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At least 1,657 records · Page 92
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Sensitivity of Simulated Deep Convection to a Stochastic Ice Microphysics Framework

Ice microphysics parameterizations in models must make major simplifications relative to observations, typically employing empirical relationships to represent average functional properties of particles. However, previous studies have established that ice particle properties vary even in similar cloud types and thermodynamic environments, and it remains unclear how this so-called “natural variability” impacts simulated deep convection. This uncertainty is addressed by implementing a stochastic framework into the Predicted Particle Properties microphysics scheme in the Weather Research and Forecasting model. The approach stochastically varies the coefficients of the mass-size (m-D) relationship (m=aD b ) for unrimed and partially rimed ice. Using guidance from aircraft in situ measurements obtained during the Midlatitude Continental Convective Clouds Experiment (MC3E), the scheme samples from distributions of the prefactor (a) and the exponent (b) of the m-D relationship. Simulations of two MC3E deep convective cases indicate that the stochastic m-D scheme produces considerable variability of anvil cirrus cloud optical depth (τ) distributions, even for the same ice water path (IWP). Thus, the stochastic scheme produces variable cloud radiative forcing that is independent of IWP. This τ-IWP relationship variability is nonexistent using the deterministic m-D ensemble. Additional sensitivity tests are performed in which the fallspeed-size relationship (V=cD d ) is stochastically varied, resulting in variable precipitation amounts and rain rate distributions. Results are presented in the context of satellite and precipitation observations and include comparison with other ensemble configurations using perturbed initial and lateral boundary conditions and small-amplitude noise added to the potential temperature field.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2006

Spectral Measurements of PMCs from SBUV/2 Instruments

The SBUV/2 (Solar Backscattered Ultraviolet, model 2) instrument is designed to monitor ozone stratospheric profile and total column ozone using measurements of the Earth's backscattered ultraviolet albedo. We have previously demonstrated that the normal radiance measurements from SBUV/2 instruments, which sample 12 discrete wavelengths between 252 and 340 nm during each scan, can be used to identify polar mesospheric clouds (PMCs). Some SBUV/2 instruments also periodically view the earth in continuous scan mode, covering the wavelength range 160-400 nm with 0.15 nm sampling. Analysis of these data show PMC occurrence rates similar to the normal discrete scan results, although the observation technique reduces the number of daily measurements by a factor of six. PMC observed by SBUV/2 instruments show a monotonic variation in the residual spectral albedo over the wavelength range 250 300 nm, with maximum enhancements of 10 15% at 250 nm. This result is consistent with microphysical model predictions from Jensen [1989. A numerical model of polar mesospheric cloud formation and evolution, Ph. D. Thesis, University of Colorado]. We find no evidence for a systematic localized increase in PMC residual albedo for wavelengths near 260 nm, in contrast to the recently reported results from the MSX UVISI instrument [Carbary J.F., et al., 2004. Evidence for bimodal particle distribution from the spectra of polar mesospheric clouds. Geophysics Research. Letters 31, L13108]. This result is observed for three different SBUV/2 instruments in both Northern and Southern Hemisphere data over a 13-year span. Our Mie scattering calculations show that the location and magnitude of the 260 nm hump feature is dependent upon the specific scattering angles appropriate to the MSX measurements. Although it explains the MSX spectrum, the bimodal size distribution proposed by Carbary et al. (2004), cannot explain the lack of scattering angle dependence of the SBUV/2 spectral shapes. The spectral signature of the SBUV/2 continuous scan PMC data is thus inconsistent with the bimodal particle size distribution suggested by Carbary et al. (2004).

DeLand, Matthew T.↗
NASA NTRS2012

Microphysics in Multi-scale Modeling System with Unified Physics

Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (1) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model), (2) a regional scale model (a NASA unified weather research and forecast, WRF), (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation, and cloud-land surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, a review of developments and applications of the multi-scale modeling system will be presented. In particular, the microphysics development and its performance for the multi-scale modeling system will be presented.

Tao, Wei-Kuo↗
DOE OSTI2024

Cloud micro- and macrophysical properties from ground-based remote sensing during the MOSAiC drift experiment

In the framework of the Multidisciplinary drifting Observatory for the Study of Arctic Climate Polarstern expedition, the Leibniz Institute for Tropospheric Research, Leipzig, Germany, operated the shipborne OCEANET-Atmosphere facility for cloud and aerosol observations throughout the whole year. OCEANET-Atmosphere comprises, amongst others, a multiwavelength Raman lidar, a microwave radiometer, and an optical disdrometer. A cloud radar was operated aboard Polarstern by the US Atmospheric Radiation Measurement program. These measurements were processed by applying the so-called Cloudnet methodology to derive cloud properties. To gain a comprehensive view of the clouds, lidar and cloud radar capabilities for low- and high-altitude observations were combined. Cloudnet offers a variety of products with a spatiotemporal resolution of 30 s and 30 m, such as the target classification, and liquid and ice microphysical properties. Additionally, a lidar-based low-level stratus retrieval was applied for cloud detection below the lowest range gate of the cloud radar. Based on the presented dataset, e.g., studies on cloud formation processes and their radiative impact, and model evaluation studies can be conducted.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Characterization of cumulus cloud fields using trajectories in the center of gravity versus water mass phase space: 1. Cloud tracking and phase space description

We study the evolution of warm convective cloud fields using large eddy simulations of continental and trade cumulus. Individual clouds are tracked a posteriori from formation to dissipation using a 3D cloud tracking algorithm and results are presented in the phase- space of center of gravity altitude versus cloud liquid water mass (CvM space). Here, the CvM space is shown to contain rich information on cloud field characteristics, cloud morphology, and common cloud development pathways, together facilitating a comprehensive understanding of the cloud field. In this part we show how the meteorological (thermodynamic) conditions that determine the cloud properties are projected on the CvM phase space and how changes in the initial conditions affect the clouds' trajectories in this space. This part sets the stage for a detailed microphysical analysis that will be shown in part II.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Cloud Condensation Nuclei Activity of Aerosols during GoAmazon 2014/15 Field Campaign Report

Aerosol indirect effects, which represent the impact of aerosols on climate through influencing the properties of clouds, remain one of the main uncertainties in climate predictions (Stocker et al. 2013). Reducing this large uncertainty requires both improved understanding and representation of aerosol properties and processes in climate models, including the cloud activation properties of aerosols. The Atmospheric System Research (ASR) science program plan of January 2010 states that: “A key requirement for simulating aerosol-cloud interactions is the ability to calculate cloud condensation nuclei and ice nuclei (CCN and IN, respectively) concentrations as a function of supersaturation from the chemical and microphysical properties of the aerosol.” The Observations and Modeling of the Green Ocean Amazon (GoAmazon 2014/15) study seeks to understand how aerosol and cloud life cycles are influenced by pollutant outflow from a tropical megacity (Manaus)—in particular, the differences in cloud-aerosol-precipitation interactions between polluted and pristine conditions. One key question of GoAmazon2014/5 is: “What is the influence of the Manaus pollution plume on the cloud condensation nuclei (CCN) activities of the aerosol particles and the secondary organic material in the particles?” To address this question, we measured size-resolved CCN spectra, a critical measurement for GoAmazon2014/5.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Influences of an entrainment–mixing parameterization on numerical simulations of cumulus and stratocumulus clouds

Abstract. Different entrainment–mixing processes can occur in clouds; however, a homogeneous mixing mechanism is often implicitly assumed in most commonly used microphysics schemes. Here, we first present a new entrainment–mixing parameterization that uses the grid mean relative humidity without requiring the relative humidity of the entrained air. Then, the parameterization is implemented in a microphysics scheme in a large eddy simulation model, and sensitivity experiments are conducted to compare the new parameterization with the default homogeneous entrainment–mixing parameterization. The results indicate that the new entrainment–mixing parameterization has a larger impact on the number concentration, volume mean radius, and cloud optical depth in the stratocumulus case than in the cumulus case. This is because inhomogeneous and homogeneous mixing mechanisms dominate in the stratocumulus and cumulus cases, respectively, which is mainly due to the larger turbulence dissipation rate in the cumulus case. Because stratocumulus clouds break up during the dissipation stage to form cumulus clouds, the effects of this new entrainment–mixing parameterization during the stratocumulus dissipation stage are between those during the stratocumulus mature stage and the cumulus case. A large aerosol concentration can enhance the effects of this new entrainment–mixing parameterization by decreasing the cloud droplet size and evaporation timescale. The results of this new entrainment–mixing parameterization with grid mean relative humidity are validated by the use of a different entrainment–mixing parameterization that uses parameterized entrained air properties. This study sheds new light on the improvement of entrainment–mixing parameterizations in models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2012

Comparison of PARASOL Observations with Polarized Reflectances Simulated Using Different Ice Habit Mixtures

Insufficient knowledge of the habit distribution and the degree of surface roughness of ice crystals within ice clouds is a source of uncertainty in the forward light scattering and radiative transfer simulations required in downstream applications involving these clouds. The widely used MODerate Resolution Imaging Spectroradiometer (MODIS) Collection 5 ice microphysical model assumes a mixture of various ice crystal shapes with smooth-facets except aggregates of columns for which a moderately rough condition is assumed. When compared with PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) polarized reflection data, simulations of polarized reflectance using smooth particles show a poor fit to the measurements, whereas very rough-faceted particles provide an improved fit to the polarized reflectance. In this study a new microphysical model based on a mixture of 9 different ice crystal habits with severely roughened facets is developed. Simulated polarized reflectance using the new ice habit distribution is calculated using a vector adding-doubling radiative transfer model, and the simulations closely agree with the polarized reflectance observed by PARASOL. The new general habit mixture is also tested using a spherical albedo differences analysis, and surface roughening is found to improve the consistency of multi-angular observations. It is suggested that an ice model incorporating an ensemble of different habits with severely roughened surfaces would potentially be an adequate choice for global ice cloud retrievals.

Cole, Benjamin H.↗
DOE OSTI2021

Predicting Frigid Mixed-Phase Clouds for Pristine Coastal Antarctica

Supercooled water is common in the clouds near coastal Antarctica and occasionally occurs at temperatures at or below -30°C. Yet the ice physics in most regional and global numerical models will glaciate out these clouds. This presents a challenge for the simulation of highly supercooled clouds that were observed at McMurdo, Antarctica during the Atmospheric Radiation Measurement (ARM) West Antarctic Radiation Experiment (AWARE) project during 2015–2017. The polar optimized version of the Weather Research and Forecasting model (Polar WRF) with the recently developed two-moment P3 microphysics scheme was used to simulate observed supercooled liquid water cases during March and November 2016. Nudging of the simulations to observed rawinsonde profiles and Antarctic automatic weather station observations provided increased realism and much greater cloud water amounts. Furthermore, sensitivity tests that adjust the ice physics for extremely low ice nucleating particle (INP) concentrations decrease cloud ice and increases the cloud liquid water closer to observed amounts. In these tests, a liquid layer near cloud top is simulated, in agreement with observations. Accurate representation of INP concentrations appears to be critical for the simulation of coastal Antarctic clouds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Locally narrow droplet size distributions are ubiquitous in stratocumulus clouds

Marine stratocumulus clouds are the “global reflectors,” sharply contrasting with the underlying dark ocean surface and exerting a net cooling on Earth’s climate. The magnitude of this cooling remains uncertain in part owing to the averaged representation of microphysical processes, such as the droplet-to-drizzle transition in global climate models (GCMs). Current GCMs parameterize cloud droplet size distributions as broad, cloud-averaged gammas. Here, using digital holographic measurements of discrete stratocumulus cloud volumes, we found cloud droplet size distributions to be narrower at the centimeter scale, never resembling the cloud average. These local distributions tended to form pockets of similar-looking cloud regions, each characterized by a size distribution shape that is diluted to varying degrees. These observations open the way for new modeling representations of microphysical processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

A new subgrid-scale representation of hydrometeor fields using a multivariate PDF

Abstract. The subgrid-scale representation of hydrometeor fields is important for calculating microphysical process rates. In order to represent subgrid-scale variability, the Cloud Layers Unified By Binormals (CLUBB) parameterization uses a multivariate probability density function (PDF). In addition to vertical velocity, temperature, and moisture fields, the PDF includes hydrometeor fields. Previously, hydrometeor fields were assumed to follow a multivariate single lognormal distribution. Now, in order to better represent the distribution of hydrometeors, two new multivariate PDFs are formulated and introduced.The new PDFs represent hydrometeors using either a delta-lognormal or a delta-double-lognormal shape. The two new PDF distributions, plus the previous single lognormal shape, are compared to histograms of data taken from large-eddy simulations (LESs) of a precipitating cumulus case, a drizzling stratocumulus case, and a deep convective case. Finally, the warm microphysical process rates produced by the different hydrometeor PDFs are compared to the same process rates produced by the LES.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

GCSS Idealized Cirrus Model Comparison Project

The GCSS Working Group on Cirrus Cloud Systems (WG2) is conducting a systematic comparison and evaluation of cirrus cloud models. This fundamental activity seeks to support the improvement of models used for climate simulation and numerical weather prediction through assessment and improvement of the "process" models underlying parametric treatments of cirrus cloud processes in large-scale models. The WG2 Idealized Cirrus Model Comparison Project is an initial comparison of cirrus cloud simulations by a variety of cloud models for a series of idealized situations with relatively simple initial conditions and forcing. The models (16) represent the state-of-the-art and include 3-dimensional large eddy simulation (LES) models, two-dimensional cloud resolving models (CRMs), and single column model (SCM) versions of GCMs. The model microphysical components are similarly varied, ranging from single-moment bulk (relative humidity) schemes to fully size-resolved (bin) treatments where ice crystal growth is explicitly calculated. Radiative processes are included in the physics package of each model. The baseline simulations include "warm" and "cold" cirrus cases where cloud top initially occurs at about -47C and -66C, respectively. All simulations are for nighttime conditions (no solar radiation) where the cloud is generated in an ice supersaturated layer, about 1 km in depth, with an ice pseudoadiabatic thermal stratification (neutral). Continuing cloud formation is forced via an imposed diabatic cooling representing a 3 cm/s uplift over a 4-hour time span followed by a 2-hour dissipation stage with no cooling. Variations of these baseline cases include no-radiation and stable-thermal-stratification cases. Preliminary results indicated the great importance of ice crystal fallout in determining even the gross cloud characteristics, such as average vertically-integrated ice water path (IWP). Significant inter-model differences were found. Ice water fall speed is directly related to the shape of the particle size distribution and the habits of the ice crystal population, whether assumed or explicitly calculated. In order to isolate the fall speed effect from that of the associated ice crystal population, simulations were also performed where ice water fall speed was set to the same constant value everywhere in each model. Values of 20 and 60 cm/s were assumed. Current results of the project will be described and implications will be drawn. In particular, this exercise is found to strongly focus the definition of issues resulting in observed inter-model differences and to suggest possible strategies for observational validation of the models. The next step in this project is to perform similar comparisons for well observed case studies with sufficient high quality data to adequately define model initiation and forcing specifications and to support quantitative validation of the results.

Starr, David OC.↗
DOE OSTI2017

The Effect of Ice Nuclei Efficiency on Arctic Mixed-Phase Clouds from Large-Eddy Simulations

The effects of ice nuclei (IN) efficiency on the persistent ice formation in Arctic mixed-phase clouds (AMCs) are investigated using a large-eddy simulation model, coupled to a bin microphysics scheme with a prognostic IN formulation. In the three cases where the IN efficiency is high, ice formation and IN depletion are fast. When the IN concentration is 1 and 10 g -1 , IN are completely depleted and the cloud becomes purely liquid phase before the end of the 24-h simulation. When the IN concentration is 100 g -1 , the IN supply is sufficient but the liquid water is completely consumed so that the cloud dissipates quickly. In the three cases when the IN efficiency is low, ice formation is negligible in the first several hours but becomes significant as the temperature is decreased through longwave cooling. Before the end of the simulation, the cloud is in mixed phase when the IN concentration is 1 and 10 g -1 but dissipates when the IN concentration is 100 g -1 . In the case where two types of IN are considered, ice formation persists throughout the simulation. Analysis shows that as the more efficient IN are continuously removed through ice formation, the less efficient IN gradually nucleate more ice crystals because the longwave cooling decreases the cloud temperature. This mechanism is further illustrated with a simple model. These results indicate that a spectrum of IN efficiency is necessary to maintain the persistent ice formation in AMCs.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2014

Intercomparison and Evaluation of Global Aerosol Microphysical Properties Among Aerocom Models of a Range of Complexity

Many of the next generation of global climate models will include aerosol schemes which explicitly simulate the microphysical processes that determine the particle size distribution. These models enable aerosol optical properties and cloud condensation nuclei (CCN) concentrations to be determined by fundamental aerosol processes, which should lead to a more physically based simulation of aerosol direct and indirect radiative forcings. This study examines the global variation in particle size distribution simulated by 12 global aerosol microphysics models to quantify model diversity and to identify any common biases against observations. Evaluation against size distribution measurements from a new European network of aerosol supersites shows that the mean model agrees quite well with the observations at many sites on the annual mean, but there are some seasonal biases common to many sites. In particular, at many of these European sites, the accumulation mode number concentration is biased low during winter and Aitken mode concentrations tend to be overestimated in winter and underestimated in summer. At high northern latitudes, the models strongly underpredict Aitken and accumulation particle concentrations compared to the measurements, consistent with previous studies that have highlighted the poor performance of global aerosol models in the Arctic. In the marine boundary layer, the models capture the observed meridional variation in the size distribution, which is dominated by the Aitken mode at high latitudes, with an increasing concentration of accumulation particles with decreasing latitude. Considering vertical profiles, the models reproduce the observed peak in total particle concentrations in the upper troposphere due to new particle formation, although modelled peak concentrations tend to be biased high over Europe. Overall, the multimodel- mean data set simulates the global variation of the particle size distribution with a good degree of skill, suggesting that most of the individual global aerosol microphysics models are performing well, although the large model diversity indicates that some models are in poor agreement with the observations. Further work is required to better constrain size-resolved primary and secondary particle number sources, and an improved understanding of nucleation an growth (e.g. the role of nitrate and secondary organics) will improve the fidelity of simulated particle size distributions.

Cloud physics↗
DOE OSTI2018

On the freezing time of supercooled drops in developing convective clouds over tropical ocean

Ice generation and evolution in tropical maritime convective clouds are still poorly understood and challenging to model. Aircraft measurements during the Ice in Clouds-Tropical (ICE-T) project suggest that the observed ice particles in intense convective clouds are primarily small at relatively warm temperature (between -7 °C and -10 °C), and large frozen drops are detected at a temperature colder than -10 °C. However, the ice particle size distributions (PSDs) between -7 °C and -10 °C modelled using a parcel model with spectral bin microphysics scheme are much broader than the observation. To interpret the difference in the temperature-dependent ice PSD evolution between the model simulations and the observations, the freezing times and temperatures of supercooled drops are modelled and analyzed. The results indicate that the freezing time (from the initial nucleation to fully frozen) must be considered; it is not instantaneous, and is longer for large drops than for small drops. In strong updrafts, such as that sampled by the Learjet during ICE-T, large freezing drops may be carried upwards to a temperature lower than their nucleation temperature before they are fully frozen. This offers a feasible explanation for the temperature-dependent ice particle size evolution in strong updrafts observed during ICE-T. In models, drop freezing is normally assumed to be instantaneous, which is not realistic; the models yields broader ice PSDs between -7 °C and -10 °C than is observed. The results highlight the importance to consider the freezing time of supercooled drops in interpreting the observed and modelled ice PSDs in growing turrets and in modelling ice generation in cloud resolving models. To better understand the time-dependent drop freezing and its impact on the microphysics and dynamics of convective clouds, more field measurements and laboratory experiments, as well as modelling studies are needed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Marine Boundary Layer Clouds Associated with Coastally Trapped Disturbances: Observations and Model Simulations

Modeling marine low clouds and fog in coastal environments remains an outstanding challenge due to the inherently complex ocean–land–atmosphere system. This is especially important in the context of global circulation models due to the profound radiative impact of these clouds. This study utilizes aircraft and satellite measurements, in addition to numerical simulations using the Weather Research and Forecasting (WRF) Model, to examine three well-observed coastally trapped disturbance (CTD) events from June 2006, July 2011, and July 2015. Cloud water-soluble ionic and elemental composition analyses conducted for two of the CTD cases indicate that anthropogenic aerosol sources may impact CTD cloud decks due to synoptic-scale patterns associated with CTD initiation. In general, the dynamics and thermodynamics of the CTD systems are well represented and are relatively insensitive to the choice of physics parameterizations; however, a set of WRF simulations suggests that the treatment of model physics strongly influences CTD cloud field evolution. Specifically, cloud liquid water path (LWP) is highly sensitive to the choice of the planetary boundary layer (PBL) scheme; in many instances, the PBL scheme affects cloud extent and LWP values as much as or more than the microphysics scheme. Results suggest that differences in the treatment of entrainment and vertical mixing in the Yonsei University (nonlocal) and Mellor–Yamada–Janjić (local) PBL schemes may play a significant role. The impact of using different driving models—namely, the North American Mesoscale Forecast System (NAM) 12-km analysis and the NCEP North American Regional Reanalysis (NARR) 32-km products—is also investigated.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Weak influence of anthropogenic emissions on aerosol, cloud, and rain in the wet season of the Amazon rainforest

Anthropogenic emissions have been shown to affect new particle formation, aerosol concentrations, and clouds. Such effects vary with region, environmental conditions, and cloud types. In the wet season of Amazonia, anthropogenic emissions emitted from Manaus, Brazil, can significantly increase the cloud condensation nuclei (CCN) concentrations compared to the background of mainly natural aerosols. However, the regional response of cloud and rain to anthropogenic emissions in Amazonia remains very uncertain. Here, we aim to quantify how aerosol concentration, cloud, and rain respond to changes in anthropogenic emissions through parameterized new particle formation and primary aerosol emission in the Manaus region and to understand the underlying mechanisms. We ran the atmosphere-only configuration of the HadGEM3 climate model with a nested regional domain that covers most of the rainforest region (720 km by 1200 km with 3 km resolution) under scaled regional emissions. The 7 d simulations show that, in the areas that are affected by anthropogenic emissions, when aerosol and precursor gas emissions are doubled from the baseline emission inventories, aerosol number concentrations increase by 13 %. The nucleation rate that involves sulfuric acid and biogenic compounds generally increases with pollution levels. However, nucleation is suppressed very close to the pollution source, resulting in lower nucleation and soluble Aitken mode aerosol number concentrations. We also found that doubling the anthropogenic emission can increase the cloud droplet number concentrations ( N d ) by 9 %, but cloud water and rain mass mixing ratios do not change significantly. Even very strong reductions in aerosol number concentrations by a factor of 4, which is an unrealistic condition, cause only a 4 % increase in rain over the domain. If we assume our simulation has a fine enough grid resolution and an accurate representation of the relevant atmospheric processes, the simulated weak and non-linear response of cloud and rain properties to linearly scaled anthropogenic emissions suggests that the interactions among aerosol, cloud, and precipitation in the Amazonian convective environment are buffered by microphysical processes. It also implies that the convective environment is resilient to the changes in Nd that occur in response to localized anthropogenic aerosol perturbations.

Wang, Xuemei [University of Leeds (United Kingdom)↗
NASA NTRS1980

Acid rain: Microphysical model

A microphysical model was used to simulate the case of a ground cloud without dilution by entrainment and without precipitation. The numerical integration techniques of the model are presented. The droplet size spectra versus time and the droplet molalities for each value of time are discussed.

Dingle, A. N.↗