Why do moisture convergence deep convection schemes work for more scales than those they were in principle designed for? Jean-François Geleyn ONPP/ČHMÚ & CNRM/Météo-France (on an incentive from Philippe Bougeault and using ideas of Brian Mapes(*) and Jean-Marcel Piriou) CCWS, Tartu, Estonia, (*) in ‘The physics and parameterisation of moist atmospheric convection, pp , NATO ASI Series, 1997, Kluwer Academic Publishers, Dordrecht

P. Bougeault (pers. com. - 12/1/04) n “I was well conscious about this limitation (of the moisture convergence closure) in 85, but the problem is that I mostly wanted to fit GATE data, where there is no correlation between CAPE and rainfall, while there is a strong correlation between MOCON and rainfall. But, as Mapes rightly says, the latter does not guarantee a causal link because one might mix cause and consequence. n But, since it works on this basis at Meteo- France as well as at ECMWF for 20 years, this cannot be that wrong either!”

Why is deep-convection so special in the parameterisation trade? n Because such a parameterisation automatically requires some knowledge of the model’s resolved tendencies (closure problem). n Because it is a non-hydrostatic phenomenon that we try to parameterise in a hydrostatic-type framework (for the scales -above 10km- where we need such a parameterisation). n Because the basic atmospheric state always looks at the edge of a yes/no behaviour. n Because ‘visible’ convection appears like a local auto-organised process while its ‘invisible’ influence and conditions of existence are very much of a large-scale type.

Why do we need a parameterisation of deep-convection? n Because for models that do not resolve the 10km scale, associated clouds are clearly sub-grid and look like the result of an auto-organisation process. n Because without it, resolved microphysics of clouds and precipitation takes over the vertical stabilising role, but at the wrong scale with sometimes catastrophic consequences on the modelled atmosphere. n Not because it helps maintaining the correct local vertical gradients of temperature and humidity but because it controls the intensity of larger-scale dynamical adjustment motions (Hadley cell, …).

Convective instability is a local property One GATE highly unstable profile (  e >  es aloft) => CAPE >0 For the averaged tropical situation, potential instability still (weakly) exists but the (CIN>0) barrier is high Conditional instability of the first kind

The mass-flux approach Compensating subsidence of magnitude M c Hypotheses: -steady cloud -negligible updraft area Entrainment Detrainment

The mass-flux approach (Bougeault’s 1985 variant) Hypotheses: -steady cloud -negligible updraft area Compensating subsidence of magnitude M c Entrainment Detrainment Allows to include the surface evaporation in the humidity convergence without forcing too strong a constraint on the moisture budget But no possibility of temporary storage though ?

The CISK vs. WISHE controversy Static view (there is also a wave-propagation equivalent) Conditional Instability of the Second Kind Buoyancy Updraft motion Surface pressure drop Low level convergence More moisture Condensation ? Wind Induced Surface Heat Exchange Condensation + Ascent ? Balanced profile’s maintenance Sinking in dry regions  Radiation Need of a return flow Stronger wind => evaporation More available moisture Where does the moisture comes from ? What determines the balanced profile ?

The CISK vs. WISHE main difference Conditional Instability of the Second Kind Buoyancy Updraft motion Surface pressure drop Low level convergence More moisture Condensation ? Wind Induced Surface Heat Exchange Condensation + Ascent ? Balanced profile’s maintenance Sinking in dry regions  Radiation Need of a return flow Stronger wind => evaporation More available moisture Convection drives the ‘large-scale’ circulation Convection controls the ‘large-scale’ circulation But the truth seems to be situation- and scale dependent !

The Quasi-Equilibrium (QE) concept: history n Whatever causality is at work, QE is verified at very large scale, but not necessarily below. n Study of the phenomenology of convection pushed to the concept of mass-flux formulation for convective parameterisation schemes. n This shifted the old problem of convective closure from budgets to complex questions about the dynamics of convective circulations. n But the (misleading?) answer was to replace the search of an additional convective impact under given local circumstances by that of a full convective answer to a non-convective forcing.

The Quasi-Equilibrium (QE) concept: controversy n CISK idea of QE: convective circulations are determining the ‘larger scale’ vertical velocities that in turn force convection. n WISHE idea of QE: ‘being in a lift, you are not going up because the counter-weight goes down’. n Anti-QE thinking (20 years lost, they say): –Scales are not separable (the ‘invisible’ part of convection is at the scale of the Rossby radius of deformation); –Forcing and answer are not really separable either (at least scale-dependent in a model where the return flow must be accounted for in the same grid-box)! –There is no ‘under-law’ of convective regions dynamics that aggregates local behaviours to a simple balance.

QE and causality. Le Châtelier’s principle as an answer? (1/2) n Chemical reactions QE: if the modification of some parameters does displace the equilibrium, other forces counteract the primary evolution, but only partly. n Mapes (1997): –If convective heating follows cooling by adiabatic ascent (~WISHE in full QE meaning) the resulting effect will be cooling; –If convective heating precedes cooling by adiabatic ascent (~CISK in full QE meaning) the resulting effect will be heating. n Test to be done by statistical differences between observations of active and non-active periods.

QE and causality. Le Châtelier’s principle as an answer? (2/2) BUT 300 Venezuelian soundings =>  T WISHE wins (if QE exists) More mitigated results on TOGA-COARE (and GATE) Is QE really usefull ?

QE => scale separation. Which concept to replace that? (Mapes, 97) Nature Model

Vertical velocity. Which representativeness? Which use? For any conservative quantity  one may symbolically write adiabaticconvective But In other words, the computed large-scale vertical velocity is just the average of the (rare) cloud ascents and of a slightly sinking environment everywhere. Hence the large scale vertical advection term is dynamically meaningless (but model-wise unavoidable) and has to be compensated by a good estimate of the mass flux, slightly bigger thanks to surface evaporation. Thus, if QE is doubtful, the mass-flux parameterisation should never use the diagnosed large-scale vertical velocity as input.

What else do we have as input for the closure assumption? n CAPE (Convective Available Potential Energy) n CIN (Convective INhibition energy) n Moisture convergence: a ‘good old concept’ first introduced by Kuo (1965, 1974) in order to get rid of convective adjustment n Moisture availability: an extension of the previous concept that tries to get rid of the QE constraint through adding ‘local’ auto- organised moisture sources for a bulk convective condensation (a synthesis of the 3 above ones?)

Standard ingredients of a convective parameterisation (and new ideas?) Equations Large scale + Parameterised Physical description Microphysics & Conditions of activation Cloud ascent profile(s) Simulation of the entrainment Budget regulation ‘Closure’ Cloud stationarity? Which sophistication? Which life-cycle? How do LS  local? Hidden form of QE thinking? Moist. avail. Moist. conv.

Summary n The MOCON  Rainfall link is sufficiently stronger than any equivalent (at large scale and in a steady environment) for schemes intelligently based on such a closure to be very robust and applicable even if the balance is less accurate. n Going further implies to stop thinking large-scale forcing vs. cloud balancing: –Introducing a local organisation source of moisture leads to the overall concept of (CAPE- & CIN- dependent) moisture availability; –The cloud-stationarity hypothesis might be relaxed; –What then really counts is the Bulk Convective Condensation rate (BCC). n Bougeault’s 85 scheme anticipates such steps, but not enough for ‘meso-scale-organised’ and/or ‘dry environmental’ cases.