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Entrainment as the main controling parameter of convective activity in the 3MT moist-physics unifying scheme. Trials for an extension towards a 'cold-pool mechanism-oriented memory of entrainment J.-F. Geleyn, D. Banciu, R. Brožková and L. Gerard (with strong reference to ideas of J.-M. Piriou) 26/3/09, Prague, CHMI

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A few words about 3MT Goals Main choices Implementation characteristics Grey-zone results

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Why 3MT? (i) Attacking, within a long-term perspective, the challenge of the horizontal scales (δx ~ 5 km) where precipitating convection is neither fully resolved nor likely to be correctly parameterised in a classical way. (ii) Insisting on stable (for longer t) and cost-efficient algorithmic solutions (bulk model for the drafts for instance). (iii) Having a NWP-controlled progress (novelty AND ascending compatibility). (iv) Modularity-flexibility as the essential tool to obtain a multi- scale character (being able to swap and/or tune the processes description without touching the structuring algorithmic). (v) Using a prognostic orientation for reconciliation of ideas about complex microphysics and mass-flux-type parameterisation (neither CRM nor QE).

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3MT, the acronym Three ideas/concepts: Modular, because of the ALARO-0 effort made in order to stay compatible with a general phys-dyn interfacing while searching proximity with the AROME concepts (R. Brozkova, I. Stiperski, J.-F. Geleyn, B. Catry, D. Banciu); Multi-scale, because a great deal of the architectural constraint comes from the grey-zone oriented work, initiated in 2001 by L. Gerard; Microphysics & Transport, to underline the decisive catalysing role played by the central proposal of J.-M. Pirious PhD work, made in 2004.

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Microphysics AND Transport (M-T) It is the basic idea behind all what follows. Allows to rethink around two trivial facts: Detrainment here = Entrainment somewhere else. Cloud+precipitation microphysics is anything but instantaneous (fall speed of drops ~ propagation speed of convective structures). CONSEQUENCES 3MT gets away from assumptions of a stationary cloud (neither in size nor in properties). 3MT fully takes into account the fact that microphysics has a rather long lag-time and is not only happening within the drafts.

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One key equation If we set –M c from two independent prognostic equations for c and up – up as constant (in the cloud) along the vertical => 2D-only closure –E from something (see later in the presentation) Then D cannot be parameterised (overdetermination otherwise) and it is obtained from all other computations. Piriou et al. (2007) showed that it is in fact mainly constrained by the microphysical activity => a justification for using the M-T decomposition.

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Time- and space-scale issue Basically, 3MT is a way to do as if deep convection was resolved but without needing to go to scales where this is true. This is thanks to: Prognostic and diagnostic memory of convection; A unique micro-physical treatment beyond all sources of condensation. But, owing to the peculiar role of entrainment in the M-T concept, this requires to better understand what one means when specifying entrainment in one way or the other.

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3MT

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The nice sides … NWP orientation: bulk mass-flux but fully prognostic handling of the mass-flux AND of the 2D closure. With M-T, the 2D closure and a prognostic equation for the mass-flux, no need to parameterise anymore detrainment. Facility to work on modularity for flexibility. One single microphysical-type computation, except for the condensation/re-evaporation, the latter being obtained from the sum of a resolved contribution and of a convective one. Lot of freedom for a complex fully prognostic micro- physics => more memory of past convective events. The cold-pool effects parameterisation should happen quite naturally in this framework.

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But … The handling of the cascade (neither sequential nor parallel treatment of individual contributions) is not always easy: Avoiding double-counting for updraft and downdraft closure is not trivial; The sedimentation aspect of the downdraft impact must be treated heuristically; In order not to be forced to iterate expensive computations, one must make judicious choices about which information to pass or not to pass to the next time-step (and on how to best use it). Not enough effort was devoted to the closure formulation, especially in view of its multi-scale impact. For a deep framework, a vertically constant area fraction for drafts is OK; but this does not hold anymore in the shallow case.

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Modularity for flexibility. Where? Updraft (and downdraft): Ascent computation (including the prognostic handling of an in-ascent vertical velocity); Closure (leading to a 2D field of active area fractions, also prognostic); M-T equations => (non-negociable). Microphysics: General organisation (explicit need of fall-speeds, non-advective sedimentation, geometrical overlaps impact, protection of convective condensates at the ensuing time steps, …) => (non-negociable); Type of sedimentations handling; choice of the computation (or set-up) of fall-speeds; Auto-conversion type processes; Collection type processes; Evaporation, Sublimation, Melting, Freezing of falling species. Resolved adjustment: Choice of critical relative humidity; Formulation of cloud-cover; Condensation/Evaporation rate => (separation from the other items is non-negociable; but the choice of the formulation is free).

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3MT, the backbone Convective equations in Microphysics-Transport form (Piriou et al., JAS, 2007) M c u/d (p)=- u/d (p). u/d (p), both prognostic (Gerard & Geleyn, QJRMS, 2005) Prognostic, barycentric and conservative phys-dyn interfacing (Catry et al., Tellus-A, 2007) Sequential handling of both condensation sources, but summing of their inputs for a uniquemicrophysics call This microphysics is sandwiched between up- et downdrafts computations (Gerard, QJRMS, 2007) Unique vertical loop for the microphysics, made purely local thanks to PDF-based sedimentation (Geleyn et al., Tellus-A, 2008)

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And it works quite like expected … The next viewgraph presents the structure of 6h cumulated precipitation amounts over the Alps for 4 forecasts valid at 18h range for the initial date 21/6/06 00UTC: Two with 9km mesh-size (left column) and two with 4.7km mesh-size (right column); Two with ALARO-0-minus-3MT (upper row) and two with ALARO-0 [i.e. with 3MT] (lower row). One notices the strong grey zone syndrome when trying to apply the classical diagnostic convection scheme at the 4.7km mesh-size (upper-right diagramme). On the contrary, when using the 3MT ensemble of novelties, the precipitation patterns scale correctly from one resolution to the other (bottom row).

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Scalability of precip. patterns

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Operational implementations At ~9km mesh-size: Cz (4/6/08) Si (16/6/08) Sk (19/8/08) At soon (already in LAEF set-up) Interest in Hr, Ro, Pt, Tr At ~4.5 km resolution Be (15/1/09) Interest in No

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Now about entrainment ( no need to speak about detrainment in 3MT; it is decided by microphysics ) Role with respect to the novelties of 3MT Empiricism of the diagnostic set-up value of its tuning A prognostic alternative? Some model-run diagnostics

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Two constatations Apart from the autoconversion time scales for microphysics, the parameters controlling the entrainment rate for the convective ascents computation were the only ones which needed retuning whan introducing 3MT in ALARO-0: Doubling of the min and max entrainment rates (to respectivly 0.00005 and 0.0016 m -1 ) Dividing by 1.5 the sensitivity to free ascent buoyancy (which regulates the max min adjustment) Diminishing by a factor 2.5 the account taken of ensembling entrainment All this goes in the direction of higher entrainment rates (more realistic but still below measurements)

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Entrainment matters more for convection in 3MT than in the equivalent static scheme qvqv T Standard static entrainment Doubled Entrainment Max / Min rates => 3MT choice Standard static entrainment Doubled Entrainment Max / Min rates => 3MT choice STATIC 3MT

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Reduction of the difference to the static reference via the retuning (3 aspects in it) qvqv T BEFORE AFTER Total

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Reduction of the difference to the static reference via the retuning (3 aspects in it) Entr. Detr. Diagnostic / weak entr. 3MT / strong entr. 3MT / weak entr.

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Structure of the static entrainment rate computation (Gerard & Geleyn, 2005) Very heuristic but fine tuned by more than 10 years of operational use

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Cold pool mechanism Basic entrainment is by nature strong and prevents immediate deep penetration of convective clouds But the evaporation of first convective precipitation amounts creates density currents, cold pools and thus ascent- favourable conditions at the edge between the latter ones Quickly raising plumes entrain relatively less (a mechanism already parameterised by in our static algorithm) So the idea is to encompass the effect in an hysteresis-like link between past evaporation of precipitations and current entrainment rates; the time-lag aspect calls for a prognostic algorithm, with all the associated risks and difficulties. In his PhD thesis, Piriou proposed and tested the above in a demo-fashion. 3MT in principle allows to go to a more concrete test.

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Equations of J.-M. Pirious proposal

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3MT-linked change of variable of L. Gerard downdraft is treated prognostically like its updraft equivalent and integrates all effects of previous evaporation (but resolved + convective, since the distinction disappears in 3MT)

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Improvements by D. Banciu Replacing f(p/p surf ) by an adimensional scaling (inspired by Met-Offices LES estimates) in ( - surf ) Observed value 3.5. Our min/max bracket [0.3-3.] NB: this quite useful scaling will also be used for the presentation of the results Quitting the linear relationship Advecting and reinitialising it to the static tuning when no convection is present

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Our current equations downdraft is treated prognostically like its updraft equivalent and integrates all effects of previous evaporation (but resolved + convective, since the distinction disappears in 3MT) is a fully prognostic quantity Tuning => cp =5000 s E =2 cp Hysteresis-control Mironov-type term

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First results with prognostic entrainment Diagnostic 3MT computation. Histogramme at all model levels of the (admimensional) product of the entrainment rate by the height above the ground The same but for the best tuning (so far) of Pirious proposal for a treatment of entrainment with cumulated influence of the past evaporation rates. => Correct histogramme structure but too little convective activity!

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First results with prognostic entrainment Downdraft Mass Flux Divergence Updraft Mass Flux Divergence Diagnostic entrainmentPrognostic entrainment

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(Preliminary) lessons Prognostic entrainment can mimick the well-tuned statistical structure of the static case The space- and time-averaged mass fluxes agree quite well after this tuning But the frequency of convective activation is diminished => more intermittency for the prognostic case Unfortunately, we did not get closer to observed entrainment rates (our upper bound is still just below the truth) => the problem stays!

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Two ways to look at entrainment (1/3) First definition: the positive contribution to the vertical change of mass-flux with height Second definition: the rate of mixing of cloud and environment conservative properties In 3MT, both physical processes, though not completly disconnected, are really treated separately => one may try and diagnose them independently of each other

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Two ways to look at entrainment (2/3) General agreement, except where the plumes start, but details differ, in fact rather significantly for an horizontal average E1 E2 Case without the parameterisation (forget the units)

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Two ways to look at entrainment (3/3) Distinction between the two regimes is even more marked but details elsewhere match better (let us have a closer look)! E1E2 Case with the parameterisation (forget the units)

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Pseudo mass-flux integrals of E 1 and E 2 (comparison diagnostic vs. prognostic) Diagnostic Prognostic Diagnostic Prognostic Tuning not so bad!

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Pseudo mass-flux integrals of E 1 and E 2 (comparison of the two methods) PrognosticDiagnostic E1 E2 Hidden constraint? Better parallelism

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Conclusions With the additional degrees of freedom of 3MT, the role of entrainment is increased Retuning of the static entrainement rates without touching the algorithm delivers what we believe to be a good reference target for the prognostic entrainment scheme The latter delivers some first promising results (more freedom, better dissociation between the two sources of ascent) We are very sorry that we did not manage to push the assesment any further before the workshop !

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