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We compare stochastic models of microscale surface roughness assuming uniform and Weibull distributions of crystal facet tilt angles to calculate scattering by roughened hexagonal ice crystals using the geometric optics (GO) approximation. Both distributions are determined by similar roughness parameters, while the Weibull model depends on the additional shape parameter. Calculations were performed for two visible wavelengths (864 nm and 410 nm) for roughness values between 0.2 and 0.7 and Weibull shape parameters between 0 and 1.0 for crystals with aspect ratios of 0.21, 1 and 4.8. For this range of parameters we find that, for a given roughness level, varying the Weibull shape parameter can change the asymmetry parameter by up to about 0.05. The largest effect of the shape parameter variation on the phase function is found in the backscattering region, while the degree of linear polarization is most affected at the side-scattering angles. For high roughness, scattering properties calculated using the uniform and Weibull models are in relatively close agreement for a given roughness parameter, especially when a Weibull shape parameter of 0.75 is used. For smaller roughness values, a shape parameter close to unity provides a better agreement. Notable differences are observed in the phase function over the scattering angle range from 5deg to 20deg, where the uniform roughness model produces a plateau while the Weibull model does not.

A fundamental problem in remote sensing and radiative transfer simulations involving ice clouds is the ability to compute accurate optical properties for individual ice particles. While relatively simple and intuitively appealing, the conventional geometric-optics method (CGOM) is used frequently for the solution of light scattering by ice crystals. Due to the approximations in the ray-tracing technique, the CGOM accuracy is not well quantified. The result is that the uncertainties are introduced that can impact many applications. Improvements in the Invariant Imbedding T-matrix method (II-TM) and the Improved Geometric-Optics Method (IGOM) provide a mechanism to assess the aforementioned uncertainties. The results computed by the II-TMþIGOM are considered as a benchmark because the IITM solves Maxwell's equations from first principles and is applicable to particle size parameters ranging into the domain at which the IGOM has reasonable accuracy. To assess the uncertainties with the CGOM in remote sensing and radiative transfer simulations, two independent optical property datasets of hexagonal columns are developed for sensitivity studies by using the CGOM and the II-TMþIGOM, respectively. Ice cloud bulk optical properties obtained from the two datasets are compared and subsequently applied to retrieve the optical thickness and effective diameter from Moderate Resolution Imaging Spectroradiometer (MODIS) measurements. Additionally, the bulk optical properties are tested in broadband radiative transfer (RT) simulations using the general circulation model (GCM) version of the Rapid Radiative Transfer Model (RRTMG) that is adopted in the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM, version 5.1). For MODIS retrievals, the mean bias of uncertainties of applying the CGOM in shortwave bands (0.86 and 2.13 micrometers) can be up to 5% in the optical thickness and as high as 20% in the effective diameter, depending on cloud optical thickness and effective diameter. In the MODIS infrared window bands centered at 8.5, 11, and 12 micrometers biases in the optical thickness and effective diameter are up to 12% and 10%, respectively. The CGOM-based simulation errors in ice cloud radiative forcing calculations are on the order of 10Wm(exp 2).

Halos at 22 deg from the sun attributed to randomly-orientated, pristine hexagonal crystals are frequently observed through ice clouds. These frequent sightings of halos formed by pristine crystals pose an apparent inconsistency with the dominance of distorted, nonpristine ice crystals indicated by in situ and remote sensing data. Furthermore, the 46 deg halo, which is associated with pristine hexagonal crystals as well, is observed far less frequently than the 22 deg halo. Considering that plausible mechanisms that could cause crystal distortion such as aggregation, sublimation, riming and collisions are stochastic processes that likely lead to distributions of crystals with varying distortion levels, here the presence of the 22 deg and 46 deg halo features in phase functions of mixtures of pristine and distorted hexagonal ice crystals is examined. We conclude that the 22 deg halo feature is generally present if the contribution by pristine crystals to the total scattering cross section is greater than only about 10% in the case of compact particles or columns, and greater than about 40% for plates. The 46 deg halo feature is present only if the mean distortion level is low and the contribution of pristine crystals to the total scattering cross section is above about 20%, 50% and 70%, in the case of compact crystals, plates and columns, respectively. These results indicate that frequent sightings of 22 deg halos are not inconsistent with the observed dominance of distorted, non-pristine ice crystals. Furthermore, the low mean distortion levels and large contributions by pristine crystals needed to produce the 461 halo features provide a potential explanation of the common sighting of the 22 deg halo without any detectable 46 deg halo.