Parameterisation of Cumulus Convection

Transcription

1 Parametersaton of Cmls Convecton Dmtr V. Mronov German Weather Servce, Research and Development, FE14, Offenbach am Man, Germany COSMO-CLM Tranng Corse, Langen, Germany, Febrary 2012

2 Otlne Cmls convecton and the need for parametersatons Convecton parametersaton schemes Mass-flx schemes The COSMO-model convecton parametersaton scheme(s) Crtcal Isses

3 Phenomenology Deep Cmls (ITCZ) A great varety of convectve clods far and wde Shallow Cmls (Trade wnds) Strats, stratocmls (Sb-tropcs) P B L

4 Phenomenology (cont d) Strats Broken stratocmls Cmls Berln-St. Petersbrg, 28 Agst 2007.

5 Phenomenology (cont d) Stratocmls Cmls Berln-St. Petersbrg, 28 Agst 2007.

6 Phenomenology (cont d) Spercell near Alvo, Nebraska, USA, 13 Jne (

7 Phenomenology (cont d) Spercell off Brlegh, Astrala, 31 December (

8 The Need for a Parametersaton Convecton s a sb-grd scale phenomenon. It cannot be explctly compted (resolved) by an atmospherc model. Hence, t shold be parametersed. x y

9 Recall... what a convecton parametersaton shold do (t s not a mystery, t s jst a model) Transport eqaton for a generc qantty ( ) x S x x t =... SGS flx dvergence Sorce terms Splttng of the SGS flx dvergence and of the sorce term ( ) other x conv x other conv S S x x x t =...

10 What a convecton parametersaton shold do (cont d) Temperatre and specfc-hmdty eqatons T t ( T ) x T = x conv T x trb R x rad L( c e) conv L( c e) grd scale q t ( q) x q = x conv q x trb ( e c) conv ( e c) grdscale Here, L s the specfc heat of vaporsaton, e s the rate of evaporaton, and c s the rate of condensaton. Apart from mxng (redstrbton of heat and mostre), convecton prodces precptaton

11 Convecton Parametersaton Schemes Mostre convergence schemes (e.g. Ko 1965, 1974) Convectve adjstment schemes (e.g. Betts 1986, Betts and Mller 1986) Mass-flx schemes (e.g. Arakawa and Schbert 1974; Bogealt 1985; Tedtke 1989; Gregory and Rowntree 1990; Kan and Frtsch, 1990, 1993, Kan 2004; Emanel 2001; Bechtold et al. 2001, 2004)

12 Mass-Flx Schemes. Basc Featres A trple top-hat decomposton, =1, = e d e e d d a a a a a a, d and e refer to the pdraght, downdraght and the envronment, respectvely, and a s the fractonal area coverage. In terms of the probabltes (δ s the Drac delta fncton) Vertcal flx of a flctatng qantty ). ( ) ( ) ( ) (, e e d d e e d d P P P P P P P = = δ δ δ ), ( ) ( ) ( ) )( ( ) )( ( ) )( ( M M M w w a w w a w w a w e e d d e e e d d d = = ρ ρ ρ ρ s the pdraght mass flx (smlarly for the downdraght and for the envronment). ( w) w a M = ρ

13 Mass-Flx Schemes. Basc Featres (cont d) A top-hat representaton of a flctatng qantty Updraght Only coherent top-hat part of the sgnal s acconted for Envronment After M. Köhler (2005)

14 Mass-Flx Schemes. Basc Featres (cont d) Assmpton 1: a mean over the envronment s eqal to to a horzontal mean (over a grd box), 1. 1, << << = d e a and a Assmpton 2: convecton s n a qas-steady state, ( ). 0, 0 = = a z w t a z w t Then, vertcal flx of a flctatng qantty n mass-flx approxmaton s gven by [ ] M M M M w d d d ) ( 1 = ρ

15 Mass-Flx Schemes. Basc Featres (cont d) The eqatons for convectve pdraghts ( ) ( ) ( ),,,, p G c D l z l M c D q q E z q M c L D s s E z s M D E z M ρ ρ ρ ρ = = = = where s s the dry statc energy, q s the specfc hmdty, l s the specfc clod condensate content, E and D are the rates of mass entranment and detranment per nt length, c s the rate of condensaton n the pdraghts, and G p s the rate of converson from clod condensate to precptaton.

16 The COSMO-Model Convecton Parametersaton Schemes Basc Namelst settng: lphys=.true., lconv=.true. Namelst settng: type_conv=0. Tedtke (1989) mass-flx scheme, defalt n COSMO-EU (called every 4th tme step,.e. every 264 s). Namelst settng: type_conv=1. Kan and Frtsch (1990) mass-flx scheme, optonal n COSMO-EU. Namelst settng: type_conv=3. Shallow convecton scheme [bascally, a smplfed Tedtke (1989) scheme that treats shallow non-precptaton convecton only and ncorporates a nmber of rather crde assmptons, e.g. on the convecton vertcal extent], defalt n COSMO-DE (called every 10th tme step,.e. every 250 s). The ECMWF-IFS scheme (Bechtold 2010) s mplemented nto GME (c/o Krstna Fröhlch); ths opton (type_conv=2) s not yet avalable n the COSMO model (Peter Brockhas et al., Ulrch Schättler).

17 The Tedtke (1989) Mass-Flx Convecton Scheme A set of ordnary dfferental eqatons (n z) for convectve pdraghts and downdraghts s solved (entranng-detranng plme model) Shallow, penetratve and md-level convecton are dscrmnated Trblent and organsed entranment and detranment are consdered Trblent entranment and detranment: E =εm and D = δm, ε and δ beng constants that are dfferent for dfferent types of convecton (smlarly for downdraghts) Organsed entranment s proportonal to the large-scale mostre convergence (dv of resolved scale mostre flx) and s appled n the lower part of convectve clod p to the level of strongest vertcal ascent Organsed detranment s appled above the clod top, where clod condensate evaporates nstantaneosly (snce Jly 2008, detraned clod condensate s collected and passed to other COSMO-model rotnes for frther processng) Convectve clod base and convectve clod top are determned sng the parcel method, a test parcel pertrbed wth respect to ts boyancy orgnates near the srface Updraght mass flx at the clod base M b s lnked to the sb-clod layer mostre convergence (dv of the SGS and resolved scale mostre flxes ntegrated from the srface to the clod base) Downdraght mass flx at the level of free snkng (where the downdraght orgnates) s proportonal to M b No mxed phase clod condensate s ether water or ce dependng on whether the temperatre s above or below the freezng pont (mxed phase s ntrodced n Jly 2008) Hghly smplfed mcrophyscs: G p l (the rate of converson from clod condensate to precptaton s proportonal to the amont of clod condensate) Evaporaton of convectve precptaton n the sb-clod layer s consdered Fnally, convectve tendences n T, q, and v, and convectve precptaton rate are compted

18 The Tedtke (1989) Mass-Flx Convecton Scheme (cont d) Organsed detranment of clod ar Converson of clod condensate to precptaton Organsed entranment of envronment ar de to mostre convergence Trblent detranment of clod ar Trblent entranment of envronment ar Assmptons of the T89 scheme are many and vared! Mostre convergence n the sb-clod layer Evaporaton of precptaton n the sb-clod layer

19 Crtcal Isses Possble doble-contng of energy-contanng scales Drnal cycle of convecton Coplng of cmls convecton scheme wth other physcal parametersaton schemes of the COSMO model...

20 Possble doble-contng of energy-contanng scales Convectve precptaton: model vs. observatons Convectve precptaton Possble doble contng de to the assmpton a <<1 Precptaton over Germany, mean over Aprl COSMO-EU (ca. 7 km mesh sze) vs. observatons. Lnes - total precptaton, hatched areas - convectve precptaton.

21 Possble doble-contng of energy-contanng scales (cont d) SON 2007 DJF Mxed phase ntrodced MAM 2008 JJA 2008 Precptaton over Germany, September 2007 throgh Agst COSMO-EU (ca. 7 km mesh sze) vs. observatons. Lnes - total precptaton, hatched areas - convectve precptaton. [Mxed-phase snce Jly 2008.]

22 Possble doble-contng of energy-contanng scales (cont d) SON 2008 DJF MAM 2009 JJA 2009 Precptaton over Germany, September 2008 throgh Agst COSMO-EU (ca. 7 km mesh sze) vs. observatons. Lnes - total precptaton, hatched areas - convectve precptaton.

25 Drnal cycle of convecton Srface latent heat flx Srface sensble heat flx Precptaton Typcal daly evolton of srface latent (thck sold lne) and sensble (thn sold lne) heat flx, and precptaton (dotted lne) drng a mdlattde or tropcal smmer day over reasonably hmd land (from Bechtold 2010)

26 Drnal cycle of convecton (cont d) Observatons precptaton (mm/h) GME Maxmm of convectve actvty (precptaton) closely follows srface flxes and occrs too early, possbly de to d/dt=0 ( beng a qantty treated by convecton scheme) local tme (h) Drnal cycle of precptaton n the Rondôna area n Febrary. GME forecasts vs. LBA 1999 observatonal data (Slva Das et al. 2002). The model crves show area-mean vales, emprcal crve shows pont measrements. Both nmercal and emprcal crves represent monthly-mean vales.

27 Coplng of convecton scheme wth other parametersaton schemes Inconsstent treatment of fractonal clod cover, convectve clod cover s nsenstve to mxng rate Trblence Dvergence of SGS flxes (mxng), fractonal clod cover sng statstcal clod scheme No nteracton between trblent and convectve mxng, no resolton senstvty of convectve mxng SGS Clod Cover Fractonal clod cover sng relatve hmdty scheme Cmls Convecton Dvergence of SGS flxes (mxng), convectve precptaton, fractonal cover of convectve clods Mcrophyscs Grd-scale precptaton, resolved scale amont of clod condensate Althogh a feedback of evaporaton/condensaton de to convecton on the resolved scale amont of clod condensate s now ntrodced, a flly consstent treatment s not yet acheved. Grd-Scale Satraton Adjstment Evaporaton/condensaton sng resolved scale qanttes No nteracton between grd-scale and convectve precptaton

28 Otlook Exstng convecton schemes s dffclt to mprove... However, a better coplng of cmls convecton scheme wth other parametersaton schemes of the COSMO model shold be attempted Longer term prospects Relax crcal assmptons of the exstng mass-flx schemes (no tme-rate-of-change terms, small area fracton of convectve clods); the model of Lappen and Randall (2001) holds promse Acheve a nfed descrpton of shallow-convecton and trblence (see Mronov 2009, for dscsson) EU COST Acton ES0905 Basc Concepts for Convecton Parameterzaton n Weather Forecast and Clmate Models (

29 References Arakawa, A., 2004: The cmls parameterzaton problem: past, present, and ftre. J. Clmate, 17, Bechtold, P., 2010: Atmospherc most convecton. ECMWF Lectre Notes, 77 pp. ( Emanel, K. A., 1994: Atmospherc Convecton. Oxford Unv. Press, Oxford, 580 pp. Fedorovch, E., R. Rotnno, and B. Stevens (Eds.), 2004: Atmospherc Trblence and Mesoscale Meteorology. Cambrdge Unv. Press, Cambrdge, 280 pp. Frank, W. M., 1983: The cmls parameterzaton problem. Mon. Weather Rev., 111, Hoze, R. A., 1993: Clod Dynamcs. Academc Press, San Dego, etc., 573 pp. Mronov, D. V., 2009: Trblence n the lower troposphere: second-order closre and mass-flx modellng frameworks. Interdscplnary Aspects of Trblence, Lect. Notes Phys., 756, W. Hllebrandt and F. Kpka, Eds., Sprnger-Verlag, Berln, Hedelberg, Plant, R. S., 2010: A revew of the theoretcal bass for blk mass flx convectve parameterzaton. Atmos. Chem. Phys., 10, Smth, R. K., 2000: The role of cmls convecton n hrrcanes and ts representaton n hrrcane models. Rev. Geophys., 38, Stensrd, D. J., 2007: Parameterzaton Schemes: Keys to Understandng Nmercal Weather Predcton Models. Cambrdge Unv. Press, Cambrdge, 478 pp. Stevens, B., 2005: Atmospherc most convecton. Ann. Rev. Earth Planet. Sc., 33, Tedtke, M., 1988: The Parameterzaton of Most Processes. Part 2: Parameterzaton of Cmls Convecton. Meteorologcal Tranng Corse, Lectre Seres, Eropean Centre for Medm-Range Weather Forecasts, Readng, U.K., 78 pp.

30 References (cont d) Arakawa, A., and W. H. Schbert, 1974: Interacton of a cmls clod ensemble wth the large-scale envronment, Part I. J. Atmos. Sc., 31, Bechtold, P., E. Bazle, F. Gchard, P. Mascart, and E. Rchard, 2001: A mass-flx convecton scheme for regonal and global models. Qart. J. Roy. Meteorol. Soc., 127, Bechtold, P., J.-P. Chaborea, A. Beljaars, A. K. Betts, M. Köhler, M. Mller, and J.-L. Redelsperger, 2004: The smlaton of the drnal cycle of convectve precptaton over land n a global model. Qart. J. Roy. Meteorol. Soc., 130, Betts, A. K., 1986: A new convectve adjstment scheme. Part I: Observatonal and theoretcal bass. Non-precptatng cmls convecton and ts parameterzaton. Qart. J. Roy. Meteorol. Soc., 112, Betts, A. K., and M. J. Mller, 1986: A new convectve adjstment scheme. Part II: Sngle colmn tests sng GATE wave, BOME, ATE and arctc ar-mass data sets. Qart. J. Roy. Meteorol. Soc., 112, Bogealt, P., 1985: A smple parameterzaton of the large-scale effects of cmls convecton. Mon. Weather Rev., 113, Emanel, K. A., 2001: A scheme for representng cmls convecton n large-scale models. J. Atmos. Sc., 48, Gregory, D., and P. R. Rowntree, 1990: A mass flx convecton scheme wth representaton of clod ensemble characterstcs and stablty-dependent closre. Mon. Weather Rev., 118, Kan, J. S., 2004: The Kan-Frtsch convecton parameterzaton: an pdate. J. Appl. Meteorol., 43, Kan, J. S., and J. M. Frtsch, 1990: A one-dmensonal entranng/detranng plme model and ts applcaton n convectve parameterzaton. J. Atmos. Sc., 47, Kan, J. S., and J. M. Frtsch, 1993: Convectve parameterzaton for mesoscale models: the Kan-Frtsch scheme. The Representaton of Cmls Convecton n Nmercal Models, Meteorol. Monogr. No. 24, Amer. Meteor. Soc., Ko, H. L., 1965: On formaton and ntensfcaton of tropcal cyclones throgh latent heat release by cmls convecton. J. Atmos. Sc., 22, Ko, H. L., 1974: Frther stdes of the parameterzaton of the nflence of cmls convecton on large-scale flow. J. Atmos. Sc., 31, Tedtke, M., 1989: A comprehensve mass flx scheme for cmls parameterzaton n large-scale models. Mon. Weather Rev., 117,

31 Thanks for yor attenton! COSMO-CLM Tranng Corse, Langen, Germany, Febrary 2012

32 Geändertes Tedtke-Konvektonsschema Detraned-Wolkenwasser nd Detraned-Wolkenes werden als Tendenzen von q_c nd q_ den anderen Parametrserngsschemata übergeben Wasser-Es Mschng exstert m Temperatrberech zwschen 0 C nd -23 C Verbesserte Kopplng des Konvektonsschemas mt den anderen Parametrserngsschemata Hochrechende Konvekton wrd etwas gebremst

34 Possble doble-contng of energy-contanng scales (cont d) SON 2008 DJF Precptaton over Germany, September 2008 throgh Febrary COSMO-EU (ca. 7 km mesh sze) vs. observatons. Lnes - total precptaton, hatched areas - convectve precptaton.

35 Possble doble-contng of energy-contanng scales (cont d) JJA 2007 JJA 2008 Precptaton over Germany, JJA 2007 verss JJA COSMO-EU (ca. 7 km mesh sze) vs. observatons. Lnes - total precptaton, hatched areas - convectve precptaton. In JJA 2008 Mod < Obs? (*) Changes were ntrodced nto the T89 scheme n Jly (*) Smmer 2008 was dry.

36 Parametersaton of Cmls Convecton Dmtr V. Mronov German Weather Servce, Research and Development, FE14, Offenbach am Man, Germany COSMO-CLM Tranng Corse Langen, Germany, Febrary 2012

37 Thanks for yor attenton!