Quoted from: Prieto Herráez, D., María Isabel Asensio Sevilla, Luis Ferragut Canals, José Manuel Cascón Barbero, and A. Morillo Rodríguez. "A GIS-based fire spread simulator integrating a simplified physical wildland fire model and a wind field model." International Journal of Geographical Information Science 31, no. 11 (2017): 2142-2163. https://doi.org/10.1080/13658816.2017.1334889 

The origin of the HDWM lies in an asymptotic approximation of the primitive Navier–Stokes equations considering that the horizontal dimensions are much larger than the vertical ones. The aim is to provide a 3D wind velocity field in the air layer over the surface of study, solving only 2D linear equations so that it can be coupled with the 2D fire spread model. This idea was first published in Asensio et al. (2002), where the coupling of wind and fire models had already been considered. The details of how this model stems from an asymptotic approximation of the Navier–Stokes equations can be found in Asensio et al. (2005). Roughly speaking, the HDWM locally provides a detailed 3D wind velocity field in an air layer over the surface, above which the surface temperature and topography have not effect, solving only 2D equations depending on the temperature on the ground surface  (or  in the absence of fire), topography h, and the horizontal component of the meteorological wind  on the boundary of the simulation air layer. The model depends on a single parameter, the friction coefficient , which is related to the surface roughness length   using the Davenport classification of terrain (Davenport et al. 2000). The model takes into account slope effects, mass conservation and buoyancy forces that enable the effect of wind temperature to be included. In Ferragut et al. (2011), the wind velocity field obtained by the model is adjusted to several wind velocity measurements  at different points in the 3D domain. This adjustment requires solving an optimal control problem in which the wind flow on the surface boundary is the control. Our wind field model does not therefore require measuring the meteorological wind on the boundary, as it suffices to provide the meteorological wind at certain points in the domain, for example, the data from weather stations. Our model is an alternative for wind resource estimation in local terrains using mesoscale–microscale coupling techniques (Gopalan et al. 2014).

The HDWM equations are not shown in this paper due to their mathematical complexity. Interested readers can find the details in the aforementioned papers. The implementation of the HDWM is entered in the Spanish Registry of Intellectual Property on 16 July 2015 under record entry 00/2015/4721.