Above a thin boundary layer, most atmospheric convection involved phase change of water: Moist Convection Moist Convection • Significant heating owing to phase changes of water • Redistribution of water vapor – most important greenhouse gas • Significant contributor to stratiform cloudiness – albedo and longwave trapping Water Variables Mass concentration of water vapor (specific humidity): q≡ MH O 2 M air Vapor pressure (partial pressure of water vapor): Saturation vapor pressure: C-C: e* 17.67(T −273) T +30 e* = 6.112 hPa e Relative Humidity: H ≡ e e* e The Saturation Specific Humidity Ideal Gas Law: R *T p=ρ m R*T e = ρv mv mv e ρ v q= ρ = m p mv e* q* = m p Phase Equilibria Bringing Air to Saturation e = qp  m m   v e* = e *(T ) 1. Increase q (or p) 2. Decrease e* (T) When Saturation Occurs… • Heterogeneous Nucleation • Supersaturations very small in atmosphere • Drop size distribution sensitive to size distribution of cloud condensation nuclei Ice Nucleation Problematic ICE NUCLEATION PROBLEMATIC 4 3 100 Percentage of clouds with ice particle concentrations above detectable level 15 16 16 80 7 1 2 1 1 1 8 23 60 14 25 40 12 10 20 33 15 20 1 0 0 25 1 -5 -10 -15 Cloud top temperature (oC) -20 -25 Precipitation Formation: • Stochastic coalescence (sensitive to drop size distributions) • Bergeron-Findeisen Process • Strongly nonlinear function of cloud water concentration • Time scale of precipitation formation ~10 30 minutes Stability No simple criterion based on entropy: T   p sd = c p ln   − Rd ln    T0   p0  α = α ( sd , p ) T   p  q + L s = c ln   − R ln  − qR ln ( H p T  d  p  vT v  0  0 α = α ( s, p, qt ) ) Trick: Define a saturation entropy, s* : s* ≡ s (T , p, q *) α = α ( s*, p, qt ) We can add an arbitrary function of qt to s* such that α ≅ α ( s*', p ) Stability Assessment using Tephigrams: Convective Available Potential Energy (CAPE): CAPEi ≡ ∫ p (α p − α e )dp pi n ( ) = ∫ p Rd Tρ − Tρ d ln ( p ) pi p e Other Stability Diagrams: Tropical Soundings “Air-Mass” Showers: Precipitating Convection favors Widely Spaced Clouds (Bjerknes, 1938) Properties: • Convective updrafts widely spaced • Surface enthalpy flux equal to vertically integrated radiative cooling c pT ∂θ M = −Q • θ ∂z • Precipitation = Evaporation = Radiative Cooling • Radiation and convection highly interactive Simple Radiative-Convective Model Enforce convective neutrality: T1 = T2 + ∆T , Ts = T2 + 2∆T TOA : T2 = Te → T1 = Te + ∆T , Ts = Te + 2∆T Surface : Fs + σ Ts 4 = σ Te 4 + σ T14 Layer 2 : 2σ Te = σ T + Fc 4 Define x ≡ ∆T Te 4 1 , 4 4  Fs = σ Te 1 + (1+ x ) − (1 + 2 x )  ,   4 4  Fc = σ Te 2 − (1 + x )    4 Manabe and Strickler 1964 calculation: Effect of Moist Convective Adjustment on Climate Sensitivity