Galerkin Approximations to Vertical Temperature Profiles Across the Earth's Surface

Abstract

The Galerkin method is used to solve numerically the nonlinear initial-boundary value problem describing the vertical temperature profile for a thermally coupled soil-atmosphere boundary layer in a simple physical setting. The basic physical processes modeled, including conduction and free convection, are simple, yet the solution to the model problem illustrates the Galerkin procedure. The numerical simulation requires special mathematical techniques for handling interior boundary or coupling conditions. The physical interpretation of the internal conditions includes consideration of time-dependent insolational heating and the thermal interaction between the atmosphere and the soil. Comparisons between the exact solutions and the Galerkin solutions for several linear problems show agreement for all cases studied.