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Feedback and Sensitivity in Climate

Frédéric Hourdin June 18, 2009

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Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection

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Boundary layer processes in climate Boundary layer as a boundary condition

Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection

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Boundary layer processes in climate Boundary layer as a boundary condition

ps2pdf OK.

Figure: ClimSI WV feedback model responses.

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Boundary layer processes in climate Boundary layer and clouds

Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection

university-logo Feedback

Boundary layer processes in climate Boundary layer in the "Earth Systemp"

Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection

university-logo Feedback

Approaches to the parametrization of the boundary layer Scale decomposition

Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection

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Approaches to the parametrization of the boundary layer Scale decomposition

Scale decomposition of the conservation equation

Conservation equation v : wind field c : conserved quantity (dc/dt = 0),

Advective form :  \frac{∂c}{∂t} + vgrad c = 0  (1)
Flux form :  \frac{∂ρc}{∂t} + div(ρvc) = 0  (2)

Scale decomposition \overline{X}: "average" or "large scale" variable X′ = X − \overline{X}: turbulent fluctuation \overline{vc} = \overline{v}\overline{c} + \overline{v′c′}

\frac{∂\overline{q}}{∂t} + \overline{V}.grad \overline{q} + \frac{1}{ρ}div(\overline{ρv′c′}) = 0  (3)

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Approaches to the parametrization of the boundary layer Scale decomposition

Under boundary layer approximations (∂/∂x << ∂/∂z) :

\frac{∂c}{∂t} + v.grad c + \frac{1}{ρ} \frac{∂}{∂z}\overline{w′c′} = 0  (4)

Turbulent closure : Construct a model relating \overline{w′c′} to the large scale variables.

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Approaches to the parametrization of the boundary layer Diffusive approaches and their limitations

Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection

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Approaches to the parametrization of the boundary layer Diffusive approaches and their limitations

Diffusive or local formulations for the PBL

\overline{w′c′} = −K_{z} \frac{∂c}{∂z}  ⟶  \frac{∂c}{∂t} = \frac{∂}{∂z} (K_{z} \frac{∂c}{∂z})  (5)

Analogy with molecular viscosity. Down-gradient fluxes. Turbulence acts as a "mixing"

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Approaches to the parametrization of the boundary layer Diffusive approaches and their limitations

Turbulent diffusivity K_{z}

Prandlt (1925) mixing length : K_{z} = l\overline{|w′|}or K_{z} = l^{2} \frac{∂||v||}{∂z} Accounting for static stability (Ex. Louis 1979)

K_{z} = f (Ri)l^{2} |\frac{∂v}{∂z}| ,  with Ri = \frac{g}{θ} \frac{\frac{∂θ}{∂z}}{(\frac{∂v}{∂z})2}  (6)

Turbulent kinetic energy \overline{w′}^{2} ≃ e = \frac{1}{2} [\overline{u^{′2}} + \overline{v^{′2}} + \overline{w^{′2}}]

\frac{∂e}{∂t} = −\overline{w′u′} \frac{∂u}{∂z} − \overline{w′v′}\frac{∂v}{∂z} − −\frac{g}{θ}\overline{w′θ′}− \frac{1}{ρ} \frac{∂\overline{w′p′}}{∂z} − \frac{∂\overline{w′e}}{∂z} − ϵ (7)

Ex : Mellor and Yamada \overline{w′ϕ′} = −K_{ϕ} \frac{∂ϕ}{∂z} with K_{ϕ} = l\sqrt{2e}S_{ϕ}(Ri) Note : Imposing \frac{∂e}{∂t} gives a coefficient of the form Eq. 6

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Approaches to the parametrization of the boundary layer

Diffusive approaches and their limitations

Limitations of turbulent diffusion

Diffusive approach : Random process Small scale turbulence of size l << h with h = [\frac{1}{c} \frac{∂c}{∂z}]^{−1}

Real turbulence Long range vertical transport (from the bottom to PBL top) Organized structures

Cloud streets on North of France (March 2009, MSG)

Radar echos in a dry convective boundary layer

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Approaches to the parametrization of the boundary layer Alternatives to diffusive approaches

Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection

university-logo Feedback

Boundary layer, clouds and convection Could schemes in climate models

Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection

university-logo Feedback

Boundary layer, clouds and convection Cumulus clouds and mass flux parametrisations

Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection

university-logo Feedback

Boundary layer, clouds and convection Boundary layer and deep convection

Outline

1 Boundary layer processes in climate

Boundary layer as a boundary condition Boundary layer and clouds Boundary layer in the "Earth Systemp"

2 Approaches to the parametrization of the boundary layer

Scale decomposition Diffusive approaches and their limitations Alternatives to diffusive approaches

3 Boundary layer, clouds and convection

Could schemes in climate models Cumulus clouds and mass flux parametrisations Boundary layer and deep convection