# Vertical wind interpolation

*Back to the WRF-SFIRE user guide*.

## 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/z _{0}**, where

**z**is the

_{0}*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**need to be known at every point of the fire mesh.

_{0}In BEHAVE, the wind is measured at 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* (Baughman and Albini, 1980), which we denote by **windrf**.

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

## Implementation

In the code, we thus have two choices:

- Interpolate to 6.096m and apply the wind reduction factors. This is much simpler and faster.
- 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 fuel roughness height **fz0**, the wind reduction factors **windrf** for each fuel category, and the BEHAVE height **fire_wind_height**, are specified 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.

Note that the roughness height **z0** from land use and **fz0** will be generally different, and besides they are given on different meshes.

## Options

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

Supported combinations of the options are listed below. In particular, do not use **fire_use_windrf**=1, which is for experiments only.

### Interpolation to common height and wind reduction factors

**fire_wind_log_interp**=4,**fire_use_windrf**is not used: vertical log interpolation on the atmospheric mesh to**fire_wind_height**with**z0**from land use, the interpolated wind speed is then multiplied by**windrf**at every fire mesh node. The values of**fwh**and**fz0**are ignored.

### Interpolation to different heights on the fire mesh

The following group of combinations of options controls the interpolation by the wind reduction factor **windrf**; **fwh** is not used.

**fire_wind_log_interp**=1,**fire_use_windrf**=2: use the roughness height**fz0**from fuel categories, ignore**fwh**and set it automatically to the height that corresponds to the given**windrf**.**fire_wind_log_interp**=2,**fire_use_windrf**=2: the same, but using roughness height**z0**interpolated from land use as piecewise constant, ignore**fz0**.**fire_wind_log_interp**=3,**fire_use_windrf**=2: the same, but using roughness height**z0**interpolated from land use as piecewise bilinear, ignore**fz0**.

The above options will produce similar results as the interpolation to common height and using wind reduction factors; the only difference is from the wind not obeying the log profile exactly. In particular, if the first WRF level is above the **fire_wind_height** (of 6.096m, which is usually the case), these three option will give *the same result as the interpolation on the atmospheric mesh and multiplication by the wind reduction factors*, except for slight differences caused by a different technique used for the interpolation of the atmospheric variables, and by rounding errors.

The combinations of options below control the interpolation by the midflame height **fwh**, and all three will again produce similar results; **windrf** is not used.

**fire_wind_log_interp**=1,**fire_use_windrf**=0: Use the values of**fwh**and**fz0**as given.**fire_wind_log_interp**=2,**fire_use_windrf**=3: Interpolate**z0**as piecewise constant and adjust**fwh**for a similar result as with**fz0**.**fire_wind_log_interp**=3,**fire_use_windrf**=3: Interpolate**z0**as piecewise bilinear and adjust**fwh**for a similar result as with**fz0**.

The adjustment of **fwh** is done by first computing the wind reduction factor when going from **fire_wind_height** to the given height **fwh** with the given roughness **fz0**, then changing **fwh** to the value that corresponds to the same wind reduction factor but with the interpolated **z0**.

## Diagnostics

You can use function **vprofile** in Matlab (**cd em_fire**, **matlab**, help **vprofile**) to view the resulting wind profiles and the computed value of **fwh**. See How to visualize vertical profiles from WRF in Matlab for details.

## References

- 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
- 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

## Works with

- SFIRE July 31, 2011. In particular, note that these options are not present in WRF-Fire in WRF 3.3 release; the interpolation to different heights on the fire mesh was not implemented yet, and the wind factors were removed from the release.
- Matlab 2011a