  The radar scattering properties of realistic aggregate snowflakes have been
calculated using the Rayleigh-Gans theory. We find that the effect of the
snowflake geometry on the scattering may be described in terms of a single
universal function, which depends only on the overall shape of the aggregate
and not the geometry or size of the pristine ice crystals which compose the
flake. This function is well approximated by a simple analytic expression at
small sizes; for larger snowflakes we fit a curve to our numerical data. We
then demonstrate how this allows a characteristic snowflake radius to be
derived from dual-wavelength radar measurements without knowledge of the
pristine crystal size or habit, while at the same time showing that this detail
is crucial to using such data to estimate ice water content. We also show that
the `effective radius', characterising the ratio of particle volume to
projected area, cannot be inferred from dual-wavelength radar data for
aggregates. Finally, we consider the errors involved in approximating
snowflakes by `air-ice spheres', and show that for small enough aggregates the
predicted dual wavelength ratio typically agrees to within a few percent,
provided some care is taken in choosing the radius of the sphere and the
dielectric constant of the air-ice mixture; at larger sizes the radar becomes
more sensitive to particle shape, and the errors associated with the sphere
model are found to increase accordingly.
