Earth sciences
10 topics
Earth sciences
Meteorology
Meteorology uses the Navier-Stokes equations and thermodynamics to model the atmosphere. Numerical weather prediction is one of the great triumphs of applied mathematics.
Topics in this field
Atmospheric Boundary Layer
The turbulent lowest kilometre of the atmosphere that mediates exchanges of heat, moisture, and momentum between the surface and free troposphere.
Atmospheric Thermodynamics
The thermodynamic laws governing temperature, stability, and phase change in the atmosphere.
Atmospheric Waves
Rossby waves, gravity waves, and their dispersion relations that govern large-scale energy propagation in the atmosphere.
Data Assimilation
Combining model forecasts with observations using Bayesian estimation to produce optimal initial conditions for NWP.
Ensemble Forecasting
Quantifying forecast uncertainty by running multiple model simulations from perturbed initial conditions.
Mesoscale Convection
The organisation of thunderstorms into mesoscale convective systems driven by CAPE, wind shear, and cold pool dynamics.
Numerical Weather Prediction
How finite-difference and spectral methods solve the atmospheric PDEs that drive operational weather forecasts.
Primitive Equations
The governing equations of atmospheric motion on a rotating sphere, forming the backbone of all global weather and climate models.
Tropical Cyclones
The dynamics of warm-core rotating vortices that form over tropical oceans and can reach devastating intensities.
Weather Radar
How radar equations, reflectivity, Doppler velocity, and dual-polarisation moments are used to observe precipitation and storms.