A study of the moist Entropy in Meteorology.

Transcription

1 Workshop on the Atmospheric Modelling 8-10 February, 2011.Toulouse, France. A study of the moist Entropy in Meteorology. Pascal MARQUET (Météo-France. DPrévi / LABO)

2 Contents 1) Motivations : to study and compute the moist Entropy / why? 2) Theoretical results : s = Cste + c pd ln(θ s ) ; with θ s 3) Applications : Strato-cumulus FIRE-I ; [θ l ;θ E ; ] 4) Turbulence : 3D-diagrams non-conservative variables? 5) Conclusions - Outlooks 2

3 Contents 1) Motivations : to study and compute the moist Entropy / why? 2) Theoretical results : s = Cste + c pd ln(θ s ) ; with θ s 3) Applications : Strato-cumulus FIRE-I ; [θ l ;θ E ; ] 4) Turbulence : 3D-diagrams non-conservative variables? 5) Conclusions - Outlooks 3

4 Motivations (see the extended abstract) Work on Available Energy (LMD-Polytechnic school, ). «Exergy» and «Available Enthalpy» : (h h 0 ) T env (s s 0 ) Applications to the African Monsoon (?) ; «Lorenz Cycle» ; Impacts of a 2xCO2 ; Moist Norm but still with no answer to the question of Alan Thorpe (1990) : link Exergy & CAPE? 4

5 Motivations - A. Thorpe (1990) : Exergy & CAPE? T e = Cste Convection : w 2 /2 exergy? t t+dt t t+dt (e k ) in (e k ) out h in, s in W max? h out, s out θ v,env θ v, part θ v,env T e = Cste W max (h out h in ) +T e (s out s in ) [ (e k ) out (e k ) in ] Moist PBL & Turbulence W max = ( h T e s ) (e k ) A steam machine : the maximum shaft work W? B θ = D w D t v, part θ θ v, env w v, env w z D w D t ; 2 w 2 = z 2 D ( w 2 + a D t ( h Tenv s)? z h ) 0 5

6 Motivations There seems to be a need to compute the moist entropy But this has already be done! why another approach? Hauf & Höller (87), Marquet (93), Emanuel (94) : a weighted sum of partial entropies : but s r, c r, θ sr variables! s r, c r, θ sr constants Entering all the r t, q t et q d within the ln(...)? then θ s would becomes a true synonym of Entropy, even for varying r t q t q d... 6

7 Contents 1) Motivations : to study and compute the moist Entropy / why? 2) Theoretical results : s = Cste + c pd ln(θ s ) ; with θ s Marquet (QJRMS, 2011) 3) Applications : Strato-cumulus FIRE-I ; [θ l ;θ E ; ] 4) Turbulence : 3D-diagrams non-conservative variables? 5) Conclusions - Outlooks 7

8 Computations of : s θ s θ s complex? In fact, similar to HH87, M93 ou E94, except... 8

9 Computations of : s θ s The leading term : Generalization / A mixed of : absolute values of partial entropies The 3 rd Law 9

10 Contents 1) Motivations : to study and compute the moist Entropy / why? 2) Theoretical results : s = Cste + c pd ln(θ s ) ; with θ s 3) Applications : Strato-cumulus FIRE-I ; [θ l ;θ E ; ] A new formula : is there new consequences? is there new physical properties? if yes, a need of validations against measurements! 4) Turbulence : 3D-diagrams non-conservative variables? 5) Conclusions - Outlooks 10

11 Applications / FIRE-I : [ θ l ; q t ; q l ] RF03B-hom. Data flights NASA S. De Roode 10 K 6 g/kg θ l q t q l Same results as Roode & Wang (2007) clear-air cloud (entrain. region) Large jumps in θ l and q t (entrain. region) 11

12 Applications / FIRE-I : [ θ l ; q t ; q l ] RF03B-hom. θ l q t Unexpected results q l constant with z clear-air = cloud! for No jump in! 12

13 FIRE-I 03B 02B-04B-08B : OK + 3 other Sc cases : OK constant profiles for No (or small) jump (top-pbl) 13

14 Comparisons [θ l ;θ E ; ]? différent from all other Pot. Temp.! E94 TC81 GB81 L68 HH87 M93 θ E 2/3-1/3 between θ l & θ E θ l 14 K θ l 14

15 Contents 1) Motivations : to study and compute the moist Entropy / why? 2) Theoretical results : s = Cste + c pd ln(θ s ) ; with θ s 3) Applications : Strato-cumulus FIRE-I ; [θ l ;θ E ; ] 4) Turbulence : 3D-diagrams non-conservative variables? 5) Conclusions - Outlooks 15

16 Turbulent Fluxes : (θ l ; q t ) variables? θ s Approximated formula for the flux of moist entropy : Isentropic diffusion The fluxes of Betts variables would be linked (proportional) in the «moist isentropic case»? 16

17 Turbulent Fluxes : ( c pd T + φ ; L v q v ; L v q l ) variables? Flux de S m But how to go further? What are the links between entropy and turbulence? A crude idea: to replace S or θ l by S m or? But what about q t??? 17

18 z Thermodynamic Diagrams z Curve seen in profile! z θ l d ln = d ln(θ l ) + Λ dq t = θ l exp(λ q t ) d ln(θ X ) = d ln(θ l ) dq t /Λ q t θ l θ l θ X = θ l exp( q t /Λ) Maximum jump in θ X q t θ l Slope d q t /dθ l = 1 / (Λ θ l ) q t θ X 3D-Diagram: «conservatives» variables Mininum jump in Pascal MARQUET (june 2010) 18

19 Turbulents fluxes: the [ ; θ X ] variables? z = θ l exp(λ q t ) θ X = θ l exp( q t /Λ) θ l Isentropic mixing in : reduce the departure terms (grey lines) a relaxation? Mixing in θ X : other diabatic or irreversible physical processes (radiation, ) q t θ X A wish to switch to non-conservatives (natural) variables (θ, q v, q l )? 19

20 α = L v /(c pd T) Λ iso-q t in violet α q l Just like 2 slantwise roofs... q v θ l iso-θ l in green ln(θ l ) = ln(θ ) (α +Λ) q l q t =q v +q l ln = ln(θ ) + Λ q v α q l The iso- in red q v = 0 q l = 0 Pascal MARQUET (July 2010) A 3D-Diagram with the «non-conservatives» variables (θ, q v, q l ) : but how to represent θ l, q t,? θ The line iso - θ l iso - q t 20 20

21 α q l q t q v isentropes α = L v /(c pd T) Λ ln = ln(θ ) + Λ q v α q l Clear SBL Inversion & clear-air cloud The points are not scattered at random! Is it interesting for moist turbulence? q sat (T) is missing go from θ to T! Pascal MARQUET (January 2011) A 3D-diagram with nonconservatives variables Application : FIRE-I 03B? θ l clear q l = 0 cloud q l 0 along iso-(θ l, q t ) θ dry clear-air above the inversion 21 21

22 ln = (R d /c pd ) ln(p/p 0 ) + ln(t ) + Λ q v α q l T-ln(p) emagram FIRE-I / RF03B α = L v /(c pd T) Λ q v α q l Continuous + angular points! Proposition : (1) switch from black to red points define (T)* q v (on plane q l =0) ; (2) Mixing in (T)* q v with iso- (??) ; (3) If saturation: q l 0 => (T, q v, q l )(z) (T)* = T exp( α q l ) Pascal MARQUET (January 2011) A 3D-diagram with nonconservatives variables z p (q v ) sat (T,p) z p z p Go from θ to T T Slope of red lines : d(α q l )/dt = 1/T (with constant other terms). Unsolved problems : Be careful : homogeneous Sc N=100%? And what about : N<100 %? An the sub-grid variability: σ s? 22 22

23 Contents 1) Motivations : to study and compute the moist Entropy / why? 2) Theoretical results : s = Cste + c pd ln(θ s ) ; with θ s 3) Applications : Strato-cumulus FIRE-I ; [θ l ;θ E ; ] 4) Turbulence : 3D-diagrams non-conservative variables? 5) Conclusions - Outlooks : I will not show. 23

24 L.E.S. EUCAARI J.L. Brengier O. Thouron r l θ l r t 24

25 Radio Soundings : Bermuda θ w θ w Alignment! alignment

26 No influence at all of ( T r, p r, q r ) on s and θ s! 26

27 850 hpa 2D fields? (French Anasyg-Presyg) = 2K et 1g/kg θ w θ θ X q vap 27

28 Contents 1) Motivations : to study and compute the moist Entropy / why? 2) Theoretical results : s = Cste + c pd ln(θ s ) ; with θ s 3) Applications : Strato-cumulus FIRE-I ; [θ l ;θ E ; ] 4) Turbulence : 3D-diagrams non-conservative variables? 5) Conclusions - Outlooks : I will finish by. 28

29 Conclusions - Outlooks Get an analytical formulation for the moist entropy θ s Validations against observations (FIRE, EPIC, + R.S.) Paper accepted: QJRMS (2011) Sc analyses : global & local budget of (h, s) / IPCC? Improve Setup : LES CRM SCM NWP / GCM (Euclipse) NWP & GCM simulations : applications = moist turbulence θ X or for horizontal = front gradients : max in ; min in θ X θ l θ What about links ( s, θ s ) CAPE? Shallow? Deep? J. F. Geleyn + my own speculations : links Exergy S.V.? Q.G.? P.V.? 29

30 Thanks a lot for your attention Questions? J. W. GIBBS «A method of geometrical representation of the thermodynamic properties of substance by means of surfaces» - Gibbs (1873) 30