The Atmosphere: Part 3: Unsaturated convection Composition / Structure Radiative transfer Vertical and latitudinal heat transport Atmospheric circulation Climate modeling Suggested further reading: Hartmann, Global Physical Climatology (Academic Press, 1994)

Full calculation of radiative equilibrium surface much too warm tropopause too cold stratosphere about right tropospheric lapse rate too large

Atmospheric energy balance

Hydrostatic balance

Pressure and density profiles in a compressible atmosphere hydrostatic balance perfect gas law Isothermal atmosphere More generally, H=H(z) and gas constant for dry air R = 287 J kg -1 K -1

Pressure and density profiles in a compressible atmosphere hydrostatic balance perfect gas law Isothermal atmosphere More generally, H=H(z) and (T=237K)

Convection I: Incompressible fluid, no condensation T and ρ are conserved under adiabatic displacement stable unstable

Thermodynamics of dry air C p = 1005 J kg -1 K -1

Thermodynamics of dry air C p = 1005 J kg -1 K -1 specific entropy

Thermodynamics of dry air C p = 1005 J kg -1 K -1 p 0 = 1000 hPa κ = R/c p = 2/7 (diatomic ideal gas) potential temperature (+ constant) specific entropy

Thermodynamics of dry air C p = 1005 J kg -1 K -1 p 0 = 1000 hPa κ = R/c p = 2/7 (diatomic ideal gas) potential temperature Adiabatic processes : θ is conserved under adiabatic displacement (N. B. θ=T at p =p 0 = 1000 hPa) (+ constant) specific entropy

Convection II: Compressible ideal gas, no condensation adiabatic displacement

Convection II: Compressible ideal gas, no condensation hydrostatic balance adiabatic displacement

Convection II: Compressible ideal gas, no condensation hydrostatic balance adiabatic displacement — adiabatic lapse rate Following displaced parcel

Convection II: Compressible ideal gas, no condensation hydrostatic balance adiabatic displacement — adiabatic lapse rate Following displaced parcel unstable stable

Convection II: Compressible ideal gas, no condensation hydrostatic balance adiabatic displacement — adiabatic lapse rate Following displaced parcel unstable stable

Stability of Radiative Equilibrium Profile Radiative equilibrium is unstable in the troposphere -10 K/km radiative equilibrium solution

Effects of convection Model aircraft observations in an unsaturated convective region (Renno & Williams)

Effects of convection radiative-convective equilibrium

Effects of convection radiative-convective equilibrium TROPOSPHERE STRATOSPHERE

Radiative-Convective Equilibrium Radiative equilibrium is unstable in the troposphere Re-calculate equilibrium subject to the constraint that tropospheric stability is rendered neutral by convection. -10 K/km radiative equilibrium solution

Radiative-convective equilibrium (unsaturated) Better, but: surface still too warm tropopause still too cold

Moist convection Above a thin boundary layer, most atmospheric convection involves phase change of water: condensation releases latent heat