APPM Instructor Search - Eric Thaler

Quasigeostrophic Theory – Applying Mathematics to Applied Meteorology

Quasigeostrophic (QG) theory has been the cornerstone of dynamic meteorology for well over half a century. It has been used as a research tool for understanding the dynamics of weather systems, served as the basis of some early numerical weather prediction models and is used in operational weather prediction as a key component in producing day-to-day forecasts.

One of the benefits of theory is its ability to include many of the important physical processes responsible for synoptic scale weather in a compact package of mathematical equations. These equations have been applied qualitatively in operational weather forecasting for a very long time. More 
recently, quantitative applications of the solutions of these equations have been developed and are now in operational use.

These quantitative techniques include a rich application of many mathematical ideas, ranging from describing physically-based conservation laws to approximating solutions of three-dimensional partial differential equations. Obtaining these solutions involves solving gigantic linear systems of equations (~105 equations/unknowns) which, in turn, requires numerical techniques that can accomplish the task in time frames dictated by real time weather forecasting constraints.

This talk will provide a brief look into how a variety of mathematical concepts ranging from vector calculus through differential equations, linear algebra and numerical analysis are applied to a real world problem that affects essentially all of humanity.