3-D modelling of wind field adjustment using finite differences in a terrain conformal coordinate system

Abstract

A mass consistent model is developed in order to obtain a wind field which adjusts to an initial one. For the construction of the initial field, horizontal interpolation is considered at the level of the measure stations over the terrain. From these values, vertical wind profiles are built according to atmospheric stability conditions, terrain roughness, geostrophic wind, atmospheric stratification. The problem is formulated in terms of an incompressible fluid with no-flow-through conditions on the terrain. The adjustment is carried out by minimizing a least-square function. Lagrange multipliers technique leads to an elliptic problem, which is discretized using finite-differences schemes after applying a proposed system of terrain conformal coordinate. This change not only simplifies the mesh generation, but leads to simpler boundary conditions and allows the definition o:F the vertical spacing with more resolution near the terrain without affecting the efficiency. Finally, the numerical model is applied to realistic data corresponding to the Island of La Palma (Canary Islands).