Why do moisture convergence deep convection schemes work for more scales than those they were in principle designed for?

Transcription

1 Why do moisture onvergene deep onvetion shemes work for more sales than those they were in priniple designed for? J.-F. Geleyn 1 and J.-M. Piriou 2 1 Czeh HydroMeteorologial Institute, Prague, Czeh Republi, on leave of absene from Météo-Frane 2 Centre National de Reherhes Météorologiques, Météo-Frane, Toulouse, Frane I) Introdution The title of this note is intentionally provoative, but it reflets two underlying realities. First of all it stems out of the ontent of a mail written (on 12/01/2004, personal ommuniation) by Philippe Bougeault (who proposed twenty years ago the first operational deep onvetive parameterisation that ombined a mass-flux approah with a single-loud profile and a Kuo-type losure, Bougeault (1985)) and that will be reprodued (after translation) here. I was well onsious about this limitation (authors note: of the moisture onvergene losure) in 1985, but the problem is that I mostly wanted to fit GATE data, where there is no orrelation between CAPE and rainfall, while there is a strong orrelation between moisture onvergene and rainfall. But, as Mapes rightly says, the latter does not guarantee a ausal link beause one might mix ause and onsequene. But, sine it works on this basis at Meteo-Frane as well as at ECMWF for 20 years, this annot be that wrong either! Seond, and prolonging the ideas expressed by Mapes (1997), it is our opinion that the heavy debate about whih measure of Quasi-Equilibrium (QE thereafter) is the most appropriate one for any parameterisation sheme s losure (loud work funtion, CAPE-CIN, moisture onvergene, ) is illplaed and reflets a wrong hoie of priority. We believe that future parameterisation shemes will put this question to the seond rank and first address a far more fundamental one. The aim of this note is thus to introdue this hange of emphasis and to explore some traks about how to onretise it without throwing away muh of the progress that deep onvetive parameterisation made in the past twenty to thirty years on others aspets. For this reason, our referene tool, when needed, will be the urrent operational version of the Bougeault sheme. For differenes with the 1985 published version, the reader is referred to Gerard and Geleyn (2005). In Setion 2 the basi onepts leading to the mass flux approah and to its above-mentioned ombination with a single asent and a moisture onvergene losure will be realled. Setion 3 will be a short introdution on ontroversies around losure and QE issues. In Setion 4 we shall introdue our own searh of traks meant to go around the underlying problems (those of the basi analysis by Mapes), before a short onluding Setion 5. II) Bougeault s mass-flux approah and its partiularities We start from the following priniples: any deep-onvetive parameterisation requires some knowledge of the host model s resolved tendenies for its losure; given the sales we are targeting at, we must parameterise in an hydrostati-type framework an essentially non-hydrostati phenomenon (the integral link between pressure and geopotential annot be the same for the environment and the loud if they have the same basis and top); parameterised onvetion is basially intermittent at a given grid-point and we must aount for that fat (onditional ativity); 47

2 most importantly, while visible onvetion appears like a loal auto-organised proess, its invisible onditions of existene and bak-influenes on the basi flow are very muh of a large-sale type. Hene, even if parameterisation shemes look at first glane like being built to maintain the orret loal vertial gradients of temperature and humidity, we must onsider that their main role in the host model is to ultimately interat with the intensity and with the horizontal sale of larger-sale dynamial adjustment motions, up to those of the Hadley ell in ase of the ITCZ. The need to establish this distintion is emphasised by tropial observations (Fig. 1): while the onvetively ative areas are haraterised by unstable profiles (the loal return to neutrality is all but instantaneous), the averaged tropial situation is hardly favourable to a global onvetive ativity (the time-rate of return to neutrality annot therefore be ditated only by the intensity of loal imbalanes). Figure 1: Tephigrams of a GATE sounding (left) and of the averaged tropial state (right). CAPE being proportional to the area on the right of the most right urve but older than the warmest point below on the urve next to the left, one sees a lot of onditional instability (of the first kind ) in the perturbed ase (left) and relatively little in the mean one (right). We now look at the most basi version of the single-asent mass-flux framework, obtained under the hypothesis (i) of steady loud-asent behaviour and (ii) of negligible updraft area: ψ = t CV M = D E M ψ = E ( ψ ψ ) [ M ( ψ ψ )] where the first equation expresses the sole onvetive tendeny with ψ a generi notation for any onservative property, M represents the mass-flux expressed in units of a negative omega vertial veloity, D and E are respetively the detrainment and entrainment rates expressed in inverse time units. The subsript marks the loud-asent speifi properties and the averaging sign the host model resolved ( large-sale (LS)) values. We don t address here the question of deriving an expression for ψ. So, assuming that ψ has been omputed by some existing method, the losure problem beomes that of expressing two out of the 48

3 three quantities M, D and E. In Bougeault (1985) the approah is somewhat different and an be symbolised (on the basis of the same notations) as follows: dψ = ω dt LS ψ M ψ + D.( ψ ψ ) g Ψ g M h ψ D E but = 0 D ; M = E ( ) ψ ψ dt CV q q q M = LS g ( Closure) ω where the braketed terms of the first equation orrespond to the full RHS of the first equation of the previous set, the seond equation of the previous set has been replaed by an integral onstraint on a now uniform detrainment rate and the losure indeed expresses the loal onsumption (LHS) of the total moisture onvergene (RHS). Jψ represents the non-onvetive sub-grid sale fluxes (turbulent ones in general) and, for the sake of simpliity, horizontal advetion has been omitted. Basially, for the onvetive parameterisation alone, the straight link between M, D and E has been replaed by a rule of ompensation between onvetive motions and the turbulent part of their feeding. This has the important onsequene that the ω LS +M residual value (what the large sale feels as effetive vertial motion) reates terms that are in balane with all loal motions while, at steady state, the ontrolling moisture budget beomes independent of this effetive vertial motion: q D.( q q ) g. This is in essene the way in whih the basi Bougeault sheme tries to make the above-mentioned ruial distintion (illustrated by Figure 1) and probably one of the main reasons of its long-lasting value. Indeed all improvements made later to the sheme never touhed this ruial point. But we must also point out that the assoiated advantage bears in itself its own limitations, beause it is obtained only under the too restritive onditions of (a) loud stationary behaviour, (b) no possible storage or destorage of moisture from one time step to the next and () independene of the moisture soure from loal onvetive ativity. Ψ III) Some ontroversies and their link with this note As any phenomenon being in quasi-equilibrium with its environment -at least at some sales-, deep onvetion needs both a dissipative mehanism (frition) and a self-enhaning-type ativation. Conerning the latter, two theories (CISK for Conditional Instability of the Seond Kind & WISHE for Wind Indued Surfae Heat Exhange) have been fighting for reognition in the past twenty years. We shall here limit ourselves to the stati view of the problem (already ompliated enough), therefore without referene to wave propagation arguments. The CISK approah is to say ondensation buoyany updraft motion surfae pressure drop low level onvergene more moisture ondensation, but the WISHE advoates then ask Where does the moisture omes from?. The WISH approah is to say ondensation + asent balaned profile maintenane sinking in dry regions balaned by radiation need of a return flow stronger wind leading to more evaporation more available moisture ondensation + asent, but the CISK advoates then ask What determines the balaned profile?. 49

4 In fat the truth seems to be situation- and sale-dependent, but there is an important indued differene in the link between what we named earlier the visible and invisible parts of the onvetive irulations. In the CISK ase, onvetion drives the large-sale irulation while, in the WISHE ase, onvetion ontrols the large-sale irulation. This brings us bak to the question of the separation between loal and larger-sale properties of a given parameterisation sheme. Experimentally it an be shown (Geleyn and Rohas, 1987) that the Bougeault sheme, although having a losure assumption learly of the CISK type, an have both CISK and WISHE behaviours, something surely related to our previous remark about the virtue of replaing the link between M, D and E by a rule of ompensation. Given this reassuring pratial result and sine, when oming to parameterisation issues, the CISK/WISHE ontroversy boils down to something we already announed as of seond importane, it is time to ome to the seond and more reent ontroversy, about the nature and role of QE in understanding and parameterising deep onvetion. Historially speaking, the evolution of the QE onept is roughly the following (f. Mapes, 1997): whatever feedbak and ausality might be at work, it was realised quite early that QE is verified at large sales but not neessarily at sales below; studying the phenomenology of onvetion did lead to the mass-flux onept that helped to odify the issues around QE (Arakawa and Shubert, 1974); this shifted the old problem of onvetive losure from budgets to omplex questions about the dynamis of onvetive irulations; but the (likely misleading) answer was to replae a tratable question whih onvetive louds are likely to develop in a given environment and whih feedbak do they have on this environment? by a more diffiult one whih are the quantities that QE onvetion leaves unhanged?. Beside that last issue, there is also the problem that QE is not onsidered under the same angle of view depending whether one prefers the CISK or WISHE theory. In the CISK ase, onvetive irulations are determining the larger-sale vertial motions that in turn fore onvetion. In the WISHE ase, only the residual aspets matter (weight and ounter-weight motions need a small additional push orresponding to the targeted additional transport, if we take a mehanial analogy). All this giving the impression that the QE onept has been over-used and/or over-interpreted, it is not surprising that some anti-qe thinking started to appear. Mapes (2003) synthesises it as follows: sales are not separable sine the invisible part of onvetion is at the sale of the Rossby radius of deformation; foring and answer are not really separable either (even if we may add that the return flow must be aounted for at the grid-box sale in any parameterisation sheme); there is no under-law of onvetive regions dynamis that aggregates loal behaviours to a simple balane. We shall see later how to try and onvert these negative statements into some positive proposals, but let us mention here that this way to bring bak QE to its simplest expression indiretly onfirms some impossibility to arbitrate between CISK and WISHE ideas. Indeed, following Le Châtelier s hemial rule, if onvetive heating follows ooling by adiabati asent (somehow equivalent to the ontrol role of onvetion) the resulting effet would be ooling but if onvetive heating preedes ooling by adiabati asent (somehow equivalent to the driving role of onvetion) the resulting effet would be heating. Testing this on the basis of statistial observed differenes between ative and non-ative periods at some tropial loations however shows onfliting results (see Figure 2, adapted from Mapes (1997)). 50

5 Figure 2: Left, ~300 Venezuelian sounding (Betts, 1974); right, TOGA-COARE experiment. The left urves of both diagrams represent the differene between onvetive and non-onvetive periods in terms of averaged temperatures. One sees that, away from the PBL where turbulene might bias the results, the trend is ambiguous. IV) A possible path to revise the basi parameterisation onepts If believing in the need for a new perspetive, Figure 3, also adapted from Mapes (1997), shows how to link the hanges in our nature s understanding to hanges in modelling paradigms. Figure 3: Top row, nature s understanding; bottom row, parameterisation shemes boundary hoies. Left olumn, impossible (?) problemati; right olumn, path not yet enough explored. A first immediate onsequene is that there is an important intermediate result that is missing (in the physial sense sine there is always a mathematial equivalent) in urrent deep onvetive parameterisation shemes: the vertial distribution of the ondensation rate inside the loud-asent. Let us all it BCC (Bulk Convetive Condensation) and remark that, if we make it an obliged path for parameterisation alulations, (A) the moist-dry separation of Fig. 3 beomes far easier to trak and (B) the distintion between resolved and onvetive types of preipitation may be ironed out via an appropriate addition of both forms of ondensation before other omputations relying on this quantity. 51

6 This mention of the large-sale-type preipitations (linked to negative large sale ω LS ) brings us to the question of the representativity of the large-sale vertial veloity for the parameterisation of subgrid sale ondensation. Let us go bak to the first equation of Bougeault s interpretation of the massflux onept. In deep onvetive onditions the absolute value of M will be slightly greater than that of ω LS and both will be muh bigger than the absolute value of the environmental vertial veloity ω e =ω LS +M. In other words, the omputed large-sale vertial veloity is just the average of the (rare but intense) loud asents and of a slightly sinking environment everywhere. Hene the large sale vertial advetion term is dynamially meaningless (but model-wise unavoidable) and has to be ompensated by a good estimate of the mass flux, slightly bigger thanks to surfae evaporation. Thus, if QE is doubtful, the mass-flux parameterisation shemes should not use the diagnosed large-sale vertial veloity as input, to avoid the risk of a double ounting or of an unontrolled feedbak loop. But what is then left as possible input for the losure assumption? Basially we have CAPE (Convetive Available Potential Energy), CIN (Convetive INhibition energy) and moisture onvergene (the good old onept introdued by Kuo (1965) in order to get rid of the onvetive adjustment framework and that still shows some usefulness when skilfully used, f. Setion 2). If we ome bak to our new BCC goal, there is an obvious link with moisture onvergene but one that ertainly should not lead to identity. Hene the idea to find a moisture availability that goes bak to moisture onvergene in the ideal ase of fulfilled QE but that also enompasses the CAPE and CIN information in the more general ase of an evolving behaviour of onvetive ativity. But we may even go further in the way to eradiate hidden QE thinking from the design of parameterisation shemes if we deide to relax the first hypothesis of the basi mass-flux equations, i.e. the one about steady loud-asent behaviour. For reasons that would be too long to develop here, this beomes possible if the parameterisation sheme is organised around the provision of BCC to further alulations, this losing a hopefully virtuous irle. V) Conlusion The ideas expressed in Setion 4 are for the time being not yet fully onretised or tested. There are however enouraging signs that they may lead to a positive evolution of deep onvetion parameterisation. Furthermore they are not ontraditing what was the answer to our title question, namely that the link between moisture onvergene and onvetive rainfall is strong enough to allow shemes arefully based on suh a losure to be robust and appliable even when the balane is less aurate. Hene we may onlude that Bougeault s speial appliation of the mass-flux onept somehow antiipated the steps we are now advoating, the present proposal being an evolution of the former in order to over meso-sale-organised and/or rapidly evolving environmental onditions. Referenes: Arakawa, A. and W.H. Shubert, 1974: Interation of a umulus loud ensemble with the large-sale environment; Part I. J. Atmos. Si., 31, pp Betts, A.K., 1974: Thermodynami lassifiation of tropial onvetive soundings. Mon. Wea. Rev., 102, pp Bougeault, P., 1985: A simple parameterisation of the large-sale effets of umulus onvetion. Mon. Wea. Rev., 113, pp Geleyn J.-F. and G. Rohas, 1987: A study of the feed-bak aspets of diabati foring in the Frenh large-sale hemispheri model Emeraude. Diabati foring ECMWF Workshop, pp Gerard, L. and J.-F. Geleyn, 2005: Evolution of a subgrid deep onvetion parameterisation in a Limited Area Model with inreasing resolution. To appear in Q. J. R. Meteorol. So.. Kuo, H.L., 1965: On formation and intensifiation of tropial ylones through latent heat release by umulus onvetion. J. Atmos. Si., 22, pp Mapes, B.E., 1997: Equilibrium vs. ativation ontrol of large-sale variations of deep onvetion. In The physis and parameterisation of moist onvetion, Kluwer Aademi Publishers, pp Mapes, B.E., 2003: An information-based approah to onvetive losure. In Current issues in the parameterisation of onvetion, BMRC Researh Report N 93, pp