Dwnscalng Geptental Heght Usng Lapse Rate Chrana Surawut and Dusadee Sukawat 2* Earth Sstem Scence, Kng Mngkut s Unverst f Technlg Thnur, Bangkk, Thaland 2* Department f Mathematcs, Kng Mngkut s Unverst f Technlg Thnur, Bangkk, 00, Thaland Astract In rder t utlze the utput frm a glal clmate mdel, relevant nfrmatn fr the area f nterest must e etracted. Ths s called "dwnscalng". In ths paper, the dervatn f a lcal geptental heght n terms f lapse rate s presented. The man assumptns are hdrstatc alance, perfect gas, cnstant gravt, and cnstant lapse rate. Tw sets f data are requred fr ths methd, smulatn utputs frm the Educatn Glal Clmate Mdel (EdGCM) and the served data at the pnts f nterest (Changma, Bangkk, Un Ratchathan, Phuket and Sngkla). The results shw that dwnscalng f the geptental heghts usng lapse rate dnamc equatn are clser t the served data than the geptental heghts frm EdGCM. Kewrds: Dwnscalng, Geptental heght, Lapse rate. Intrductn Clmate change data are smulatn utputs frm glal clmate mdels (GCMs). Outputs f GCMs are carse reslutn, s t must e dwnscaled fr use n regnal applcatns dwnscalng []. The startng pnt fr dwnscalng s a larger scale atmspherc r cupled ceanc atmspherc mdel run frm a GCM [2]. There are tw majr knds f dwnscalng, statstcal and dnamcal methds. Statstcal dwnscalng methds use hstrcal data and archved frecasts t prduce dwnscaled nfrmatn frm large scale frecasts. Dnamcal dwnscalng methds nvlve dnamcal mdels f the atmsphere nested wthn the grds f the large scale frecast mdels []. The term dwnscalng refer t the use f ether fne spatal scale numercal atmspherc mdel (dnamcal dwnscalng), r statstcal relatnshp (statstcal dwnscalng) n rder t acheve detaled regnal and lcal atmspherc data [2]. Ths paper fcuses n dnamcal dwnscalng that used utputs data frm the Educatn Glal Clmate Mdel (EdGCM), n whch all prcesses f hdrstatc alance, perfect gas, cnstant gravt, and lapse rate are cnsdered. A dnamc equatn s derved t calculate geptental heght. Geptental heght s the heght f pressure surface and t can e used t dentt th speed and drectn f wnd [3]. Interplatn s an mprtant methd t tan relevant data fr the area f nterest frm knwn data pnts that cver the area []. The papers nvlved nverse dstance weghted nterplatn nclude [5-8]. * Crrespndng authr: Tel: 02-70882 Fa: 02-28025 E-mal: dusadee.suk@kmutt.ac.th 0
In ths paper three dfferent tpes f data are used fr cmparsn. The frst tpe s the smulatn utputs frm EdGCM. The secnd tpe s data frm the dnamc equatn. The thrd tpe s served data (frm meterlgcal statns) at the pnts f nterest (Changma, Bangkk, Un Ratchathan, Phuket, Sngkla) as shwn n Fgure. Fgure The pnts f nterest, Changma, Bangkk, Un Ratchathan, Phuket and Sngkla, and the grd pnts f EdGCM that cver the pnts f nterest. The remander f ths paper s rganzed as fllws. materals and methds are descred n secnd sectn. In the thrd sectn, the results are analzed and dscussed. In the furth sectn, the cnclusn s presented. 2. Materals and Methds 2. EdGCM Sftware The clmate mdel used the EdGCM sftware was develped at NASA s Gddard Insttute fr Space Studes (NASA/GISS). Ths 3 dmensnal cmputer mdel s knwn as a grd-pnt GCM. A grd pnt GCM dvdes the atmsphere nt a seres f dscrete grd cells. EdGCM s mdel has 7776 grd cells n the atmsphere, wth each hrzntal clumn crrespndng t 8 lattude 0 lngtude and cntanng 9 vertcal laers. The cmputer mdel numercall slves fundamental phscal equatns, whch descre the cnservatn f mass, energ, mmentum, and msture n each cell, whle takng nt accunt the transprt f quanttes etween cells [9]. 02
2.2 Eperment Case Lcatns f the pnts used n ths research are shwn n Fgure 2. 2 3 ( Changma ) 2( Un Ratchathan ) ( Phuket ) ( Bangkk ) ( Sngkla ) 3 5 3 5 6 Fgure 2 Lcatns f the data pnts frm EdGCM and the pnts fnterest (, 2, 3, and 5 ) Fgure 2 shws the data pstns, 2, 3,, and 5 6 frm EdGCM at the lattudes and lngtudes, (20N,95E), (20N,05E), (2N,95E), (2N,05E), (N,95E) and (N,05E), respectvel, whch cver the pnts f nterest, 2, 3, and 5 at the lattudes and lngtudes (8.7N,98.59E), (5.5N,0.53E), (3.N,00.3E), (8.8N,95.9E) and (7.N,00.37), respectvel. Tw sets f data are requred fr ths methd. The frst set cnssts f surface pressure, temperature, tpgraph and 850 hpa geptental heght f August mnthl mean etween 2000-2009 frm EdGCM wth the reslutn f 8 lattude and 0 lngtude. The secnd set cnssts f served 850 hpa geptental heght f August mnthl mean etween 2000-2009 at the pnts f nterest (Changma, Bangkk, Un Ratchathan, Phuket, Sngkla). 03
2.3 Eperment Desgn The steps fr the eperment are shwn n Fgure 3. Start. Derve the dnamc equatn fr calculatn f 850 hpa geptental heghts 2. Calculate 850 hpa geptental heghts at the EdGCM grd pnts, 2, 3,, 5 and 6 usng the dnamc equatn 3. Usng nverse dstance weghted nterplatn t apprmate 850 hpa geptental heghts at the pnts f nterest ( t 5 ) frm (a) the values at the pnts t 6 frm Step 2 () the 850 hpa geptental heghts at the pnts t 6 frm EdGCM. Cmpare mean average errr f 850 hpa geptental heghts taned frm (a) and () n Step 3 End Fgure 3 The sequence fr estmatn f the geptental heghts at the pnts f nterest The eperment desgn s started dervng the dnamc equatn usng the man assumptns whch are hdrstatc alance, perfect gas, cnstant gravt, and cnstant lapse rate. Net, calculate geptental heghts at the EdGCM grd pnts t 6 usng the dnamc equatn taned frm the frst step. The varales used as nputs n the dnamcal equatn cnsst f surface pressure, surface temperature, tpgraph and 850 hpa geptental heght frm utputs f the EdGCM. Net, appl the nverse dstance weghted nterplatn fr the pnts f nterest usng the results frm the dnamc equatn and the utputs fr EdGCM. Fnall, cmpare mean average errr f geptental heghts taned frm the dnamc equatn and EdGCM utputs. 0
2. Dnamc Equatn The dnamc equatn s derved frm a flud laer. The flud mtn s determned the vertcal mmentum equatn usng the hdrstatc equatn, perfect gas, cnstant gravt, and cnstant lapse rate. Fr flud laer n Fgure, s the heght f the free surface, s the heght f the tpgraph, T s temperature, T s sea level temperature, pressure, p s sea level pressure, p s surface pressure. s s T s surface ar temperature, p s p, T, Fgure The dnamc equatn sstem [0] In the hdrstatc equatn, the change n pressure wth alttude must ppse the gravtatnal frce n the ar, that s dp g dz () where p s pressure z s alttude s ar denst g s gravtatnal acceleratn The deal gas law states that where R s gas cnstant fr dr ar, T s temperature p RT (2) Cmnng Equatns () and (2), can e elmnated dp P g (3) dz RT g dp dz p R T Cnsder dz n Eq. () T p ps dp p 0 g dz RT g ln p ln ps dz R () T 05
Susttutng Eq. () Eq. (5) dz dz T T z T ln T p g T ln ln p R T p p R g s s T T p T ps T g R p T T ps R g (5) The dnamc equatn fr geptental heght s R g p T T p s where dt, dz T zts P T, ps srts, s z RTs T g R (6) s lapse rate s 850 hpa geptental heght s tpgraph z s alttude g s gravtatnal acceleratn R s gas cnstant T s temperature T s sea level temperature Ts s surface ar temperature p s pressure p s sea level pressure p s surface pressure s 06
2.5 Inverse Dstance Weghted Interplatn An eample f 850 hpa geptental heght apprmatn at the pnt n Fgure 2 s shwn n Fgure 5. 2 d d 2 d 3 d 3 Fgure 5, 2, and 3 are 850 hpa geptental heghts at the pnts, 2, and 3 n Fgure 2 that are used t apprmate geptental heghts at the pnt f nterest n Fgure 2. Inverse dstance weghted s a methd fr nterplatn, a prcess f assgnng values t nterest pnts usng values frm a set f knwn pnts. The mprtance f servatns s represented the nn-negatve numercal ceffcent and the sum f wetght s equal t ne. In ths research, weghtng s determned frm dstance etween the EdGCM grd pnts and the pnts f nterest whch s cvered the EdGCM grd pnts. That s, the nverse dstance weghted nterplatn s defned as / d / d where s the geptental heght at the pnt f nterest. d s dstance etween the pnt f nterest and the EdGCM grd pnt. 2 2 d lat lat ln ln s the 850 hpa geptental heght at the EdGCM grd pnt. 3. Results and Dscussn Tale shws dstance and weght numer f the pnts f nterest. The mnmal dstance has the mamum weght ecause the nearest served pnt has the mst nfluence. 07
Tale Dstance (km) and weghts fr Changma, Bangkk, Un Ratchathan, Phuket, Sngkla. Changma Bangkk Un Ratchathan Phuket Sngkla Dstance Weght Dstance Weght Dstance Weght Dstance Weght Dstance Weght 659.007 0.232 806.992 0.97 87.272 0.288 036.627 0.36 673.7 0.237 390.2 0.392 83.38 0.89 069.35 0.3 320.306 0. 726.285 0.220 739.926 0.207 59.2 0.290 003.70 0.0 80.20 0.29 620.556 0.257 90.763 0.68 9.565 0.32 38.87 0. 096.629 0.29 557.75 0.286 Tales 2-6 cmpare the errrs f geptental heghts at 850 hpa taned frm the dnamc equatn and EdGCM fr Changma, Bangkk, Un Ratchathan, Phuket and Sngkla. At Changma, Bangkk and Un Ratchathan the errrs the dnamc equatn are much less than the errrs EdGCM. Fr Phuket and Sngkla, the errrs the dnamc equatn are nl slghtl less than the errrs EdGCM. Ths ma e ecause Phuket and Sngkla are surrunded the sea whch can results n dfference lapse rates frm Changma, Bangkk and Un Ratchathan. Tale 2 Cmparsn f geptental heght (m) at 850 hpa the dnamc equatn and EdGCM fr Changma. Changma Dnamc Dnamc Eq. EdGCM EdGCM Oserved Equatn errr errr 2000 3 377 63 29 86 200 3 383 60 29 77 2002 35 380 68 33 88 2003 387 68 2 8 200 38 376 62 2 86 2006 35 38 62 27 78 2007 38 376 6 26 88 2009 385 83 2 98 Tale 3 Cmparsn f geptental heght (m) at 850 hpa the dnamc equatn and EdGCM fr Bangkk. Bangkk Dnamc Dnamc Eq. EdGCM EdGCM Oserved Equatn errr errr 2000 20 86 5 66 200 2 9 87 5 68 2002 7 2 502 55 8 2003 55 30 98 3 68 200 5 23 9 3 7 2006 9 23 77 28 5 2007 8 23 80 32 57 2008 6 26 90 6 2009 20 90 9 70 08
Tale Cmparsn f geptental heght (m) at 850 hpa the dnamc equatn andedgcm fr Un Ratchthan. Un Ratchathan Dnamc Dnamc EdGCM Oserved Equatn Eq. errr 2000 38 76 38 62 200 38 6 75 37 59 2002 5 6 87 2 7 2003 52 28 87 35 59 200 9 22 82 33 60 2006 6 2 7 28 53 2007 5 8 57 72 99 2009 3 7 72 29 55 EdGCM errr Tale 5 Cmparsn f geptental heght (m) at 850 hpa the dnamc equatn and EdGCM fr Phuket. Phuket Dnamc Dnamc EdGCM EdGCM Oserved Equatn Eq. errr errr 200 3 32 56 82 8 2002 37 35 52 75 77 2003 7 5 505 58 60 Tale 6 Cmparsn f geptental heght (m) at 850 hpa the dnamc equatn andedgcm f Sngkla. Sngkla Dnamc Dnamc EdGCM EdGCM Oserved Equatn Eq. errr errr 2000 39 37 96 57 59 200 39 37 9 55 57 2002 3 99 55 56 200 8 6 50 56 58 2006 5 99 5 55 2007 5 3 508 63 65 2009 2 87 3 5. Cnclusns Ths research s amed t tan dwnscaled geptental heghts usng a dnamc equatn fr Changma, Bangkk, Un Ratchathan, Phuket and Sngkla. The dnamc equatn s derved frm the man assumptns f hdrstatc alance, perfect gas, cnstant gravt, and lapse rate. The nverse dstance weghted nterplatn s used fr nterplatn frm the EdGCM grd pnts t the pnts f nterest. The mean aslute errr f geptental heghts frm the dnamcal equatn apprmatn fr all pnts f nterest are less than that f EdGCM. Hwever, fr Phuket and Sngkla there are less dfferences etween the dnamc equatn and EdGCM values. Ths culd e ecause these tw lcatns are surrunded the sea whch result s dfference lapse rates frm ther lcatns whch are n land. 09
5. Acknwledgements The frst authr wuld lke t thanks the Earth Sstem Scence f Kng Mngkut s Unverst f Technlg Thnur fr the fnancal supprt and the Department f Mathematcs, Facult f Scence, Kng Mngkut s Unverst f Technlg Thnur fr cmputer facltes. References [] http://www.hrc-la.rg/prjects/prjectpdfs/inform_reports/final_phase_i [2] Castr, C. L., Pelke Sr, R. A. and Lencn, G., 2005. Dnamcal dwnscalng: Assesssment f value retaned and added usng the Regnal Atmspherc Mdelng Sstem (RAMS), Jurnal f Gephscal Research, 0, -2. [3] Nelsen-Gammn, J., 2000. Weather Oservatn and Analss. Curse ntes ATMO25, Teas A & M. [] Dejmal, K. and Kratchvl, V., 200. Interplatn methds f weather phenmena, WSEAS Transactns n Envrnment and Develpment, 2(6), -52. [5] Jade, Sr. and Vjaan, M.S.M., 2008. GPS-ased atmspherc precptale water vapr estmatn usng meterlgcal parameters nterplated frm NCEP glal reanalss data, Jurnal f Gephscal Research, 3, -2. [6] Wllmtt, C.J., 995. Clmatlgcall aded nterplatn (CAI) f terrestral ar temperature, Internatnal Jurnal f Clmatlg, 5, 22-229. [7] Mendes, V.B., Prates, G., Santa, L. and Langle, R.B., 2000. An evaluatn f the accurac f mdels fr the determnatn f the weghted mean temperature f the atmsphere, Prc. ION Natl. Tech. Meet., C, 33-38. (Avalale at http://w3.uagl.pt/gprates/ion2000.pdf) [8] Wang, J., Zhang, L. and Da, A., 2005. Glal estmates f water-vapr-weghted mean temperature f the atmsphere fr GPS applcatns, Jurnal f Gephscal Research, 0, -7. [9] Chandler, M. and Shl, L., 20. NASA Clmate Mdelng and Data Applcatn, Gddard Insttute fr Space Studes, New Yrk. [0] Valls, G., 2006. Atmspherc and Oceanc Flud Dnamcs Fundamentals and Large-Scale Crculatn, Camrde, pp. 2. 0