General and Dynamic Meteorology
KMA Grade 9 meteorology candidates are tested on general and dynamic meteorology: the primitive equations, balance laws, vorticity, and scale analysis. Questions often ask you to derive a wind from a pressure field or to judge which force dominates at a given scale, so keep units and signs explicit.
Core balances
- Hydrostatic balance: dp/dz = -ρg. The hypsometric equation, Δz = (Rd T_v/g) ln(p1/p2), converts thickness to mean virtual temperature.
- Geostrophic balance: f k × Vg = -(1/ρ)∇p, with f = 2Ω sinφ. In the Northern Hemisphere, low pressure is to the left of the geostrophic wind.
- Thermal wind: ∂Vg/∂ln p = (R/f) k × ∇T. Wind veering with height indicates warm advection in the Northern Hemisphere.
- Vorticity ζ = ∂v/∂x - ∂u/∂y; divergence and deformation complete the kinematic description. Rossby wave phase speed depends on the beta effect and the zonal mean flow.
Worked example
At 45°N, ρ = 1.1 kg m⁻³, and pressure decreases northward by 2 hPa per 100 km. Convert the gradient: 200 Pa / 100,000 m = 0.002 Pa m⁻¹. f = 2(7.292×10⁻⁵) sin45° = 1.03×10⁻⁴ s⁻¹. Then Vg = (1/(ρf))|∇p| = 0.002/(1.1×1.03×10⁻⁴) ≈ 17.6 m s⁻¹. Because low pressure lies north, the NH geostrophic wind blows from west to east. Keeping hPa out of the denominator is the key step.
Traps
Using pressure in hPa without converting to Pa; omitting density; reversing the sign of f in the Southern Hemisphere; applying geostrophic balance near the equator, where f → 0; confusing the thermal wind with the actual wind; and treating the hypsometric equation as a temperature profile rather than a layer mean.