Convection Parameterization

Transcription

1 Convecton Parameterzaton Bob Plant Wth thanks to: all nvolved n COST Acton ES0905! NWP Physcs Lectures 4 and 5 Nanjng Summer School July 2014

2 Outlne Motvaton The mass flux dea Justfcatons for bulk schemes Man ngredents of a typcal bulk scheme: Vertcal structure of convecton Overall amount of convecton Other new deas Convecton parameterzaton p.1/91

3 Motvaton Convecton parameterzaton p.2/91

4 Tropcal T budget Budget wthn ECMWF model Convecton parameterzaton p.3/91

5 Importance of entranment entranment parameter s one of the most senstve aspects of GCMs plot shows varaton n clmate senstvty explaned by varyng dfferent parameters n UM (Knght 2007) Convecton parameterzaton p.4/91

6 The mass flux dea Convecton parameterzaton p.5/91

7 Basc equatons θ θ ΠL = v. θ w w θ + (c e) + Qrad t cp Large-scale forcng produced by modelled advecton Convecton scheme needs to provde the balance to that wth contrbutons to vertcal turbulent transport w θ and net condensaton, c e Analogous equatons for mosture and momentum Convecton parameterzaton p.6/91

8 The am Interactons of convecton and large-scale dynamcs crucal Need for a convectve parameterzaton n GCMs and (most) NWP Assume we are thnkng of a parent model wth grd length 20 to 100km Basc dea: represent effects of a set of hot towers / plumes / convectve clouds wthn the grd box Convecton parameterzaton p.7/91

9 Startng Assumptons Assume that there exsts a meanngful large-scale wthn whch the convectve systems are embedded Assume that the large-scale s well descrbed by the grd box state n the parent model ths s a lttle suspect Am of the parameterzaton s to determne the tendences of grd-box varables due to convecton, gven the grd-box state as nput Convecton parameterzaton p.8/91

10 Startng Pcture Convecton charactersed by ensemble of non-nteractng convectve plumes wthn some area of tolerably unform forcng Indvdual plume equatons formulated n terms of mass flux, M = ρσ w Convecton parameterzaton p.9/91

11 Top hat decomposton splt between convectve updraught and weakly-subsdng envronment updraught and envronment both assumed unform Convecton parameterzaton p.10/91

12 Homogenety n-cloud? w from arcraft data LES dagnoses = tophat representaton captures 90% of the turbulent transport Convecton parameterzaton p.11/91

13 Defnng the mass flux For some varable χ = T, q, ql... χ = σχu + (1 σ)χe where σ s the fractonal area of the updraught. Vertcal flux of a fluctuatng varable: ρw χ = ρσ(wu w)(χu χ) + ρ(1 σ)(we w)(χe χ) For σ 1 and wu w then ρw χ ρσ(wu w)(χu χ) ρσwu (χu χe ) = M(χu χe ) wth M = ρσwu Convecton parameterzaton p.12/91

14 Basc questons Supposng we accept all the above, we stll need to ask How should we formulate the entranment and detranment? e, what s the vertcal structure of the convecton? 2. How should we formulate the closure? e, what s the ampltude of the convectve actvty? 3. Do we really need to make calculatons for every ndvdual plume n the grd box? e, s our parameterzaton practcal and effcent? We consder 3 frst, because the answer has mplcatons for 1 and 2. Convecton parameterzaton p.13/91

15 Do we really need to make calculatons for every ndvdual plume n the grd box? Convecton parameterzaton p.14/91

16 Basc dea of spectral method Group the plumes together nto types defned by a labellng parameter λ In Arakawa and Schubert (1974) ths s the fractonal entranment rate, λ = E/M, but t could be anythng e.g. cloud top heght λ = zt s sometmes used a generalzaton to multple spectral parameters would be trval Convecton parameterzaton p.15/91

17 Basc dea of bulk method Sum over plumes and approxmate ensemble wth a representatve bulk plume Ths can only be reasonable f the plumes do not nteract drectly, only wth ther envronment And f plume equatons are almost lnear n mass flux Summaton over plumes wll recover equatons wth the same form so the sum can be represented as a sngle equvalent plume Convecton parameterzaton p.16/91

18 Mass-flux weghtng We wll use the mass-flux-weghtng operaton (Yana et al. 1973) M χ χbulk = M χbulk s the bulk value of χ produced from an average of the χ for each ndvdual plume Convecton parameterzaton p.17/91

19 Plume equatons ρσ M = E D t M s ρσ s = E s D s + Lρc + ρqr t M q ρσ q = E q D q ρc t M l ρσ l = D l + ρc R t s = c p T + gz s the dry statc energy QR s the radatve heatng rate R s the rate of converson of lqud water to precptaton c s the rate of condensaton Convecton parameterzaton p.18/91

20 Usng the plume equatons Average over the plume lfetme to get rd of / t : M E D =0 M s E s D s + Lρc + ρqr = 0 M q E q D q ρq = 0 M l D l + + ρc + R = 0 Integrate from cloud base zb up to termnatng level zt where the n-cloud buoyancy vanshes Convecton parameterzaton p.19/91

21 Effects on the envronment Takng a mass-flux weghted average, ρχ w M (χ χ) = M(χbulk χ) where M = M Recall that the am s for the equatons to take the same form as the ndvdual plume equatons but now usng bulk varables lke M and χbulk Convecton parameterzaton p.20/91

22 Equvalent bulk plume I Now look at the weghted-averaged plume equatons M E D =0 Msbulk + Lρc + ρqr = 0 Es D s Mqbulk Eq D q ρc = 0 Mlbulk + ρc R = 0 D l The same bulk varables feature here Convecton parameterzaton p.21/91

23 Equvalent bulk plume II M E D =0 Msbulk + Lρc + ρqr = 0 Es D s Mqbulk Eq D q ρc = 0 Mlbulk D l + ρc R = 0 where E = E ; D = D Convecton parameterzaton p.22/91

24 The entranment dlemma E and D encapsulate both the entranment/detranment process for an ndvdual cloud and the spectral dstrbuton of cloud types Is t better to set E and D drectly or to set E and D together wth the dstrbuton of types? Convecton parameterzaton p.23/91

25 Equvalent bulk plume III Msbulk + Lρc + ρqr = 0 Es D s where QR (sbulk, qbulk, lbulk,...) = QR (s, q, l,...) s somethng for the cloud-radaton experts to be conscous about Convecton parameterzaton p.24/91

26 Equvalent bulk plume IV Msbulk Es D s + Lρc + ρqr = 0 Mqbulk ρc = 0 Eq D q Mlbulk D l + ρc R = 0 where c(sbulk, qbulk, lbulk,...) = c (s, q, l,...) R(sbulk, qbulk, lbulk,...) = R (s, q, l,...) s somethng for the mcrophyscs experts to be conscous Convecton parameterzaton p.25/91 about

27 A Note on Mcrophyscs In Arakawa and Schubert 1974, the ran rate s R = C0 M l where C0 s a constant. Hence, R = C0 Mlbulk If C0 were to depend on the plume type then we couldn t wrte R as a functon of the bulk quanttes but would need to know how lbulk s parttoned across the spectrum = A bulk scheme s commtted to crude mcrophyscs But mcrophyscs n any mass-flux parameterzaton has ssues anyway Convecton parameterzaton p.26/91

28 Equvalent bulk plume V M E D =0 Msbulk Es D s + Lρc + ρqr = 0 Mqbulk ρc = 0 Eq D q Mlbulk D l + ρc R = 0 How can we handle these terms? (a) Below the plume tops? (b) At the plume tops? Convecton parameterzaton p.27/91

29 (a) Below the plume tops One opton s to consder all the consttutent plumes to be entranng-only (except for the detranment at cloud top) If D = 0 then D χ = 0 and the problem goes away! Ths s exactly what Arakawa and Schubert dd Convecton parameterzaton p.28/91

30 (a) Below the plume tops If we retan entranng/detranng plumes then we have Dχ Dχχbulk D χ Dχ = M M χ The detranment rate s 6= D.e., t s dfferent from the D that we see n the vertcal mass flux profle equaton and t s dfferent for each n-plume varable = A bulk parameterzaton can only be fully equvalent to a spectral parameterzaton of entranng plumes Convecton parameterzaton p.29/91

31 (b) At the plume tops There are the contrbutons to D χ from plumes the that have reach neutral buoyancy at the current level But the expressons smplfy here because of the neutral buoyancy condton Msbulk Es Db s =0 Mqbulk Eq Db q =0 Mlbulk b Dl =0 so now these equatons use the same D as n the mass flux b, b profle equaton. But what about sb, q l? Convecton parameterzaton p.30/91

32 (b) At the plume tops Because of the neutral buoyancy condton: Lε s = sb = s δ(q q) b l 1 + γεδ γε q = qb = q δ(q q) b l 1 + γεδ ; l = b l where L, ε, γ and δ are thermodynamc functons of the envronment Everythng on the RHS s known n the bulk system, apart from b l b l(z) can only be calculated by ntegratng the plume equatons for a plume that detrans at z = z Convecton parameterzaton p.31/91

33 Key bulk assumpton At the heart of bulk models s an ansatz that the lqud water detraned from each ndvdual plume s gven by the bulk value l = lbulk Yana et al (1973): gross assumpton but needed to close the set of equatons Convecton parameterzaton p.32/91

34 Spectral decomposton of bulk system Output from UM bulk scheme of convecton embedded wthn cold front Construct plume ensemble usng mn M(z) c M (z) wth M plumes c 0 for entranng Convecton parameterzaton p.33/91

35 Spectral decomposton Convecton parameterzaton p.34/91

36 Other transports Contrbutons to D χ from detranment at plume top can be smplfed for s, q and l from the neutral-buoyancy condton (wth l ansatz) But no smplfcaton occurs for other transports (e.g., tracer concentratons, momentum) Needs further ansatze, b χ = χbulk Or decompose bulk plume nto spectrum of plumes Convecton parameterzaton p.35/91

37 Example for passve scalar Passve scalar dstrbuton for bulk and spectral systems From decomposton of ZM outputs (Lawrence and Rasch 2005) Convecton parameterzaton p.36/91

38 Conclusons I A bulk model of plumes does not follow mmedately from averagng over bulk plumes, but requres some extra assumptons Entranment formulaton s a bg ssue In bulk systems, cloud-radaton nteractons have to be estmated usng bulk varables In bulk systems, mcrophyscs has to be calculated usng bulk varables Ths mples very smple, lnearzed mcrophyscs But mcrophyscs s problematc for mass flux methods anyway, owng to non-separaton of σ and w Convecton parameterzaton p.37/91

39 Conclusons II A bulk plume s an entranng/detranng plume that s equvalent to an ensemble of entranng plumes A bulk system needs a gross assumpton that l = lbulk not often recognzed, but relevant when detraned condensate s used as a source term for prognostc representatons of stratform cloud (for example) Detraned condensate from a bulk scheme s an overestmate Bulk schemes are much more effcent, but they do have ther lmtatons Convecton parameterzaton p.38/91