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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Stochastic Kinetics of Nanocatalytic Systems

Catalytic reaction events occurring on the surface of a nanoparticle constitute a complex stochastic process. Although advances in modern single-molecule experiments enable direct measurements of individual catalytic turnover events occurring on a segment of a single nanoparticle, we do not yet know how to measure the number of catalytic sites in each segment or how the catalytic turnover counting statistics and the catalytic turnover time distribution are related to the microscopic dynamics of catalytic reactions. Here, we address these issues by presenting a stochastic kinetics for nanoparticle catalytic systems. We propose a new experimental measure of the number of catalytic sites in terms of the mean and variance of the catalytic event count. By considering three types of nanocatalytic systems, we investigate how the mean, the variance, and the distribution of the catalytic turnover time depend on the catalytic reaction dynamics, the heterogeneity of catalytic activity, and communication among catalytic sites. This work enables accurate quantitative analyses of single-molecule experiments for nanocatalytic systems and enzymes with multiple catalytic sites.

Statistical Physics↗
DOE OSTI2020

Ultrafast Relaxations in Ruthenium Polypyridyl Chromophores Determined by Stochastic Kinetics Simulations

Maximizing the efficiency of solar energy conversion using dye assemblies rests on understanding where the energy goes following absorption. Transient spectroscopies in solution are useful for this purpose, and the time-resolved data are usually analyzed with a sum of exponentials. This treatment assumes that dynamic events are well separated in time, and that the resulting exponential prefactors and phenomenological lifetimes are related directly to primary physical values. Such assumptions break down for coincident absorption, emission, and excited state relaxation that occur in transient absorption and photoluminescence of tris(2,2'-bipyridine)ruthenium(2+) derivatives, confounding the physical meaning of the reported lifetimes. Here, we use inductive modeling and stochastic chemical kinetics to develop a detailed description of the primary ultrafast photophysics in transient spectroscopies of a series of Ru dyes, as an alternative to sums of exponential analysis. Commonly invoked three-level schemes involving absorption, intersystem crossing (ISC), and slow nonradiative relaxation and incoherent emission to the ground state cannot reproduce the experimentally measured spectra. The kinetics simulations reveal that ultrafast decay from the singlet excited state manifold to the ground state competes with ISC to the triplet excited state, whose efficiency was determined to be less than unity. The populations predicted by the simulations are used to estimate the magnitudes of transition dipoles for excited state excitations and evaluate the influence of specific ligands. The mechanistic framework and methodology presented here are entirely general, applicable to other dye classes, and can be extended to include charge injection by molecules bound to semiconductor surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1989

Turbulent hydrocarbon combustions kinetics - Stochastic modeling and verification

Idealized reactors, that are designed to ensure perfect mixing and are used to generate the combustion kinetics for complex hydrocarbon fuels, may depart from the ideal and influence the kinetics model performance. A complex hydrocarbon kinetics model that was established by modeling a jet-stirred combustor (JSC) as a perfectly stirred reactor (PSR), is reevaluated with a simple stochastic process in order to introduce the unmixedness effect quantitatively into the reactor system. It is shown that the comparisons of the predictions and experimental data have improved dramatically with the inclusion of the unmixedness effect in the rich combustion region. The complex hydrocarbon kinetics is therefore verified to be mixing effect free and be applicable to general reacting flow calculations.

Wang, T. S.↗
DOE OSTI2024

Versatile stochastic model for predictive KMC simulation of fcc metal nanostructure evolution with realistic kinetics

Stochastic lattice-gas models provide the natural framework for analysis of the surface diffusion-mediated evolution of crystalline metal nanostructures on the appropriate time scale (often 10 1 –10 4 s) and length scale. Model behavior can be precisely assessed by kinetic Monte Carlo simulation, typically incorporating a rejection-free algorithm to efficiently handle the broad range of Arrhenius rates for hopping of surface atoms. The model should realistically prescribe these rates, or the associated barriers, for a diversity of local surface environments. However, commonly used generic choices for barriers fail, even qualitatively, to simultaneously describe diffusion for different low-index facets, for terrace vs step edge diffusion, etc. We introduce an alternative Unconventional Interaction–Conventional Interaction formalism to prescribe these barriers, which, even with few parameters, can realistically capture most aspects of behavior. Here, the model is illustrated for single-component fcc metal systems, mainly for the case of Ag. It is quite versatile and can be applied to describe both the post-deposition evolution of 2D nanostructures in homoepitaxial thin films (e.g., reshaping and coalescence of 2D islands) and the post-synthesis evolution of 3D nanocrystals (e.g., reshaping of nanocrystals synthesized with various faceted non-equilibrium shapes back to 3D equilibrium Wulff shapes).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Coupled Interfacial and Bulk Kinetics Govern the Timescales of Multiphase Ozonolysis Reactions

Chemical transformations in aerosols impact the lifetime of particle phase species, the fate of atmospheric pollutants, and both climate- and health-relevant aerosol properties. Timescales for multiphase reactions of ozone in atmospheric aqueous phases are governed by coupled kinetic processes between the gas phase, the particle interface, and its bulk, which respond dynamically to reactive consumption of O 3 . However, models of atmospheric aerosol reactivity often do not account for the coupled nature of multiphase processes. Herein, to examine these dynamics, we use new and prior experimental observations of aqueous droplet reaction kinetics, including three systems with a range of surface affinities and ozonolysis rate coefficients ( trans -aconitic acid (C 6 H 6 O 6 ), maleic acid (C 4 H 4 O 4 ), and sodium nitrite (NaNO 2 )). Using literature rate coefficients and thermodynamic properties, we constrain a simple two-compartment stochastic kinetic model which resolves the interface from the particle bulk and represents O 3 partitioning, diffusion, and reaction as a coupled kinetic system. Our kinetic model accurately predicts decay kinetics across all three systems, demonstrating that both the thermodynamic properties of O 3 and the coupled kinetic and diffusion processes are key to making accurate predictions. An enhanced concentration of adsorbed O 3 , compared to gas and bulk phases is rapidly maintained and remains constant even as O 3 is consumed by reaction. Multiphase systems dynamically seek to achieve equilibrium in response to reactive O 3 loss, but this is hampered at solute concentrations relevant to aqueous aerosol by the rate of O 3 arrival in the bulk by diffusion. As a result, bulk-phase O 3 becomes depleted from its Henry's law solubility. This bulk-phase O 3 depletion limits reaction timescales for relatively slow-reacting organic solutes with low interfacial affinity (i.e., trans-aconitic and maleic acids, with k rxn ≈ 10 3 -10 4 M -1 s -1 ), which is in contrast to fast-reacting solutes with higher surface affinity (i.e., nitrite, with k rxn ≈ 10 5 M -1 s -1 ) where surface reactions strongly impact the observed decay kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Constraining the Reaction Rate of Criegee Intermediates with Carboxylic Acids during the Multiphase Ozonolysis of Aerosolized Alkenes

Criegee intermediates (CIs) are central to the ozonolysis of unsaturated organic compounds, controlling the formation of small fragmentation reaction products and higher molecular weight oligomeric compounds through competing unimolecular and bimolecular pathways. In particular, the reaction of thermalized CI with carboxylic acids (RCOOH) to produce oligomeric α-acyloxyalkyl hydroperoxides (AAHPs) is of interest to the chemical transformation of organic compounds in the atmosphere. In the gas phase, the CI + RCOOH reaction proceeds at supercollisional rates, consistent with a barrierless reaction mechanism. However, the rate of this reaction in condensed phases remains uncertain. Here, we report the results of aerosol flow tube studies of the ozonolysis of submicron organic aerosol containing mixtures of an internal n-alkene (Z-9-tricosene, tri) and a saturated acid (2-hexyldecanoic acid, HDA). The decay of the reactants and formation of reaction products are monitored using atmospheric pressure chemical ionization mass spectrometry (APCI–MS). A 6-fold decrease in the reactive uptake of ozone is observed with increasing acid concentration, consistent with a previous study using alcohol additives. The decay of HDA with ozone exposure shows that HDA scavenges CIs at rates comparable to competing unimolecular pathways involving CIs. The decay kinetics of HDA are analyzed using a simple kinetic model in order to constrain the ratio of the CI + RCOOH and unimolecular CI rate constants. Empirical fitting to this model, combined with theoretical estimates of the unimolecular loss rate, yields a CI + RCOOH rate constant of 1.85 ± 0.27 × 10 –19 cm 3 molec –1 s –1 , which is six orders of magnitude slower than the expected diffusion limit in a liquid organic matrix. Stochastic kinetic simulations are conducted with different values of the CI + RCOOH rate constant to validate this result and show that the diffusion-limited rate is indeed much too rapid to reproduce the experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1985

Does nucleation theory apply to the formation of refractory circumstellar grains?

It is pointed out that kinetic factors inherent in cosmic systems will prevent the attainment of an approximate equilibrium precondensation cluster distribution, and that therefore such systems will violate one of the most fundamental assumptions of nucleation theory. More importantly, it is shown that of the 11 refractory metal/metal oxide systems which have been studied experimentally none are consistent with the predictions of either classical nucleation theory or the Lothe-Pound modification. Since no valid method is known by which these deficiencies can be circumvented, it is concluded that nucleation theory cannot be made to work in expanding circumstellar shells. However, a stochastic, kinetic treatment which makes use of experimental and theoretical data for specific refractory systems does appear to be feasible.

Donn, B.↗
DOE OSTI2025

The role of the droplet interface in controlling the multiphase oxidation of thiosulfate by ozone

Predicting reaction kinetics in aqueous microdroplets, including aerosols and cloud droplets, is challenging due to the probability that the underlying reaction mechanism can occur both at the surface and in the interior of the droplet. Additionally, few studies directly measure the surface activities of doubly charged anions, despite their prevalence in the atmosphere. Here, deep-UV second harmonic generation spectroscopy is used to probe surface affinities of the doubly charged anions thiosulfate, sulfate, and sulfite, key species in the thiosulfate ozonation reaction mechanism. Thiosulfate has an appreciable surface affinity with a measured Gibbs free energy of adsorption of -7.3 ± 2.5 kJ mol -1 in neutral solution, while sulfate and sulfite exhibit negligible surface propensity. The Gibbs free energy is combined with data from liquid flat jet ambient pressure X-ray photoelectron spectroscopy to constrain the concentration of thiosulfate at the surface in our model. Stochastic kinetic simulations leveraging these novel measurements show that the primary reaction between thiosulfate and ozone occurs at the interface and in the bulk, with the contribution of the interface decreasing from ~65% at pH 5 to ~45% at pH 13. Additionally, sulfate, the major product of thiosulfate ozonation and an important species in atmospheric processes, can be produced by two different pathways at pH 5, one with a contribution from the interface of >70% and the other occurring predominantly in the bulk (>98%). The observations in this work have implications for mining wastewater remediation, atmospheric chemistry, and understanding other complex reaction mechanisms in multiphase environments. Future interfacial or microdroplet/aerosol chemistry studies should carefully consider the role of both surface and bulk chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

The Impact of Stochastic Perturbations in Physics Variables for Predicting Surface Solar Irradiance

We present a probabilistic framework tailored for solar energy applications referred to as the Weather Research and Forecasting-Solar ensemble prediction system (WRF-Solar EPS). WRF-Solar EPS has been developed by introducing stochastic perturbations into the most relevant physical variables for solar irradiance predictions. In this study, we comprehensively discuss the impact of the stochastic perturbations of WRF-Solar EPS on solar irradiance forecasting compared to a deterministic WRF-Solar prediction (WRF-Solar DET), a stochastic ensemble using the stochastic kinetic energy backscatter scheme (SKEBS), and a WRF-Solar multi-physics ensemble (WRF-Solar PHYS). The performances of the four forecasts are evaluated using irradiance retrievals from the National Solar Radiation Database (NSRDB) over the contiguous United States. We focus on the predictability of the day-ahead solar irradiance forecasts during the year of 2018. The results show that the ensemble forecasts improve the quality of the forecasts, compared to the deterministic prediction system, by accounting for the uncertainty derived by the ensemble members. However, the three ensemble systems are under-dispersive, producing unreliable and overconfident forecasts due to a lack of calibration. In particular, WRF-Solar EPS produces less optically thick clouds than the other forecasts, which explains the larger positive bias in WRF-Solar EPS (31.7 W/m 2 ) than in the other models (22.7–23.6 W/m 2 ). This study confirms that the WRF-Solar EPS reduced the forecast error by 7.5% in terms of the mean absolute error (MAE) compared to WRF-Solar DET, and provides in-depth comparisons of forecast abilities with the conventional scientific probabilistic approaches (i.e., SKEBS and a multi-physics ensemble). Guidelines for improving the performance of WRF-Solar EPS in the future are provided.

14 SOLAR ENERGY↗
DOE OSTI2023

Quantifying the Variation in the Number of Donors in Quantum Dots Created Using Atomic Precision Advanced Manufacturing

Atomic-precision advanced manufacturing enables unique silicon quantum electronics built on quantum dots fabricated from small numbers of phosphorus dopants. The number of dopant atoms comprising a dot plays a central role in determining the behavior of charge and spin confined to the dots and thus overall device performance. Here in this work, we use both theoretical and experimental techniques to explore the combined impact of lithographic variation and stochastic kinetics on the number of P incorporations in quantum dots made using these techniques and how this variation changes as a function of the size of the dot. Using a kinetic model of PH3 dissociation augmented with novel reaction barriers, we demonstrate that for a 2 × 3 silicon dimer window the probability that no donor incorporates goes to zero, allowing for certainty in the placement of at least one donor. However, this still comes with some uncertainty in the precise number of incorporated donors (either one or two), and this variability may still impact certain applications. We also examine the impact of the size of the initial lithographic window, finding that the incorporation fraction saturates to δ-layer-like coverage as the circumference-to-area ratio decreases. We predict that this incorporation fraction depends strongly on the dosage of the precursor and that the standard deviation of the number of incorporations scales as ~√n, as would be expected for a sequence of largely independent incorporation events. Finally, we characterize an array of 36 experimentally prepared multidonor 3 × 3 nm lithographic windows with scanning tunneling microscopy, measuring the fidelity of the lithography to the desired array and the final location of PH x fragments within these lithographic windows. We use our kinetic model to examine the expected variability due to the observed lithographic error, predicting a negligible impact on incorporation statistics. We find good agreement between our model and the inferred incorporation locations in these windows from scanning tunneling microscope measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Structure–Function Relationships in Sequence-Controlled Copolymers for Rare Earth Element Chelation

The ability to tune material function through primary sequence is a defining feature of biological macromolecules, allowing precise control over structure and target interactions in complex aqueous environments. However, translating sequence–structure–function relationships to synthetic macromolecules is challenging due to their dispersity in sequence, conformation, and composition. Here, we report systematic studies of amphiphilic polymer chelators designed to probe how composition and patterning influence binding affinity and selectivity for rare earth elements (REEs), a series of technologically relevant metals with challenging separation profiles. A library of copolymers varying hydrophobic monomer composition and patterning was synthesized via reversible addition–fragmentation chain transfer (RAFT) polymerization, spanning statistical, gradient, and block architectures. REE binding was quantified using a high-throughput colorimetric assay, and reconstruction of polymer ensembles using kinetic stochastic simulations enabled quantitative comparisons of sequence heterogeneity, linking local monomer colocalization to emergent REE binding. Further, we investigated the role of different hydrophobic comonomers in tuning metal coordination, with binding trends linked to structural features that influence binding site desolvation. Complementary dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS) measurements showed that both polymer and monomer architecture modulate metal-induced conformational changes, and that multichain assembly behavior emerges beyond critical hydrophobic thresholds. Sequence control also altered REE selectivity, with nonmonotonic differences observed across compositionally identical polymers with different sequence architectures. Together, these findings establish design principles that connect polymer sequence and structure to binding performance, guiding the design of macromolecular chelators with enhanced affinity and selectivity for applications in separations, sensing, and catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2003

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e.,pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions.A spectral-bin microphysical model is very expensive from a from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region using identical thermodynamic conditions but with different concentrations of CCN: a low "clean" concentration and a high "dirty" concentration. Besides the initial differences in aerosol concentration, preliminary results indicate that the low CCN concentration case produces rainfall at the surface sooner than the high CCN case but has less cloud water mass aloft. Because the spectral-bin model explicitly calculates and allows for the examination of both the mass and number concentration of species in each size categor, a detailed analysis of the instantaneous size spectrum can be obtained for the two cases. It is shown that since the low CCN case produces fewer droplets, larger sized develop due to the greater condensational and collectional growth, leading to a broader size spectrum in comparison to the high CCN case.

Tao, Wei-Kuo↗
NASA NTRS2003

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitable affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distribution parameterized as spectral bin microphysics are needed to explicitly study the effect of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensembel (GCE) model. The formulation for the explicit spectral-bim microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e., pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), groupel and frozen drops/hall] Each type is described by a special size distribution function containing many categories (i.e., 33 bins). Atmospheric aerosols are also described using number density size-distribution functions.A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep cloud systems in the west Pacific warm pool region and in the mid-latitude using identical thermodynamic conditions but with different concentrations of CCN: a low "clean" concentration and a high "dirty" concentration. Besides the initial differences in aerosol concentration, preliminary results indicate that the low CCN concentration case produces rainfall at the surface sooner than the high CCN case but has less cloud water mass aloft. Because the spectral-bim model explicitly calculates and allows for the examination of both the mass and number concentration of cpecies in each size category, a detailed analysis of the instantaneous size spectrum can be obtained for the two cases. It is shown that since the low CCN case produces fever droplets, larger size develop due to greater condencational and collectional growth, leading to a broader size spectrum in comparison to the high CCN case.

Tao, Wei-Kuo↗
NASA NTRS2004

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-resolving Model Simulations

Cloud microphysics is inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, r d a U production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensembe1 (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e. pristine ice crystals (columnar and platelike), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and in the mid-latitude continent with different concentrations of CCN: a low "c1ean"concentration and a high "dirty" concentration. In addition, differences and similarities between bulk microphysics and spectral-bin microphysical schemes will be examined and discussed.

Tao, Wei-Kuo↗
NASA NTRS2004

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics is inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensembel (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e. pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and in the mid-latitude continent with different concentrations of CCN: a low "c1ean"concentration and a high "dirty" concentration. In addition, differences and similarities between bulk microphysics and spectral-bin microphysical schemes will be examined and discussed.

Tao, Wei-Kuo↗
NASA NTRS2004

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitably affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds. Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effects of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, two detailed spectral-bin microphysical schemes were implemented into the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bin microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles (i.e., pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail). Each type is described by a special size distribution function containing many categories (i.e. 33 bins). Atmospheric aerosols are also described using number density size-distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep cloud systems in the west Pacific warm pool region, in the sub-tropics (Florida) and in the mid-latitude using identical thermodynamic conditions but with different concentrations of CCN: a low 'clean' concentration and a high 'dirty' concentration.

Tao, Wei-Kuo↗
NASA NTRS2005

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Cloud microphysics are inevitable affected by the smoke particle (CCN, cloud condensation nuclei) size distributions below the clouds, Therefore, size distributions parameterized as spectral bin microphysics are needed to explicitly study the effect of atmospheric aerosol concentration on cloud development, rainfall production, and rainfall rates for convective clouds. Recently, a detailed spectral-bin microphysical scheme was implemented into the the Goddard Cumulus Ensemble (GCE) model. The formulation for the explicit spectral-bim microphysical processes is based on solving stochastic kinetic equations for the size distribution functions of water droplets (i.e., cloud droplets and raindrops), and several types of ice particles [i.e., pristine ice crystals (columnar and plate-like), snow (dendrites and aggregates), graupel and frozen drops/hail]. Each type is described by a special size distribution function containing many categories (i.e., 33 bins). Atmospheric aerosols are also described using number density size-distribution functions.

Tao, Wei-Kuo↗