### ASA 127th Meeting M.I.T. 1994 June 6-10

## 2pUW1. The two-scale model from the point of view of a small slope
approximation.

**A. G. Voronovich
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*NOAA/ERL/Environmental Technol. Lab. R/E/WP1, 325 Broadway, Boulder, CO
80303
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The two-scale model (TSM) is widely used for interpretation of data
concerning wave scattering at rough surfaces. On the other hand, a small slope
approximation theory (SSA) is able to consider the same situation without
introducing somewhat arbitrary scale-dividing parameter. It is shown that under
appropriate conditions the SSA reproduces the results of TSM. Dividing of
spectrum of roughness into two components can be considered in this case as a
numerical mode for calculating the corresponding integrals arising in SSA.
Moreover, statistical dependence of the small-scale component of roughness upon
shape of large-scale undulating surface is taken into account. Thus the
statistics of small-scale component of roughness is not assumed to be space
homogeneous. As a result the small-scale component of spectrum in the final
expression for scattering cross section is modified. The forms of correlation
functions of roughness which should be substituted to the presented theory are
specified. Corresponding results can be of interest for scattering of
high-frequency waves from surfaces possessing wide spectrum of roughness (as
wavy sea surface). [This work is partly supported by NRC.]