The applicability of physical optics in the millimetre and sub-millimetre spectral region. Part I: The ray tracing with diffraction on facets method

- A method of physical optics is shown to apply to size parameters as low as 18 in the mm and sub-mm-wave spectral regions.
- Including ray tracing with diffraction on facets and diffraction at the cross-section of the particle is fundamental.
- Ray tracing with diffraction on facets is shown to be generally within ± 4 K of more exact calculations at 874 GHz±4 .
- Polarised intensities in the sub-mm region are potentially sensitive up to a certain level of large-scale ice complexity.

Future satellite missions, from 2022 onwards, will obtain near-global measurements of cirrus at microwave and sub-millimetre frequencies. To realise the potential of these observations, fast and accurate light-scattering methods are required to calculate scattered millimetre and sub-millimetre intensities from complex ice crystals. Here, the applicability of the ray tracing with diffraction on facets method (RTDF) in predicting the bulk scalar optical properties and phase functions of randomly oriented hexagonal ice columns and hexagonal ice aggregates at millimetre frequencies is investigated. The applicability of RTDF is shown to be acceptable down to size parameters of about 18, between the frequencies of 243 and 874 GHz. It is demonstrated that RTDF is generally well within about 10% of T-matrix solutions obtained for the scalar optical properties assuming hexagonal ice columns. Moreover, on replacing electromagnetic scalar optical property solutions obtained for the hexagonal ice aggregate with the RTDF counterparts at size parameter values of about 18 or greater, the bulk scalar optical properties can be calculated to generally well within ±5% of an electromagnetic-based database. The RTDF-derived bulk scalar optical properties result in brightness temperature errors to generally within about ±4 K at 874 GHz. Differing microphysics assumptions can easily exceed such errors. Similar findings are found for the bulk scattering phase functions. This finding is owing to the scattering solutions being dominated by the processes of diffraction and reflection, both being well described by RTDF. The impact of centimetre-sized complex ice crystals on interpreting cirrus polarisation measurements at sub-millimetre frequencies is discussed.