# Definition of Roughness

The roughness
$\Delta {h}_{0}$
of the surface naturally influences the reflection loss in
the aforementioned Excel spreadsheet^{1}. The parameter
${\rho}_{0}$
, derived from roughness, is used to correct the reflection
coefficient.^{2}^{3}

The definition of the roughness of the surface is based on the standard deviation of the normally distributed surface roughness $\Delta {h}_{0}$ :

$${\rho}_{0}{}^{2}={e}^{-2{\delta}_{0}}$$

with
$${\delta}_{0}=\frac{4\pi \Delta {h}_{0}}{\lambda}\mathrm{sin}{\alpha}_{i}$$

^{1}Altair\2024.0\help\winprop\examples\ExampleGuide_models\Example-A03-Database_Materials.zip

^{2}G. Wölfle: Adaptive Modelle für die Funknetzplanung und zur Berechnung der Empfangsqualität in Gebäuden. (Adaptive Propagation Models for the Planning of Wireless Communication Networks and for the Computation of the Reception Quality inside Buildings). PhD Thesis, University of Stuttgart, published by Shaker Verlag, 2000.

^{3}K.A. Chamberlain and R. J. Luebbers: An Evaluation of Longley-Rice and GTD Propagation Models. IEEE transactions on Antennas and Propagation, vol. 30, no. 6, pp. 1093-1098, Nov. 1982.