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).

In the code, we thus have two choices:

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

See Mandel et al. 2011 for more details.

The vertical interpolation is somehow complicated because of the way how WRF represents the wind speed and How_to_interpret_WRF-Fire_variables#Location the vertical coordinate; in particular, because the altitude of nodes in WRF changes, the number of vertical levels needed for the interpolation is not known in advance.

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