High definition local adjustment model of 3D wind fields performing only 2D computations

Abstract

SUMMARYWe present a set of equations modelling wind velocity in a 3D domain in terms of the ground height function, the ground temperature and the wind on the boundary. The wind field is adjusted to several punctual wind velocity measurements at different points in the 3D domain by an optimal control problem in which the (unknown) wind on the boundary is the control. Using the meteorological wind punctual measures as datum, the model provides locally a detailed 3D wind that takes into account topography and thermal gradients on the surface by solving only 2D linear equations. We consider briefly the numerical approximation and two examples, including one with real data to control the accuracy of the model.

A reduced basis for a local high definition wind model

“…In this section we present the wind model. A complete description can be found in [1,2]. Our model arrives from an asymptotic analysis of Navier-Stokes equations and gives a three-dimensional convective model governed by a two-dimensional equation.…”

“…In practical applications [2], the inverse of the friction coefficient ξ is defined in terms of the roughness of the terrain. Here, we propose a quadratic adjustment:…”

“…Our starting point is a mass consistent vertical diffusion wind field model. If the significant phenomena that we want to simulate occur in a zone, where the horizontal dimensions are much larger than the vertical one, then an asymptotic approximation of the primitive Navier-Stokes equations can be derived as in the model developed in [1,2]. The most salient feature of this asymptotic approach is that it provides a three-dimensional velocity wind field (which satisfies the incompressibility condition in the air layer) governed by a two-dimensional equation, so that it can be coupled with the temperature surface distribution in order to take into account the thermal effects such as sea breezes.…”

“…The wind model presented in this paper is an adaptation of the wind model proposed in [1]. When the data are given by meteorological predictions, an optimal control problem is obtained [2], which can be solved using the adjoint equation-based method. We refer the reader to [3] for the details of this approach.…”

A Wildland Fire Physical Model Well Suited to Data Assimilation

“…We used the high definition wind model developed by the authors in ASENSIO et al (2005) andFERRAGUT et al (2011). The starting point of our wind model is a vertical diffusion wind-field model.…”