Earth sciences 10 topics
Earth sciences
Meteorology
10 topics 18 math concepts connects to 3 fields
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.
differential equations dynamical systems spectral analysis
Atmospheric Thermodynamics
The thermodynamic laws governing temperature, stability, and phase change in the atmosphere.
differential equations probability theory measure theory
Atmospheric Waves
Rossby waves, gravity waves, and their dispersion relations that govern large-scale energy propagation in the atmosphere.
partial differential equations fourier transform spectral analysis
Data Assimilation
Combining model forecasts with observations using Bayesian estimation to produce optimal initial conditions for NWP.
bayes theorem linear algebra optimization
Ensemble Forecasting
Quantifying forecast uncertainty by running multiple model simulations from perturbed initial conditions.
probability theory monte carlo methods gaussian distribution
Mesoscale Convection
The organisation of thunderstorms into mesoscale convective systems driven by CAPE, wind shear, and cold pool dynamics.
differential equations dynamical systems probability theory
Numerical Weather Prediction
How finite-difference and spectral methods solve the atmospheric PDEs that drive operational weather forecasts.
partial differential equations numerical methods fourier transform
Primitive Equations
The governing equations of atmospheric motion on a rotating sphere, forming the backbone of all global weather and climate models.
partial differential equations differential geometry dynamical systems
Tropical Cyclones
The dynamics of warm-core rotating vortices that form over tropical oceans and can reach devastating intensities.
differential equations dynamical systems variational calculus
Weather Radar
How radar equations, reflectivity, Doppler velocity, and dual-polarisation moments are used to observe precipitation and storms.
fourier transform spectral analysis probability theory