Three-Dimensional Wind Field Modeling: A Review

Abstract

Over the past several decades, the development of computer models to predict the atmospheric transport of hazardous material across a local (on the order of 10s of km) to mesoscale (on the order of 100s of km) region has received considerable attention, for both regulatory purposes, and to guide emergency response teams. Wind inputs to these models cover a spectrum of sophistication and required resources. At one end is the interpolation/ extrapolation of available observations, which can be done rapidly, but at the risk of missing important local phenomena. Such a model can also only describe the wind at the time the observations were made. At the other end are sophisticated numerical solutions based on socalled Primitive Equation models. These prognostic models, so-called because in principle they can forecast future conditions, contain the most physics, but can easily consume tens of hours, if not days, of computer time. They may also require orders of magnitude more effort to set up, as both boundary and initial conditions on all the relevant variables must be supplied. The subject of this report is two classes of models intermediate in sophistication between the interpolated and prognostic ends of the spectrum. The first, known as mass-consistent (sometimes referred to as diagnostic) models, attempt to strike a compromise between simple interpolation and the complexity of the Primitive Equation models by satisfying only the conservation of mass (continuity) equation. The second class considered here consists of the so-called linear models, which purport to satisfy both mass and momentum balances. A review of the published literature on these models over the past few decades was performed. Though diagnostic models use a variety of approaches, they tend to fall into a relatively few welldefined categories. Linear models, on the other hand, follow a more uniform methodology, though they differ in detail. The discussion considers the theoretical underpinnings of each category of the diagnostic models, and the linear models, in order to assess the advantages and disadvantages of each. It is concluded that diagnostic models are the better suited of the two for predicting the atmospheric dispersion of hazardous materials in emergency response scenarios, as the linear models are only able to accommodate gently-sloping terrain, and are predicated on several simplifying approximations which can be difficult to justify a priori. Of the various approaches used in diagnostic modeling, that based on the calculus of variations appears to be the most objective, in that it introduces the fewest number of arbitrary parameters. The strengths and weaknesses of models in this category, as they relate to the activities of Sandia's Nuclear Emergency Support Team (NEST), are further highlighted.

Improving the Reconstruction of Vector Fields Using Mixed Finite Element Methods and Optimal Preconditioning

“…w ( x , y ) depends on x explicitly), the results do depend of S . Nevertheless, many authors give recommendations about how to choose S , . The number of iterations is reduced from several hundreds to less than 10 for all the examples considered in this article, even for nonsimple domains and nonuniform meshes. Also, the number of iterations of the PCG–algorithm is almost independent with respect to mesh refinement, while the number of iterations in the nonpreconditioned algorithm doubles at each mesh refinement in most cases.…”

Preliminary estimate of the large-scale wind energy resource with few measurements available: The case of Montenegro

“…For an overview of mass-consistent models see e.g. Ratto et al (1994) or Homicz (2002). The traditional approach consists in creating 3D mass-consistent flows from 3D flow fields essentially obtained through numerical interpolation/ extrapolation from measurements in available stations in the simulated area.…”

Evaluation of a Diagnostic Model of an Air Velocity Field: The Must Wind Tunnel Case

“…Homicz [11] distinguishes four methods of solving problems which are known in the literature as using one of the algorithms: direct-differencing, point-iterative, hybrid and variational calculus.…”

“…This algorithm also requires the least number of parameters to be given arbitrarily by the performers of the simulations. As [11] further mentions, diagnostic models using variational calculus allow to compute a spatial velocity field which not only satisfies the continuity equation, but also minimises the difference between the input velocity field (obtained by interpolation) and the resulting field. The algorithm is based on solving the minimisation problem of the functional representing the difference between the initial velocity field which is obtained from the measurements and the adjusted velocity field which satisfies the continuity equation.…”

“…Diagnostic models use a procedure of adjusting the velocity field to the measurement data [11]. The procedure comprises two stages.…”