Jean-Fran ç ois Geleyn ONPP/ČHMÚ & CNRM/Météo-France

1. 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, 24-1-2005 (*) in ‘The physics and parameterisation of moist atmospheric convection, pp.321-358, NATO ASI Series, 1997, Kluwer Academic Publishers, Dordrecht

2. P. Bougeault (pers. com. - 12/1/04) • “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. • But, since it works on this basis at Meteo-France as well as at ECMWF for 20 years, this cannot be that wrong either!”

3. Why is deep-convection so special in the parameterisation trade? • Because such a parameterisation automatically requires some knowledge of the model’s resolved tendencies (closure problem). • 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). • Because the basic atmospheric state always looks at the edge of a yes/no behaviour. • 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.

4. Why do we need a parameterisation of deep-convection? • 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. • 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. • Not because it helps maintaining the correct local vertical gradients of temperature and humiditybutbecause it controls the intensity of larger-scale dynamical adjustment motions (Hadley cell, …).

5. 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 Convective instability is a local property Conditional instability of the first kind

6. Detrainment Compensating subsidence of magnitude Mc Entrainment The mass-flux approach • Hypotheses: • steady cloud • negligible updraft area

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

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

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

10. The Quasi-Equilibrium (QE) concept: history • Whatever causality is at work, QE is verified at very large scale, but not necessarily below. • Study of the phenomenology of convection pushed to the concept of mass-flux formulation for convective parameterisation schemes. • This shifted the old problem of convective closure from budgets to complex questions about the dynamics of convective circulations. • 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.

11. The Quasi-Equilibrium (QE) concept: controversy • CISK idea of QE: convective circulations are determining the ‘larger scale’ vertical velocities that in turn force convection. • WISHE idea of QE: ‘being in a lift, you are not going up because the counter-weight goes down’. • 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.

12. QE and causality. Le Châtelier’s principle as an answer? (1/2) • Chemical reactions QE: if the modification of some parameters does displace the equilibrium, other forces counteract the primary evolution, but only partly. • 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. • Test to be done by statistical differences between observations of active and non-active periods.

13. 300 Venezuelian soundings => T<0 => WISHE wins (if QE exists) BUT More mitigated results on TOGA-COARE (and GATE) Is QE really usefull ? QE and causality. Le Châtelier’s principle as an answer? (2/2)

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

15. adiabatic convective But Vertical velocity. Which representativeness? Which use? For any conservative quantity  one may symbolically write 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.

16. What else do we have as input for the closure assumption? • CAPE (Convective Available Potential Energy) • CIN (Convective INhibition energy) • Moisture convergence: a ‘good old concept’ first introduced by Kuo (1965, 1974) in order to get rid of convective adjustment • 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?)

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

18. Summary • 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. • 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). • Bougeault’s 85 scheme anticipates such steps, but not enough for ‘meso-scale-organised’ and/or ‘dry environmental’ cases.