Climate Modeling

Mathematical Modeling · Axiom Academy

How spatial mathematical models help us understand and predict Earth's climate system The Challenge of Modeling Earth's Climate Climate modeling is one of the most ambitious applications of spatial mathematical models. Scientists must simulate the complex interactions of atmosphere, oceans, ice, land, and life across the entire planet, using partial differential equations that capture how heat, moisture, and momentum flow through space and time. A climate model is a system of mathematical equations that describes the physical, chemical, and biological processes governing Earth's climate. Modern climate models divide the Earth into a three-dimensional grid and solve conservation equations for energy, mass, and momentum at each grid cell. Dividing Earth into a Computational Grid At the heart of climate modeling is spatial discretization - dividing the continuous Earth system into discrete grid cells where equations can be solved numerically. This is the same technique used for any spatial PDE model. Climate models use a three-dimensional grid that covers the entire globe: Here is a simplified representation of a horizontal climate model grid. Each cell stores values for temperature, pressure, humidity, and other variables: Coarse grids (100+ km) : Computationally fast, but miss local features like individual storms Medium grids (25-50 km) : Balance between detail and computational cost Fine grids (<10 km) : Resolve hurricanes, mountain effects, but require supercomputers

This is the written version of the interactive lesson above. See the full Mathematical Modeling course.