A Mass Consistent Approach to Improve Wind Downscaling for Real Time Fire Spread Simulations ^†

Fire propagation is mainly influenced by three elements: slope of the terrain, vegetation, and wind. The most dangerous fires events occur with strong wind conditions. Even small differences in wind field predictions can imply relevant variations in burned areas; therefore, particular attention should be dedicated to feed the fire model with reliable wind field information.

In this work, the downscaling approach consists of a first guess wind field, in order to respect the constrains imposed by a higher resolution orography, relaxing the constrains derived from general conservation principle of energy, momentum, and mass in regards to this last conservation law. The mass-consistent approach, therefore, adjusts a first-guess wind field by individuating, among the non-divergent scalar field, the closest to the first-guess. The approximation of incompressibility of the air is also introduced.

The implementation of the method follows the variational method, and deals with a generalization of the Lagrangian multiplier for the L² Hilbert space. To solve the Poisson equation, a finite difference method with horizontal regular squared cells was adopted and, in order to give a better representation of the lower part of the planetary boundary layer, the distribution of the vertical levels follows an exponential law. “Terrain following” vertical coordinates are introduced.

To speed up the solution of equations, in order to support an operational use of the model, a multi grid technique is implemented; it allows for different treatment of errors characterized by different wavelength.

Preliminary results show a relevant improvement in the wind field data accuracy within an elaboration time compatible with operational needs.