Physical Meteorology and Atmospheric Thermodynamics
Core concepts
A candidate must command the equation of state for dry air (p = ρRdT) and moist air, the hydrostatic equation, and the hypsometric equation used to derive thickness and heights. Understand the first law of thermodynamics in both forms, potential temperature (θ = T(1000/p)^(Rd/cp)), the Exner function, and the stability criteria dθ/dz. Moist processes are decisive: mixing ratio, saturation vapour pressure (Clausius–Clapeyron), dew point, relative humidity, equivalent potential temperature, and the wet-bulb temperature. Know the lapse rates: dry adiabatic 9.8 °C/km, saturated adiabatic 4–7 °C/km, and environmental averages. Study CAPE and CIN, the parcel method, and the thermodynamic diagram (T–log p, skew-T) with its dry and moist adiabats and mixing-ratio lines.
Traps
Questions often mix virtual temperature with actual temperature; always use Tv where buoyancy is at stake. Watch whether θ or θe is required (θe is conserved in saturated ascent). Distinguish the tropopause definition (lapse-rate and isothermal criteria) from the tropopause break. Be careful with units: hPa versus Pa, g/kg versus kg/kg, and °C versus K in the equation of state. Latent heat values (Lv ≈ 2.5×10^6 J/kg, Lf ≈ 3.34×10^5 J/kg) are frequently tested.
Worked example
A parcel at 1000 hPa and 20 °C is lifted to 900 hPa dry adiabatically. Using θ conservation: θ = 293.15 × (1000/1000)^0.286 = 293.15 K. At 900 hPa, T = θ(p/1000)^0.286 = 293.15 × (0.9)^0.286 ≈ 293.15 × 0.970 ≈ 284.4 K ≈ 11.3 °C. The dry-adiabatic cooling is about 8.7 °C, consistent with ~9.8 °C/km over roughly 0.9 km.