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h Ý 95 ž ž åž À d º ß r h Õ v Œ ½ Õ ³v Œ n½ î Ä fäååå³ ³ äî Ø w f³ ¹nz ³pÄ fäå ƒ Œ ³Ä f îh³ f Œ ½ WRF w ½ ˆš y ˆš ö p ˆš g w 40 Ä ˆ ³Ä õሠw fo w ˆ š Î îh³ f w Œ ³ eä fäå õ Ä f ³pÅåŽ á õáä fäå Î æ Š y p õá æ Ä îh h¼v Ø Î³³ «æ Ä fäå³ fî v ½Å º w ˆ š 40 ÄÄ f ¼v î º ˆšp î ƒ îh Ä f vp î Œ ùo Ä ˆwõáo æ ŒŒ õ Ä f Ä ˆw ýn Ä fäå

96 Í ˆ h fäå n Æzõ¼ yo³é ³Œ ÎoÐ få th ³t Ì fäå n æh ¹nz j숳çt nê³ wäå ³ Îõ w få ³ ¹nz ųˆ h f w f ŒŒ ³ jìˆ «x w få õ½ nz ³ f šn ƒƒ fõ¼ ³ ¹nz Š šƒ fõ¼ ³ ¹nzìå ŒŒ wƒƒœ γh é Œ v Ä f³³p xâ w f³ î Ú h ³Ä f ŒŒÄÅ Î w f³ ¹nz o ¹nzù ƒ Œ ³ f «³pÄ fäå Œ ³Ä f ù o e w Ä f ³ˆš Ú jf ³ ö t ³ w ˆš ³ 䳈 h f y ç p w e w Õ ³pÄ f ÄÅ i ë y ECMWF y 51 å v T399 15 h f³ Ä f æä oˆ ïx fƒ nä³ f ¹nz h ëp f yo f ùä³åò Ê o f f y NCEP T190 å v 88 Ä ƒ 16 h³ f Œ ëw JMA ³ Medium-Range Ensemble Prediction Model ƒ ³ f Œ 51 Ä T319 ³ w fõáä f æ d ˆ 40 p ëp KMA T213 ³ w fõáä f d ˆ 40 p f Œ 32 Ä eä fäåˆ y ³³p î Ó š h NCEP h w³ f ³p SREF Short Range Ensemble Forecast ³ f áõá eä ¾h ³ f Œ³ vå v 32 ù ÄÅ ETA Regional Spectral Model ø Breeding method Toth et al., 1997 âõ jf³ 10 ÄÄ ˆ 2001 v j ³ f Du et al. 2004 å w ˆš ³ oä fä ųx o w ˆš ³ˆ Œ³ Œ eä fäå 15 ÄÄ õá fo Ž ½Å ³ w ˆš³ x ΃ SREF ÄÅoˆ f ¹nz³ƒƒ x NCEP SREF ÄÅ Èõá ˆ Du et al., 2006, 2009 ÄÅ WRF-NMM WRF-ARW Ä ÄÅ Œ 21 ÄÄ õá f åhù w³ä få Zhou and Du 2010 ùo ³ fõáä f³ ½ Ä f e w WRF-NMM WRF-ARW ø Breeding method 10 Ä få º hù w³ä f Å «f v ˆ w ³Ä få h Ä g Š oˆ «få Œ Ä g Ì Fujita et al. 2007 ùo Ä

h Ý 97 ˆwõáo ò ˆš ö jf Ë Ä Å ³ ˆš f Ÿv Ÿv f³ ¼ v òhˆ jf f v f ¼v oˆ jf Å Ì Ë Ä Î h³ ¼ v Ϋx ³ få Toth et al. 2003 Zhou et al. 2005 Zhu et al. 2008 ÄÄ f ½Ž ˆš Root mean square error and ensemble spread Histogram distribution Continuous Ranked Probability Skill Score and Ranked Probability Skill Score Ì Zhou et al. 2005 õ Ž ˆš õá p Ä f³ž žæ ŒæhnËõáÄ f³ ½ Yang et al. 2004 Chien and Jou 2004 MM5 õá 2000 vð 2002 v n³ f ½ õõ ³½ ˆš y ˆ š ÄÄ õá f åà ³ fv h õõæzô š näž ò õá ovˆô åà x f ù ˆ ùåà f Ì ˆšÎ xò ³ få  2005 ùo 2003 v Œ õáä f w jf ½ ˆš y ˆš x 17 ÄÄ õá f Ä v få º ç ho oˆ nz fœò ³Å Ë} Œé x òi³å ÌË}³é ž o Ä få ét Ì é é jf Œ ˆÄ f ½ ˆš x y ˆš Œ ½ WRF wõá fo ø w ˆš w½ ˆš y ˆš ö p ˆšÑ g w 40 ÄÄ ƒå ˆš w Ä fäå³ fåå z å Ä ³ˆšÎ ƒ õ Ä f æ i¾ ( ) î Œo WRF wõáo vå vån 45 km Æ ˆ 222 128 wá i 1 º d å vån 45 p w 30 hpa WPS WRF Œ 3.1.1 o šœõáìˆ ƒ jf Åõ ìˆ NCEP w f fw ë ½ pv w jf ëp³ ½ NCEP w jf WRF f Œ v³ fî Ì NCEP wå v 0.5 fœ Ð 2008 v 6 Œ 1 Ð 6 Œ 27 h 00 UTC 12 UTC õá 72 oš f WRF wƒ h½ ˆš ˆš ån ˆš ƒ wä ù õìx w éˆ f Œ ½o é w ˆš Ú g w y ö p ½ ˆš 40 Ä w ˆšÄ ³ fo ½ g w NOAH Land-Surface Model LSM Rapid Update Cycle Model LSM RUC Pleim-Xiu LSM PX

98 æ! 1 w³ fá Ž Á ½y ˆš WSM3 WSM5 Thompson et al. Goddard Cumulus Ensemble Model GCE ½ö p ˆš Yonsei University (YSU) PBL Mellor-Yamada-Janjic MYJ PBL Betts-Miller-Janjic ½½ ˆš Grell-Devenyi ensemble GD Grell-3 G3 Kain-Fritsch KF Â Ä ˆš t ˆš æä Äæä WRF Skamarock et al. 2008 g w ä t géˆ gpˆ NOAH LSM géˆ Ÿv gpˆ 4 p RUC LSM géˆ Ÿv gpˆ 6 p PX LSM géˆ Ÿv v gpˆ 2 p y ˆš t ˆ ˆš é ˆ ½y õ¼ ƒô WSM3 y ˆš Ø éˆ o Œ 3 ½ WSM5 y ˆš 5½éˆ Thompson y ˆšoñ 6 ½éˆ o éˆ xd}ë}õ GCE y ˆš ñ 7 ½éˆ ½ö ˆš ˆšƒôö p YSUö p ˆšõõ Ÿv õù ø K nö p ½n õ¼ Ìö p œ õù n hˆö p õ p MYJ ö p ˆš õõ Î TKE nö p õ¼ ½ ˆš ½ õ¼ å೜ Betts-Miller-Janjic ½ ˆšˆ o w¾š o w vç Ð Ÿvá ª} KF ½ ˆš o ¼v õõ

h Ý 99 o Î n CAPE GD ½ ˆš Ä ½ ˆš o ƒ CAPE pd vò n G3 ½ ˆš GD ½ ˆš ˆ Œ ä é ˆ ˆšƒô šõ¼îx Ð ôæ á o åå h Ä n g w Noah Land-Surface Model ø ½ ˆš³ é õá 32 Äo PH01~PH32 æ g wš 2006 ½ y ˆšoÄ f³ x o Ä ny ˆš Æ ån Goddard Cumulus Ensemble Model scheme ø ½ g w Äö p ˆš ̽ ˆšö Grell-3 Kain-Fritsch ½ PH27 PH28 PH31 PH32 PH33~PH40 Ç 40 Äo ( ) i¾ õ³ä f õõž ˆ ÄÄ õ õáä fäå æ Š p õáæ æ Ä f îh h¼ v Ø Î³³ «Šƒ Talagrand Rank Histogram ensemble spread Ñ member equallikelihood æ Ä fäå³ f Î v ƒ Continuous Ranked Probability Skill Score CRPSS õá fî ³ Ž væ ƒ Reliability diagram 1. Talagrand Rank Histograms Hamill, 2001; Toth et al., 2003 ùot ³ µ Ìå Talagrand Rank Histogram Îæ Ä fäå oˆæµ ³ ¼v z Î åä f³ t Bias {x Ä fäå åœ M Œ M få ƒ o f oðhƒ M+1 Rank oˆ o f M+1 hˆ h f f ѵ õá ò Äüµ Ö ˆ æ Ä ÅånŒ Š Æ ³ìˆx x Rank Histogram ÓÅåÅ º x U d t ẠÄÅ ¼v î µ Ç Öˆòh ò o ³ f š ØŒ γ ³ «Ó x A d t Ạ¼vhh ÄÅ Œ³ ¹nzhˆµo{x x v ẠÄÅ ¼v ³{x 2. Ensemble spread (SPRD) (Toth et al., 2003; Zhu et al., 2008) Rank Histogram oˆ ¼v³æ ò n z ˆ õõ ensemble spread ƒ nù ³ˆ ˆ ensemble spread Ÿt á³ Ë f fv ³t õáv åà À Ä ³ ¼ v wi 1 SPRD = f f n N 2 ( ( )) (1) N 1 n= 1 f (n) f SPRD šœ µ õá ò Îå À v šx v õõ fv µ ò õõ Root Mean Square Error RMSE åà x fv µ ³t Ó RMSE SPRD Š áº

100 æ á 1 w ˆ šo åå

h Ý 101 á 1 w ˆ šo åå È ensemble spread ¼v RMSE hˆ SPRD Š Ạî RMSE oˆ SPRD Š áºõv 3. Member equal-likelihood (Zhou et al., 2005) ÑÌå i³ä fäå ŒŒ Ä oˆµ ³ f «v ³ Ì Rank Histogram šx å{ õ member equal-likelihood õáž š³ µ f õá ò ÓÄ f µ ƒô Ä Ä Åån ŒŠ Æ ³ìˆ x x i 5 ˆŒŒ oˆµ ³ f «Ð xv Š ³{x 4. Continuous Ranked Probability Score (CRPS) «Continuous Ranked Probability Skill Score (CRPSS) (Hersbach, 2000; Toth et al., 2003) CRPS Brier score éì ÎåÀ «fçt Brier score ³åÀ ån åà f hˆ ³ «µ hˆ ³ «t Ì CRPS ùoœ Î ³ (x)õá f «äž «t ½ wi 2 [ ( ) ( )] = CRPS P x O x dx (2) P( x) ρ ( y) dy = (3) (4) 0 x < xa O( x) = 1 x > xa O( x½ äž «) P( x ) t ρ ( y) «ov t x a Ľ «äž Ó CRPS ö Îx fî Î õ «fçt Ó fî y ŒÎh ò³ˆ Reference Continuous Ranked Probability Score CRPS r åà ³ CRPS x ³¹nz f deterministic forecast Åõ ò x fî ½ Continuous Ranked Probability Skill Score CRPSS

102 CRPSS CRPS CRPS r = (5) CRPSr Ó CRPSS hˆ 0Šáº ÄÅ Œ fî Ó CRPSS 1 Š {x 5. Reliability diagram (Hamill, 1997; Toth et al., 2003; Bröcker, 2007) Reliability diagram Î fäå³ v ånž ³ Ž Œ Ååhˆ Ä ˆ åà Ç ˆ f «Œ f «³ Œ Ååäž hˆ ³ ˆ Ì ˆ Œˆ äž «Reliability o f «o~³äž «Çˆ ò f «Çò äž «Óäž «ˆ f «áº fäå Œ v x~ oåæ ( ) v Œ ½ ³Ž µ ECMWF w fìˆ å v 0.25 v õõ WRF w j oìˆ ƒðæ ìˆõ áž h 2007 Ð 2009 v ECMWF TIGGE the THORPEX Interactive Grand Global Ensemble THORPEX The Observing System Research and Predictability Experiment ì ˆ å v 0.5 v ³v ¾ˆ ƒš bicubic oìˆ ƒð w 45 km Æ õá Reference Continuous Ranked Probability Score åà e¼ 2 ECMWF f Œo 40 ÄÄ f 72 oš f Œv œv g æ f y x o få n t io PH01 PH02 PH04 fœ Œæh få ³ io PH02 PH03 f Ó ff š ˆ ¼v îh õõž Ä Åõá Œ ½ùo 40 ÄÄ o õõ ¾ Ä Ž ˆšõá Œ ½ ù æ Ä fäåˆ ô Åäh Äų fî Š uœ ùžo wö ³x ùoœ fo ³ ná i 1 õáž Œ ½oùo 1 Á õá Ÿvf 500 hpa vf œv g fž ä ~Ä fo Å äpv f 3 Ÿvf 500 hpa vf œv gf Rank Histogram º éˆ fš ³ hð U d t áº Ä fo ³ ¼v î õ 500 hpa vf³ Rank Histogram º Œ h³ «t³ Œò ³ «º fo µ Ö òo f ³ «òh Ð Œ f o Ạ500 hpa v f h œv gf³ º ³ Œò ³ «x Œ h³ «áºµ Ö òh f ³ «ò Ð Œ f h ẜv gf f o õõ 500 hpa v fœ h³{x Ìœv gœ f o h ùo éˆf ¼v fš ³é õáåç 3 éˆf³ x t fš é h ˆ Rank Histogram Î

h Ý 103!

104 æ! 2 40 ÄÄ f 72 oš Œv œv gf ECMWF Œv œv gf j Ä f t å Ä ³ÆÜ 1 Ạo PH01 72 oš f³œv œv gf ƒ ÅåÅ ³xª i U d A dv nz ˆÄ f³ ¼v šƒ nù³ìå ˆ nùæ Ä ³ ¼v åà fš RMSE SPRD Lj w i 4 4(A)Ð(C) Ÿvf 500 hpa ù vf œv gf³ RMSE SPRD ³ ò º éˆ fš g SPRD ³oˆ RMSE Ạfœ Œ š Å Rank Histogram ³ Å Ð 4(A) Ÿv f º RMSE SPRD fš ³t hð t h ẠŸvf ¼v î ¼v î {š žo 4(B) 500 hpa vf º f 24 oš x SPRD fš g Ìg Ä Ä v ¼v f Š g Ìg õoˆä f³ ¼v Œu ³ fš g RMSE g õ Ä v µ ³ï fš g

h Ý 105! 3 Rank Histogram ò Rank ÆÜ Çò «(A)Ð(C) Ÿvf f 24 48 72 oš³ Rank Histogram (D)Ð(F) 500 hpa vf f 24 48 72 oš³ Rank Histogram (G)Ð(I) œv gf f 24 48 72 oš³ Rank Histogram

106 æ! 4 (A)Ð(C) Ÿvf 500 hpa ù vf œv gf³ RMSE SPRD ³ ò ò fš oæ RMSE ÜÆ SPRD

h Ý 107 Ìg õ ˆÄ fäå³ ¼v 4(B) º SPRD fš g Ì RMSE g ³ h áºä f Ø ¹nz v g g uv î w fçt õ ¼v î {š ¼v î ä Ä v µ ³t oð ƒå Ä ÄÅ ŒŽ½ t {x t Î ˆ w³ ˆ õ ¼ j ö ¹nzõ Ì Å 500 hpa vf Rank Histogram ³ Å Ð 3(D)Ð(F) 4(C) œv gf º fš g RMSE SPRD t Œ æg é {x i 500 hpa vf Ž Å RMSE ³g î ¼hˆ SPRD Î tõ 5(A) (C) Ÿvf 500 hpa ù vf œv gf f 72 oš³ member equal-likelihood ùo o µ ³ f «õáƒå i³ä f Œ Œ ³ f «Ð º oˆµ ³ f «Ð Œ ò Œ òt ẠÄÅ Ä Ä öœx 6 ùo Ÿvf 500 hpa vfõ á f v³ž Ÿvf Ž 293K 298K Ì 500 hpa vf Ž 5820 p 6(A) (B) Ÿ vf 500 hpa ù vf Ž Å x ò f «ò äž «Ó Å x oåæ x Ạf «äž «f v 6 º ç  Ÿvf 500 hpa vf x³ oåæ oåæœ ï º o ³ f v î f «³Àš f «ò Ë áºhhˆ³ä f ò hˆ ³ ˆòo f «ò Ÿv f «ò Ë Ÿ ä fò ŸË f «ò Ëä fò Ÿ 6(A) º Ÿvf f «ò Ë äž «hˆ f «Ÿ fò ŸËŒ ³ t{x Ì f «ò Ë äž «oˆ f «ä fò ŸË Ÿv fœ ³î ˆ fò ŸËŒ ³î fò ŸËŒ ³î Å 3(C) U d t³å Ð 6(B) º 500 hpa vf³äž «³oˆ f «áº 500 hpa vf f h Rank Histogram Å Œ Åç 7(A)Ð(C) Ÿvf 500 hpa ù vf œv gf³ ò CRPSS Ž Ä Äų fî º h f CRPSS ³hˆ 0 Ạfo ³ «fçtoˆ ³çt fo oˆ fìå fœ Œ fî Ì NCEP Ä fäå CRPSS NCEP fäå fì ˆ 40 v v ìˆ Ž e NCEP Å ä Ë NCEP Ä fäå f 500 hpa vf ˆ 72 oš³ CRPSS Ä 0.7 ŸvfÄ 0.5 œv gfšœõáž Œ ½ 500 hpa vfˆ 72 oš³ CRPSS Ä 0.5  ŸvfÄ 0.25 ò º Œ ½ Ä f ÄÅ Œ fî Œ ½ h 7(D)Ð(F) Ÿvf 500 hpa ù

108 æ! 5 (A) (C) Ÿvf 500 hpaù vf œv gf f 72oŠ³ member equal-likelihood ò Ä ÆÜ Çò «

h Ý 109! 6 Reliability Diagram ò f «Çò äž «(A) Ÿvf Reliability diagram oæ 293K Š Æ ÜÆ 298K Š Æ (B) 500 hpa ù vf Reliabilitydiagram 5820 ù p ³ ÜÆ Š³ Æ

110 æ! 7 (A)Ð(C) Ÿvf 500 hpa ù vf œv gf ³ CRPSS fš é (D)Ð(F) Ÿvf 500 hpa ù vf œv gf w f ëp WRF wæ f ³ CRPSS fš é ò fš vf œv gf³ ëp WRF wæ f ò CRPSS Å º CRPSS ³hˆ 0 áº Ä f ˆ w f 8(A)Ð(C) Ÿvf 500 hpa ù vf œv gf RMSE ÒoÆ Ä RMSE ÒoÆ Ä fv RMSE fš ³g ³t jéh º Ä fäå n ³ RMSE hð f g Ìg h Ä fv RMSE Ä f RMSE ò º Ä fv fî ˆh Ä f ƒžä v ˆ n ˆš jf få Ì Å wõá CRPSS Ž Å Ð åä ŒÄÅzt æ o õá Ä ò i 8(D) o ˆ 500 hpa vf RMSE ½ ˆšõá Ä Å º ˆ õ RMSE ³t Ó Kain-Fritsch ½ ˆš RMSE òh h Grell-Devenyi ensemble Grell-3 ½ ˆ š RMSE ô Ì ˆ Ÿvf RMSE g w x òh i 8(E)

h Ý 111! 8 (A)Ð(C) Ÿvf 500 hpa ù vf œv gf RMSE ÒoÆ RMSE ÒoÆ Ä v RMSE (D)500 hpa vf ½ ˆš o RMSE Ä ÒÄoÆ Kain-Fritsch ½ ˆš ÒÃoÆ Betts-Miller-Janjic ½ ˆš ÒoÆ Grell-Devenyi ensemble ½ ˆš Ò ÜÆ Grell-3 ½ ˆš (E) Ÿv f g w Ä ÒoÆ Noah LSM ÒoÆ Pleim-Xiu LSM Ò ÜÆ Rapid Update Cycle Model LSM º ö Ä Ä PH27 PH28 PH31 PH32 ò ½ g w(noah LSM Rapid Update Cycle Model LSM Pleim-Xiu LSM* x ˆ ³ ³{š Ó Rapid Update Cycle Model LSM RMSE òh gf ˆ Œõ RMSE ŒÄÅ z³x q t ý Œ ½ƒ WRF wõáo Ú w ³ ˆšÄ õá 40 Ä³Ä fo få õõ ³Ž á Ä ˆš Î õ Ä õáä fo æ Š p õ áæ æ Ä îh h¼v Ø Î³³ «ƒ Rank

112 Histogram member equal-likelihood ensemble spread Ž á æ Ä f³ fî v Continuous Ranked Probability Skill Score õá fî Ž f v ƒ Reliability diagram õá Œ ½ùo Ÿvf 500 hpa vf œ v gfž ä ~Ä f o Åäpv f Å º š Ä ¼v î oˆµ ³ f «v f vž Å º f vp î f Î Ž Å º Ä fo Œ fî w fõá ò Å ä Ä f ˆ w f ÌõõÄ v ³ˆw x ÄÄ v f åà RMSE Ñ Ä f RMSE õá ò Å º Ä fv fî ˆh Ä f áº Ä v ˆš Ϋx ˆ f få òå fî Ž Å Ð h õ ³ Ä w f³ 500 hpa v œv g f o «ò Ì ÂŸvf 293K 298K ³ ån f ˆ ËŒ ³ t f ˆ ËŒŸv ³î Œˆ ä n ƒå ˆš w Ä fä ų fåå z Œ 500 hpa v f h œv g f o³ «ò Åç ä ƒå t ³ ³ «õ Åç î åù Ä f³äåz t Ì Åå Å ³¹ ~ Ä ÄÅ ÎŽ Œ 500 hpa v œv g f æ o³äåz t ÄÅz t Î w ³ ˆ õ¼ j ö ¹n zoð Œ ùo w fìˆõá t Ž ùož õ³å õáž Œ ½Å Œ³o ååoåäh f š îh³ Ì o Å x ˆ oˆ få ŒÄ Åz x n ä 40 Ä õ ¼v h õh³ Îx ¼v³åÀÅ õ ¼ vž Å Œ o õ ˆš ån Œ ³ h ˆš šƒ îh Ä Î ˆ jf ö ³ŒŒ Œ oùo ³Ä ˆw õáo jf ö EAKF Ensemble Adjustment Kalman Filter system Ä ç š á jf ŒŒø w ˆš jf ö Î Ä ˆ w w i Ä fäå ë Œ ½ h ëp ëìå yƒ å À ¼ å NSC 99-2625-M-052-006 -MY3 n i ÂÒÕ Ž¼ r šæ Šp Ù 2005 2003 v n MM5 Ä f h ¼n 33 255-275

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h Ý 115 The Study of Regional Ensemble Forecast: Physical Perturbations Jhih-Sin Li and Jing-Shan Hong Central Weather Bureau (manuscript received 25 August 2010 in final form 25 March 2011) ABSTRACT In order to represent the forecast uncertainties, the spread-enough ensemble products from a robust ensemble forecast system (EFS) became more and more important in the numerical weather prediction centers. The goal of this paper is to evaluate the forecast spread based on the physical perturbations from WRF model. One-month regional forecast experiment from 40 members was conducted in this paper, including the cumulus, microphysics, planetary boundary layer parameterization schemes, and land-surface models. Verification techniques were applied to evaluate the ensemble spread qualitatively and quantitatively. The results show that there exist systematic bias in the ensemble system and therefore result in the not enough forecast spread from the physical perturbation based on WRF model. To further apply a bias correction and perturbed the ensembles from the other technique is under assessment to implement an effective EFS in Central Weather Bureau. Key Words: ensemble forecast system, spread

116 æ