Matrix Analysis of Tracer Transport

We review matrix methods as applied to tracer transport. Because tracer transport is linear, matrix methods are an ideal fit for the problem. A gridded, Eulerian tracer simulation can be approximated as a system of linear ordinary differential equations (ODEs). The first-order stretching and deformation of Lagrangian space can also be calculated using a system of linear ODEs. Solutions to these equations are reviewed as well as special properties. Using matrices to model Eulerian tracer transport can also help understand and improve the stability of numerical solutions. Detailed derivations are included.