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Variability of ice microphysical properties like crystal size and density in cirrus clouds is important for climate through its impact on radiative forcing, but challenging to represent in models. For the first time, recent laboratory experiments of particle growth (tied to crystal morphology via deposition density) are combined with a state‐of‐the‐art Lagrangian particle‐based microphysics model in large‐eddy simulations to examine sources of microphysical variability in cirrus. Simulated particle size distributions compare well against balloon‐borne observations. Overall, microphysical variability is dominated by variability in the particles' thermodynamic histories. However, diversity in crystal morphology notably increases spatial variability of mean particle size and density, especially at mid‐levels in the cloud. Little correlation between instantaneous crystal properties and supersaturation occurs even though the modeled particle morphology is directly tied to supersaturation based on laboratory measurements. Thus, the individual thermodynamic paths of each particle, not the instantaneous conditions, control the evolution of particle properties. Plain Language Summary Thin, high‐altitude ice clouds—cirrus—are critical to climate through their interactions with incoming solar radiation and outgoing longwave radiation. With a zoomed‐in view, observations show that cirrus comprise ice crystals of diverse sizes and shapes. These crystal properties determine the bulk properties of the clouds, like their ice water content. What controls this diversity of crystal properties? To address this question, we performed numerical simulations using a state‐of‐the‐art model that tracks the growth of individual particles, informed by laboratory crystal growth experiments, in a realistic turbulent cloud flow. We show that variability in the local environmental conditions (e.g., relative humidity) that particles experience in a turbulent environment is a primary driver of crystal diversity in cirrus. Diversity is also driven by different shapes of newly formed crystals, leading to different growth characteristics. This diversity drives spatial variability of properties like mean crystal density across the cloud layer. Climate models that represent cirrus using simple relationships based on observations that are essentially snapshots of average crystal properties cannot capture this variability. Overall, our analysis indicates that the history of environmental conditions along particle trajectories, not just instantaneous conditions, are required to understand crystal growth and variability in cirrus. Key Points Variability in the thermodynamic histories of ice crystals are a primary driver of particle variability in cirrus Diversity in crystal morphology also drives spatial variability of mean particle size and density, particularly at mid‐levels in the cloud Thermodynamic histories along particle trajectories, not just local conditions, are required to understand crystal growth in cirrus

In the atmosphere, microphysics refers to the microscale processes that affect cloud and precipitation particles and is a key linkage among the various components of Earth's atmospheric water and energy cycles. The representation of microphysical processes in models continues to pose a major challenge leading to uncertainty in numerical weather forecasts and climate simulations. In this paper, the problem of treating microphysics in models is divided into two parts: (i) how to represent the population of cloud and precipitation particles, given the impossibility of simulating all particles individually within a cloud, and (ii) uncertainties in the microphysical process rates owing to fundamental gaps in knowledge of cloud physics. The recently developed Lagrangian particle‐based method is advocated as a way to address several conceptual and practical challenges of representing particle populations using traditional bulk and bin microphysics parameterization schemes. For addressing critical gaps in cloud physics knowledge, sustained investment for observational advances from laboratory experiments, new probe development, and next‐generation instruments in space is needed. Greater emphasis on laboratory work, which has apparently declined over the past several decades relative to other areas of cloud physics research, is argued to be an essential ingredient for improving process‐level understanding. More systematic use of natural cloud and precipitation observations to constrain microphysics schemes is also advocated. Because it is generally difficult to quantify individual microphysical process rates from these observations directly, this presents an inverse problem that can be viewed from the standpoint of Bayesian statistics. Following this idea, a probabilistic framework is proposed that combines elements from statistical and physical modeling. Besides providing rigorous constraint of schemes, there is an added benefit of quantifying uncertainty systematically. Finally, a broader hierarchical approach is proposed to accelerate improvements in microphysics schemes, leveraging the advances described in this paper related to process modeling (using Lagrangian particle‐based schemes), laboratory experimentation, cloud and precipitation observations, and statistical methods. Plain Language Summary In the atmosphere, microphysics—the small‐scale processes affecting cloud and precipitation particles such as their growth by condensation, evaporation, and melting—is a critical part of Earth's weather and climate. Because it is impossible to simulate every cloud particle individually owing to their sheer number within even a small cloud, atmospheric models have to represent the evolution of particle populations statistically. There are critical gaps in knowledge of the microphysical processes that act on particles, especially for atmospheric ice particles because of their wide variety and intricacy of their shapes. The difficulty of representing cloud and precipitation particle populations and knowledge gaps in cloud processes both introduce important uncertainties into models that translate into uncertainty in weather forecasts and climate simulations, including climate change assessments. We discuss several specific challenges related to these problems. To improve how cloud and precipitation particle populations are represented, we advocate a “particle‐based” approach that addresses several limitations of traditional approaches and has recently gained traction as a tool for cloud modeling. Advances in observations, including laboratory studies, are argued to be essential for addressing gaps in knowledge of microphysical processes. We also advocate using statistical modeling tools to improve how these observations are used to constrain model microphysics. Finally, we discuss a hierarchical approach that combines the various pieces discussed in this article, providing a possible blueprint for accelerating progress in how microphysics is represented in cloud, weather, and climate models. Key Points Microphysics is an important component of weather and climate models, but its representation in current models is highly uncertain Two critical challenges are identified: representing cloud and precipitation particle populations and knowledge gaps in cloud physics A possible blueprint for addressing these challenges is proposed to accelerate progress in improving microphysics schemes

A novel bulk microphysics scheme that predicts the evolution of ice properties, including aspect ratio (shape), mass, number, size, and density is described, tested, and demonstrated. The scheme is named the Ice-Spheroids Habit Model with Aspect-Ratio Evolution (ISHMAEL). Ice is modeled as spheroids and is nucleated as one of two species depending on nucleation temperature. Microphysical process rates determine how shape and other ice properties evolve. A third aggregate species is also employed, diversifying ice properties in the model. Tests of ice shape evolution during vapor growth and riming are verified against wind tunnel data, revealing that the model captures habit-dependent riming and its effect on fall speed. Lagrangian parcel studies demonstrate that the bulk model captures ice property evolution during riming and melting compared with a bin model. Finally, the capabilities of ISHMAEL are shown in a 2D kinematic framework with a simple updraft. A direct result of predicting ice shape evolution is that various states of ice from unrimed to lightly rimed to densely rimed can be modeled without converting ice mass between predefined ice categories (e.g., snow and graupel). This leads to a different spatial precipitation distribution compared with the traditional method of separating snow and graupel and converting between the two categories, because ice in ISHMAEL sorts in physical space based on the amount of rime, which controls the thickness and therefore fall speed. Predicting these various states of rimed ice leads to a reduction in vapor growth rate and an increase in riming rate in a simple updraft compared with the traditional approach.

Observations and measurements show that crystals remain relatively compact at low ice supersaturations, but become increasingly hollowed and complex as the ice supersaturation rises. Prior measurements at temperatures >−25°C indicate that the transition from compact, solid ice to morphologically complex crystals occurs when the excess vapor density exceeds a threshold value of about 0.05 g m −3 . A comparable threshold is not available at low temperatures. A temperature-dependent criterion for the excess vapor density threshold (Δ ρ thr ) that defines morphological transformations to complex ice is derived from laboratory measurements of vapor grown ice at temperatures below −40°C. This criterion depends on the difference between the equilibrium vapor density of liquid ( ) and ice ( ρ ei ) multiplied by a measurement-determined constant, . The new criterion is consistent with prior laboratory measurements, theoretical estimates, and it reproduces the classical result of about 0.05 g m −3 above −25°C. Since Δ ρ thr defines the excess vapor density above which crystals transition to a morphologically complex (lower density) growth mode, we can estimate the critical supersaturation ( s crit ) for step nucleation during vapor growth. The derived values of s crit are consistent with previous measurements at temperatures above −20°C. No direct measurements of s crit are available for temperatures below −40°C; however, our derived values suggest some measurement-based estimates may be too high while estimates from molecular dynamics simulations may be too low.

Bulk microphysical schemes use the capacitance model for ice vapor growth in combination with mass–size relationships to determine the evolution of ice water content (IWC) and ice particle maximum dimension in time. These approaches are limited since a single axis length is used, the aspect ratio is usually held constant and mass–size relations have many available coefficients for similar ice types. Fixing the crystal aspect ratio severs the nonlinear link between aspect ratio changes and increased growth rates that occur during crystal growth. A method is presented here for predicting two crystal axes and the crystal aspect ratio in bulk models. Evolution of the ice mass mixing ratio is tied to the evolution of two axis length mixing ratios through the use of a historical axis ratio parameter containing memory of crystal shape. This parameter links the distributions of the two axes, allowing characterization of particle lengths using a single distribution. The method uses four prognostic variables: the mass and number mixing ratios, and two axis length mixing ratios. Development of the method is presented, with testing described in Part II.

This study investigates droplet size distribution (DSD) characteristics from condensational growth and transport in Eulerian dynamical models with bin microphysics. A hierarchy of modeling frameworks is utilized, including parcel, one-dimensional (1D), and three-dimensional large-eddy simulation (LES). The bin DSDs from the 1D model, which includes only vertical advection and condensational growth, are nearly as broad as those from the LES and in line with observed DSD widths for stratocumulus clouds. These DSDs are much broader than those from Lagrangian microphysical calculations within a parcel framework that serve as a numerical benchmark for the 1D tests. In contrast, the bin-modeled DSDs are similar to the Lagrangian microphysical benchmark for a rising parcel in which Eulerian transport is not considered. These results indicate that numerical diffusion associated with vertical advection is a key contributor to broadening DSDs in the 1D model and LES. This DSD broadening from vertical numerical diffusion is unphysical, in contrast to the physical mixing processes that previous studies have indicated broaden DSDs in real clouds. It is proposed that artificial DSD broadening from vertical numerical diffusion compensates for underrepresented horizontal variability and mixing of different droplet populations in typical LES configurations with bin microphysics, or the neglect of other mechanisms that broaden DSDs such as growth of giant cloud condensation nuclei. These results call into question the ability of Eulerian dynamical models with bin microphysics to investigate the physical mechanisms for DSD broadening, even though they may reasonably simulate overall DSD characteristics.

Models of ice crystal vapor growth require estimates of the deposition coefficient α when surface attachment kinetics limit growth and when ice crystal shape is predicted. Parametric models can be used to calculate α for faceted growth as long as characteristic supersaturation values are known. However, previously published measurements of are limited to temperatures higher than −40°C. Estimates of at temperatures between −40° and −70°C are provided here through reanalysis of vapor growth data. The estimated follow the same functional temperature dependence as data taken at higher temperatures. Polynomial fits to are used as inputs to a parameterization of α suitable for use in cloud models. Comparisons of the parameterization with wind tunnel data show that growth at liquid saturation and constant temperatures between −3° and −20°C can be modeled by ledge nucleation for larger (hundreds of micrometers) crystals; however, comparisons with free-fall chamber data at −7°C suggest that dislocation growth may be required to model the vapor growth of small crystals (~20 μ m) at liquid saturation. The comparisons with free-fall chamber data also show that the parameterization can reproduce the measured pressure dependence of aspect-ratio evolution. Comparisons with a hexagonal growth model indicate that aspect-ratio evolution based on the theory of Chen and Lamb produces unrealistically fast column growth near −7°C that is mitigated if a theory based on faceted growth is used. This result indicates that the growth hypothesis used in habit-evolving microphysical models needs to be revised when deposition coefficients are predicted.

This paper describes and tests a single-particle ice growth model that evolves both ice crystal mass and shape as a result of vapor growth and riming. Columnar collision efficiencies in the model are calculated using a new theoretical method derived from spherical collision efficiencies. The model is able to evolve mass, shape, and fall speed of growing ice across a range of temperatures, and it compares well with wind tunnel data. The onset time of riming and the effects of riming on mass and fall speed between −3° and −16°C are modeled, as compared with wind tunnel data for a liquid water content of 0.4 g m −3 . Under these conditions, riming is constrained to the more isometric habits near −10° and −4°C. It is shown that the mass and fall speed of riming dendrites depend on the liquid drop distribution properties, leading to a range of mass–size and fall speed–size relationships. Riming at low liquid water contents is shown to be sensitive to ice crystal habit and liquid drop size. Moreover, very light riming can affect the shape of ice crystals enough to reduce vapor growth and suppress overall mass growth, as compared with those same ice crystals if they were unrimed.

A quasi-idealized 3D squall-line case is simulated using a novel bulk microphysics scheme called the Ice-Spheroids Habit Model with Aspect-ratio Evolution (ISHMAEL). In ISHMAEL, the evolution of ice particle properties (e.g., mass, shape, maximum diameter, density, and fall speed) are predicted during vapor growth, sublimation, riming, and melting, allowing ice properties to evolve from various microphysical processes without needing separate unrimed and rimed ice categories. ISHMAEL produces both a transition zone and an enhanced stratiform precipitation region, and ice particle properties are analyzed to determine the characteristics of ice that lead to the development of these squall-line features. Rimed particles advected rearward from the convective region produce the enhanced stratiform precipitation region. The transition zone results from hydrometeor sorting; the evolution of ice particle properties in the convective region leads to fall speeds that favor ice advecting rearward of the transition zone before reaching the melting level, causing a local minimum in precipitation rate and reflectivity there. Sensitivity studies show that the fall speed of ice particles largely determines the location of the enhanced stratiform precipitation region and whether or not a transition zone forms. The representation of microphysical processes, such as rime splintering and aggregation, and ice size distribution shape can impact the mean ice particle fall speeds enough to significantly impact the location of the enhanced stratiform precipitation region and the existence of the transition zone.

Snow aggregates evolve into a variety of observed shapes and densities. Despite this diversity, models and observational studies employ fractal or Euclidean geometric measures that are assumed universal for all aggregates. This work therefore seeks to improve understanding and representation of snow aggregate geometry and its evolution by characterizing distributions of both observed and Monte Carlo–generated aggregates. Two separate datasets of best-fit ellipsoid estimates derived from Multi-Angle Snowflake Camera (MASC) observations suggest the use of a bivariate beta distribution model for capturing aggregate shapes. Product moments of this model capture shape effects to within 4% of observations. This mathematical model is used along with Monte Carlo simulated aggregates to study how combinations of monomer properties affect aggregate shape evolution. Plate aggregates of any aspect ratio produce a consistent ellipsoid shape evolution whereas thin column aggregates evolve to become more spherical. Thin column aggregates yield fractal dimensions much less than the often-assumed value of 2.0. Ellipsoid densities and fractal analogs of density (lacunarity) are much more variable depending on combinations of monomer size and shape. Simple mathematical scaling relationships can explain the persistent triaxial ellipsoid shapes that appear in both observed and modeled aggregates. Overall, both simulations and observations prove aggregates are rarely oblate. Therefore, the use of the proposed bivariate ellipsoid distribution in models will allow for similar-sized aggregates to exhibit a realistic dispersion of masses and fall speeds.