Gamma distributions represent particle size distributions (SDs) in mesoscale and cloud-resolving models that predict one, two, or three moments of hydrometeor species. They are characterized by intercept (N0), slope (λ), and shape (μ) parameters prognosed by such schemes or diagnosed based on fits to SDs measured in situ in clouds. Here, ice crystal SDs acquired in arctic cirrus during the Indirect and Semi-Direct Aerosol Campaign (ISDAC) and in hurricanes during the National Aeronautic and Space Administration (NASA) African Monsoon Multidisciplinary Analyses (NAMMA) are fit to gamma distributions using multiple algorithms. It is shown that N0, λ, and μ are not independent parameters but rather exhibit mutual dependence. Although N0, λ, and μ are not highly dependent on choice of fitting routine, they are sensitive to the tolerance permitted by fitting algorithms, meaning a three-dimensional volume in N0–λ–μ phase space is required to represent a single SD. Depending on the uncertainty in the measured SD and on how well a gamma distribution matches the SD, parameters within this volume of equally realizable solutions can vary substantially, with N0, in particular, spanning several orders of magnitude. A method to characterize a family of SDs as an ellipsoid in N0–λ–μ phase space is described, with the associated scatter in N0–λ–μ for such families comparable to scatter in N0, λ, and μ observed in prior field campaigns conducted in different conditions. Ramifications for the development of cloud parameterization schemes and associated calculations of microphysical process rates are discussed.

Remote sensing retrievals and ice microphysical parameterizations in global climate models typically use assumptions about the distribution of ice mass as a function of particle size using mass‐dimensional (m‐D) relationships. This study investigates the ice crystal m‐D properties of tropical anvil cirrus during the Tropical Composition, Cloud and Climate Coupling Experiment (TC4) to better document the distribution of ice mass with size in this particular class of tropical ice clouds. Two optimal estimation algorithms (XIWC and MZ) are used to estimate the m‐D relationship for each particle size distribution (PSD) collected in situ. The XIWC algorithm minimizes the difference between measured ice water content (IWC) and PSD calculated IWC, while the MZ algorithm minimizes the difference between measured radar reflectivity factors and those calculated from the in situ PSDs. Results from these algorithms are compared to previous studies to establish consistency of the methodologies. The XIWC results show that both parameters in the m‐D relationship increase with temperature. Changes in m‐D with temperature have substantial implications for remote sensing retrievals. With the prefactor varying by a factor of 5 and the exponent varying by some 16% over a typical range of ice cloud temperatures, forward modeling errors in radar reflectivity could be typically in excess of 5 dB, further suggesting that retrievals of IWC and precipitation rates from radar measurements in ice clouds be in error by factors easily exceeding 3.

Interpretations of remote sensing measurements collected in sample volumes containing ice‐phase hydrometeors are very sensitive to assumptions regarding the distributions of mass with ice crystal dimension, otherwise known as mass‐dimensional or m‐D relationships. How these microphysical characteristics vary in nature is highly uncertain, resulting in significant uncertainty in algorithms that attempt to derive bulk microphysical properties from remote sensing measurements. This uncertainty extends to radar reflectivity factors forward calculated from model output because the statistics of the actual m‐D in nature is not known. To investigate the variability in m‐D relationships in cirrus clouds, reflectivity factors measured by CloudSat are combined with particle size distributions (PSDs) collected by coincident in situ aircraft by using an optimal estimation‐based (OE) retrieval of the m‐D power law. The PSDs were collected by 12 flights of the Stratton Park Engineering Company Learjet during the Small Particles in Cirrus campaign. We find that no specific habit emerges as preferred, and instead, we find that the microphysical characteristics of ice crystal populations tend to be distributed over a continuum‐defying simple categorization. With the uncertainties derived from the OE algorithm, the uncertainties in forward‐modeled backscatter cross section and, in turn, radar reflectivity is calculated by using a bootstrapping technique, allowing us to infer the uncertainties in forward‐modeled radar reflectivity that would be appropriately applied to remote sensing simulator algorithms.

Mesoscale models that predict the evolution of tropical cyclones (TCs) are sensitive to the representation of cloud microphysical processes. Bulk cloud parametrizations used in such models make assumptions about the particle size distributions (PSDs) of different ice species, and their representativeness for TCs is not well known. In situ cloud probe data acquired in tropical storms, depressions and waves during the NASA African Monsoon Multidisciplinary Analyses (NAMMA) project are used to define PSDs of snow and graupel, and of all ice hydrometeors combined. These PSDs are fitted to gamma functions to determine how the intercept (N0), shape (μ), and slope (λ) vary with cloud and environmental conditions. Families of PSDs are determined for each condition (e.g. PSDs found in updraughts, downdraughts and stratiform regions, for different ranges of ice water content (IWC) and temperature (T), and for differing stages of TC development). A volume of equally plausible solutions in (N0‐μ‐λ) phase space is defined for each environmental condition sampled based on the goodness of the fits and the uncertainty in the measured PSDs due to statistical sampling. Per cent overlap between two families in each environmental and cloud condition was calculated, and results show that areas with sustained vertical velocity with a magnitude of at least 1 m·s−1 lie in a different phase space than stratiform regions, and PSDs corresponding to IWC < 0.01 g·m−3 lie in a different phase space than PSDs corresponding to IWC > 0.1 g·m−3. All other environmental and cloud conditions did not have significant impacts on either the location or uncertainty in the family of ellipsoids.

Radio occultation (RO) measurements have little direct sensitivity to clouds, but recent studies have shown that they may have an indirect sensitivity to thin, high clouds that are difficult to detect using conventional passive space-based cloud sensors. We implement two RO-based cloud detection (ROCD) algorithms for atmospheric layers in the middle and upper troposphere. The first algorithm is based on the methodology of a previous study, which explored signatures caused by upper tropospheric clouds in RO profiles according to retrieved relative humidity, temperature lapse rate, and gradients in log-refractivity (ROCD-P), and the second is based on inferred relative humidity alone (ROCD-M). In both, atmospheric layers are independently predicted as cloudy or clear based on observational data, including high performance RO retrievals. In a demonstration, we use data from 10 days spanning seven months in 2020 of FORMOSAT-7/COSMIC-2. We use the forecasts of NOAA GFS to aid in the retrieval of relative humidity. The prediction is validated with a cloud truth dataset created from the imagery of the GOES-16 Advanced Baseline Imager (ABI) satellite and the GFS three-dimensional analysis of cloud state conditions. Given these two algorithms for the presence or absence of clouds, confusion matrices and receiver operating characteristic (ROC) curves are used to analyze how well these algorithms perform. The ROCD-M algorithm has a balanced accuracy, which defines the quality of the classification test that considers both the sensitivity and specificity, greater than 70% for all altitudes between 6 and 10.25 km.