Novel Parameterization of Ice Cloud Effective Diameter from Collocated CALIOP-IIR and CloudSat Retrievals
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54 ENVIRONMENTAL SCIENCES↗
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On the importance to consider the cloud dependence in parameterizing the albedo of snow on sea ice
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54 ENVIRONMENTAL SCIENCES↗
Assessing Clouds Using Satellite Observations Through Three Generations of Global Atmosphere Models
Abstract Clouds are parameterized in climate models using quantities on the model grid‐scale to approximate the cloud cover and impact on radiation. Because of the complexity of processes involved with clouds, these parameterizations are one of the key challenges in climate modeling. Differences in parameterizations of clouds are among the main contributors to the spread in climate sensitivity across models. In this work, the clouds in three generations of an atmosphere model lineage are evaluated against satellite observations. Satellite simulators are used within the model to provide an appropriate comparison with individual satellite products. In some respects, especially the top‐of‐atmosphere cloud radiative effect, the models show generational improvements. The most recent generation, represented by two distinct branches of development, exhibits some regional regressions in the cloud representation; in particular the southern ocean shows a positive bias in cloud cover. The two branches of model development show how choices during model development, both structural and parametric, lead to different cloud climatologies. Several evaluation strategies are used to quantify the spatial errors in terms of the large‐scale circulation and the cloud structure. The Earth mover's distance is proposed as a useful error metric for the passive satellite data products that provide cloud‐top pressure‐optical depth histograms. The cloud errors identified here may contribute to the high climate sensitivity in the Community Earth System Model, version 2 and in the Energy Exascale Earth System Model, version 1.
54 ENVIRONMENTAL SCIENCES↗
An Improved Convection Parameterization with Detailed Aerosol–Cloud Microphysics for a Global Model
Abstract A new microphysical treatment that includes aerosol–cloud interactions and secondary ice production (SIP) mechanisms is implemented in the convection scheme of the Community Atmosphere Model, version 6 (CAM6). The approach is to embed a 1D Lagrangian parcel model in the bulk convective plume of the existing deep convection parameterization. Aerosol activation, growth processes including collision/coalescence, and three processes of SIP mechanisms, two of which are normally overlooked in atmospheric models, are represented in this embedded parcel model. These microphysical processes are treated with a hybrid bin/bulk scheme and a high spatial and temporal resolution for the integration of the embedded parcel in 1D, allowing vertical velocity to determine the microphysical evolution following the in-cloud motion during ascent. Simulations of an observed case (Midlatitude Continental Convective Clouds Experiment) of a mesoscale convective system in Oklahoma, United States, with a single-column model (SCAM) version of CAM, are compared with aircraft in situ and ground-based observations of microphysical properties from the convection and precipitation. Results from the validation show the new microphysical scheme has a good representation of the ice initiation in the bulk convective plume, including the known and empirically quantified pathways of primary and secondary initiation, with benefits for the accuracy of properties of its supercooled cloud liquid. The sensitivity simulations and use of tagging tracers for the validated simulation confirm that the newly included SIP mechanisms are of paramount importance for convective microphysics and can be successfully treated in the global model.
54 ENVIRONMENTAL SCIENCES↗
Coupling Warm Rain With an Eddy Diffusivity/Mass Flux Parameterization: 1. Model Description and Validation
A new version of the stochastic multiplume Jet Propulsion Laboratory Eddy-Diffusivity/Mass-Flux (JPL-EDMF) parameterization which consistently couples the simplified Khairoutdinov and Kogan (2000), https://doi.org/10.1175/1520-0493(2000)128<0229:ANCPPI>2.0.CO;2, warm phase cloud microphysical parameterization with the parameterization of cloud macrophysical and subgrid scale dynamical processes is described. The new parameterization combines the EDMF approach with an assumed shape of a joint probability density function of thermodynamic and kinematic variables which provide the basis for the computation of all parameterized processes. As far as we are aware this is the first attempt to consistently couple all of these parameterized processes in the EDMF framework. This paper is part one of a two paper series. Here, the JPL-EDMF parameterization is described and benchmark simulations of precipitating stratocumulus and cumulus convection are performed in a single-column-model framework. The parameterization results compare favorably to the reference large-eddy-simulation results. In the second part (Smalley et al., 2022, https://doi.org/10.1029/2021MS002729) the JPL-EDMF parameterization is validated for a wide range of observation-based scenarios covering the continuous transition from subtropical stratocumulus to cumulus convection derived from global reanalysis, and parameterization uncertainties are studied in detail.
54 ENVIRONMENTAL SCIENCES↗
Parameterization and Explicit Modeling of Cloud Microphysics: Approaches, Challenges, and Future Directions
Cloud microphysical processes occur at the smallest end of scales among cloud-related processes and thus must be parameterized not only in large-scale global circulation models (GCMs) but also in various higher-resolution limited-area models such as cloud-resolving models (CRMs) and large-eddy simulation (LES) models. Instead of giving a comprehensive review of existing microphysical parameterizations that have been developed over the years, this study concentrates purposely on several topics that we believe are understudied but hold great potential for further advancing bulk microphysics parameterizations: multi-moment bulk microphysics parameterizations and the role of the spectral shape of hydrometeor size distributions; discrete vs “continuous” representation of hydrometeor types; turbulence-microphysics interactions including turbulent entrainment-mixing processes and stochastic condensation; theoretical foundations for the mathematical expressions used to describe hydrometeor size distributions and hydrometeor morphology; and approaches for developing bulk microphysics parameterizations. Also presented are the spectral bin scheme and particle-based scheme (especially, super-droplet method) for representing explicit microphysics. Their advantages and disadvantages are elucidated for constructing cloud models with detailed microphysics that are essential to developing processes understanding and bulk microphysics parameterizations. Particle-resolved direct numerical simulation (DNS) models are described as an emerging technique to investigate turbulence-microphysics interactions at the most fundamental level by tracking individual particles and resolving the smallest turbulent eddies in turbulent clouds. Outstanding challenges and future research directions are explored as well.
54 ENVIRONMENTAL SCIENCES↗
Advancing the Understanding of Cloud Microphysical Processes and Aerosol Indirect Effects in High-Latitude Mixed-Phase Clouds by Linking ARM Measurements with Climate Model Simulations (Final Report)
The key objectives of this project were to advance our understanding of cloud microphysical characteristics and aerosol indirect effects on mixed-phase clouds in high latitudes. To improve the representation of ice and mixed-phase clouds in Earth System Models (ESMs), we propose an integrated observation and modeling study of cloud macro- and microphysical properties, including spatial heterogeneities, mass partitioning between ice crystals and supercooled liquid water, effects of ice nucleating particles (INPs), and efficiency of secondary ice production (SIP), etc. Specifically, we took four main approaches in this project: (1) examining macro- and microphysical properties of ice and mixed-phase clouds based on in-situ and ground-based observations from multiple field campaigns funded by the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program, including the Mixed-Phase Arctic Cloud Experiment (M-PACE), Indirect and Semi-Direct Aerosol Campaign (ISDAC), Ice Nucleating Particle Sources at Oliktok Point (INPOP), ARM West Antarctic Radiation Experiment (AWARE), Measurements of Aerosols, Radiation, and Clouds over the Southern Ocean (MARCUS), and Macquarie Island Cloud and Radiation Experiment (MICRE); (2) evaluating the DOE Energy Exascale Earth System Model (E3SM) simulations based on observations, particularly for ice and mixed-phase cloud microphysical properties; (3) examining the impacts of INPs on ice and mixed-phase clouds. Specifically, a series of comparisons were conducted using observations over the Arctic, Southern Ocean, and Antarctica, including comparisons between the lower and higher southern latitudes as well as comparisons between the northern and southern hemispheres. In addition, aerosol indirect effects from distinct sources of dust particles were examined; and (4) investigating the impacts of SIP. Ultimately, these results helped to improve cloud microphysics and aerosol-cloud interaction parameterizations in the E3SM model. Overall, the project provided improved understanding regarding various factors, including thermodynamic, dynamic, and aerosol conditions, on the micro- and macrophysical properties of ice and mixed-phase clouds in the high latitudes. Resulting analysis helped to provide an improved physical basis for refining the current cloud microphysics parameterizations related to ice and mixed-phase clouds in E3SM.
54 ENVIRONMENTAL SCIENCES↗
A Machine‐Learning‐Assisted Stochastic Cloud Population Model as a Parameterization of Cumulus Convection
Abstract A machine‐learning‐assisted stochastic cloud population model is coupled with the Advanced Research Weather Research and Forecasting (WRF) model to represent fluctuations in the cloud‐base mass flux associated with the life cycles and interactions among cumulus convection cells. In this cloud population model, the size distribution and the associated cloud‐base mass flux of the convective cells are related to their previous state and to the change in the total convective area via a transition function. The convective area tendency in turn is assumed to depend on the cloud‐base mass flux that is resolved by the host WRF model. The transition function is represented by a single hidden‐layer neural network trained by the evolution of convective cell size distributions in a 1‐km grid‐spacing WRF simulation run over the Australian Monsoon region. At every grid point of the host model, the cloud population model predicts the cell size and cloud‐base mass flux distributions from which a random sample of cells is fed to an entraining parcel model that calculates precipitation as well as the associated liquid water potential temperature and total moisture tendencies. These tendencies are averaged over the cells and provided to the host model. Several regional simulations are performed over tropical and midlatitude domains to test this as a potential approach to scale‐aware parameterization. It is shown that such an approach could be a new promising path to simulating realistic precipitation statistics and propagation of precipitation associated with the Madden‐Julian Oscillation while maintaining realistic depictions of the diurnal cycle over both land and ocean.
54 ENVIRONMENTAL SCIENCES↗
Downward Convective Moisture Transport Dominated by a Few Overshooting Clouds in Marine and Continental Shallow Convection
Abstract In a previous study (Xiao et al., 2023, https://doi.org/10.1029/2022ms003526 ), we found that ignoring the moist convective downdrafts associated with overshooting clouds in parameterizations can lead to significant biases in the simulated depth and liquid water content of a shallow cloud layer. In this study, we seek to better quantify the properties of the clouds responsible for these moist downdrafts to help improve shallow convection parameterizations. We apply a 3‐D cloud‐tracking algorithm to large‐eddy simulations (LESs) of marine and continental shallow convection. We find that top 1% and 2% of the tracked cloud population ranked by lifetime‐mean cloud‐base mass flux can explain 90%–95% of the total downward moisture transport in the upper cloud layer whereas top 10%–20% is required to explain 90%–95% of the total upward moisture transport near mean cloud base. The vertical structure of the clouds in the top 1% and 2% (the overshooting “deep mode”) is also distinctively different from that of the rest of the cloud population (the “shallow mode”). Shallow convection parameterizations need to capture accurately the properties and convective transports of the clouds in both the deep and shallow modes. To do that, our results suggest that mass‐flux parameterizations need to (a) accurately predict the size and number of the deep‐mode clouds and (b) explicitly represent overshooting cloud updrafts and associated moist downdrafts.
54 ENVIRONMENTAL SCIENCES↗
Physics or Knob‐Tuning? Tropical Anvil Peak Is Captured by GCMs
Tropical anvil clouds peak near 200 hPa and significantly impact Earth's climate, yet its physical realism in coarse‐resolution General Circulation Models (GCMs) remains debated. We examine anvil cloud formation by performing simulations with a GCM with a hierarchy of cloud fraction schemes ranging from a complex prognostic Tiedtke scheme to a simple binary scheme. All schemes consistently reproduce the anvil peak. The robust anvil peak arises because extremely cold temperatures at the upper troposphere facilitate frequent saturation events, producing clouds that disproportionately influence mean cloud fraction. Sensitivity experiments with enhanced evaporation of cloud condensate unexpectedly show increased anvil coverage, highlighting how slight evaporative moistening reinforces local saturation in cold upper‐tropospheric conditions. These results demonstrate that the tropical anvil cloud peak emerges from fundamental thermodynamic constraints, rather than specific cloud fraction parameterization choices.
54 ENVIRONMENTAL SCIENCES↗
Development of a triple-moment ice-phase cloud microphysics scheme and its application to the Single Column Atmosphere Model
Parameterization of cloud microphysics is critical for accurate simulation of weather and climate, in which the characteristics of cloud particle spectrum inevitably further affect climate simulation by changing the cloud evolution and cloud radiation effects. The popular currently used double-moment cloud microphysics schemes in numerical models can predict the intercept (N 0 ) and slope (λ) parameters of cloud particle spectrum but cannot predict the spectral shape parameter (μ), which hinders accurate description of cloud physical processes in climate models. Therefore, in the present study, we built upon the ideas of previously developed triple-moment cloud microphysics scheme, considered radar reflectivity factor as the third predictor in addition to number and mass concentration, and introduced its related prediction equation to the Single Column Atmosphere Model Version 5.3 (SCAM5.3). Moreover, the relevant microphysical process formulas in the model were revised, and a triple-moment ice-cloud microphysics scheme was constructed to predict the μ of ice particle spectrum. Based on this model, a 29-day case of the Atmospheric Radiation Measurement Program in the summer of 1997 (ARM97) was simulated, and the differences in cloud fraction and radiation simulations between the double- and triple-moment schemes were analysed. The μ of ice particle spectrum predicted by the triple-moment scheme mainly ranged from 0 to 4; the peak value was around 2, and at least 85% of the μ values were greater than the default 0. Therefore, the μ=0 setting in the double-moment scheme is unreasonable. Moreover, the developed triple-moment ice-cloud microphysics scheme yielded a narrower ice particle spectrum, which was closer to the observation results of previous studies, than the double-moment cloud microphysics scheme (e.g., height=233 hPa). Furthermore, compared with the double-moment scheme, the triple-moment scheme achieved closer simulations of the cloud fraction observations, particularly for ice clouds in the upper levels. Considering the close association between cloud fraction and radiation, the error with the triple-moment scheme was smaller than that with the double-moment scheme regardless of the shortwave (surface downward shortwave radiation, net downward shortwave radiation at the top of the atmosphere, and net shortwave radiation at the surface) or longwave (surface downward longwave radiation and net longwave radiation at the surface) flux density. Finally, the improvement mechanism of the triple-moment scheme on cloud fraction and radiation simulations was explored. The major reason is that the triple-moment scheme weakens the autoconversion of ice crystal to form snow and enhances the growth process of ice crystal deposition, thereby increasing the mass concentration of ice crystals and ice cloud fraction. Overall, the developed triple-moment ice-cloud microphysics scheme can help improve the simulation ability of models for cloud-climate feedback and other processes.
54 ENVIRONMENTAL SCIENCES↗
Assessing Clouds in GFDL's AM4.0 With Different Microphysical Parameterizations Using the Satellite Simulator Package COSP
We evaluate cloud simulations using satellite simulators against multiple observational data sets. These simulators have been run within the Geophysical Fluid Dynamics Laboratory's Atmosphere Model version 4.0 (AM4.0), as well as an alternative configuration where a fully two‐moment Morrison‐Gettelman cloud microphysical parameterization with prognostic precipitation (MG2) is applied, denoted as AM4‐MG2. The modeled cloud spatial distributions, vertical profiles, phase partitioning, cloud‐to‐precipitation transitions, and radiative effects compare reasonably well with satellite observations. Model biases include the under‐prediction of total and low‐level clouds, especially optically thin/intermediate clouds with cloud optical depth of less than 23, but the over‐prediction of thick clouds, indicating “too few, too bright” biases. These biases counteract each other, and give rise to reasonable estimates of cloud radiative effects. The underestimate of low‐level clouds is associated with too early and too frequent drizzle/precipitation formation. The precipitation bias is improved in AM4‐MG2, where the autoconversion scheme initiates the precipitation more realistically. There also exist discrepancies between models and observations for midlevel and high‐level clouds. Additional biases include the underestimate of liquid cloud fraction and the overestimate of ice cloud fraction.
54 ENVIRONMENTAL SCIENCES↗
An Intercomparison of Large‐Eddy Simulations of a Convection Cloud Chamber Using Haze‐Capable Bin and Lagrangian Cloud Microphysics Schemes
Abstract Recent in situ observations show that haze particles exist in a convection cloud chamber. The microphysics schemes previously used for large‐eddy simulations of the cloud chamber could not fully resolve haze particles and the associated processes, including their activation and deactivation. Specifically, cloud droplet activation was modeled based on Twomey‐type parameterizations, wherein cloud droplets were formed when a critical supersaturation for the available cloud condensation nuclei (CCN) was exceeded and haze particles were not explicitly resolved. Here, we develop and adapt haze‐capable bin and Lagrangian microphysics schemes to properly resolve the activation and deactivation processes. Results are compared with the Twomey‐type CCN‐based bin microphysics scheme in which haze particles are not fully resolved. We find that results from the haze‐capable bin microphysics scheme agree well with those from the Lagrangian microphysics scheme. However, both schemes significantly differ from those from a CCN‐based bin microphysics scheme unless CCN recycling is considered. Haze particles from the recycling of deactivated cloud droplets can strongly enhance cloud droplet number concentration due to a positive feedback in haze‐cloud interactions in the cloud chamber. Haze particle size distributions are more realistic when considering solute and curvature effects that enable representing the complete physics of the activation process. Our study suggests that haze particles and their interactions with cloud droplets may have a strong impact on cloud properties when supersaturation fluctuations are comparable to mean supersaturation, as is the case in the cloud chamber and likely is the case in the atmosphere, especially in polluted conditions.
54 ENVIRONMENTAL SCIENCES↗
Insights of warm-cloud biases in Community Atmospheric Model 5 and 6 from the single-column modeling framework and Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) observations
There has been a growing concern that most climate models predict precipitation that is too frequent, likely due to lack of reliable subgrid variability and vertical variations in microphysical processes in low-level warm clouds. In this study, the warm-cloud physics parameterizations in the singe-column configurations of NCAR Community Atmospheric Model version 6 and 5 (SCAM6 and SCAM5, respectively) are evaluated using ground-based and airborne observations from the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign near the Azores islands during 2017–2018. The 8-month single-column model (SCM) simulations show that both SCAM6 and SCAM5 can generally reproduce marine boundary layer cloud structure, major macrophysical properties, and their transition. The improvement in warm-cloud properties from the Community Atmospheric Model 5 and 6 (CAM5 to CAM6) physics can be found through comparison with the observations. Meanwhile, both physical schemes underestimate cloud liquid water content, cloud droplet size, and rain liquid water content but overestimate surface rainfall. Modeled cloud condensation nuclei (CCN) concentrations are comparable with aircraft-observed ones in the summer but are overestimated by a factor of 2 in winter, largely due to the biases in the long-range transport of anthropogenic aerosols like sulfate. We also test the newly recalibrated autoconversion and accretion parameterizations that account for vertical variations in droplet size. Compared to the observations, more significant improvement is found in SCAM5 than in SCAM6. This result is likely explained by the introduction of subgrid variations in cloud properties in CAM6 cloud microphysics, which further suppresses the scheme's sensitivity to individual warm-rain microphysical parameters. The predicted cloud susceptibilities to CCN perturbations in CAM6 are within a reasonable range, indicating significant progress since CAM5 which produces an aerosol indirect effect that is too strong. The present study emphasizes the importance of understanding biases in cloud physics parameterizations by combining SCM with in situ observations.
54 ENVIRONMENTAL SCIENCES↗
Coupled Climate Simulations With E3SM‐MMF
Simulations of the recent historical period from 1950 to 2014 are conducted with E3SM‐MMF, which uses an embedded 2D cloud resolving model that runs efficiently on GPUs in place of traditional parameterizations for cloud and turbulence. Analysis of the climate and variability reveal several aspects where E3SM‐MMF produces smaller biases compared to E3SMv2, including better agreement with the observed evolution of global mean surface temperature, although the representation of ENSO is too weak and fast. Three idealized abrupt CO 2 experiments were also conducted to assess climate sensitivity and feedbacks. These yield three estimates of effective climate sensitivity (4.38, 5.21, and 6.06 K), with a corresponding spread in the shortwave cloud feedbacks. These estimates are on the higher end of sensitivity estimates from CMIP ensembles, and the spread indicates substantial state‐dependent feedbacks. These results demonstrate how multiscale modeling framework (MMF) models can be used for climate relevant experiments and projections by leveraging modern GPU enabled computational platforms. The unique qualities of E3SM‐MMF shown in previous literature are largely still present, but various instances of reduced biases suggest that MMF models have utility in improving future projections.
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Acceleration of the Parameterization of Unified Microphysics Across Scales (PUMAS) on the Graphics Processing Unit (GPU) With Directive-Based Methods
Cloud microphysics is one of the most time-consuming components in a climate model. In this study, we port the cloud microphysics parameterization in the Community Atmosphere Model (CAM), known as Parameterization of Unified Microphysics Across Scales (PUMAS), from CPU to GPU to seek a computational speedup. The directive-based methods (OpenACC and OpenMP target offload) are determined as the best fit specifically for our development practices, which enable a single version of source code to run either on the CPU or GPU, and yield a better portability and maintainability. Their performance is first examined in a PUMAS stand-alone kernel and the directive-based methods can outperform a CPU node as long as there is enough computational burden on the GPU. A consistent behavior is observed when we run PUMAS on the GPU in a practical CAM simulation. A 3.6× speedup of the PUMAS execution time, including data movement between CPU and GPU, is achieved at a coarse horizontal resolution (8 NVIDIA V100 GPUs against 36 Intel Skylake CPU cores). This speedup further increases up to 5.4× at a high resolution (24 NVIDIA V100 GPUs against 108 Intel Skylake CPU cores), which highlights the fact that GPU favors larger problem size. This study demonstrates that using GPU in a CAM simulation can save noticeable computational costs even with a small portion of code being GPU-enabled. Therefore, we are encouraged to port more parameterizations to GPU to take advantage of its computational benefit.
54 ENVIRONMENTAL SCIENCES↗
Polar Cloud Microphysics and Surface Energy Budget from AWARE (Final Technical Report)
This was a collaborative project between the Scripps Institution of Oceanography at the University of California San Diego (SIO), Byrd Polar and Climate Research Center at The Ohio State University (BPCRC), The Department of Meteorology and Atmospheric Science at The Pennsylvania State University (Penn State), and Brookhaven National Laboratory (BNL). The project’s over-arching objectives involved maximizing the scientific potential of the ARM West Antarctic Radiation Experiment (AWARE) data set, in two respects: (1) application of polar-optimized climate models to test the most current and comprehensive cloud microphysical parameterizations; and (2) analysis of the most advanced ARM Mobile Facility sensors (e.g., cloud radar, spectroradiometer, and aerosol observing system data) to advance understanding of Antarctic cloud microphysical and radiative properties, particularly on a climatological basis with emphasis on contrasts with the high Arctic. The team’s efforts have resulted in 16 peer-review publications, in addition to an overview of the AWARE campaign in the Bulletin of the American Meteorological Society. Our emphasis throughout this program was to go beyond the traditional “case study” approach to model evaluation, in which a “classical” or otherwise well-characterized surface-atmosphere-cloud system of short duration is simulated by several climate models. Instead, we attempted analysis of longer time series in the AWARE data, both climatologically and with models. We have numerous successful results from both AWARE locations: The main AMF-2 deployment at McMurdo Station on Ross Island (13 months duration), and the extended facility at the West Antarctic Ice Sheet (WAIS) Divide Ice Camp (40 days during austral summer 2015-16).
54 ENVIRONMENTAL SCIENCES↗
The Ice Particle and Aggregate Simulator (IPAS). Part II: Analysis of a Database of Theoretical Aggregates for Microphysical Parameterization
Abstract Bulk ice-microphysical models parameterize the dynamic evolution of ice particles from advection, collection, and sedimentation through a cloud layer to the surface. Frozen hydrometeors can grow to acquire a multitude of shapes and sizes, which influence the distribution of mass within cloud systems. Aggregates, defined herein as the collection of ice particles, have a variety of formations based on initial ice particle size, shape, falling orientation, and the number of particles that collect. This work focuses on using the Ice Particle and Aggregate Simulator (IPAS) as a statistical tool to repetitively collect ice crystals of identical properties to derive bulk aggregate characteristics. A database of 9 744 000 aggregates is generated with resulting properties analyzed. After 150 single ice crystals (monomers) collect, the most extreme aggregate aspect ratio calculations asymptote toward and ϕ ca ≈ 0.50 for aggregates composed of quasi-horizontally oriented and randomly oriented monomers, respectively. The results presented are largely consistent with both a previous theoretical study and estimates derived from ground-based observations from two different geographic locations. Particle falling orientation highly influences newly formed aggregate aspect ratios from the collection of particles with extreme aspect ratios; quasi-horizontally oriented particles can produce aggregate aspect ratios an order of magnitude more extreme than randomly oriented particles but can also produce near-spherical aggregates as the number of monomers comprising the aggregate reach approximately 100. Finally, a majority of collections result in aggregates that are closer to prolate than oblate spheroids.
54 ENVIRONMENTAL SCIENCES↗