3D Spectral Energetics Analysis and Rossby Wave Saturation Theory

Transcription

1 3D Spectral Eergetcs Aalyss ad Rossby Wave Saturato Theory Hrosh L. Taaka Uversty of Tsukuba Japa Presetato at MODES 015

2 Lorez Eergy Box Dagram Eergy accumulates at zoal wave 0 Potetal Eergy Ketc Eergy Zoal Box Zoalzato Eddy Box Barotropzato Eergy accumulates at vertcal wave 0 Kug ad Taaka 1983, JAS

3 Lorez cycle, Saltzma cycle Saltzma 1957; ,, 1,, 0, 0 3,, 1,, 0, G C S R t P G C R t P D C L M t K D C M t K N Z N Z P0 P K0 K expx p p

4 Saltzma cycle G: Geerato of P P: Avalable potetal eergy R: zoal-wave teracto of P S: wave-wave teracto of P C: Baroclc coverso from P to K K: Ketc eergy M: zoal-wave teracto of K L: wave-wave teracto of K D: Dsspato of K Saltzma 1957 & 1970 Kug ad Taaka 1983 &1984

5 Data JRA-5.5.5, 3 levels hpa NCEP/NCAR reaalyss.5.5, 17 levels hpa ERA-40 JRA-5 Reaalyss by JMA NOAA CDC ECMWF.5.5, 3 levels hpa 1990/91 DJF 3 Moth u, v, T, q

6 Avalable Potetal Eergy P Ketc eergy K Potetal eergy NCEP up to 35 ERA up to 60 Ketc eergy total eergy [10 4 Jm - ] NCEP JRA ERA P E K E

7 Wave-wave teractos S, L Eergy Flux ~7 Dow-scale cascade 1 S Up-scale cascade 1 L 6~11 Dow-scale cascade

8 D Spectral model 1D: Expaso Fourer harmocs D: Expaso sphercal harmocs x p x p x p p exp exp,, exp, θ λ θ λ λ θ θ λ l L l l N N l l Y p p P Y

9 3D Spectral model Vertcal ormal mode Horzotal ormal mode: Hough harmocs Expaso 3D Normal Mode Fuctos,,,, exp G,, 0 0 m σ θ λ σ θ λ λ σ θ σ θ λ lm L l m lm M m N N lm lm X w U Π Θ Π lm m s k j jk jk w w w h p E f w w r w d dw +, 1 1,,3,..., σ τ

10 G G m Vertcal eergy spectrum Vertcal modes σ C σ + C σ 0 σ σ r1 r 1 Barotropc ad baroclc modes 1 C s µ lσ + C cos µ lσ µ λm σ σ 1 Gm σ + λ G m m 0, λ m K:Barotropc Rγ gh m 1 4 P:Baroclc mode -3 Terasak ad Taaka 007 Vertcal Waveumber

11 Barotropzato by baroclc stablty Barotropc mode Eergy flux of Ketc eergy エネルギーフラックス Terasak ad Taaka 007

12 Sphercal harmocs 0 Hough harmocs Kelv mode Mxed Rossby-gravty mode

13 Zoal Eergy Spectrum Vertcal Eergy Spectrum m Taaka 1985

14 Merdoal Eergy Spectrum l Taaka 1985

15 Eergy spectrum the 3D waveumber space c + β l + m β k, l, m : zoal, merdoal ad vertcal waves k : total wave c σ / dw dτ σ w jk r jk w j w k + f Use c for the scale place of 3D waveumber

16 Observed eergy spectrum c-doma Frequecy doma Phase speed doma Shgehsa mode 0 Taaka 1985 Taaka ad Kasahara 199

17 Frequecy doma Taaka ad Kmura 1996 Vertcal mode m0 Vertcal mode m1 Vertcal mode m Vertcal mode m3

18 Eergy flow box dagram barotropc-baroclc decomposto Zoalzato D turbulece Barotropzato Baroclc stablty We ca costruct a barotropc model wth baroclc stablty

19 Numercal smulatos of blockg ad AO Prmtve Equato Model

20 Numercal smulatos of blockg ad AO dw dτ E σ w jk 1 p s h m w jk w w Barotropc S-Model Taaka 003, JAS r j k + f

21 NCEP/NCAR Barotropc S-Model Barotropc eergy Perpetual Jauary

22 Arctc Oscllato Barotropc heght EOF-1 NCEP/NCAR Barotropc S-Model

23 Sgular Egemode Theory of AO Egemode EVP- EVP-1 EOF-1 5 Days 0 Days Eddy Feedback Effect Taaka ad Matsueda 005

24 Blockg the model

25 Blockg formato by Rossby wave breakg Taaka ad Watara 1999 Taaka 1998

26 Rossby wave breakg ad saturato Basc state of 0 Eddes breakg saturato Taaka ad Watara 1999 Mudrck 1974

27 Zoalzato Rossby wave breakg for 6 Growthrate 1.7

28 3D eergy spectrum By 3D ormal mode expaso dw dτ σ w r jk jk w w j k + f E c 1 w 0 psh σ / Phase speed Rhes scale E mc? c Taaka et al. 004 GRL

29 Saturato theory gravty waves Saturato spectrum Breakg gravty waves -3/5 power θ < 0 z Breakg codto Frtts 1984

30 q y y u Saturato theory Rossby waves < < 0, Basc state ψ + β + l q f c ψ + u f + β Taaka ad Watara 1999 PV barotropc model < 0 Breakg codto q y < 0 Eddy eergy saturato

31 Saturato eergy spectrum u < u v E q y 1 g p g s 0 β p s c + l 1 u mc c Taaka ad Kasahara v < 0 E mc dp m p / s g Mass for ut area Ku Kv Shepherd 1987

32 Observed eergy spectrum c-doma FGGE SOP1 E mc Taaka 1985 Taaka ad Kug 1988

33 Global eergy spectrum of E mc Taaka et al. 004 GRL Up-scale cascade q y < 0 E mc Rhes scale c m p / s Rossby phase speed g Mass of the ar turbulece waves

34 Rhes sclae o a sphere dw σ w dτ R r jk σ w w j w turbulece waves turbulace R > 1 k jk r jk w j w k + f Rhes rato Rhes scale waves R < 1 Rhes scale R 1 Taaka et al. 004 GRL

35 Eergy flux c-doma Eergy accumulates at phase speed 0 Source of eergy cascade Up-scale cascade There s a eergy source the mddle of the spectrum: ertal subrage theory fals. wave-wave Theory of Rossby wave saturato

36 Exctato of blockg ad AO by up-scale eergy cascade wave-wave Taaka ad Terasak 004 zoal-wave

37 Blockg AO Low-frequecy varablty of the atmosphere Cycloes Up-scale cascade Eergy source Meso Syoptc Plaetary Zoal

38 Summary 1 Eergy spectrum s examed the 3D waveumber doma usg phase speed c. Eergy spectrum of Emc s obtaed ad explaed by Rossby wave saturato 3 Up-scale eergy cascade to Rhe s scale forms blockg 4 Further up-scale cascade to zoal eergy forms the Arctc Oscllato

39 END Thak you.

40 Model descrpto Barotropc S-Model

41 Barotropc forcg