Atmospheric Thermodynamics and Physical Meteorology
Atmospheric thermodynamics and physical meteorology covers the first law, moisture variables, adiabatic processes, stability, and cloud microphysics. The exam expects numerical fluency with potential temperature, mixing ratio, and CAPE, plus a physical picture of phase change.
Core rules
- First law: dq = cp dT - α dp. For dry adiabatic motion, θ = T(p0/p)^(Rd/cp) is conserved, with Rd/cp ≈ 0.286. The dry adiabatic lapse rate is g/cp ≈ 9.8 K km⁻¹.
- Mixing ratio: w = 0.622 e/(p - e). Relative humidity is w/ws (or e/es); dewpoint is the temperature at which saturation occurs. Clausius-Clapeyron gives roughly 7% more saturation vapor pressure per 1 K warming.
- Equivalent potential temperature θe is conserved in moist adiabatic ascent; CAPE = ∫ g (Tv,parcel - Tv,env)/Tv,env dz, and CIN is the negative area below the level of free convection.
Worked example
A parcel has T = 10°C (283.15 K) at 850 hPa. Find θ with p0 = 1000 hPa: θ = 283.15 × (1000/850)^0.286. The ratio is 1.176; ln(1.176) = 0.162; multiplied by 0.286 gives 0.0464; exp(0.0464) = 1.0475. Thus θ ≈ 296.6 K (23.5°C). If lifted dry-adiabatically back to 850 hPa from a 1000-hPa reference, the parcel would return to about 283 K, confirming conservation.
Traps
Putting Celsius into Poisson's equation; inverting the pressure ratio; treating mixing ratio and specific humidity as identical at high humidity; assuming RH stays constant when temperature changes at fixed w; using environmental temperature instead of virtual temperature in CAPE; and forgetting that θe, not θ, is the conserved quantity in saturated ascent.