An analytical solution for a low barrier in a turbulent atmosphere

Journal article, 2004

The work presented here uses a previously developed substitute sources method (SSM) as the starting point for solving the problem with a low barrier in a turbulent atmosphere. The formulation of the SSM involves a double integral and the numerical solution is computationally demanding. The SSM results are here used as reference. As an intermediate step toward an analytical solution, an expression containing a single integral is found. Its implementation is computationally much less demanding and is here called the fast method. The analytical solution involves further approximations and has a smaller range of validity than the fast method, but could nonetheless be useful. Both the fast method and the analytical solution assume a flat geometry, whereby they can be useful as a complement to scattering cross-section based methods. Moreover, two-dimensional (2-D) modelling is done and no ground surface is considered. Agreement between the SSM and the fast method is reasonably good, and additional restraints are formulated for the applicability of the analytical solution.