7.3 Numerical Weather Prediction
NWP models solve the primitive equations on a 3D grid to forecast weather. Modern models have ~10 km resolution globally.
Primitive Equations
Momentum: $\frac{D\vec{v}}{Dt} = -\frac{1}{\rho}\nabla p - f\hat{k}\times\vec{v} + \vec{g} + \vec{F}$
Continuity: $\frac{\partial \rho}{\partial t} + \nabla\cdot(\rho\vec{v}) = 0$
Thermodynamic: $\frac{D\theta}{Dt} = \frac{\dot{Q}}{c_p\Pi}$
Moisture: $\frac{Dq}{Dt} = S_q$
Major NWP Models
GFS
NOAA global model, ~13 km
ECMWF IFS
European, ~9 km, gold standard
NAM/HRRR
Regional US, 3 km
ICON
German DWD, icosahedral grid