Keywords: parameter estimation, genetic algorithms, wind field modelling, mass consistent models, adaptive mesh refinement, finite element method.

A three-dimensional finite element model for wind field adjustment is developed. In general, these problems are defined over regions with complex terrain, therefore a suitable discretization of the studied zone will be necessary. Here, we have used a technique for constructing tetrahedral meshes which are adapted to the terrain orography and have a higher density of nodes near the terrain surface. Our mass consistent model generates a velocity field for an incompressible fluid which adjusts to an initial one obtained from experimental measures and physical considerations. The first step for building the initial field is to carry out an horizontal interpolation at the height over the terrain of the measurement stations. From these data, vertical profiles are constructed taking into account the atmospheric stability, the roughness of the terrain, the geostrophic wind and the atmospheric stratification. Once the initial field is computed, we formulate the mass continuity equation of an incompressible fluid with non-flow-through boundary condition on the terrain surface. The adjustment is carried out by a least square function. The Lagrange multipliers technique leads to an elliptic problem which is solved by using the finite elements method. However, there may exist some zones of the domain where more accuracy of the numerical solution is required due to the irregularity of the terrain as well as to strong variations of the solution. In order to improve the solution, an adaptable refinement of the three-dimensional mesh is proposed. First, for each element of the mesh to be refined, an error indicator is computed attending to the current numerical solution. These point out what elements must be refined. The proposed refinement technique, based on the subdivision in 8-subtetrahedra, allows a higher discretization of the selected zones without an excessive propagation along the mesh. This process may be repeated until the error of the numerical solution satisfies the imposed tolerance. Nevertheless, the efficiency of this mass consistent model for wind field adjustment depends on several parameters that arise in various stages of the process. On one hand, those involved in the construction of the initial wind field using horizontal interpolation and vertical extrapolation of the wind measures registered at meteorological stations. On the other hand, the Gauss precision moduli which allow from a strictly horizontal wind adjustment to a pure vertical one. In general, the values of all of these parameters are based on empirical laws. The main goal of this work is the estimation of these parameters using genetic algorithms, such that some of the wind velocities observed at the measurement stations are regenerated as accurately as possible by the model. In addition, we study the effect of the mesh refinement on the parameter estimation in several numerical experiments.

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