Parameterization in large-scale atmospheric modelling

Transcription

1 Paameeaon n lage-sale amose modellng Geneal aameeaon oblem: Ealaon of ems nolng aeaged qada and ge ode ods of nesoled deaons fom lage-sale aables Examles: a blen ansfe n e bonday laye b Effes of nesoled wae moons e.g. gay-wae dag Cmls aameeaon Oe knds of aameeaon oblems: adae ansfe, lod moysal oesses*, emal oesses

2 age-sale aables and eqaons e an oeba denoe e esl of an aeagng o fleng oeaon w sesses flaons w emoal and saal sales smalle an e-defned lms. e.g. fo some aoaely smoo and bonded aable afe aeagng: ,,, τ τ τ x x y y y x x x y y dy dx d d y x We efe o s as e lage-sale aable and assme a o model as sffen saal and emoal esolon o eesen e aaon of s aable one we ae deemned e eqaons goenng and an aoae solon meodology.

3 yally, f e aable, as e followng goenng eqaon: ; Q, And e mass onny eqaon s: 0; en alyng e aeagng oeaon ges, aoxmaely: 1 Q f <<1 In ases o be onsdeed e.g. mls aameeaon w and deemnng s em s e goal of e aameeaon n s ase

4 oon Amose Eqaons 1 2 fkˆ P gkˆ ν 0 1 e F S 1 gw e k 2 ; S ass onny emodynam O: [ ] 2 k ad ˆ ˆj kw ˆ Φ Φ gw ao Condensed wae q q w e e P Eqaon of Sae deal gas 1.61q qw P R

5 E / 2 Enegy Conseaon e.g., Gll, 1982,. 4 kne enegy q Φ mos sa enegy E μ 2 E k 2 Fad [ E ] [ E μ E k ] F ad ] ν μ, ν olela dynam and knema sosy x y Fo a ν m / s a 15C, 100Pa Kolmogoo sales fo w sosy and 3 dssaon ae ndeenden aamees: ν ; ν 1/ 4 K U K ese ae small fo e amosee ~ 1mm,.1 m/s. eefoe s emssble o negle sos ems fo aameeaon oses b no o gnoe effes/oesses a lead o dssaon and assoaed eang 1/ 4

6 Qas-anelas aoxmaons fo GC aameeaon Bakgond sae: -ydosaally balaned - slowly ayng on e smalle, nesoled oonal and emoal sales - e.g. a of qas- balaned laneay sale laon egme. - deaons fom ae small enog o allow lneaaon of e eqaon of sae deal gas law o deemne elaonss beween key emodynam aables: R g 1 1 > R g g R R g 1 1 > g g g g

7 ems nolng wll also be negleed omaed o ny. Ge eqaons fo e bakgond sae by aeagng: w fk H H H ˆ R Q Q g B w B w w Q H H { } fk k d d H H ˆ ˆ Φ q Q g w d d H H 1 Usng ese esls leads o e followng: neglgble fo e aameeed sales b no fo e esoled sales oe s ems

8 Paameeaon of e effes of os Coneon n GCs ass flx semes Bas ones and qanes Qas-seady Enanng/deanng lmes Aakawa&Sbe and smla aoaes Boyany song Raymond-Blye, Emanel Kan-Fs Close Condons, ggeng Adjsmen Semes anabe Bes-lle

9 adonal Assmons fo Cmls Paameeaon: 1. Qas-seady assmon: effes of aeagng oe a mls lfeyle an be eesened n ems of seady-sae onee elemens. [ansen lod lfe-yle fomlaons: Ko 1964, 1974; Faed1974, Bes1975, Co1977, on Salen&Falane 2002.] 2. Pesse ebaons and effes on momenm gnoed [Some of ese effes ae been enoded n moe een wok, b no neessaly n an enegeally onssen manne]

10 Sang eqaons negle ems n ly and oe small ems bakes and assme mlly a e bakgond sae s slowly ayng on e aameeed sales: w w H H 0 Paameeaon of os Coneon H g k ˆ [ ] Q g w H ls smla eqaons fo ao, ondensed wae, and oe sala qanes Fo e adonal fomlaon gnoe ossed-o ems

11 A σ, A A e 1 σ A A

12 Saal Aeages Fo a gene sala aable, : age-sale aeage: Conee-sale aeage fo a snglemls /downdaf : Enonmen aeage sngle onee elemen: Wee σ A A << 1 e 1 A A A 1 1 A da A A da Ae da, e / O1 * σ 1σ σ 1 σ ˆ eal eloy: e w σw 1σ w e Ensemble of mls lods: σ σ w >> w, w e σ 1σ e

13 Cmls effes on e lage-sales Sa w a geneal onseaon eqaon fo w Pls e assmon: H Q smla o sng anelas assmon fo onee-sale moons Aeage oe e lage-sale aea assmng fxed bondaes: w Q ass flx ose fo dafs: σw σw σ w * * oes Also: * * Q σ ; o a assmon: w 0 Q 1 σ Q e In ae e.g. n a GC e ognos aables ae also mlly me aeages oe onee lod lfe-yles

14 Aly mls sale sb-aeage o e geneal onseaon eqaon, aonng fo emoally and saally ayng bondaes ebn le: σ σ A σ ass onny ges: n dl b σ[ w w * * ] σ Q σ σ A σ n dl aw 0 n ; e owad deed nomal flow eloy elae o e lod bonday Enanmen nflow/deanmen oflow: σ E A efne: σ n [ 1 H n ] dl σ E n b[ 1 H n] dl EA σ 1; nh n dl H f A { 0; σ f f 0 < 0 σ nbh n dl A o a: E e ; ;

15 Smmay fo a gene sala, : seady and o a n lod dafs: negle ossed-o ems oe Q w Q w E E oe Q w w e σ σ σ σ σ σ 1 0 ] [ * * * * Wen bo dafs and downdafs ae esen, bo enanng enonmenal a: d d d d d d d E E E w σ ; ; ;

16 Bas mls daf eqaons o-a, adonal 0 0 E P l l q q E q s s E s E {y sa enegy: sc g; os sa enegy : sq; } mass onseaon dy Sa Enegy mos Sa Enegy ondensae ao w σ κ θ o ; l q al emeae R / κ ;

17 Enanmen/eanmen adonal oganed e.g.lme enanmen assmon: E [1 H ] dl < n n P E α A n > P αw P σw λ 2α σw R P dl daf emee Aakawa & Sbe 1974 and desendans, e.g. RAS, Z-: - λ s a onsan fo ea daf [saaed omogeneos o-a enanng lmes] - deanmen s onfned o a naow egon nea e o of e daf, w s loaed a e leel of eo boyany deemnes λ Kan & Fs 1990 and desendans, e.g. Beeon e al, 2004 : - R s sefed onsan o ayng w eg fo a gen mls - enanmen/deanmen onolled by boyany song.e. e effee ale of α s onsaned by boyany song Esod Enanmen and non-omogeneos mxng Raymond&Blye, Emanel, Emanel&Zko-Roman: -No based on oganed enanmen/deanmen - enanmen a a gen leel ges se o an ensemble of mxes of ndled and enonmenal a w asend/desend o leels of neal boyany and dean

18

19

20 b

21 λ b b, * λ d b b b ] ex[ ] ex[ * λ λ λ eemnng faonal enanmen aes e.g. wen a e o of an daf 2 * * * 1, O q q q Noe a sne dafs ae saaed w ese o wae ao aboe e C: s deemnes e daf emeae and w.. mxng ao gen s mse. e

22 Faonal enanmen aes fo daf ensembles a Sngle ensemble membe deanng a E λ ; 0 < ex λ b [ ] b b eanmen oe a fne de Δ : b see ensemble based on a ange of os / Δ E, λ ; λ λ λ λ Δλ Δ

23 Boyany Song Enanmen odes mxes of a faon, f, of enonmenal a and 1-f of lody saaed mls daf a. Some of e mxes may be osely boyan w ese o e enonmen, some negegaely boyan, some saaed w ese o wae, some nsaaed θ saaed lody θ osely boyan θ e f f* 0 1 f

24 Kan-Fs 1990 see also Beeon e al, 2003: Sose a enanmen no a mls daf n a laye of kness δ leads o mxng of λ d of enonmenal a w an eqal amon of lody a. K-F assmed a all of e negaely boyan mxes f>f wll be ejeed fom e daf mmedaely wle osely boyan mxes wll be nooaed no e daf. e Pf be e df of mxng faons. en: E 2λ o f 0 fp f df 1 2λ 0 1 f P f df f s assmes a negaely boyan a deans bak o e enonmen wo eqng o desend o a leel of neal boyany fs. Emanel: xes ae all ombnaons of enonemen a and ndled lod-base a. Ea mxe asendsosely boyan/desends negaely boyan, yally wo fe mxng o a leel of neal boyany wee deans.

25 Close and ggeng ggeng: I s feqenly obseed a mos oneon does no o een wen ee s a ose amon of CAPE. Poesses w oeome onee nbon ms also o. Close: e smle lod models sed n mass flx semes do no flly deemne e mass flx. yally an addonal onsan s needed o lose e fomlaon. e lose oblem s enly sll ooly onsaned by eoy. Bo may nole soas oesses

26 Close Semes In Use yally o deemne e ne mass flx a e base of e onee laye ose onegene~ Peaon Ko, fo dee eang oneon Qas-eqlbm [Aakawa and Sbe, 1974 and desendans RAS, Z-, Zang&, 2005] Pognos mass-flx loses Pan & Randall, 1998;Snoa&Falane, 2004 Closes based on bonday-laye fong Emanel&Zko-Roman, 1998; Beeon e al., 2004