 990). The man advantage of the regresson-based downscalng methods s the relatve ease of ther applcaton. However, these models often explan only a fracton of the observed clmate varablty as they are unable to capture the extremes, especally when the predctand s precptaton (Wlby et al. 2004; Trpath et al. 2006; Anandh et al. 2008). Downscalng future extreme hydrologc events usng regresson based models may be problematc, because these events usually tend to be stuated at the margns or beyond the range of the extremes n the calbraton data set (Wlby et al. 2002). Artfcal Neural Network (ANN) based downscalng technques have ganed wde recognton owng to ther ablty to capture nonlnear relatonshps between predctors and predctand (Tatl et al. 2005). Mathematcally, an ANN s often vewed as a unversal approxmator. The ablty to generalze a relatonshp from gven patterns makes t possble for ANNs to solve large-scale complex problems such as pattern recognton, nonlnear modelng and classfcaton. The ANNs have been extensvely used n a varety of physcal scence applcatons, ncludng hydrology (ASCE Task Commttee 2000; Govndaraju and Rao 2000). Despte a number of advantages, the tradtonal neural network models have several drawbacks ncludng possblty of gettng trapped n local mnma and 33

7 subjectvty n the choce of model archtecture (Suykens 200). (Vapnk 995; Vapnk 998) poneered the development of a novel machne learnng algorthm, called support vector machne (SVM), whch provdes an elegant soluton to these problems. The SVM has found wde applcaton n the feld of pattern recognton and tme seres analyss. Introductory materal on SVM s avalable n a number of books (Cortes and Vapnk 995; Vapnk 995; Schölkopf et al. 998; Vapnk 998; Crstann and Shawe-Taylor 2000; Haykn 2003; Sastry 2003). Most of the tradtonal neural network models seek to mnmze the tranng error by mplementng the emprcal rsk mnmzaton prncple, whereas the SVMs mplement the structural rsk mnmzaton prncple, whch attempts to mnmze an upper bound on the generalzaton error, by strkng a rght balance between the tranng error and the capacty of the machne (.e., the ablty of the machne to learn any tranng set wthout error). The soluton of tradtonal neural network models may tend to fall nto a local optmal soluton, whereas global optmum soluton s guaranteed n SVM (Haykn 2003). Further, the tradtonal ANNs have consderable subjectvty n model archtecture, whereas for SVMs the learnng algorthm automatcally decdes the model archtecture (number of hdden unts). Moreover, tradtonal ANN models do not gve much emphass on generalzaton performance, whle SVMs seek to address ths ssue n a rgorous theoretcal settng. The flexblty of the SVM s provded by the use of kernel functons that mplctly map the data to a hgher, possbly nfnte, dmensonal space. A lnear soluton, n the hgher dmensonal feature space, corresponds to a non-lnear soluton n the orgnal lower dmensonal nput space. Ths makes SVM a plausble choce for solvng a varety of problems n hydrology, whch are non-lnear n nature Least-Square Support Vector Machne (LS-SVM) The Least-Square Support Vector Machne (LS-SVM) provdes a computatonal advantage over standard SVM (Suykens 200). Ths subsecton presents the underlyng prncple of the LS-SVM and s extracted from Anandh et al. (2008) and Trpath et al. (2006). Consder a fnte tranng sample of N patterns x, y,,, N, where x representng the -th pattern n n-dmensonal space (.e., x n x,, xn ) consttutes the nput to LS-SVM, and y s the correspondng value of the desred model output. Further, let the learnng machne be defned by a set of possble mappngs x f ( x, w), where f () s a determnstc functon whch, for a gven n nput pattern x and adjustable parameters w ( w ), always gves the same output. The tranng phase of the learnng machne nvolves adjustng the parameter w. These parameters are estmated by mnmzng the cost functon w, e). L ( w, e) w 2 T w C 2 N 2 e subject to the equalty constrant L ( 332

8 N e y y,..., ˆ (Eq. 2.) b x w y T ) ( ˆ (Eq. 2.2) where C s a postve real constant, and ŷ s the actual model output. The frst term of the cost functon represents weght decay or model complexty-penalty functon. It s used to regularze the weght szes and to penalze the large weghts. Ths helps n mprovng the generalzaton performance (Hush and Horne 993). The second term of the cost functon represents penalty functon. The soluton of the optmzaton problem s obtaned by consderng the Lagrangan as N N y e y e C b L 2 T ˆ 2 2 ),,, ( w w e w (Eq. 2.3) where are Lagrange multplers, and b s the bas term defned n eq. 2. The condtons for optmalty are gven by N y e y L N Ce e L b L L N N,.., 0 ˆ,..., x w w (Eq. 2.4) The above condtons of optmalty can be expressed as the soluton to the followng set of lnear equatons after elmnaton of w and e. y I 0 C 0 - T b (Eq. 2.5) where N 2 y y y y ; N ; N 2 ; NN I In Eq. 2.5, s obtaned from the applcaton of Mercer s theorem. 333

9 T, j K( x, x j ) ( x ) ( x j ), j (Eq. 2.6) where ( ) represents nonlnear transformaton functon defned to convert a nonlnear problem n the orgnal lower dmensonal nput space to lnear problem n a hgher dmensonal feature space. f The resultng LS-SVM model for functon estmaton s: x Kx, x b (Eq. 2.7) where and b are the solutons to Eq. 2.5 and K ( x, x) s the nner product kernel functon defned n accordance wth Mercer s theorem (Mercer 909; Courant and Hlbert 970) and b s the bas. There are several choces of kernel functons, ncludng lnear, polynomal, sgmod, splnes and Radal bass functon (RBF). The lnear kernel s a specal case of RBF (Keerth and Ln 2003). Further, the sgmod kernel behaves lke RBF for certan parameters (Ln and Ln 2003). In ths study RBF s chosen to map the nput data nto hgher dmensonal feature space, whch s gven by: 2 x x j K ( x, x j ) exp (Eq. 2.8) where, s the wdth of RBF kernel, whch can be adjusted to control the expressvty of RBF. The RBF kernels have localzed and fnte responses across the entre range of predctors. The advantage wth RBF kernel s that t maps the tranng data non-lnearly nto a possbly nfnte-dmensonal space, and thus, t can effectvely handle the stuatons when the relatonshp between predctors and predctand s nonlnear. Moreover, the RBF s computatonally smpler than polynomal kernel, whch requres more parameters. It s worth mentonng that developng LS-SVM wth RBF kernel nvolves a judcous selecton of RBF kernel wdth and parameter C. 2.3 Study Regon and Data Used The study regon s the catchment of Malaprabha Rver, upstream of Malaprabha reservor n Inda. The regon covers an area of km 2 stuated between 5 30'N and 5 56' N lattudes, and 74 2' E and 75 8' E longtudes. It les n the extreme western part of the Krshna Rver basn n Inda, and ncludes parts of Belgaum, Bagalkot and Dharwad dstrcts of North Karnataka (Fgure 2.2). Analyss of temporal varaton of ranfall showed that, n general, the clmate of the study regon s dry, except n monsoon months (June September) when warm wnds blowng from Indan Ocean cause copous amount of ranfall. Isohyetal map prepared for the regon showed consderable varaton n spatal dstrbuton of annual ranfall. Heavy ranfall (more than 3000 mm) s recorded at gaugng statons n the upstream reaches of the Malaprabha catchment, whch forms a part of the western Ghats. In 334

10 contrast, the average annual ranfall n the reservor command area (.e., downstream of the dam) s 576 mm. The average annual ranfall n the basn s 05 mm. It may be noted that the Malaprabha Rver orgnates n a regon of hgh ranfall, and t s the man source of surface water for ard and sem-ard regons downstream of Malaprabha reservor. The data adopted for ths study conssts of monthly mean atmospherc varables smulated by Canadan Center for Clmate Modelng and Analyss s (CCCma) thrd generaton Coupled Global Clmate Model (CGCM3). The data comprsed of the 20 th century smulatons (20C3M) for the perod of , and future smulatons forced by four SRES scenaros namely, AB, A2, B and COMMIT for the perod of Reanalyzed data of the monthly mean atmospherc varables prepared by Natonal Centers for Envronmental Predcton (NCEP) for the perod were used. The data on observed precptaton were obtaned from the Department of Economcs and Statstcs, Government of Karnataka, Inda, for the perod of The data on observed temperature were obtaned from Inda Meteorologcal Department (IMD) for the perod of The detals of the data are furnshed n Table 2.. For the sake of analyss, the GCM data were re-grdded to NCEP grd usng Grd Analyss and Dsplay System (GrADS) (Doty and Knter 993). 2.4 Methodology The development of a downscalng model begns wth the selecton of probable predctors, followed by ther stratfcaton (whch s optonal and varable dependant), and tranng and valdaton of the model. The developed model s subsequently used to obtan projectons of predctand for smulatons of GCM Selecton of Probable Predctors The selecton of approprate predctors s one of the most mportant steps n a downscalng exercse (Fowler et al. 2007). The choce of predctors could vary from regon to regon dependng on the characterstcs of the large-scale atmospherc crculaton and the predctand to be downscaled. Any type of varable can be used as predctor as long as t s reasonable to expect that there exsts a relatonshp between the varable and the predctand. Often, n clmate mpact studes, only such varables are chosen as predctors that are: () relably smulated by GCMs and are readly avalable from archves of GCM output and reanalyss data sets; () strongly correlated wth the predctand; and () based on prevous studes. The number of probable predctors s referred to as m n ths chapter Stratfcaton of Predctors For the sake of stratfcaton of predctors, the m 2 clmate varables (potental predctors), whch are realstcally smulated by the GCM, were selected from the m 335

11 probable predctors, by specfyng a threshold value (T ng ) for correlaton between the probable predctor varables n NCEP and GCM data sets. For the estmaton of correlaton, product moment correlaton (Pearson 896), Spearman's rank correlaton (Spearman 904a and b) and Kendall's tau (Kendall 95) were consdered. Table 2. The detals of the meteorologcal data used n the study Data type Source of data Perod Detals Tme scale Observed data of precptaton Observed data of temperature CGCM3 T/47 data on atmospherc varables NCEP reanalyss data of atmospherc varables NCEP reanalyss data of atmospherc fluxes Dept. of Economcs & Statstcs, Government of Karnataka (GOK), Inda Inda Meteorologcal Department (IMD) c.ca/cg-bn/data/cgcm Data at gaugng statons are used to arrve at representatve values of precptaton for the basn Data at 2 gaugng statons namely Santhebasthewad and Gadag ; baselne: 2 grd ponts for atmospherc 20C3M ( ); varables, wth grd spacng future: SRES AB, Lattudes range: 9.28 N to 20.4 N. A2, B & COMMIT Longtudes range: 7.25 E to ( ) E Kalnay et al. (996) grd ponts for atmospherc varables, wth grd spacng 2.5. Lattudes range: 2.5 N to 7.5 N. Longtudes range: 72.5 E to 77.5 E Kalnay et al. (996) grd ponts for atmospherc fluxes wth grd spacng.9. Lattudes range: 2.3 N to 20.0 N longtude range : 7.6 E to 77.5 E Daly Daly Monthly Monthly Monthly Fgure 2.2. Locaton of the study regon n Karnataka State, Inda. The lattude, longtude and scale of the map refer to Karnataka State. The data extracted at CGCM3 and.9 NCEP grd ponts are re-grdded to the nne 2.5 NCEP grd ponts. Among the nne grd ponts, 4 and 7 are on Araban Sea, and the remanng ponts are on land 336

12 Dependng on the predctand varable to be downscaled, the stratfcaton of the correspondng potental predctors was carred out n space (land and ocean) or n tme (e.g., wet and dry seasons). When precptaton was consdered as predctand, the stratfcaton of the predctors was carred out n tme doman to form clusters correspondng to wet and dry seasons. When maxmum and mnmum temperatures were consdered as predctands, the stratfcaton of predctors was carred out n space doman. The followng part of ths subsecton outlnes fner detals on the procedure suggested for stratfcaton of potental predctors n the context of downscalng precptaton and temperature. Stratfcaton of Predctors for Downscalng Precptaton. The clmate of a regon can be broadly classfed nto seasons for analyzng precptaton. The predctor varables for downscalng a predctand could vary from season to season. Further the relatonshp between the predctor varables and the predctand vares seasonally because of the seasonal varaton of the atmospherc crculaton (Karl et al. 990). Hence seasonal stratfcaton has to be performed to select the approprate predctor varables for each season to facltate development of a separate downscalng model for each of the seasons. The seasonal stratfcaton can be carred out by defnng the seasons as ether conventonal (fxed) seasons or as floatng seasons. In fxed season stratfcaton, the startng dates and lengths of seasons reman the same for every year. In contrast, n floatng season stratfcaton, the date of onset and duraton of each season s allowed to change from year to year. Past studes have shown that floatng seasons are better than the fxed seasons, as they reflect natural seasons, especally under altered clmate condtons (Wnkler et al. 997). Therefore dentfcaton of the floatng seasons under altered clmate condtons helps to effectvely model the relatonshps between predctor varables and predctands for each season, thereby enhancng the performance of the downscalng model. Hence, for the case study presented n ths chapter, the floatng method of seasonal stratfcaton s consdered to dentfy dry and wet seasons n a calendar year for both NCEP and GCM data sets. In the floatng method of seasonal stratfcaton, the NCEP data are parttoned nto two clusters depctng wet and dry seasons by usng the K-means clusterng method (MacQueen 967), whereas the GCM data are parttoned nto two clusters by usng the nearest neghbor rule (Fx and Hodges 95). From NCEP data on the m 2 varables, n prncpal components (PCs), whch preserve more than 98% of the varance, are extracted usng prncpal component analyss (PCA). The PCs correspondng to each month are used to form a feature vector for the month. The PCs are also extracted from GCM data, but along the prncpal drectons obtaned for the NCEP data. They are used to form feature vectors for GCM data. Each feature vector (representng a month) can be vsualzed as an object havng a specfc locaton n multdmensonal space, whose dmensonalty s defned by the number of PCs. The feature vectors of the NCEP data are parttoned nto two clusters (depctng wet and dry seasons) usng the K-means cluster analyss. The clusterng 337

13 should be such that the feature vectors wthn each cluster are as close to each other as possble n space, and are as far as possble n space from the feature vectors of the other clusters. The dstance between each par of feature vectors n space s estmated usng Eucldan measure. Subsequently, each feature vector of the NCEP data s assgned a label that denotes the cluster (season) to whch t belongs. Followng ths, the feature vectors prepared from GCM data (past and future) are labeled usng the nearest neghbor rule to get the past and future projectons for the seasons. As per ths rule, each feature vector formed usng the GCM data s assgned the label of ts nearest neghbor from among the feature vectors formed usng the NCEP data. To determne the nearest neghbors for ths purpose, the dstance between each par of NCEP and GCM feature vectors s computed usng Eucldean measure. Comparson of the labels of contemporaneous feature vectors formed from NCEP and GCM past data s useful n checkng f the GCM smulatons represent the regonal clmate farly well, durng the past perod. Optmal T ng s dentfed as a value for whch the wet and dry seasons formed for the study regon usng NCEP data are well correlated wth the possble true seasons for the regon. For ths analyss, the plausble true wet and dry seasons n the study regon are dentfed usng a method based on truncaton level (TL). In ths method, the dry season s consdered as consstng of months for whch the estmated Thessen Weghted Precptaton (TWP) values for the regon are below the specfed TL, whereas the wet season s consdered as consstng of months for whch the estmated TWP values are above the TL. Heren, two optons have been used to specfy the TL. In the frst opton, the TLs are chosen as varous percentages of the observed mean monthly precptaton (MMP) (70 to 00% of MMP at ntervals of 5%). In the second opton, the TL s chosen as the mean monthly value of the actual evapotranspraton n the rver basn. The actual evapotranspraton s obtaned for Krshna basn from Gosan et al. (2006). The potental predctors correspondng to optmal T ng are noted. Stratfcaton of Predctors for Downscalng Surface Temperature. The surface temperature n a regon s domnated by local effects such as evaporaton, sensble heat flux and vegetaton n the regon. Therefore the potental predctor varables nfluencng surface temperature n the study regon are stratfed based on the locaton of grd ponts (land and/or ocean) correspondng to the varables, to assess the mpact of ther use on downscaled temperature. Out of the nne 2.5 NCEP grd ponts consdered n the study regon, sx are above land and the remanng three are over sea. As there are no dstnct seasons based on temperature, seasonal stratfcaton as n the case of precptaton s not relevant SVM Downscalng Model For downscalng the predctand, the m probable predctors at each of the NCEP grd ponts wll be consdered as probable predctors. Thus, there are m 3 (= m number of NCEP grd ponts) probable predctor predctors. The potental predctors (m 4 ) are selected from the m 3 probable predctor varables. For ths 338

14 purpose, the cross-correlatons are computed between the probable predctor varables n NCEP and GCM data sets, and the probable predctor varables n NCEP data set and the predctand. A pool of potental predctors s then dentfed for each season by specfyng threshold values for the computed cross-correlatons. The threshold value for cross-correlaton between varables n NCEP and GCM data sets s denoted hereafter by T ng2, whereas the same between NCEP varables and predctand s depcted as T np. The T np should be reasonably hgh to ensure choce of approprate predctors for downscalng the predctand. Smlarly, T ng2 should also be reasonably hgh to ensure that the predctor varables used n downscalng are realstcally smulated by the GCM n the past, so that the future projectons of the predctand obtaned usng GCM data would be acceptable. The downscalng model s calbrated to capture the relatonshp between NCEP data on potental predctors and the predctand. The data on potental predctors s frst standardzed for each season or locaton separately for a baselne perod. Such standardzaton s wdely used pror to statstcal downscalng to reduce systemc bas (f any) n the mean and varance of the predctors n the GCM data, relatve to those of the same n the NCEP reanalyss data (Wlby et al. 2004). Ths step typcally nvolves subtracton of mean and dvson by the standard devaton of the predctor for the baselne perod. The standardzed NCEP predctor varables are then processed usng PCA to extract such PCs whch are orthogonal and whch preserve more than 98% of the varance orgnally present n them. A feature vector s formed for each month usng the PCs. The feature vector forms the nput to the SVM model, and the contemporaneous value of predctand s ts output. The PCs account for most of the varance n the nput and also remove the correlatons, f any, among the nput data. Hence, the use of PCs as nput to a downscalng model helps n makng the model more stable and at the same tme reduces the computatonal load. To develop the SVM downscalng model, the feature vectors formed are parttoned nto a tranng set and a testng set. The parttonng was ntally carred out usng multfold cross-valdaton procedure, whch was adopted from Haykn (2003) n an earler work (Trpath et al. 2006). In ths procedure, about 70% of the feature vectors are randomly selected for tranng the model, and the remanng 30% are used for valdaton. However, n ths study the multfold cross-valdaton procedure s found to be neffectve because the tme span consdered for analyss s small and there are more extreme events n the past decades than n the recent decade. Therefore, the feature vectors formed from approxmately frst 70% of the avalable data are chosen for calbratng the model and the remanng feature vectors are used for valdaton. The normalzed mean square error s used as an ndex to assess the performance of the model. The tranng of SVM nvolves selecton of the model parameters and C. The wdth of RBF kernel gves an dea about the smoothness of the derved functon. Smola et al. (998), n ther attempt to explan the regularzaton capablty of RBF kernel, have shown that a large kernel wdth acts as a low-pass flter n frequency doman. It attenuates the hgher order frequences, resultng n a smooth functon. Alternately, RBF wth a small kernel wdth retans most of the hgher order frequences leadng to an approxmaton of a complex 339

15 functon by the learnng machne. In ths study, grd search procedure (Gestel et al. 2004) s used to fnd the optmum range for each of the parameters. Subsequently, the optmum values of the parameters are obtaned from wthn the selected ranges, usng the stochastc search technque of genetc algorthm (Haupt and Haupt 2004). The feature vectors prepared from GCM smulatons are processed through the valdated SVM downscalng model to obtan future projectons of the predctand, for each of the four emsson scenaros consdered (.e., SRES AB, A2, B and COMMIT). Subsequently, for each scenaro, the projected values of the predctand are chronologcally dvded nto fve parts ( , , , and ) to determne the trend n the projected values of the predctand. The procedure s llustrated n the flowchart n Fgure Results The results of the downscaled precptaton, maxmum and mnmum temperatures are dscussed n ths secton Predctor Selecton For downscalng precptaton, the predctor varables are screened on the twn bass that monsoon ran s dependent on dynamcs through advecton of water from the surroundng seas and thermodynamcs through effects of mosture and temperature, both of whch can modfy the local vertcal statc stablty. In a changed clmate scenaro, both the thermodynamc and dynamc parameters may undergo changes. Therefore n the present study, only such probable predctor varables, whch ncorporate both the effects, are chosen. Wnds durng south-west monsoon season advect mosture nto the regon whle temperature and humdty are assocated wth local thermodynamc stablty and hence are useful as predctors. Zonal wnd s the response to heatng n the monsoon trough n the North Inda. Merdonal wnd has more local effects, and together the wnds are responsble for convergence of mosture and hence related to precptaton. Temperature affects the mosture holdng capacty and the pressure at a locaton. The pressure gradent affects the crculaton whch n turn affects the mosture brought nto the place and hence the precptaton. Hgher precptable water n the atmosphere means more mosture, whch n turn causes statcally unstable atmosphere leadng to more vgorous overturnng, resultng n more precptaton. Lower pressure leads to more wnds and so more precptaton. At 925 mb pressure heght, the boundary layer (near surface effect) s mportant. The 850 mb pressure heght s the low level response to regonal precptaton. The 200 mb pressure level depcts the global scale effects. Temperature at 700 mb and 500 mb represent the heatng process of the atmosphere due to monsoonal precptaton whch s maxmum at md-troposphere on a constant pressure heght. Geopotental heght represents the pressure varaton, whch reflects the flow, based on whch the mosture changes. Due to these reasons, ffteen probable predctors are extracted from the NCEP reanalyss and CGCM3 data sets. They are the ar temperature at 925 mb 340

16 Select (m 3 ) probable predctors (PPs) Prepare scatter plots, and compute cross-correlatons (CCs) between PPs n NCEP and GCM data sets, and between PPs n NCEP and the predctand Select/update thresholds T ng2 & T CCs thresholds Yes Select (m 4 ) potental predctors (POPs) for Downscalng No Standardze the monthly data of POPs extracted from NCEP and GCM data sets NCEP Extract PCs and PDs from standardzed NCEP data of POPs to prepare feature vectors (FVs) GC Obtan PCs of standardzed GCM data of POPs along PDs extracted from NCEP data to prepare feature vectors (depctng 75% of FVs form the tranng set 25% of FVs form the valdaton set Calbraton and verfcaton of SVM Model Grd search method to fnd optmum parameter range Genetc algorthm to determne optmum parameter Comparson of downscaled values wth observed values from past record and SVM Model Is the valdaton performance accepted Yes No Valdated SVM Future projectons of predctand Fgure 2.3. Methodology followed for SVM downscalng. PCs and PDs denote prncpal components and prncpal drectons, respectvely. T ng2 s the threshold between predctors n NCEP and GCM data sets. T np denotes the threshold between predctors n NCEP data and the predctand 34

17 (Ta 925), 700 mb (Ta 700), 500 mb (Ta 500) and 200 mb (Ta 200) pressure levels, geo-potental heght at 925 mb (Zg 925), 500 mb (Zg 500) and 200 mb (Zg 200) pressure levels, specfc humdty at 925 mb (Hus 925) and 850 mb (Hus 850) pressure levels, zonal (Ua) and merdonal wnd veloctes (Va) at 925 mb (Ua 925, Va 925) and 200 mb (Ua 200, Va 200) pressure levels, precptable water (prw) and surface pressure (ps). For downscalng temperature, large scale atmospherc varables, namely ar temperature, zonal and merdonal wnd veloctes at 925 mb, whch are often used, are consdered as predctors. Surface flux varables, namely latent heat, sensble heat, shortwave radaton and longwave radaton fluxes can also be consdered for downscalng temperature as they control the temperature of the earth s surface. The ncomng solar radaton heats the surface, whle latent heat flux, sensble heat flux, and longwave radaton cool the surface. Due to these reasons, seven probable predctors are extracted from the NCEP reanalyss and CGCM3 data sets to downscale temperature. They are ar temperature, zonal, and merdonal wnd veloctes at 925 mb, and four fluxes: latent heat (LH), sensble heat (SH), shortwave radaton (SWR), and longwave radaton (LWR) SVM Downscalng Models From the selected potental predctors for each season, prncpal components are extracted to form feature vectors. These feature vectors are provded as nput to develop SVM downscalng model followng the procedure descrbed n Secton 2.4. For obtanng the optmal range of each of the SVM parameters (kernel wdth, and penalty term C), the grd search procedure s used. Typcal results of the doman search performed to estmate the optmal ranges of the parameters for wet and dry seasons are shown n Fgure 2.4. From ths fgure, the range of and C havng the least NMSE (Normalzed Mean Square Error) s selected as the optmum parameter range. The NMSE values are ndcated n the bar code provded close to the two parts of the fgure. Usng Genetc algorthm, the optmum parameter s selected from the optmum parameter range. The optmal values of SVM parameters C and thus obtaned are 550 and 50 for wet season, and 850 and 50 for dry season, respectvely. For maxmum temperature the optmal values of SVM parameters C and are 2050 and 50 whle for mnmum temperature 050 and 50 were the optmal values of SVM parameters. The results of downscalng are compared wth observed varables and showed n fgure 2.5 The detals of the downscaled varables were elaborated n Anandh et al. (2008, 2009) Projected Future Scenaros The future projectons of three meteorologcal varables (precptaton, maxmum and mnmum temperatures) were obtaned for each of the four SRES scenaros (AB, A2, B and COMMIT) usng the developed SVM downscalng models. The projectons were subsequently dvded nto fve 20-year ntervals ( , , , , ). The mean monthly values of 342

18 observed and projected precptaton for the study area were estmated usng the Thessen method. For each of the four SRES scenaros, average of the mean monthly values of Thessen weghted precptaton, maxmum and mnmum temperatures are presented as bar plots, for all the fve 20-year ntervals n Fgures 2.6, 2.7 and 2.8 respectvely. These plots facltate n assessng the projected changes n each meteorologcal varable across twenty-year ntervals over the perod of , wth respect to the past (20C3M), for each SRES scenaro. Secondly, for each of the fve 20-year ntervals, the average of the mean monthly values of the aforementoned varables are plotted ndvdually, for all the fve scenaros (20C3M, SRES AB, A2, B and COMMIT) n Fgures 2.9, 2.0 and 2. respectvely. These plots facltate comparson of the past and projected mean monthly values of each meteorologcal varable across SRES scenaros, for each 20-year nterval, and thus, help n assessng the changes n the varables across all the months n a year. Fgure 2.4. Illustraton of the doman search performed to estmate optmal values of kernel wdth () and penalty (C) for the SVM, for dry and wet seasons From the fgures t s observed that precptaton, and maxmum and mnmum temperatures are projected to ncrease n future for AB, A2 and B scenaros, whereas no trend s dscerned wth the COMMIT. The projected ncreases are hgh for A2 scenaro, whereas they are least for B scenaro. Ths s because among the scenaros consdered, the scenaro A2 has the hghest concentraton of carbon doxde (CO 2 ) equal to 850 ppm, whle the same for AB, B2 and COMMIT scenaros are 720 ppm, 550 ppm and 370 ppm respectvely. Rse n the concentraton of CO 2 n atmosphere causes the earth s average temperature to ncrease, whch n turn causes ncrease n evaporaton especally at lower lattudes. The evaporated water would eventually precptate. In the COMMIT scenaro, where the emssons are held the same as n the year 2000, no sgnfcant trend n the pattern of projected future precptaton could be dscerned. From a perusal of Fgures 2.6, 2.7 and 2.8 t can be observed that, n general, for the meteorologcal varables, the change from past to future s gradual, and the change s more for AB scenaros, whle t s the least for B scenaro. In A2 scenaro the change s more and dfferent from AB. In the case of COMMIT no clear pattern change s vsble. 343

19 (a) Precptaton (mm) Observed (TWP) Pptn Downscaled NCEP Pptn 0 Jan-7 Jan-73 Jan-75 Jan-77 Jan-79 Jan-8 Jan-83 Jan-85 Jan-87 Jan-89 Jan-9 Jan-93 Jan-95 Jan-97 Jan-99 Month (b) Maxmum Temperature (deg C) Observed Tmax Downscaled NCEP Tmax 25 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Month (c) Mnmum Temperature (deg C) Observed Tmn Downscaled NCEP Tmn 4 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Fgure 2.5. Comparson of the monthly observed meteorologcal varable wth the correspondng smulated varable usng SVM downscalng model for NCEP data (a) Thessen weghted precptaton (TWP) (b) maxmum temperature (Tmax) (c) mnmum temperature (Tmn) Jan-90 Month Jan-92 Jan-94 Jan-96 Jan-98 Jan

20 Fgure 2.6. Mean monthly precptaton n the study regon for the perod , for the four scenaros consdered 345

21 Fgure 2.7. Mean monthly maxmum temperatures n the study regon for the perod , for the four scenaros consdered 346

22 Fgure 2.8. Mean monthly mnmum temperatures n the study regon for the perod , for the four scenaros consdered 347

23 Fgure 2.9. Projectons obtaned for mean monthly precptaton n the study regon for the four scenaros are compared wth the past (20C3M) value of the statstc, for dfferent future perods 348

24 Fgure 2.0. Projectons obtaned for mean monthly maxmum temperature n the study regon for the four scenaros are compared wth the past (20C3M) value of the statstc, for dfferent future perods 349

25 Fgure 2.. Projectons obtaned for mean monthly mnmum temperature n the study regon for the four scenaros are compared wth the past (20C3M) value of the statstc, for dfferent future perods 350

26 From the Fgures 2.9, 2.0 and 2. t can be nferred that the change n the varables s least n the frst 20-year nterval ( ) and maxmum n the last 20-year nterval ( ) Impacts of Clmate Change on Hydrology The varables precptaton and temperature play an mportant role n the hydrology of a rver basn and are commonly used for mpact studes. Some of the possble mpacts of changes n the aforementoned varables are dscussed n the followng part of ths subsecton. In general, changes n clmate varables (precptaton and temperature) cause changes n the water balance, by changng the varous components of hydrologc cycle such as runoff, evapotranspraton, sol mosture, nfltraton and groundwater recharge. Changes n precptaton and temperatures can affect the magntude and tmng of runoff, whch n turn affect the frequency and ntensty of hydrologc extremes such as floods and droughts. Changes n precptaton could be n the amount, dstrbuton, ntensty and frequency. Most of the precptaton n the regon occurs n the monsoonal months (June to October). An ncreased precptaton amount, ntensty and frequency durng monsoon perod could affect the frequency of floods whle a decreased precptaton durng the perod could affect the frequency of drought. In general, the ncrease n surface temperatures modfy the hydrologc cycle through changes n the volume, ntensty, or type of precptaton (ran versus snow), and through shfts n the seasonal tmng of stream flow (Regonda et al. 2005). In ths regon, wth no snow cover, changes n temperature may not drectly affect the runoff, but wll cause changes n precptaton patterns and other clmate varables and may also affect the evaporaton and hence the runoff of the regon. The changes n runoff affect the water resources nfrastructure such as reservors. Reduced flow wll mean less supply and potental economc damages, and ncreased flow may mean an under-desgned reservor or spllway wth potental flood rsk. A change n temperature affects the evaporaton, evapotranspraton, and desertfcaton processes and s also consdered as an ndcator of envronmental degradaton and clmate change. These changes affect sol mosture content. Apart from temperature, the other factors that affect the evaporatve demand of the atmosphere nclude vapor-pressure defct, wnd speed and net radaton. Therefore mplcatons of the change n all these factors on evaporatve demand should be carefully analyzed. Increased temperature ncreases evaporaton from the reservors and evapotranspraton from plants. Further, ncreased temperatures can cause warmng of reservor and rvers n the regon whch n turn wll ncrease evaporaton as well as wll affect ther thermal structure and water qualty. Wth changes n the varous components of the hydrologc cycle, agrculture and the natural ecosystems n the rver basns are affected. The growth of bologcal 35

27 pests and dseases ncreases as temperature and relatve humdty levels ncrease wth ncrease n precptaton. Natural ecosystems such as forests, pastures, deserts, mountan regons, lakes, streams, wetlands, coastal systems and oceans may face dffcultes n adaptng, and t s also possble to lose some of the flora and fauna. Wth ncrease n populaton, the demand of freshwater for domestc, ndustral and agrcultural uses defntely ncreases. Ths stuaton makes t prudent to assess the senstvty of hydrologcal processes to the potental future changes n clmate and populaton to meet the requrements. Incdent solar radaton, relatve humdty and wnd speed are other varables that are also worth analyzng owng to ther sgnfcance n effectng hydrologcal processes. 2.6 Conclusons The Support Vector Machne (SVM) based models are developed to downscale monthly sequences of hydrometeorologcal varables (precptaton, maxmum and mnmum temperatures) n Malaprabha rver catchment (upstream of Malaprabha reservor) of Krshna rver basn, Inda. The large scale atmospherc varables smulated by the thrd generaton coupled Canadan GCM for varous IPCC scenaros (SRES AB, SRES A2, SRES B and COMMIT) were used to prepare nputs to the SVM models. The varables, whch nclude both the thermodynamc and dynamc parameters, and whch have a physcally meanngful relatonshp wth the precptaton, are chosen as the probable predctors for downscalng precptaton. For downscalng temperatures, large-scale atmospherc varables often used for downscalng maxmum and mnmum temperatures, and fluxes whch control the temperature at the earth s surface are chosen as plausble predctor varables n ths study. Precptaton, maxmum and mnmum temperatures are projected to ncrease n future for AB, A2 and B scenaros, whereas no trend s dscerned wth the COMMIT. The projected ncrease n predctands s hgh for A2 scenaro and s least for B scenaro. The mplcatons of clmate change on monthly values of each of the hydrometeorologcal varables are assessed. The changes n the ntensty, frequency of extreme values need to be consdered. Further, the uncertantes n the projectons to the choce of downscalng methods and GCMs should also be consdered to draw relable conclusons about the possble mpacts of clmate change n the study regon, whch would help polcy makers for realstc assessment, management and mtgaton of natural dsasters, and for sustanable development. Investgatng these uncertantes s a future scope of the study. 352

28 Acknowledgements Ths work s partally supported by Dept of Scence and Technology, Govt. of Inda, through AISRF project no. DST/INT/AUS/P-27/2009. Thrd author acknowledges support from Mnstry of Earth Scences, Govt. of Inda, through project no. MoES/ATMOS/PP-IX/ References Anandh, A. (200). "Assessng mpact of clmate change on season length n Karnataka for IPCC Scenaros." Journal of Earth System Scence, 9(4), Anandh, A., Srnvas, V. V., Kumar, D. N., and Nanjundah, R. S. (2009). "Role of Predctors n Downscalng Surface Temperature to Rver Basn n Inda for IPCC SRES Scenaros usng Support Vector Machne." Internatonal Journal of Clmatology, 29(4), Anandh, A., Srnvas, V. V., Nanjundah, R. S., and Kumar, D. N. (2008). "Downscalng Precptaton to Rver Basn n Inda for IPCC SRES Scenaros usng Support Vector Machne." Internatonal Journal of Clmatology, 28(3), ASCE Task Commttee (2000). "ASCE Task Commttee, Artfcal neural network n hydrology." Journal of Hydrologc Engneerng, 5(2), Breman, L., Fredman, J., Ohlsen, R., and Stone, J. (984). Classfcaton and Regresson Trees. Wadsworth and Brooks, 358. Brnkmann, W. (999). "Applcaton of non-herarchcally clustered crculaton components to surface weather condtons: Lake Superor basn wnter temperatures." Theoretcal and Appled Clmatology, 63, Conway, D., and Jones, P. D. (998). "The use of weather types and ar flow ndces for GCM downscalng." Journal of Hydrology, 22-23, Conway, D., Wlby, R., and Jones, P. (996). "Precptaton and ar flow ndces over the Brtsh Isles." Clmate Research, 7, Cortes, C., and Vapnk, V. (995). "Support vector networks." Machne Learnng, 20, Courant, R., and Hlbert, D. (970). Methods of Mathematcal Physcs, vols. I and II. Wley Interscence, New York, USA. Crstann, N., and Shawe-Taylor, J. (2000). An Introducton to Support Vector Machnes and other kernel-based learnng methods. Cambrdge Unversty Press, Cambrdge. Doty, B., and Knter, J. I., (993). "The Grd Analyss and Dsplay System (GrADS): a desktop tool for earth scence vsualzaton." Amercan Geophyscal Unon 993 Fall Meetng, San Fransco, CA, 6 0 December, 993. Enke, W., and Spekat, A. (997). "Downscalng clmate model outputs nto local and regonal weather elements by classfcaton and regresson." Clmate Research, 8,