Outline. university-logo. Boundary layer parameterization Introduction. university-logo. Boundary layer parameterization Introduction.

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1 and climate s in climate models Frédéric Hourdin June, 009 Boundary layer in te climate system Boundary layer in te "Eart System" Driven by te Global Cange studies, climate models are more and more complex : CO cycle, CH, oone cemistry, aerosols, effect of land use = coupling between atmospere, ocean, cemistry, vegetation... Leading to so-called "Eart System Models". Boundary layer is central for most of tose components. Te boundary layer : controls energy and water excanges wit surfaces drives te oceanic circulation is associated wit a large fraction of clouds «Eart System Models» Atmosperic cemistry Atmospere Ocean Sea ice Vegetation Soil Hydrologie Ocean Bio geo cemistry Boundary layer in te "Eart System" Boundary layer in large scale models Example of well indentified uncertainty source in Eart-System models. Te diurnal (seansonal) cycle of plant respiration is modulated by te diurnal (seasonal) cycle of te boundary layer dept Current climate models : oriontal mes of 0 to 00 km. Boundary layer processes are subgrid-scale = must be "parameteried" 0 00 km Parameteriations describe te effect of subgrid-scale processes on large scale state variables troug a set of approximate equations based on some internal variables must relate tose internal variables to large scale variables (closure) closely linked to te numerical world. of te conservation equation Conservation equation v : wind field c : conserved quantity Lagrangian form : Advective form : Flux form : s in climate models dc =0 dt + vgradc = 0 ρc + div (ρvc) = 0 X : "average" or "large scale" variable = vc = v c + v0 c0 X 0 = X X : turbulent fluctuation q + V.grad q + div ρv0 c0 = 0 ρ

2 Under boundary layer approximations ( / x << /) : v.grad c = Sc wc ρ D Dynamical core s in climate models Pysical parametriations 0 km One grid mes or atmosperic column.? 00 km v and c are now te large scale variables. c :, u, v, water (vapor and oters), cemical compounds... Diffusive or local formulations for te PBL Turbulent diffusivity K Prandlt (95) mixing lengt : K = l w0 or K = l v w0 c0 = K Accounting for static stability (Ex. Louis 979) = K K = f (Ri)l Analogy wit molecular viscosity (Brownian motion turbulence) v, wit Ri = Turbulent kinetic energy w0 ' e = Down-gradient fluxes. Limitations of turbulent diffusion Assumption leading to te diffusive approac : Idealied view of te dry convective boundary layer. Turbulence as a random process Small scale turbulence, i.e. of sie l << wit = In te planetary boundary layer Potential temperature initial final c Radar ecoes dry convective boundary layer Florida, Hiop Campaign Cloud streets on Nort of France (Marc 009, MSG) Weckwert et al., 997 Termal plume 0 w eating by te surface w0 0 0 ' (Cste > 0) e d wd K Unstable surface layer u wu w 0 = 0 or sligtly < 0 Compensating subsidence d funiform Neutral (sligtly stable) mixed layer α Turbulent diffusion w0 0 ' 0 0 w0>0 Inversion layer w0 0 = K Diffusive formulation α Organied structures 5km In te mixed layer Heat flux Long range vertical transport (from te bottom to PBL top) () i u0 + v0 + w0 Limitations of turbulent diffusion v e u v g 0 0 w0 p0 w0 e = w0 u0 w0 v0 + w ρ Ex : Mellor and Yamada w0 φ0 = Kφ φ wit Kφ = l esφ (Ri) Note : e = 0 (stationarity) = K of form Eq. Turbulence acts as a "mixing" g Extension of diffusive formulations of a countergradient term w0 0 = K Γ = 0 wit Γ ' K/km () Imposed countergradient Deardorf, 966 Revisited by Troen & Mart, 986, Holtlag & Boville, 99, based on a similarity approac. s in climate models Non local mixing lengt (Bougeault) Higer order closures - Mellor & Yamada 97, ierarcy at successive orders. Complex and still local. - Abdella & Mc Farlane, 997, Introduce a mass flux approac to compute te rd order moments in a Mellor and Yamada sceme.

3 "Bulk" models Transilient matrices Mellor and Yamada (MY) i Constant value (or prescribed profiles) c ML wit discontinuities c at boundaries. Potential temperature Water q i ML = [ w c 0 w c ] () Numerical formalism (after Stull 98) C : Air mass excange rate matrices between model layers For turbulent diffusions l = «K K l+/ `cl+ c l Kl / `cl c l δ = C l,l+ = K l+/ δt δ, C l,l = (K l / + K l / ) δt δ, C l,m = 0 for l m > wit w c = C c () Betts, Albrect, Wang, Suare et al 98 ML Surf. q Randall et al. 99 and Lapen and Randall, 00: Combination of bulk models wit iger order closures l+ l l Turbulent diffussion Rising plume Slow compensating subsidence Assymetric Convective Model of Pleim and Cang 99 Mass flux scemes combined wit turbulent diffusion Potential temperature initial final 0 Inversion layer Neutral (sligtly stable) mixed layer Unstable surface layer Heat flux w w 0 α Termal plume w u u f d α Compensating subsidence e d wd K Turbulent diffusion Separation into sub-colums : X = αx u + ( αx d ) ascending plume of mass flux f = αρw u f = e d f c u = ec d dc u ρw c = ρk + f (c u c d ) (5) Catfield and Brost, 987, Hourdin et. al., 00, Siebesma, Soare et al, 00 Mass flux scemes combined wit turbulent diffusion Comparison wit LES Dry convective boundary layer. Forcing : w 0 = 0.K m/s geostropic wind of 0 m/s Termal Plume model (Hourdin et al. 00). LES SCM (D GCM) MY+Termal Plume (K) W' ' (K m/s) B Heat flux decomposition for Te «MY+termiques» case Total Termal Plume MY MY = ρk TP = f (c u c d ) wit Mass flux scemes combined wit turbulent diffusion s in climate models Zonal wind (m/s) Holtlag Mellor M& Y & Boville & Yamada + Termals w 0=0. K m/s, strongly inversion w 0=0.05 K m/s, weak inversion Tracer B H&B M& Y MY+TH Tracer B H&B M& Y MY+TH s in climate models s in climate models Statistical cloud scemes s in climate models Extension of mass flux scemes to cumulus clouds All or noting sceme 0 km 0 km 00 km Statistical sceme 00 km q > q sat (T) q < q sat (T) α Computation of condensation in te ascending plume Additional eating by condensation witin te updraft Feedback on te mass flux f and transport Computation of te water PDF Probability Distribution Function of te subrid-scale water. Cloud = fraction of te mes were water vapor exceeds saturation. = New requirement for boundary layer sceme : give information on te subrid-scale distribution 0 km 00 km

4 s in climate models D test of te cloudy termal plume model s in climate models D test of te cloudy termal plume model Continental diurnal cycle wit cumulus ARM EUROCS case (US Oklaoma) Rio et al. 008 LES SCM (D GCM) Test of te a new pysical package in te LMDZ global climate model Impact on te coverage by low clouds Specific umidity (g/kg) Turbulent diffusion + mass flux + clouds - LES Local time () Cloud base eigt (m) Cloud top eigt (m) Cloud cover Local time () Local time () Local time () s in climate models Cloud cover and satelite observations s in climate models A train Low Clouds cover Calipso LMDZ «new observations pysics» LMDZ grid + Calispo simulator 9 et 0 février Visite du Comité d'experts 8 s in climate models s in climate models Parameteriation of deep convection s in climate models A systematic biais of parameteried convection Classical parameteriations : Mass flux scemes Importance of cloud pase canges and rainfall Controled by instability above cloud base Example of te Emanuel (99) sceme : Level of Neutral Buoyancy Level of Free convection Condensation Level CIN CAPE Mb v Trigerring : B (LCL+0Pa) > CIN Closure : M B = f(cape)) CAPE : Convective Available Potential Energy CIN : Convective INibition. Climate models wit parameteried convection tend to predict continental convection in pase wit insolation, wile it peaks in late afternoon in reality and in Cloud Resolving Models (mes km). An idealied case of continental cycle wit deep convection ARM, Oklaoma, after Guicard et al. 00 CRMs SCMs Deep convection preceeded by a pase of sallow cumulus convection Boundary layer : preconditioning and trigerring of deep convection s in climate models ARM case wit te standard LMD SCM s in climate models Control of deep convection by sub-cloud processes 0km Emanuel (99) 0km km Termal plume model Emanuel ALP closure (Grandpeix et al.) km 00m Mellor & Yamada 6 9 LMD standard 5 8 Local time () CRMs 00m Mellor & Yamada New approac (Grandpeix et al. 009) : Control of deep convection by sub-cloud processes. By analogy wit a nole above a wall of eigt. Power P (W/m) ~ v Kinetic energy K=v / Local time () Triggering : K>g Closure : M=P/K

5 s in climate models s in climate models ALP closure Statistical cloud scemes New convection Avaliable Lifting Energy for te convection Scaling wit w. Trigerring : ALE > CIN Mature convection Precipitating downdraugts lifting Gust front Avaliable Lifting Power for te convection Scaling wit w. Closure : MB = f (ALP) Wake Density currents Cold pool New requirements for te boundary layer sceme : give reasonable estimates of w0 and w0. s in climate models s in climate models ARM case wit ALP closure, termals and wakes 0km ARM case wit ALP closure, termals and wakes Convective eating rate (K/day) LMDZ, old pysics Termal plume model Mellor & Yamada Ema. + MY + Term. + wakes Local time () New pysics LMD standard version CRM/MesoNH Pressure ( Pa) 6 Emanuel + MY + termal plume Pressure (Pa) Emanuel ALP closure (Grandpeix et al.) km 00m CRMs Rio & al., GRL, 008 s in climate models eure locale eure locale s in climate models Diurnal cycle of deep convection in te D LMDZ GCM LMDZ New pysical package s in climate models 0 km 00 km D test Diurnal cycle Of rainfall over Senegal (Sept. 006, AMMA) Raingauge network s in climate models s in climate models Boundary layer and transport of atmosperic tracers Boundary layer and transport of atmosperic tracers Test of Rn transport : emitted on conitnents only Contribution of te biospere to te CO latitudinal contrasts Idealied seasonal cycle for surface emission (null annual mean) GCM and transport models from te Transcom exercie After Dargaville et al. Mace Head Zingst Heidelberg (may) days of year (june) Test wit various parameteriations of te planetary boundary layer * Radon is a tracer of continental air masses, emited almost uniformely by continents only. Life time of about days. (may) days of year (june)

6 s in climate models Boundary layer and transport of atmosperic tracers Concluding remarks NOX computation at Dome C, Antartica MAR Regional model Parameteriation of boundary layer processes is a key issue for climate modeling and climate cange studies. Climate models are more and more complex but te realism of te "new components" (cemistry, vegetation,...) igly depends on te representation of atmosperic processes in general and boundary layer in particular. In current climate models (and still for a wile), boundary layer processes must be parameteried. Boundary layer scemes must be valid from equator to pole, and from dry stable atmospere to deep convection conditions. Te "new components" put new constraints on boundary layer scemes. Tere is a large place for improvement of boundary layer parameteriation. Te combined use of a turbulent diffusion for small scales and mass flux scemes for organied structures seems a proming way. A ierarcy of approaces are available to improve and evaluate boundary layer parameteriations : D versus LES, D, nudged, weater forecast and climate, etc.