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We provide a parameterization of the extinction efficiency, single-scattering albedo, and asymmetry parameter of single ice crystals with any combination of particle volume, projected area, component aspect ratio, and crystal distortion at any wavelength between 0.2 and 100 μm. The parameterization is an extension of the one previously published by van Diedenhoven et al. In addition, the parameterized optical properties are integrated over size distributions yielding bulk extinction efficiencies, single-scattering albedos, and asymmetry parameters for large ranges of effective radii, particle component aspect ratios, and crystal distortion values. The parameterization of single-particle optical properties is evaluated with a reference database. The bulk optical properties are evaluated against the ice model selected for the Moderate Resolution Imaging Spectroradiometer (MODIS) collection 6 products, for which accurate optical properties are available. Mean absolute errors in parameterized extinction efficiency, asymmetry parameter, and single-scattering albedo are shown to be 0.0272, 0.008 90, and 0.004 68, respectively, for shortwave wavelengths, while they are 0.0641, 0.0368, and 0.0200 in the longwave. Shortwave and longwave asymmetry parameters and single-scattering albedos are shown to vary strongly with particle component aspect ratio and distortion, resulting in substantial variation in shortwave fluxes, but relatively small variations in longwave cloud emissivity. The parameterization and bulk optical properties are made publicly available.

A parameterization is presented that provides extinction cross section σe, single-scattering albedo ω, and asymmetry parameter g of ice crystals for any combination of volume, projected area, aspect ratio, and crystal distortion at any wavelength in the shortwave. Similar to previous parameterizations, the scheme makes use of geometric optics approximations and the observation that optical properties of complex, aggregated ice crystals can be well approximated by those of single hexagonal crystals with varying size, aspect ratio, and distortion levels. In the standard geometric optics implementation used here, σe is always twice the particle projected area. It is shown that ω is largely determined by the newly defined absorption size parameter and the particle aspect ratio. These dependences are parameterized using a combination of exponential, lognormal, and polynomial functions. The variation of g with aspect ratio and crystal distortion is parameterized for one reference wavelength using a combination of several polynomials. The dependences of g on refractive index and ω are investigated and factors are determined to scale the parameterized g to provide values appropriate for other wavelengths. The parameterization scheme consists of only 88 coefficients. The scheme is tested for a large variety of hexagonal crystals in several wavelength bands from 0.2 to 4 μm, revealing absolute differences with reference calculations of ω and g that are both generally below 0.015. Over a large variety of cloud conditions, the resulting root-mean-squared differences with reference calculations of cloud reflectance, transmittance, and absorptance are 1.4%, 1.1%, and 3.4%, respectively. Some practical applications of the parameterization in atmospheric models are highlighted.

Satellite measurements are used to evaluate the glaciation, particle shape, and effective radius in cloud-resolving model simulations of tropical deep convection. Multidirectional polarized reflectances constrain the ice crystal geometry and the thermodynamic phase of the cloud tops, which in turn are used to calculate near-infrared reflectances so as to constrain the simulated ice effective radius, thereby avoiding inconsistencies between retrieval algorithms and model simulations. Liquid index values derived from Polarization and Directionality of the Earth’s Reflectances (POLDER) measurements indicate only ice-topped clouds at brightness temperatures (BTs) lower than −40°C, only liquid clouds at BT > −20°C, and both phases occurring at temperatures in between. Liquid index values calculated from model simulations generally reveal too many ice-topped clouds at BT > −20°C. The model assumption of platelike ice crystals with an aspect ratio of 0.7 is found consistent with POLDER measurements for BT < −40°C when very rough ice crystals are assumed, leading to an asymmetry parameter of 0.74, whereas measurements indicate more extreme aspect ratios of ~0.15 at higher temperatures, yielding an asymmetry parameter of 0.84. MODIS-retrieved ice effective radii are found to be 18–28 μm at BT < −40°C, but biased low by about 5 μm owing primarily to the assumption of pristine crystals in the retrieval. Simulated 2.13-μm reflectances at BT < −40°C are found to be about 0.05–0.1 too large compared to measurements, suggesting that model-simulated effective radii are 7–15 μm too small. Two simulations with contrasting ice nucleation schemes showed little difference in simulated effective radii at BT < −40°C, indicating that homogeneous nucleation is dominating in the simulations. Changes around −40°C in satellite observations suggest a change in cloud-top ice shape and/or size in natural deep convection possibly related to a change in the freezing mechanism.

Observations of long-lived mixed-phase Arctic boundary layer clouds on 7 May 1998 during the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE)–Arctic Cloud Experiment (ACE)/Surface Heat Budget of the Arctic Ocean (SHEBA) campaign provide a unique opportunity to test understanding of cloud ice formation. Under the microphysically simple conditions observed (apparently negligible ice aggregation, sublimation, and multiplication), the only expected source of new ice crystals is activation of heterogeneous ice nuclei (IN) and the only sink is sedimentation. Large-eddy simulations with size-resolved microphysics are initialized with IN number concentration NIN measured above cloud top, but details of IN activation behavior are unknown. If activated rapidly (in deposition, condensation, or immersion modes), as commonly assumed, IN are depleted from the well-mixed boundary layer within minutes. Quasi-equilibrium ice number concentration Ni is then limited to a small fraction of overlying NIN that is determined by the cloud-top entrainment rate we divided by the number-weighted ice fall speed at the surface υf. Because wc < 1 cm s−1 and υf > 10 cm s−1, Ni/NIN ≪ 1. Such conditions may be common for this cloud type, which has implications for modeling IN diagnostically, interpreting measurements, and quantifying sensitivity to increasing NIN (when we/υf < 1, entrainment rate limitations serve to buffer cloud system response). To reproduce observed ice crystal size distributions and cloud radar reflectivities with rapidly consumed IN in this case, the measured above-cloud NIN must be multiplied by approximately 30. However, results are sensitive to assumed ice crystal properties not constrained by measurements. In addition, simulations do not reproduce the pronounced mesoscale heterogeneity in radar reflectivity that is observed.