Influence of Gravity Waves on the Atmospheric Climate

Transcription

1 Influence of Gravity Waves on the Atmospheric Climate François Lott, LMD/CNRS, Ecole Normale Supérieure, Paris 1)Dynamical impact of mountains on atmospheric flows )Representations of mountains in General Circulation Models 3)Non-orographic gravity waves sources 4)Impact of gravity waves on the middle atmosphere dynamics

2 Influence of Gravity Waves on the Atmospheric Climate 1)Dynamical impact of mountains on atmospheric flows a)heuristic dimensional analysis b)linear mesoscale dynamics c)non-interaction theorem d)few nonlinear effects e)synoptic and planetary scales

3 a) Heuristic linear analysis Dimensional analysis: Background flow parameters N,, l, (and f ) Mountain dimensions d and h Param. controlling the linear dynamics: 1 Fr = and low level «trapped waves»: L= Mesoscale dynamics (incl. Gravity waves) Trapped waves Drag on~ Earth Ro 1 = fd Nl Param. controlling the non-linear dynamics: Boundary layer dynamics Nd S= h max d H ND = C d h max Fr 1=1 max Cg N h Synoptic scale and planetary scale dynamics «Vortex Stretching» N h max C l f h max d Rossby wave drag (almost perpendicular to ) Ro 1 =1 d

4 a) Heuristic linear analysis -X 0 +X~400km Section of the Alps at the latitude φ=45.9 N, and according to 3 different dataset The mean corresponds to the truncature of a high resolution GCM (T13, x~75km)

5 a) Heuristic linear analysis l h max Section of the Alps at the latitude φ=45.9 N, zoom to evaluate the scale of the individual mountain peaks: l~5-10km, hmax~1km!

6 a) Heuristic linear analysis In the linear case the response to the mountain can be analysed in terms of Fourier series M X 1 h x = h K cos K x K, h K = h x cos K x K dx X X X X K =0 h k The GCM orography resolves the first six harmonics quite well, do the others matter (here the model is T13!).

7 a) Heuristic linear analysis Linear response in terms of vertical velocity (stationnary D response with uniform and N!), for each harmonics: d w K z dz N k k w K z =0 with boundary condition: k f w K 0 =kh K vertical structure of disturbances with horizontal intrinsic phase velocity : horizontal wavelength π/ k= X/K, and intrinsic frequency: K f 1 m K z w x, z = kh K e K =1 KN sin kx K K=Kf Evanescent «long» disturbances K f 4 mk = k M h K sin m K z kx K Gravity waves fx c = = K = K N 1 m K z khk e sin kx K Evanescent «short» disturbances K N 4 N k k f NX where the + sign ensures positive vertical group velocity for the gravity waves and exponential decay with altitude for the evanescent solutions

8 a) Heuristic linear analysis X 1 dh Heuristic linear analysis, prediction for the mountain drag: Dr= p X X dx 1 Dr= KN K= K f 0 N k k f h K Only the gravity waves contribute to the drag! N k k f A drag due to the Alps of 1Pa corresponds to a zonal mean tendency of around 1 m/s/day (a barotropic zonal flow of 10m/s is stopped In 10 days). This is large! The difference between the T13 drag and the High Res datasets drag tells that there is a large need to parameterized Subgrid Scales Orographies!

9 b) linear mesoscale dynamics (f<k<n) X 1 dh The D linear analysis of Queney (1947), mountain drag: Dr= p X X dx =10m/s, N=0.01 s, f=10 s h x = h max x 1 d Case (a): d=10km, non rotating and hydrostatic Cgz>0 (remember mk>0 ^ ^ Cgx~Cx=- Intrinsic Group velocity Intrinsic Phase velocity

10 b) linear mesoscale dynamics (f<k<n) X 1 dh The D linear analysis of Queney (1947), mountain drag: Dr= p X X dx =10m/s, N=0.01 s, f=10 s h x = h max x 1 d Case (b): d=1km, non-hydrostatic, non-rotating Cgz>0 (remember mk>0 ^ >C^ =- C gx x Intrinsic Group velocity Intrinsic Phase velocity

11 b) linear mesoscale dynamics (f<k<n) X 1 dh The D linear analysis of Queney (1947), mountain drag: Dr= p X X dx =10m/s, N=0.01 s-1, f=10-4 s-1 h x = h max x 1 d Ro 1 = fd Results for the drag as a function of d: (c) (b) Dr N h max (a) 1 Fr = Nd

12 b) linear mesoscale dynamics (f<k<n) Trapped lee-waves and critical levels ((z) and N(z) varies) D-Boussinesq linear non-rotating theory zz w w N w=0 x z S(z) Non Hydrostatic Scorer parameter Fourier decomp: w x, z = w k, z e i k x dk w N zz k w=0 z WKB theory: Critical level m k z =S z k Scorer (1949) + Gossard and Hooke (1975) S z c =, z c =0 WKB theory predicts: lim m z k z zc Breaking and/or dissipation below zc Turning heigh: S z c k =0 lim mk z 0 z z Total or partial reflection around zc WKB theory predicts c Free modes such that w(k,z=0)=0 can be resonantly excited leeding to trapped lee waves

13 c) Non interaction theorem Non-Interaction theorem in the D Boussinesq non-rotating framework = r 0 z t, x, z, p= pr z p0 z p t, x, z In-flow eqs.: 1 p G x r x r G 1 p D t w= g z r r r z Flux form: D t u= t r u x r u u z r u w= x p G x x u z w=0 J D t w Oz = r Bound. cond.: w h =u h x h (free slip, but no-slip Would be OK) Momentum budget over the domain [-X,+X] x [h, Z] : XZ X Z X X t r u dz dx r u w dx r u u p dz X = X h X h X XZ dh dx G x dz dx p h dx X h Dr

14 c) Non interaction theorem Non-Interaction theorem in the D Boussinesq non-rotating framework Momentum budget over a periodic domain (again to simplify the maths, but the formalism is general if we take for the temporal derivative the tendency of the large scale flow including advective terms, and include lateral fluxes of momentum): XZ X XZ t r u dz dx r u w Z dx= Dr G x dz dx X H X H X In flow momentum budget at a given altitude: X t r u= z r u w G x where What makes z r u w 0 Linear theory: 1 u= u dx X X? u=u 0 z u ' t, x, z u t, z... ; w=w ' t, x, z... O 1 O O α small parameter

15 c) Non interaction theorem Non-Interaction theorem in the D Boussinesq non-rotating framework Disturbance equations written using the vorticity: ' = z u ' x w ' ' G ' G ' t u 0 x ' u 0zz w ' g x r = z x r x z J' t u0 x ' 0z w ' = r X r X r ' 0z ' ' u0zz 0z 0z ' ' u 0zz ' u A g ' w ' u ' u ' w '= G ' G ' ' J ' u ' ' x z z x r r r r r 0zz t 0z x 0 r 0z z 0z 0z 0z 0z F A A is the Action (here the pseudo-momentum) F x is the flux of Action Fz P P is the diabatic dissipative The budget of action can be written in the conservative form: production of Action t A F=P

16 c) Non interaction theorem Non-Interaction theorem in the D Boussinesq non-rotating framework A being a quadratic quantity in the disturbance amplitude, its sign being also well defined (in the absence of critical levels): A z,t can measures the wave amplitude. Its evolution satisfies: t A z F z=p

17 c) Non interaction theorem Non-Interaction theorem in the D Boussinesq non-rotating framework A being a quadratic quantity in the disturbance amplitude, its sign being also well defined (in the absence of critical levels): A z,t can measures the wave amplitude. Its evolution satisfies: t A z F z=p For a steady wave, :

18 c) Non interaction theorem Non-Interaction theorem in the D Boussinesq non-rotating framework A being a quadratic quantity in the disturbance amplitude, its sign being also well defined (in the absence of critical levels): A z,t can measures the wave amplitude. Its evolution satisfies: t A z F z=p For a steady wave, without dissipative and diabatic effects:

19 c) Non interaction theorem Non-Interaction theorem in the D Boussinesq non-rotating framework A being a quadratic quantity in the disturbance amplitude, its sign being also well defined (in the absence of critical levels): A z,t can measures the wave amplitude. Its evolution satisfies: t A z F z=p For a steady wave, without dissipative and diabatic effects: z F z=0

20 c) Non interaction theorem Non-Interaction theorem in the D Boussinesq non-rotating framework A being a quadratic quantity in the disturbance amplitude, its sign being also well defined (in the absence of critical levels): A z,t can measures the wave amplitude. Its evolution satisfies: t A z F z=p For a steady wave, without dissipative and diabatic effects: z F z=0 At the same level of approximation, the inflow momentum budget at a given altitude becomes: u G = F z =0 x z t r The wave does not modify the mean flow in the linear adiabatic non dissipative case (which includes the absence of critical levels and of waves breaking) XZ X XZ From the angular momentum budget t r u dz dx r u w dx = Dr G x dz dx X h X X h z and from t r u G x = z F =0, we can deduce that in the same conditions: X 1 z r u ' w ' Z dx=f =Dr X X The Eliasen Palm flux at all altitudes balances the surface pressure drag

21 c) Non interaction theorem Consequence of the wave Action conservation law for steady trapped non-dissipated mountain lee waves. t A F =P The general wave action law integrated over a non periodic domain when t A=P=0 gives: X X Z F Z dx 0 F X dz =Dr z N(z) F (z) Z l X Nl L= x 1 Fr = Nd and w'

22 c) Non interaction theorem X Z X F z Z dx 0 F x X dz =Dr F z Z dx Z 0 F x dz The trapped lee waves can transport downstream and at low level a substantial fraction of the mountain drag As the integral X F z Z dx is little sensitive to X (not shown and as far as X is sufficiently large), X Eliasen Palm flux vertical profile the one predicted by a linear non-dissipative we can take for the theory, and assumes that the horizontal transport at low level is dissipated.

23 d) Few non linear effects Heuristic definition of a «Blocking Height» ZB Linearity condition : ZB>>hmax From the vertical wavenumber definition: mk = k N k k f ZB can be written: d Z B~ = m1 / d 1 Ro Fr 1 For large Rossby number the linearity condition writtes: h max / d Fr 1 1 Ro 1 = fd 1 Fr = Nd

24 d) Few non linear effects Neutral or Fast Flows : Fr 1= The linearity condition becomes (for large Rossby number) Nd 1 h max / d Fr 1 ~ h max d S is the slope parameter, it is almost never small! =S 1

25 d) Few non linear effects Neutral or Fast Flows : Fr 1= Nd 1 Nonlinear dynamics for S=hmax/d~0(1) S is the slope parameter, it is almost never small! Streamlines from a D Neutral Simulations From Wood and Mason (QJ 1993) S=0., Fr-1=0 Note the separation streamline H(x) Hydrodynamic «bluff body»drag: h max Dr~ C d d (if the valley is ventilated!)

26 d) Few non linear effects Neutral or Fast Flows : Fr 1= Nd 1 Nonlinear dynamics for S=hmax/d~0(1) The dynamics at these scales explain the formation of the «banner» clouds alee of elevated and narrow mountain ridges (Reinert and Wirth, BLM 009) Large eddy simulation

27 d) Few non linear effects Stratified or «slow» Flows :Fr 1= N d 1 The linearity condition becomes (for large Rossby number) h max / d Fr 1 ~ h max N =H ND 1 HND is the non-dimensional mountain height, again it is almost never small! l h Here, hmax~1km, so for =10m/s, N=0.01s-1 : HND~1!

28 d) Few non linear effects Stratified or «slow» Flows Fr : 1= N d 1 Single obstacle simulation with h~1km, =10m/s, N=0.01s-1 : HND=1! Note: (Miranda and James 199) Quasi vertical isentropes at low level downstream: Wave breaking occurs. The strong Foehn at the surface downstream Residual GWs propagating aloft Apparent slow down near the surface downstream, And over a long distance Question: How to quantify the reversible motion that is due to the wave, from the irreversible one that is related to the breaking and that affect the large scale? Answer: On the Potential Vorticity (I am sure Ron Smith did a Very good job in explaining that to you)

29 d) Few non linear effects Analogy between low level breaking waves and Hydraulic jumps in shallow water flow (Schar and Smith 199) The Potential vorticity tells where the waves is dissipated and/or break: a steady non-dissipative wave do not produce Potential Vorticity anomalies Note the analogy with the non-interaction theorem The effect of mountains and obstacles is to produce an inflow force (F,G) at the place where the surface pressure drag due to the presence of the waves is given back to the flow. That is where the waves break. A very comparable effect occurs when The mountain intersect the free surface in shallow water, or intersect isentropes In the continuously startified case

30 d) Few non linear effects Analogy between low level breaking waves and Hydraulic jumps in shallow water flow (Schar and Smith 199), case where the mountain pierces the free surface.

31 e) Synoptic and planetary scales Basic mechanism: The vortex compression over large scale mountains produces anticyclonic circulations (linear, QG, non-dissipative view): d f z =0 dt QG vorticity: = x v g y u g No diabatic effect and the surface stays an isentrope (inherent to a steady linear theory): d =0 dt

32 e) Synoptic and planetary scales Basic mechanism: The force exerted on the mountain is almost perpendicular to the low level incident wind (like a lift force!). y It follows that the mountain felt the backgound pressure meridional gradient in geostrophic equilibrium with the background wind : Dr P=Ps f y Y Y X 1 h dx dy Dr= p 4XY Y X X x In the linear case: Dr= f h y

33 e) Synoptic and planetary scales A case of lee-cyclogenesis (NCEP Data) This basic mechanism is in part operand during the triggering of lee Cyclogenesis. The lift force therefore needs to be well represented in models

34 e) Synoptic and planetary scales Composites of surface maps keyed to -Dy (NCEP Data, 40 cases out of 8 years) Almost the structure of the cold surges. Patterns affecting cold surge onset and monsoon precipitations (not shown, but very significant over the South-China sea) SFP anomaly (contours, Student index),significant surfacetem perature anomalies (blue=cold, red=warm) Mailler and Lott (009, 010) The peaks of -DY are due high pressures and low temperatures over the Tibet to the North of the Himalayas These structures are few days systematic precusors of the Cold Surges, the cold surges ptoducing high negative values in DX

35 e) Synoptic and planetary scales How can a lateral force supplement the orographic forcing? Ps=cte H P g Dr LP g: Geostrophic wind Dr: Drag Mountain is in green Ps: Surface pressure

36 e) Synoptic and planetary scales How can a lateral force supplement the orographic forcing? H P f ua =G y G ga t P s 0 t P s 0 LP G=-Dr: the force on the atmosphere is opposite to the drag a ageostrophic wind: Equilibrate G via Coriolis Transport mass from left to the right here

37 e) Synoptic and planetary scales How can a lateral force supplement the orographic forcing? H P G t P s 0 a t P s 0 LP G=-Dr: the force on the atmosphere is opposite to the drag a ageostrophic wind: Equilibrate G via Coriolis Transport mass from left to the right here

38 e) Synoptic and planetary scales How can a lateral force supplement the orographic forcing? P H G t P s 0 a t P s 0 LP G=-Dr: the force on the atmosphere is opposite to the drag a ageostrophic wind: Equilibrate G via Coriolis Transport mass from left to the right here

39 e) Synoptic and planetary scales Winter planetary stationnary wave Ridges (ξ<0) Troughs (ξ>0) NCEP reanalysis, géopotentiel à 700hPa, average over winter months