Scale aware deep convection parameterization

Transcription

1 Scale aware deep convection parameterization Luc Gerard Royal Meteorological Institute of Belgium 3 September 26

2 Convective clouds in a model grid box Quasi-Equilibrium hypothesis: Large subgrid population, all stages represented, adjusts faster than larger-scale forcing

3 Convective clouds in a model grid box Quasi-Equilibrium hypothesis: Large subgrid population, all stages represented, adjusts faster than larger-scale forcing Equilibrium vs small subset Smaller variability no more steady state. prognostic scheme

4 Convective clouds in a model grid box Quasi-Equilibrium hypothesis: Large subgrid population, all stages represented, adjusts faster than larger-scale forcing Equilibrium vs small subset Smaller variability no more steady state. prognostic scheme Equilibrium vs short time steps Full development up to equilibrium level in t? Precipitation reaching surface in t?. prognostic microphysics

5 Convective clouds in a model grid box Quasi-Equilibrium hypothesis: Large subgrid population, all stages represented, adjusts faster than larger-scale forcing Equilibrium vs small subset Smaller variability no more steady state. prognostic scheme Equilibrium vs short time steps Full development up to equilibrium level in t? Precipitation reaching surface in t?. prognostic microphysics Other phenomena: radiation (e.g. anvils), evolution of boundary layer, are not slower than the convective adjustment.. prognostic closure

6 Convective clouds in a model grid box Quasi-Equilibrium hypothesis: Large subgrid population, all stages represented, adjusts faster than larger-scale forcing Equilibrium vs small subset Smaller variability no more steady state. prognostic scheme Equilibrium vs short time steps Full development up to equilibrium level in t? Precipitation reaching surface in t?. prognostic microphysics Other phenomena: radiation (e.g. anvils), evolution of boundary layer, are not slower than the convective adjustment.. prognostic closure Complementarity between parameterizations: large σ u w > resolved apparent updraft ( < w < w u ): Cloud scheme also represents a part of updraft condensation. sequential physics, neat separation, single microphysics

7 Convective clouds in a model grid box Quasi-Equilibrium hypothesis: Large subgrid population, all stages represented, adjusts faster than larger-scale forcing Equilibrium vs small subset Smaller variability no more steady state. prognostic scheme Equilibrium vs short time steps Full development up to equilibrium level in t? Precipitation reaching surface in t?. prognostic microphysics Other phenomena: radiation (e.g. anvils), evolution of boundary layer, are not slower than the convective adjustment.. prognostic closure Complementarity between parameterizations: large σ u w > resolved apparent updraft ( < w < w u ): Cloud scheme also represents a part of updraft condensation. sequential physics, neat separation, single microphysics Mean grid box properties ψ ψ e plume model departs from real-world conditions reduced buoyancy, CAPE,.... perturbation approach

8 Convective clouds in a model grid box Quasi-Equilibrium hypothesis: Large subgrid population, all stages represented, adjusts faster than larger-scale forcing Equilibrium vs small subset Smaller variability no more steady state. prognostic scheme Equilibrium vs short time steps Full development up to equilibrium level in t? Precipitation reaching surface in t?. prognostic microphysics Other phenomena: radiation (e.g. anvils), evolution of boundary layer, are not slower than the convective adjustment.. prognostic closure Complementarity between parameterizations: large σ u w > resolved apparent updraft ( < w < w u ): Cloud scheme also represents a part of updraft condensation. sequential physics, neat separation, single microphysics Mean grid box properties ψ ψ e plume model departs from real-world conditions reduced buoyancy, CAPE,.... perturbation approach Grid spacing resolving a phenomenon of size l: x l/6

9 Bulk parameterization z z σ u Equivalent bulk updraft ensemble effect, decreasing together with x detrainment profile effect on bulk updraft properties: h u increases upwards σ u profile: σ u = σ B ν(z, σ B ) x σ B x

10 Prognostic approach Why: reduced subgrid variability, short time steps Allows feedback/interaction of other parameterizations: Downdraft PBL, cold pools triggering, CAPE Downdraft, evaporation entrainment/mixing Anvils radiation modified ψ e

11 Prognostic approach Why: reduced subgrid variability, short time steps Allows feedback/interaction of other parameterizations: Downdraft PBL, cold pools triggering, CAPE Downdraft, evaporation entrainment/mixing Anvils radiation modified ψ e How: Updraft velocity equation ωu t = drag buoyancy (ω = ṗ ρgw). Updraft gradual elevation (not in 3MT) Closure on base mesh fraction σ B : at steady state prognostic evolution towards it updraft thermodynamical properties: steady-state estimation.

12 Sequential moist physics Each parameterization updates the state passed to the next: temperature, contents of water phases.. no double counting

13 Sequential moist physics Each parameterization updates the state passed to the next: temperature, contents of water phases.. no double counting Updraft detrains condensates, combined with those from cloud scheme single prognostic microphysics: allows a smooth transition towards fully explicit convection condensates from convection are more localized: equivalent cloud fraction to compute intensive values passing thresholds in microphysics keep memory of convective area to be protected against re-evaporation by cloud scheme next time step relaxation in time of detrainment area ( stratiform cloud) partial cloudiness and overlap rules in precipitation sedimentation

14 Sequential moist physics Each parameterization updates the state passed to the next: temperature, contents of water phases.. no double counting Updraft detrains condensates, combined with those from cloud scheme single prognostic microphysics: allows a smooth transition towards fully explicit convection condensates from convection are more localized: equivalent cloud fraction to compute intensive values passing thresholds in microphysics keep memory of convective area to be protected against re-evaporation by cloud scheme next time step relaxation in time of detrainment area ( stratiform cloud) partial cloudiness and overlap rules in precipitation sedimentation Separated downdraft scheme computed after microphysics lives independently of subgrid updraft scheme retrospective adjustment of precipitation contents

15 3MT Convection scheme main features Handles complementarity, evolution and mesh fraction Sequential organization of parameterizations, one single microphysics. Cloud scheme prevented to affect condensates in convective part. Evolution in time with prognostic variables Direct expression of DC effects through convective condensation and transport fluxes.

16 3MT Convection scheme main features Handles complementarity, evolution and mesh fraction Ignores direct effects of resolved updraft DC scheme ignores w, assumes w e. DC scheme pretends to represent the absolute updraft.

17 3MT Convection scheme main features Handles complementarity, evolution and mesh fraction Ignores direct effects of resolved updraft Protection of convective area hinders explicit representation Prevents cloud scheme to evaporate but also to condense on convective area

18 3MT Convection scheme main features Handles complementarity, evolution and mesh fraction Ignores direct effects of resolved updraft Protection of convective area hinders explicit representation Moisture convergence closure, no explicit triggering Extremely cheap. A CAPE closure cannot be used. Reducing the forcing at small mesh fraction appears to improve the diurnal cycle (slowing down the onset of convection, hence leaving more CAPE accumulate).

19 3MT Convection scheme main features Handles complementarity, evolution and mesh fraction Ignores direct effects of resolved updraft Protection of convective area hinders explicit representation Moisture convergence closure, no explicit triggering Complementarity seems realized, down to 2km resolution...

20 3MT Convection scheme main features Handles complementarity, evolution and mesh fraction Ignores direct effects of resolved updraft Protection of convective area hinders explicit representation Moisture convergence closure, no explicit triggering Complementarity seems realized, down to 2km resolution.... but not in a way that the subgrid part would fade out.

21 Parameterization method (LCVCSD=T) triggering (LUSL=T): detect deep or shallow (LCVSHCU=T) cumulus and determine cloud base

22 Parameterization method (LCVCSD=T) triggering (LUSL=T): detect deep or shallow (LCVSHCU=T) cumulus and determine cloud base guess mesh fraction

23 Parameterization method (LCVCSD=T) triggering (LUSL=T): detect deep or shallow (LCVSHCU=T) cumulus and determine cloud base guess mesh fraction plume model: build entraining and braked ascent turbulent mixing TENTR (deep) or TENTRX (shallow), GENVSRH dependence on RH, braking TUDFR, mass coefficient GCVALBU reference properties actual CSD properties: T u, q u, q cu, buoyancy, ωu assumptions on normalized ud area profile ν organized entrainment NFSIG ν = σ u /σ B 2 ( [max(, 2z )] 2 [ min(, 2σ B ) 2 ]), with z = p b p p b p t Organized entrainment limited by GCVENDYMX assumption on hanging detrained condensates (ECMNP/ECMNPI) criterion to continue ascent: upwards velocity, MoCon (if LCVGQ=T)

24 Parameterization method (LCVCSD=T) triggering (LUSL=T): detect deep or shallow (LCVSHCU=T) cumulus and determine cloud base guess mesh fraction plume model: build entraining and braked ascent NFSIG TENTR, TENTRX, GENVSRH,TUDFR, GCVALBU,ECMNP, ECMNPI steady-state closure and base mesh-fraction LCAPE, LCVGQ, LCAMOD=F=LCOMOD, RTCAPE<, GCVKSKV, NCLOMIX, LCVGQM=F

25 Parameterization method (LCVCSD=T) triggering (LUSL=T): detect deep or shallow (LCVSHCU=T) cumulus and determine cloud base guess mesh fraction plume model: build entraining and braked ascent NFSIG TENTR, TENTRX, GENVSRH,TUDFR, GCVALBU,ECMNP, ECMNPI steady-state closure and base mesh-fraction LCAPE, LCVGQ, LCAMOD=F=LCOMOD, RTCAPE<, GCVKSKV, NCLOMIX, LCVGQM=F prognostic evolution of base mesh-fraction GCVTAUSIG

26 Parameterization method (LCVCSD=T) triggering (LUSL=T): detect deep or shallow (LCVSHCU=T) cumulus and determine cloud base guess mesh fraction plume model: build entraining and braked ascent NFSIG TENTR, TENTRX, GENVSRH,TUDFR, GCVALBU,ECMNP, ECMNPI steady-state closure and base mesh-fraction LCAPE, LCVGQ, LCAMOD=F=LCOMOD, RTCAPE<, GCVKSKV, NCLOMIX, LCVGQM=F prognostic evolution of base mesh-fraction GCVTAUSIG prognostic updraught velocity and gradually rising top (LUDEVOL=T)

27 Parameterization method (LCVCSD=T) triggering (LUSL=T): detect deep or shallow (LCVSHCU=T) cumulus and determine cloud base guess mesh fraction plume model: build entraining and braked ascent NFSIG TENTR, TENTRX, GENVSRH,TUDFR, GCVALBU,ECMNP, ECMNPI steady-state closure and base mesh-fraction LCAPE, LCVGQ, LCAMOD=F=LCOMOD, RTCAPE<, GCVKSKV, NCLOMIX, LCVGQM=F prognostic evolution of base mesh-fraction GCVTAUSIG prognostic updraught velocity and gradually rising top (LUDEVOL=T) final updraught mass flux,

28 Parameterization method (LCVCSD=T) triggering (LUSL=T): detect deep or shallow (LCVSHCU=T) cumulus and determine cloud base guess mesh fraction plume model: build entraining and braked ascent NFSIG TENTR, TENTRX, GENVSRH,TUDFR, GCVALBU,ECMNP, ECMNPI steady-state closure and base mesh-fraction LCAPE, LCVGQ, LCAMOD=F=LCOMOD, RTCAPE<, GCVKSKV, NCLOMIX, LCVGQM=F prognostic evolution of base mesh-fraction GCVTAUSIG prognostic updraught velocity and gradually rising top (LUDEVOL=T) final updraught mass flux, Horizontal momentum profile (TUDGP)

29 Parameterization method (LCVCSD=T) triggering (LUSL=T): detect deep or shallow (LCVSHCU=T) cumulus and determine cloud base guess mesh fraction plume model: build entraining and braked ascent NFSIG TENTR, TENTRX, GENVSRH,TUDFR, GCVALBU,ECMNP, ECMNPI steady-state closure and base mesh-fraction LCAPE, LCVGQ, LCAMOD=F=LCOMOD, RTCAPE<, GCVKSKV, NCLOMIX, LCVGQM=F prognostic evolution of base mesh-fraction GCVTAUSIG prognostic updraught velocity and gradually rising top (LUDEVOL=T) final updraught mass flux, Horizontal momentum profile (TUDGP) Condensation fluxes with freezing/melting correction (NIMELIT), transport fluxes, detrainment area evolution GCVTAUDE

30 Significant mesh fraction Environment properties and mixing ψ u ψ e = ψ u ψ ( σ u )

31 Significant mesh fraction Environment properties and mixing ψ u ψ e = ψ u ψ ( σ u ) Larger-scale updraft environment: no longer limited to a single grid column, e.g. resolved vertical velocity w may not follow immediately σ u w u ; w = σ u w u + ( σ u )w e ω u σ u ω u * ω ω e actual updraft environment at rest w e (compensating subsidence distributed over wider area)

32 Significant mesh fraction Environment properties and mixing ψ u ψ e = ψ u ψ ( σ u ) Larger-scale updraft environment: no longer limited to a single grid column, e.g. resolved vertical velocity w may not follow immediately σ u w u ; ω u ω w = σ u w u + ( σ u )w e ω e σ u ωu* large downwards w e to fulfill geometrical constraints no physical meaning (should induce strong adiabatic heating)

33 Significant mesh fraction Environment properties and mixing ψ u ψ e = ψ u ψ ( σ u ) Larger-scale updraft environment: no longer limited to a single grid column, e.g. resolved vertical velocity w may not follow immediately σ u w u ; Buoyancy: (T vu T v ) becomes zero when σ u CAPE vanishes how to close in a way that σ u?

34 Significant mesh fraction Environment properties and mixing ψ u ψ e = ψ u ψ ( σ u ) Larger-scale updraft environment: no longer limited to a single grid column, e.g. resolved vertical velocity w may not follow immediately σ u w u ; Buoyancy: (T vu T v ) becomes zero when σ u CAPE vanishes how to close in a way that σ u? Partially resolved updraft: Increased condensation in cloud scheme, subgrid scheme must only produce a complement Subgrid vertical transport must be a complement to resolved transport (Arakawa & Wu 23).

35 Significant mesh fraction Environment properties and mixing ψ u ψ e = ψ u ψ ( σ u ) Larger-scale updraft environment: no longer limited to a single grid column, e.g. resolved vertical velocity w may not follow immediately σ u w u ; Buoyancy: (T vu T v ) becomes zero when σ u CAPE vanishes how to close in a way that σ u? Partially resolved updraft: Increased condensation in cloud scheme, subgrid scheme must only produce a complement Subgrid vertical transport must be a complement to resolved transport (Arakawa & Wu 23).

36 Significant mesh fraction Environment properties and mixing ψ u ψ e = ψ u ψ ( σ u ) Larger-scale updraft environment: no longer limited to a single grid column, e.g. resolved vertical velocity w may not follow immediately σ u w u ; Buoyancy: (T vu T v ) becomes zero when σ u CAPE vanishes how to close in a way that σ u? Partially resolved updraft: Increased condensation in cloud scheme, subgrid scheme must only produce a complement Subgrid vertical transport must be a complement to resolved transport (Arakawa & Wu 23). Must account for w in w u equation.

37 Perturbation approach Complemetary subgrid draft (CSD) Gerard (25), to appear in Mon. Wea. Rev. ψ j = ψ j ψ, σ u ψ u + ( σ u )ψ e = Perturbation draft is a closed circulation in the grid column w w e w w u w w x

38 Perturbation approach Complemetary subgrid draft (CSD) Gerard (25), to appear in Mon. Wea. Rev. ψ j = ψ j ψ, σ u ψ u + ( σ u )ψ e = Perturbation draft is a closed circulation in the grid column Formal derivation from anelastic equation Perturbation updraft properties account for mesh fraction, for grid-column environment vertical lapse rate. Distinction between organized entrainment and turbulent mixing.

39 Plume model Perturbation updraft properties ψ u p = Λ u ( σ u ) ψ u + [ ] [δψ a ψ, p = ψ u = ψ b exp ( Λ u p σ u ) + ( σ u ) Λ u( p) Prognostic vertical perturbation velocity equation ω u t = Λ w (ω sg u) 2 ωu }{{} c/δt δψ a : either δq ca net condensate production or heating. Λ u: turbulent mixing and organized entrainment. Λ w : drag, turbulent mixing and organized entrainment. [ ] δψ a (ψ l ψ l+ ) ( exp ( Λ u p ) ) σ u ωu ( ω p p ω d ln ρ ) ωu α b ρ g 2 T vu dp T }{{}}{{ v } d/δt B

40 ETR closure: eddy transport reduction Arakawa & Wu 23: eddy transport is a fraction of the value producing full adjustment (w h ) E responding to grid-scale destabilization: w h = ( σ u ) 2 (w h ) E, w h = σ u ( σ u )(w u w e )(h u h e ) (w h ) E = value at negligible σ u

41 ETR closure: eddy transport reduction Arakawa & Wu 23: eddy transport is a fraction of the value producing full adjustment (w h ) E responding to grid-scale destabilization: w h = ( σ u ) 2 (w h ) E, w h = σ u ( σ u )(w u w e )(h u h e ) (w h ) E = value at negligible σ u + assumes (ψ u ψ e ) does not depend on σ u when w and h are fixed...

42 ETR closure: eddy transport reduction Arakawa & Wu 23: eddy transport is a fraction of the value producing full adjustment (w h ) E responding to grid-scale destabilization: w h = ( σ u ) 2 (w h ) E, w h = σ u ( σ u )(w u w e )(h u h e ) (w h ) E = value at negligible σ u + assumes (ψ u ψ e ) does not depend on σ u when w and h are fixed which is wrong: ψ u ψ e = ψu ψ ( σ u).

43 ETR closure: eddy transport reduction Arakawa & Wu 23: eddy transport is a fraction of the value producing full adjustment (w h ) E responding to grid-scale destabilization: w h = ( σ u ) 2 (w h ) E, w h = σ u ( σ u )(w u w e )(h u h e ) (w h ) E = value at negligible σ u + assumes (ψ u ψ e ) does not depend on σ u when w and h are fixed which is wrong: ψ u ψ e = ψu ψ ( σ u). one should explicitly account that mean grid-box ψ substantially departs from real environment ψ Real updraft partly represented in cloud-scheme condensation, and the complement is given by subgrid condensation.

44 ETR closure: eddy transport reduction Arakawa & Wu 23: eddy transport is a fraction of the value producing full adjustment (w h ) E responding to grid-scale destabilization: w h = ( σ u ) 2 (w h ) E, w h = σ u ( σ u )(w u w e )(h u h e ) (w h ) E = value at negligible σ u + assumes (ψ u ψ e ) does not depend on σ u when w and h are fixed which is wrong: ψ u ψ e = ψu ψ ( σ u). one should explicitly account that mean grid-box ψ substantially departs from real environment ψ Real updraft partly represented in cloud-scheme condensation, and the complement is given by subgrid condensation. Environmental CAPE closure or Moisture Convergence closure

45 ETR closure: eddy transport reduction Arakawa & Wu 23: eddy transport is a fraction of the value producing full adjustment (w h ) E responding to grid-scale destabilization: w h = ( σ u ) 2 (w h ) E, w h = σ u ( σ u )(w u w e )(h u h e ) (w h ) E = value at negligible σ u + assumes (ψ u ψ e ) does not depend on σ u when w and h are fixed which is wrong: ψ u ψ e = ψu ψ ( σ u). one should explicitly account that mean grid-box ψ substantially departs from real environment ψ Real updraft partly represented in cloud-scheme condensation, and the complement is given by subgrid condensation. Environmental CAPE closure or Moisture Convergence closure Possible mixed closure, e.g. CAPE at small σ B, MoCon at large σ B.... and ETR can help to combine them

46 CAPE closure formulation Approximation of larger-scale environment: CAPE = R a p t p b (T vu ˆT v ) dp p t p R a p b (T vu T v ) dp ( σ B ) p

47 CAPE closure formulation Approximation of larger-scale environment: CAPE = R a p t p b (T vu ˆT v ) dp p t p R a p b (T vu T v ) dp ( σ B ) p Cape relaxation (sole updraft) CAPE t ud = CAPE, τ turnover time-scale H τ w u H = σ B p b p t { νω u CAPE R a t ud δq } ca dp p (Lk s k q ) p } {{ } subgrid ud cond p t p b p b g p t T v t ud F cs p f (ω)(lk s k q ) dp p } {{ } resolved ud cond

48 Moisture convergence closure formulation example σ B p t p b ν(ω u+ω)lδq ca = p t p b L [mocon g Jtur ] q dp p where moisture vertical turbulent diffusion flux Jq tur convection transport (BL scheme). includes shallow Closure preferred where shallow convection detected.

49 Physically based generalized mixed closure 2(3) different closures : CAPE or Moisture? or Eddy Transport Reduction? 2 or 3 different scaling for a same reality

50 Physically based generalized mixed closure 2(3) different closures : CAPE or Moisture? or Eddy Transport Reduction? 2 or 3 different scaling for a same reality which one is right and when... or none of them?

51 Physically based generalized mixed closure 2(3) different closures : CAPE or Moisture? or Eddy Transport Reduction? 2 or 3 different scaling for a same reality which one is right and when... or none of them? homogenize the CAPE and MoCon formulas to combine them in a single relation

52 Physically based generalized mixed closure 2(3) different closures : CAPE or Moisture? or Eddy Transport Reduction? 2 or 3 different scaling for a same reality which one is right and when... or none of them? homogenize the CAPE and MoCon formulas to combine them in a single relation A single coefficient α modulates the forcing from % Moisture (α =) to % CAPE (α =) : σ B (U αn) }{{} subgrid ud consumption + }{{} R = ( α) resolved condensation B/τ ( σ B ) }{{} CAPE forcing + αm }{{} MoCon forcing

53 Physically based generalized mixed closure 2(3) different closures : CAPE or Moisture? or Eddy Transport Reduction? 2 or 3 different scaling for a same reality which one is right and when... or none of them? homogenize the CAPE and MoCon formulas to combine them in a single relation A single coefficient α modulates the forcing from % Moisture (α =) to % CAPE (α =) : σ B (U αn) }{{} subgrid ud consumption + }{{} R = ( α) resolved condensation B/τ ( σ B ) }{{} CAPE forcing + αm }{{} MoCon forcing Modulation coefficient given by the ratio of Moisture forcing to the total forcing when using an estimate σ M obtained by a third closure (ETR): /{ α = M M + B/τ } ( σ M )

54 Steady-state closure selection LCAPE LCVGQ F F ETR closure T F CAPE closure F T MoCon closure T T Mixed closure

55 Steady-state closure selection LCAPE LCVGQ F F ETR closure T F CAPE closure F T MoCon closure T T Mixed closure B/τ σ B (U αn) = R + αm + ( α) ( σ M ) σ B ( σ M )(U αn) = [ R + αm]( σ B ) + ( α)b/τ (2) approximation (2) advantageous if σ M ()

56 Steady-state closure selection LCAPE LCVGQ F F ETR closure T F CAPE closure F T MoCon closure T T Mixed closure B/τ σ B (U αn) = R + αm + ( α) ( σ M ) σ B ( σ M )(U αn) = [ R + αm]( σ B ) + ( α)b/τ (2) approximation (2) advantageous if σ M NCLOMIX formula () and σ M = 2 (), σ M from ETR 3 (2), σ M from ETR 4 shallow: (), α = ; deep: (2) ()

57 Prognostic closure GCVTAUSIG<: extension from the moisture-convergence closure relation { pt (σ + B σ B ) p b ν(h u h e )dp + α k p t p b (ω u) 2 } ν 2ρ 2 g dp 2 pt = (σ B σ+ B )δt p b ν ω ul u δq ca α k GCVKSKV 3 ratio of total to vertical kinetic energy of the DC cells The prognostic relation is also the base for the stochastic closure.

58 Prognostic closure GCVTAUSIG<: extension from the moisture-convergence closure relation { pt (σ + B σ B ) p b ν(h u h e )dp + α k p t p b (ω u) 2 } ν 2ρ 2 g dp 2 pt = (σ B σ+ B )δt p b ν ω ul u δq ca α k GCVKSKV 3 ratio of total to vertical kinetic energy of the DC cells The prognostic relation is also the base for the stochastic closure. GCVTAUSIG=τ σ > : relaxation towards σ.

59 Triggering (LUSL=T) Updraft source layer (Kain & Fritsch): gtrgdpmix USL 6 hpa

60 Triggering (LUSL=T) Updraft source layer (Kain & Fritsch): gtrgdpmix LCL USL 6 hpa

61 Triggering (LUSL=T) Updraft source layer (Kain & Fritsch): gtrgdpmix LFC Τ v LCL USL 6 hpa

62 Triggering (LUSL=T) Updraft source layer (Kain & Fritsch): gtrgdpmix, gtrgdphimn LFC φ min Τ v LCL USL 6 hpa

63 Triggering (LUSL=T) Updraft source layer (Kain & Fritsch): gtrgdpmix, gtrgdphimn, gtrgpuslmn USL Ascent: physical point of view; LFC LCL Τ v independent of vertical discretization; full control on triggering: buoyancy kick (w, TKE, dd history...); iterative can be expensive. USL 6 hpa

64 Triggering (LUSL=T) Updraft source layer (Kain & Fritsch): gtrgdpmix, gtrgdphimn, gtrgpuslmn Triggering method: buoyancy kick applied at LCL T v,kick = min(t, T v,cin, T v,lcl + T v,rc ) limit the buoyancy kick to the minimum required for overcoming CIN barrier T v,cin

65 Triggering (LUSL=T) Updraft source layer (Kain & Fritsch): gtrgdpmix, gtrgdphimn, gtrgpuslmn Triggering method: buoyancy kick applied at LCL T v,kick = min(t, T v,cin, T v,lcl + T v,rc ) limit the buoyancy kick to the minimum required for overcoming CIN barrier T v,cin CSD-specific triggering (CGTRC= RC ) criterion based on cloud-scheme condensation: γ cs gtrgain, T gtrthrs, p x gtrthck, α LCL gtrbrc T v,rc = γ cs ( T Fcs T ), T Fcs = mean (L/c p F cs ) in layer p x starting at surface check sufficient condensation in 3hPa above LCL (α LCL T )

66 Triggering (LUSL=T) Updraft source layer (Kain & Fritsch): gtrgdpmix, gtrgdphimn, gtrgpuslmn Triggering method: buoyancy kick applied at LCL T v,kick = min(t, T v,cin, T v,lcl + T v,rc ) limit the buoyancy kick to the minimum required for overcoming CIN barrier T v,cin CSD-specific triggering (CGTRC= RC ) criterion based on cloud-scheme condensation: γ cs gtrgain, T gtrthrs, p x gtrthck, α LCL gtrbrc More classical triggering (CGTRC= KF ) modified Kain-Fritsch criterion: γ kf gtrkgain, w gtrkthrs, z gtrkthck, α LCL gtrbrc T v,kf = [ γ kf ( w LCL w min(, z LCL z ) )] /3

67 Triggering (LUSL=T) Updraft source layer (Kain & Fritsch): gtrgdpmix, gtrgdphimn, gtrgpuslmn Triggering method: buoyancy kick applied at LCL T v,kick = min(t, T v,cin, T v,lcl + T v,rc ) limit the buoyancy kick to the minimum required for overcoming CIN barrier T v,cin CSD-specific triggering (CGTRC= RC ) criterion based on cloud-scheme condensation: γ cs gtrgain, T gtrthrs, p x gtrthck, α LCL gtrbrc More classical triggering (CGTRC= KF ) modified Kain-Fritsch criterion: γ kf gtrkgain, w gtrkthrs, z gtrkthck, α LCL gtrbrc Shallow cloud diagnostic (LCVSHCU=T): φ min gtrgdphimn never reached, while other criteria fulfilled: select the USL yielding the deepest cloud use tripled turbulent entrainment in plume model Pure moisture convergence closure (with contribution from vertical turbulent moisture flux including shallow vertical transport).

68 Behavior in 3D model 5 m/s t4p54 : 25/9/ z2: +5h h rain max=36.7, mean=.36 S6 PREC.EAU.CON+EAU.GEC+NEI.CON+NEI.GEC, 4 to

69 Behavior in 3D model t4p54 : 25/9/ z2: +5h RAIN lev 6 / instanteneous rain ofs=., scal=e+3, min=., max= 2.4, mean=.9.

70 Behavior in 3D model t4p54 : 25/9/ z2: +5h CVAUX lev 2 / 6 Deep cloud ofs=., scal=, min=., max=., mean=.9.

71 Behavior in 3D model t4p54 : 25/9/ z2: +5h CVAUX lev 2 / 6 Shallow cumulus ofs=., scal=, min=., max=., mean=..

72 Comparison 3MT/CSD ( x = 4km) t4p54 : 25/9/ z2: +5h t4acru : 25/9/ z2: +5h 5 m/s m/s max=36.7, mean=.36 S6 PREC.EAU.CON+EAU.GEC+NEI.CON+NEI.GEC, 4 to max=62.2, mean=.7 S6 PREC.EAU.CON+EAU.GEC+NEI.CON+NEI.GEC, 4 to CSD -hour accumulated precipitation 3MT

73 Comparison 3MT/CSD ( x = 4km) t4p54 : 25/9/ z2: +5h t4acru : 25/9/ z2: +5h max=5.8, mean=.38 S6 PREC.EAU.CON+NEI.CON, 4 to max=45.8, mean=.7 S6 PREC.EAU.CON+NEI.CON, 4 to CSD subgrid part 3MT

74 Test in Alaro-/tr - CAOB: Cloudiness 2//3 z2: +24h : Ntot ge2 km 2//3 z2: +24h : Ntot Gez km 2//3 z2: +24h : Ntot GDZ 2 km 2//3 z2: +24h : Ntot GCA3s 4 km max=., mean=.68, sd= max=., mean=.72, sd= max=., mean=.75, sd= max=., mean=.77, sd= NOCP CSD

75 Test in Alaro-/tr - CAOB: Cloudiness 2//3 z2: +24h : Ntot ge2 km 2//3 z2: +24h : Ntot gez km 2//3 z2: +24h : Ntot gdz 2 km 2//3 z2: +24h : Ntot gca_s 4 km max=., mean=.68, sd= max=., mean=.7, sd= max=., mean=.73, sd= max=., mean=.74, sd= NOCP 3MT

76 Test in Alaro-/tr - CAOB: Cloudiness max=., mean=.68, sd=.3 2//3 z2: +24h : Ntot ge2 km NOCP max=., mean=.77, sd=.27 2//3 z2: +24h : Ntot GCA3s 4 km CSD max=., mean=.82, sd=.24 2//3 z2: +24h : Ntot GBA3s 8 km max=., mean=.85, sd=.22 2//3 z2: +24h : Ntot GAA3s 6 km

77 Test in Alaro-/tr - CAOB: Cloudiness max=., mean=.68, sd=.3 2//3 z2: +24h : Ntot ge2 km NOCP max=., mean=.74, sd=.28 2//3 z2: +24h : Ntot gca_s 4 km 3MT max=., mean=.78, sd=.26 2//3 z2: +24h : Ntot gba_s 8 km max=., mean=.83, sd=.23 2//3 z2: +24h : Ntot gaa_s 6 km

78 Alaro-/tr: 24-hour accumulated precipitation shares CSD #HAA: 24h Total rr 24 #HAA: 24h DC scheme rr 24 #HAA: 24h Cloud scheme rr x = 6 km max=7., mean= max=.3, mean= max=2.6, mean= #haa: 24h Total rr #haa: 24h DC scheme rr #haa: 24h Cloud scheme rr MT max=9., mean= max=6.6, mean= max= 5.9, mean=

79 Alaro-/tr: 24-hour accumulated precipitation shares CSD #HBA: 24h Total rr 24 #HBA: 24h DC scheme rr 24 #HBA: 24h Cloud scheme rr x = 8 km max=7.9, mean= max= 7.5, mean= max=2.8, mean= #hba: 24h Total rr #hba: 24h DC scheme rr #hba: 24h Cloud scheme rr MT max=2.5, mean= max=8.8, mean= max= 8.5, mean=

80 Alaro-/tr: 24-hour accumulated precipitation shares CSD #HCA: 24h Total rr 24 #HCA: 24h DC scheme rr 24 #HCA: 24h Cloud scheme rr x = 4 km max=8.8, mean= max= 7., mean= max=5.7, mean= #hca: 24h Total rr #hca: 24h DC scheme rr #hca: 24h Cloud scheme rr MT max=26., mean= max=9., mean= max= 9.9, mean=

81 Alaro-/tr: 24-hour accumulated precipitation shares CSD #HDZ: 24h Total rr 24 #HDZ: 24h DC scheme rr 24 #HDZ: 24h Cloud scheme rr x = 2 km max=24.9, mean= max= 7.4, mean= max=2.7, mean= #hdz: 24h Total rr #hdz: 24h DC scheme rr #hdz: 24h Cloud scheme rr MT max=26.9, mean= max=6.6, mean= max=5.7, mean=

82 Alaro-/tr: 24-hour accumulated precipitation shares #Gez: 24h DC scheme rr #gez: 24h DC scheme rr #gez: 24h Cloud scheme rr max=5.5, mean=.3 max=23.4, mean= max=24.2, mean= #gez: 24h Total rr 3MT #Gez: 24h Cloud scheme rr 24 max= 2.8, mean=. max=25.2, mean= 3. 4x = km #Gez: 24h Total rr max=7.4, mean=.74 CSD

83 ω, Vertical (instantaneous) cross section: cloud streets km/ao- model levels km/Ao-tr hdz +44: 64,52,24,24,9,87 streets omr 4. to 2.3, Mu min= omu min= 32.7, su max=.436 ω u M u =σ u ω u, cloud condensates 3MT section points model levels hca +576: 32,76,2,2,9,87 streets hba +288: 6,38,6,6,9,87 streets haa +44: 8,9,3,3,9,87 streets omr. to.6, Mu min= omu min=9., su max=.33 model levels omr. to.8, Mu min= section points 4km/Ao-tr section points 8km/Ao-tr section points 6km/Ao-tr omu min=8., su max=.3 model levels omr.2 to.6, Mu min= omu min= 43.5, su max=.26

84 ω, Vertical (instantaneous) cross section: cloud streets km/ao- model levels HDZ +44: 64,52,24,24,9,87 streets.2.6 2km/Ao-tr omr 3.6 to.9, Mu min= omu min=., su max=. ω u M u =σ u ω u, cloud condensates CSD section points model levels HCA +576: 32,76,2,2,9,87 streets HBA +288: 6,38,6,6,9,87 streets HAA +44: 8,9,3,3,9,87 streets omr.2 to.6, Mu min= omu min=., su max=. model levels omr.9 to., Mu min= section points 4km/Ao-tr section points 8km/Ao-tr section points 6km/Ao-tr omu min=., su max=. model levels omr.2 to.7, Mu min= omu min=., su max=.

85 ω, Vertical (instantaneous) cross section: cellular structures km/ao- model levels km/Ao-tr hdz +44: 84,28,8,8,9,87 core omr 7.9 to 5., Mu min= section points omu min= 35.5, su max=.95 ω u M u =σ u ω u, cloud condensates 3MT model levels hca +576: 92,4,9,9,9,87 core hba +288: 46,7,4.5,4.5,9,87 core haa +44: 23,35,2.25,2.25,9,87 core.5... omr.7 to 3.7, Mu min= omu min= 3.2, su max=.568 model levels omr.6 to 2.3, Mu min= section points 4km/Ao-tr section points 8km/Ao-tr section points 6km/Ao-tr omu min=5.3, su max=.458 model levels omr.5 to., Mu min= omu min= 42.6, su max=.359

86 ω, Vertical (instantaneous) cross section: cellular structures km/ao- model levels km/Ao-tr HDZ +44: 84,28,8,8,9,87 core omr.5 to 4.8, Mu min= section points omu min= 4.6, su max=.742 ω u M u =σ u ω u, cloud condensates CSD model levels HCA +576: 92,4,9,9,9,87 core HBA +288: 46,7,4.5,4.5,9,87 core HAA +44: 23,35,2.25,2.25,9,87 core omr 8. to 3.3, Mu min= omu min= 43., su max=.659 model levels omr 4.2 to 2.3, Mu min= section points 4km/Ao-tr section points 8km/Ao-tr section points 6km/Ao-tr omu min= 36., su max=.777 model levels omr. to.7, Mu min= omu min= 65.9, su max=.67

87 Tuning in evolving Alaro versions Triggering, updraught tuning appear stable Multiple interactions between parameterizations require to re-tune at various places. Critical Relative Humidity profile:

88 Tuning in evolving Alaro versions Triggering, updraught tuning appear stable Multiple interactions between parameterizations require to re-tune at various places. Critical Relative Humidity profile:

89 Tuning in evolving Alaro versions Triggering, updraught tuning appear stable Multiple interactions between parameterizations require to re-tune at various places. Critical Relative Humidity profile: Shallow convection from TOUCANS vs shallow cumuluses in CSD

90 Tuning in evolving Alaro versions Triggering, updraught tuning appear stable Multiple interactions between parameterizations require to re-tune at various places. Critical Relative Humidity profile: Shallow convection from TOUCANS vs shallow cumuluses in CSD Predominance of non-saturated downdraught tuning

91 Summary CSD produces a gradual transition towards explicit convection Essential features are: Sequential physics with feedbacks, e.g. convective area protection, downdraft. Plume model for perturbation-updraft Specific closure formulation Adapted/specific triggering formulation Prognostic updraft evolution (velocity, mesh fraction, rising cloud top). Single prognostic microphysics Meso-scale organization not always well rendered at high resolution: tuning of turbulent diffusion has a big impact stochastic components subgrid cold pools parameterization more results in next presentation on multi-scale behaviour