Feedback and Sensitivity in Climate

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1 Feedback and Sensitivity in Climate Frédéric Hourdin June 19, 2009

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3 Boundary layer processes in climate 2

4 Boundary layer processes in climate ps2pdf OK. Figure: ClimSI WV feedback model responses log(t y), f(x)=365*10 x -0.4 Oc Bk Tau 28j Tau prec 3m. Rep Eff "sigma.data" u (log10($1/365)): *(exp( e-02*f(x))-1) *(exp( e-03*f(x))-1) e-03*(exp( *f(x))-1) *(exp( e-02*f(x))-1) "/data/al1/pablo/cyclsta/sigma.datacysta" u (log10($1/365)):58 "/data/al1/pablo/ocblok/sigma.data" u (log10($1/365)): ClimSI : Comparaison entre Reponses efficaces

5 Boundary layer processes in climate 2

6 Boundary layer processes in climate 2

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8 of the conservation equation Conservation equation v : wind field c : conserved quantity (dc/dt = 0), Advective form : Flux form : X : "average" or "large scale" variable X = X X : turbulent fluctuation vc = vc + v c c + vgradc = 0 t (1) ρc + div (ρvc) = 0 t (2) q t + V.grad q + 1 ρ div ( ρv c ) = 0 (3)

9 Under boundary layer approximations ( / x << / z) : c t + v.grad c = S c + 1 ρ z w c (4) 3D Dynamical core 20 km Physical parametrizations One grid mesh or atmospheric column.? 200 km c : θ, u, v, water (vapor and others), chemical compounds...

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11 Diffusive or local formulations for the PBL w c = K z c z c t = ( ) c K z z z (5) Analogy with molecular viscosity. Down-gradient fluxes. Turbulence acts as a "mixing"

12 Turbulent diffusivity K z Prandlt (1925) mixing length : K z = l w or K z = l 2 v z Accounting for static stability (Ex. Louis 1979) K z = f (Ri)l 2 v z, Turbulent kinetic energy w 2 e = 1 2 with Ri = g θ θ z ( v z [u 2 + v 2 + w 2 ] ) 2 (6) e t = w u u z w v v z g θ w θ 1 w p w e ɛ (7) ρ z z Ex : Mellor and Yamada w φ φ = K φ z with K φ = l 2eS φ (Ri) Note : Imposing e t gives a coefficient of the form Eq. 6

vertical transport (from the bottom to PBL top) Organized structures 15km Cloud

13 Feedback Limitations of turbulent diffusion Diffusive approach : Random process 1 Small scale turbulence of size l << h with h = 1c c z Real turbulence Long range vertical transport (from the bottom to PBL top) Organized structures 15km Cloud streets on North of France (March 2009, MSG) Radar echoes in a dry convective boundary layer

14 Limitations of turbulent diffusion Idealized view of the dry convective boundary layer. Potential temperature initial final z h z i 0 Inversion layer Neutral (slightly stable) mixed layer Unstable surface layer θ Heat flux w θ In the mixed layer θ a Thermal plume wa Diffusive formulation w θ θ = K z = 0 or slightly < 0 α z (8) Uniform heating by the surface θ t w θ 0 z i (Cste > 0) (9) w θ z z i w z θ 0 > 0 (10) i

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16 Extension of diffusive formulations Introduction of a countergradient term [ w θ = K z Γ θ ] = 0 with Γ 1K/km (11) z Imposed countergradient Deardorf, 1966 Revisited by Troen & Mart, 1986, Holtzlag & Boville, 1993, based on a similarity approach. Higher order closures Abdella & Mc Farlane, 1997, Randall et al., 1992, Lapen & Ransall, 2002 (12)

17 Boundary layer, clouds and convection 2

18 Boundary layer, clouds and convection 2

19 Boundary layer, clouds and convection 2

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

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