The Generalized PV θ View and their applications in the Severe Weather Events

Transcription

1 Th Gnralizd PV θ Viw and thir applications in th Svr Wathr Evnts Shouting Gao Institut of Atmosphric Physics, Chins Acadmy of Scincs, Bijing, China

2 OUTLINE Background Gnralizd Potntial Tmpratur Th Scond Ordr Potntial Vorticity Thir Application in Svr Wathr Evnts Prspctiv Baroclinic Inrtial Gravity Invariant (BIG) Summary

3 Background Albrt Einstin Two basic assumptions : (1) All Physical Laws hav uninformd forms in all inrtial coordinat frams. (2) Light spd is an invariant in all th inrtial coordinat frams.

4 Background Thr ar two important invariants in th atmosphr On is potntial tmpratur( ). θ Th othr is potntial vorticity(pv). Hoskins (1985): IPV thinking Hoskins (1991): Towards a PV θ Viw of th Gnral Circulation

5 Potntial Tmpratur ( θ ) For dry atmosphr For saturatd atmosphr θ = T p p 0 ( ) L q s θ = θ xp C pm T For th ral atmosphr, nithr total dry nor saturatd anywhr, it is non uniformly moist atmosphr. So Qustion: How to dscrib th ral atmosphr? R c θ d p d

6 (Gao t. al., JGR, 2007) Gnralizd Potntial Tmpratur For ral atmosphr θ k L q s q = θ xp Cpm T q s In th absolutly dry rgion: q=0 ( q / q ) k = s 0 θ = θ (Gao t. al., GRL, 2004)

7 In th absolutly saturatd rgion: q=q s k ( q / ) = 1 θ = θ q s In th non uniformly moist rgion: ( q / ) q s k 0 θ θ ( q / ) q s k 1 θ θ

8 θ θ Rain ara θ Rain ara Rain ara Th distributions of θ,θ, θ at 20, 12 August 2004

9 Th gnralizd potntial tmpratur and havy rainfall location Th prdictd 3h prcipitation by modl Gnralizd potntial tmpratur Potntial tmpratur Equivalnt potntial tmpratur

10 Richardson numbr (R i, R i, R i, ) and Instability For dry air R i : R i = g θ θ z v z 2 θ = T R P 0 C p d ( ) P For saturatd air R i : R i = g θ θ z v z 2 θ = L q s θ x p [ ] c T p m For moist air R i : R i = g θ θ z z 2 v θ Lqs q k = θ xp[ ( ) ] c T q pm s YANG S and GAO S T, CHIN. PHYS. LETT.,2006

11 Rainfall occurrd from 00 to 12UTC 12 August 2004 R i Shadow ara R i Shadow ara Rain ara ar shadd by Purpl

12 Rainfall occurrd from 00,06,12,18UTC 12 August 2004 R i Shadow ara Rain ara ar shadd by Purpl

13 Th gnralizd frontognsis function in moist atmosphr Th traditional frontognsis function Th gnralizd frontognsis function F d = dt θ d F = θ dt Th potntial tmpratur Th gnralizd potntial tmpratur P θ =T P 0 R/ C p ( ) θ Lq s q k = θ xp[ ( ) ] c T q p s

14 Th tim avragd OLR (shadd) from 22 Jun to 2 July 1999 during Miyu priod (unit: W/M2)

15 Cas study:at 00 UTC 6 July 2003 doubl rainblts Tmpratur Th gnralizd potntial tmpratur (Blu dashd isolins) Th gnralizd frontognsis function (shadd) Th obsrvd 36h prcipitation from 00 UTC 6 to 12 UTC 7 July 2003

16 Th vrtical cross sction:at 00 UTC 6 July 2003 Th gnralizd frontognsis function (shadd), th gnralizd potntial tmpratur (blu dashd isolins), prcipitation (histogram), stram lins (rd vctors)

17 From θ to Potntial Vorticity (PV) For dry atmosphr For saturatd atmosphr v PV = α ξ θ ( ) a v MPV = α ξ θ ( ) a For moist atmosphr GMPV = α ( ξ ) a θ Gao t.al., GRL, 2004 Liang t.al., QJ, 2010 v

18 Liang t al QJ Vrtical cross sction of diagnosd MPV (units: PVU) for 0900, 1000, 1100, and 1200 UTC on 4 July 2003, corrsponding to panls a, b, c, and d rspctivly. Th contour lins ar quivalnt potntial tmpratur (K), and th color shadd rgions ar MPV and rd trangls ar rain aras

19 Liang t al QJ Th sam as abov, but th contour lins ar gnralizd potntial tmpratur (K), and color shadd rgions ar GMPV and rd Triangls ar rain aras

20 Th Scond Ordr Potntial Vorticity For Adiabatic and frictionlss flow, two invariants: θ and Q On th on hand d θ = 0 dt If V is rplacd by θ = V θ t ξ In th advction trm PV = Q = ξ θ/ ρ

21 Th Scond Ordr Potntial Vorticity ON th othr hand dq dt = 0 Q t = V Q If V is rplacd by ξ in th advction trm QS = ξ Q / ρ Qustion? Q S Invariant or not?

22 Th Scond Ordr Potntial Vorticity Proof d v 1 + 2Ω v + p + g = 0 dt ρ (1) 1 p = T s C pd T = T s H (2) ρ d v 2 v T s H 0 dt + Ω + + g = (3) whr H is th nthalpy and is th ntropy. s

23 Th Scond Ordr Potntial Vorticity curl q.(3) d ξ + 2Ω η s ξ + 2 Ω η s ( ) = ( ) v dt ρ ρ (4) W gt d ξ + 2 Ω η s ( λ ) dt ρ d ξ + 2Ω η s ξ + 2 Ω η s d = ( ) λ + [( ) λ dt ρ ρ dt (5) ξ + 2Ω η s ξ + 2 Ω η s = [( ) v] λ + [( ) [ λ + ( v )( λ )] ρ ρ t

24 Sinc and W hav = ( λ ) = t d dt d dt ( λ ) ( v λ ) ( λ ) ( v ) λ ( λ ) v ξ + 2 Ω η s [( ) v ] λ ρ λ ( v ) A ( B ) C B ( A ) C + A ( B ( C ) ) = 0 ξ + 2 Ω η s = ( ) ( λ v + λ ( v )) ρ (6) (7) (8) whr d ξ + 2 Ω η s ξ + 2 Ω η s d λ ( λ ) = ( ) dt ρ ρ dt d η dt = T d λ = dt 0 ξ + 2 Ω (9) Is absolut vorticity

25 Th Scond Ordr Potntial Vorticity From (9): d ξ + 2 Ω η s ξ + 2 Ω η s d λ ( λ ) = ( ) dt ρ ρ dt ordring ξ η s λ = θ Q = ( θ ) ρ λ = Q Q S ξ η s = ( Q ) ρ dq S dt = 0 (Scond Ordr Potntial Vorticity)

26 Mrit: Th Scond Ordr Potntial Vorticity Q S : Mrit and importanc Invariant PV gradint and vorticity ar involvd Importanc: Can b usd to diagnos instability, tropopaus, svr wathr, and so on

27 θ Applications of in Svr Q wathrs S

28 Gnralizd moist thrmal paramtr (GMTP) G ( v ) = h θ θ h whr v = ( u, v, w ) is vlocity vctor, θ is potntial tmpratur, θ is gnralizd potntial tmpratur

29 ØTo diagnos prcipitation by GMTP UTC 23 July UTC UTC 24 July 2005 Cas A UTC 12 August UTC UTC 13 August 2004 Cas B Shadd: th obsrvd 6h prcipitation Isolins: th vrtical intgral GMTP

30 Application in Svr wathr Evnts θ: In th us of th wav flow intraction Wav inducd by trrain

31 Targting th rainfall inducd by wav, Prturbation PV(= Whr ω = V Ordring ω ϕ = A + A + A u v w ω ϕ ) is constructd. ϕ is an arbitrary scalar. A u u ϕ u ϕ = z y y z A v v ϕ v ϕ = A w x z z x w ϕ w ϕ = y x x y Basd on th wav activity consrvation A + F = t S A :Wav activity dnsity F :Wav activity flux S : Sourc or Sink

32 W hav A w t w ( S ) ϕ w k = F + Wav Activity Equation Whr A w = ϕ ϕ w w x y y x Wav Activity Dnsity. ( ϕ ) F = v A + v A + G ϕ k+ v w k Wav Activity Flux w w 0 w w 0 (Gao t.al., JGR,2009; Ran and Gao, JAS,2007)

33 From 00UTC, 4 July 2003 to 00UTC, 6 July 2003 Choosing ϕ w θ w θ = θ, A w = y x x y

34 From 00UTC, 4 July 2003 to 00UTC, 6 July 2003 A dz, ϕ = θ w

35 From 00UTC, 4 July 2003 to 00UTC, 6 July 2003 A dz, ϕ = θ w

36 Diagnosd by ξ η s Q S = ( Q ) ρ Havy rainfall: shadow ara Q S : contours 26 August, 2009

37 Diagnos rainfall by QS

38 Diagnosd by QS Typhoon Morakot: 850hPa Q S : shadow ara

39 Typhoon Yunna 850hPa

40 Prspctiv Towards PV Q = ξ θ / ρ = ξ// θ θ / ρ = ξ// θ θ / ρ But ξ θ θ = 0? How to mbody th intraction of ξ θ with θ

41 On th othr hand Prspctiv q ωa θ = = 0 ρ C = ω θ 0 a q ω θ a = ρ 0 C = ω θ = 0 a

42 Prspctiv v CVV = ξ θ v ξ θ Gao t. al., JGR,2004,2007

43 Prspctiv MPV (shadd) CVV ( shadd) Havy rainfall (contour) From 20,5 Aug. to 02,6 Aug.2001

44 Prspctiv Furthr Towards PV Th schmatic diagram of th vorticity projction

45 Prspctiv q A B θ =ω ( ) q =ω p α ( ) qc = ω p α θ Potntial vorticity Th projction of CVV on th orintation along prssur gradint forc Th projction of CVV on th orintation along baroclinic trm ω = v θ = θη v = ( ηu, ηv, η w ) ρ η 1 ρ k ρ = a = L vq vs q v η = xp c T q p c vs

46 Prspctiv 06 UTC 12 UTC q q A B C (contour) Th obsrvd 6h prcipitation (shadd) q 18UTC 14 Jun 2009

47 Prspctiv Bijing Jinan Shijiazhuang Zhngzhou q A q B q C Prcipitation Rd Blu Grn Gray

48 Towards Q and θ Prspctiv Dfin: G = Q θ Vctor G is tangnt to th curv dfind by th intrsction of th two surfacs Q=const and θ=const G = ( Q) ( θ ) + ( Q ) ( θ ) t t t = curl( V G) ( QdivV ) θ

49 Summary From PV θ viw, many phnomna in th atmosphr can b dply undrstood; Gnralizd potntial tmpratur and scond ordr potntial vorticity can captur th dynamical and thrmal information bttr than PV and θ; Bsids th atmosphric circulation which can b studid from PV θ viw, many svr wathr vnts can b also studid from gnralizd PV θ viw; Ths invariants can b usd to prob into all th phnomna occurrd in atmosphr including th climat and climat chang vnts not only th svr wathrs, bcaus thy ar not constraind by scals.

50 Thank you!