Vertical wind interpolation

Vertical log interpolation and wind reduction factors

The wind speed that enters the spread rate formula is found by vertical interpolation to a specified height fwh, sometimes called midflame height, using the ideal logarithmic wind profile: the wind speed at height z is assumed to be proportional to log z/z₀, where z₀ is the roughness height (clearly, this is the height where the wind speed is zero). The special logarithmic interpolation we use preserves such functions just like linear interpolation preserves linear functions. The numbers fwh and z/z₀ need to be known at every point of the fire mesh.

In BEHAVE, the wind is measured at the 20ft (6.096m) and log interpolated to the midflame height. The interpolation is the same as multiplying the wind speed by a given wind reduction factor windrf (Baughman and Albini, 1980).

See Mandel et al. 2011 Sec. 5.2 for more details.

Implementation

In the code, we thus have two choices:

1. Interpolate to 6.096m and apply the wind reduction factors. This is much simpler and faster.
2. Interpolate the wind at each point of the fire mesh to the midflame height at that point separately. This is more complicated.

The vertical interpolation is somewhat complicated because of the way how WRF represents the wind speed and the vertical coordinate. In particular, because the altitude of nodes in WRF changes during the run, the number of vertical levels needed for the interpolation is not known in advance.

Data input

In WRF, the roughness height z0 is specified by the surface model in land use. This is typically taken from file LANDUSE.TBL. The values of the midflame height fwh, the roughness height fz0 and the BEHAVE height fire_wind_height are given in the file namelist.fire as a part of the fuel properties. If these values are not given in the file, the defaults in the code apply.

The interpolation mode is controlled by the values of the variables fire_wind_log_interp and fire_use_windrf in the file namelist.input:

 fire_wind_log_interp = 1,      ! 1 = from fuel categores, 2= roughness piecewise constant from atm, 3=bilinear from atm, 4=on atmosphere mesh 
 fire_use_windrf=2,             ! if fire_wind_log_interp.ne.4: 0=ignore wind reduction factors, 1=multiply, 2=use to set fwh, 3=adjust fwh for z0

References

1. Robert G. Baughman and Frank A. Albini, Estimating Midflame Windspeeds, Sixth Conference on Fire and Forest Meteorology, Seattle, WA April 22-24, 1980, pp. 88-92 pdf
2. Jan Mandel, Jonathan D. Beezley, and Adam K. Kochanski, Coupled atmosphere-wildland fire modeling with WRF 3.3 and SFIRE 2011, Geoscientific Model Development (GMD) 4, 591-610, 2011. doi:10.5194/gmd-4-591-2011