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At least 415 records · Page 23

Development of Numerical Codes for Modeling Electromagnetic Behavior at High Frequencies Near Large Objects

A study into the problem of determining electromagnetic solutions at high frequencies for problems involving complex geometries, large sizes and multiple sources (e.g. antennas) has been initiated. Typical applications include the behavior of antennas (and radiators) installed on complex conducting structures (e.g. ships, aircrafts, etc..) with strong interactions between antennas, the radiation patterns, and electromagnetic signals is of great interest for electromagnetic compatibility control. This includes the overall performance evaluation and control of all on-board radiating systems, electromagnetic interference, and personnel radiation hazards. Electromagnetic computational capability exists at NASA LaRC, and many of the codes developed are based on the Moment Method (MM). However, the MM is computationally intensive, and this places a limit on the size of objects and structures that can be modeled. Here, two approaches are proposed: (i) a current-based hybrid scheme that combines the MM with Physical optics, and (ii) an Alternating Direction Implicit-Finite Difference Time Domain (ADI-FDTD) method. The essence of a hybrid technique is to split the overall scattering surface(s) into two regions: (a) a MM zone (MMZ) which can be used over any part of the given geometry, but is most essential over irregular and "non-smooth" geometries, and (b) a PO sub-region (POSR). Currents induced on the scattering and reflecting surfaces can then be computed in two ways depending on whether the region belonged to the MMZ or was part of the POSR. For the MMZ, the current calculations proceed in terms of basis functions with undetermined coefficients (as in the usual MM method), and the answer obtained by solving a system of linear equations. Over the POSR, conduction is obtained as a superposition of two contributions: (i) currents due to the incident magnetic field, and (ii) currents produced by the mutual induction from conduction within the MMZ. This effectively leads to a reduction in the size of linear equations from N to N - Npo with N being the total number of segments for the entire surface and Npo the number of segments over the POSR. The scheme would be appropriate for relatively large, flat surfaces, and at high frequencies. The ADI-FDTD scheme provides for both transient and steady state analyses. The restrictive Courant-Friedrich-Levy (CFL) condition on the time-step is removed, and so large time steps can be chosen even though the spatial grids are small. This report includes the problem definition, a detailed discussion of both the numerical techniques, and numerical implementations for simple surface geometries. Numerical solutions have been derived for a few simple situations.

Joshi, R. P.↗

Giant Molecular Cloud Structure and Evolution

Bodenheimer and Burkert extended earlier calculations of cloud core models to study collapse and fragmentation. The initial condition for an SPH collapse calculation is the density distribution of a Bonnor-Ebert sphere, with near balance between turbulent plus thermal energy and gravitational energy. The main parameter is the turbulent Mach number. For each Mach number several runs are made, each with a different random realization of the initial turbulent velocity field. The turbulence decays on a dynamical time scale, leading the cloud into collapse. The collapse proceeds isothermally until the density has increased to about 10(exp 13) g cm(exp -3). Then heating is included in the dense regions. The nature of the fragmentation is investigated. About 15 different runs have been performed with Mach numbers ranging from 0.3 to 3.5 (the typical value observed in molecular cloud cores is 0.7). The results show a definite trend of increasing multiplicity with increasing Mach number (M), with the number of fragments approximately proportional to (1 + M). In general, this result agrees with that of Fisher, Klein, and McKee who published three cases with an AMR grid code. However our results show that there is a large spread about this curve. For example, for M=0.3 one case resulted in no fragmentation while a second produced three fragments. Thus it is not only the value of M but also the details of the superposition of the various velocity modes that play a critical role in the formation of binaries. Also, the simulations produce a wide range of separations (10-1000 AU) for the multiple systems, in rough agreement with observations. These results are discussed in two conference proceedings.

Hollenbach, David↗

Exploring Hypersonic, Unstructured-Grid Issues through Structured Grids

Pure-tetrahedral unstructured grids have been shown to produce asymmetric heat transfer rates for symmetric problems. Meanwhile, two-dimensional structured grids produce symmetric solutions and as documented here, introducing a spanwise degree of freedom to these structured grids also yields symmetric solutions. The effects of grid skewness and other perturbations of structured-grids are investigated to uncover possible mechanisms behind the unstructured-grid solution asymmetries. By using controlled experiments around a known, good solution, the effects of particular grid pathologies are uncovered. These structured-grid experiments reveal that similar solution degradation occurs as for unstructured grids, especially for heat transfer rates. Non-smooth grids within the boundary layer is also shown to produce large local errors in heat flux but do not affect surface pressures.

Mazaheri, Ali R.↗

Wide-Field Imaging Interferometry Spatial-Spectral Image Synthesis Algorithms

Developed is an algorithmic approach for wide field of view interferometric spatial-spectral image synthesis. The data collected from the interferometer consists of a set of double-Fourier image data cubes, one cube per baseline. These cubes are each three-dimensional consisting of arrays of two-dimensional detector counts versus delay line position. For each baseline a moving delay line allows collection of a large set of interferograms over the 2D wide field detector grid; one sampled interferogram per detector pixel per baseline. This aggregate set of interferograms, is algorithmically processed to construct a single spatial-spectral cube with angular resolution approaching the ratio of the wavelength to longest baseline. The wide field imaging is accomplished by insuring that the range of motion of the delay line encompasses the zero optical path difference fringe for each detector pixel in the desired field-of-view. Each baseline cube is incoherent relative to all other baseline cubes and thus has only phase information relative to itself. This lost phase information is recovered by having point, or otherwise known, sources within the field-of-view. The reference source phase is known and utilized as a constraint to recover the coherent phase relation between the baseline cubes and is key to the image synthesis. Described will be the mathematical formalism, with phase referencing and results will be shown using data collected from NASA/GSFC Wide-Field Imaging Interferometry Testbed (WIIT).

Lyon, Richard G.↗

Uncertainties in the Modelled CO2 Threshold for Antarctic Glaciation

frequently cited atmospheric CO2 threshold for the onset of Antarctic glaciation of approximately780 parts per million by volume is based on the study of DeConto and Pollard (2003) using an ice sheet model and the GENESIS climate model. Proxy records suggest that atmospheric CO2 concentrations passed through this threshold across the Eocene-Oligocene transition approximately 34 million years. However, atmospheric CO2 concentrations may have been close to this threshold earlier than this transition, which is used by some to suggest the possibility of Antarctic ice sheets during the Eocene. Here we investigate the climate model dependency of the threshold for Antarctic glaciation by performing offline ice sheet model simulations using the climate from 7 different climate models with Eocene boundary conditions (HadCM3L, CCSM3, CESM1.0, GENESIS, FAMOUS, ECHAM5 and GISS_ER). These climate simulations are sourced from a number of independent studies, and as such the boundary conditions, which are poorly constrained during the Eocene, are not identical between simulations. The results of this study suggest that the atmospheric CO2 threshold for Antarctic glaciation is highly dependent on the climate model used and the climate model configuration. A large discrepancy between the climate model and ice sheet model grids for some simulations leads to a strong sensitivity to the lapse rate parameter.

simulation↗

Scale resolving simulations of the NASA Juncture Flow Model using the LAVA solver

Two distinct simulation methodologies: Delayed Detached Eddy Simulation (DDES) and stress based Wall-modelled Large Eddy Simulation (WMLES) are evaluated using structured overset curvilinear grids for the NASA juncture flow model. While both methodologies are shown to mitigate the primary shortcomings of steady state Reynolds Averaged Navier Stokes(RANS) simulations, several unresolved aspects are identified. Strong sensitivity to RANS-typegrid refinement is observed in the DDES with a substantial deterioration of the solution quality with increasing spatial resolution associated with deficiencies in the shielding function. Mean profiles for attached boundary layers on the fuselage show spurious inflections suggesting modelled stress depletion on finer grids. Lower numerical dissipation in terms of spatial discretization and time step size is seen to improve the solution quality, and the advantage of using RC and QCR2000 corrections in the underlying RANS closure is demonstrated for DDES on RANS-type meshes. Equilibrium Wall-Modelled LES used grids that resolved the tripping dots over the fuselage nose and the wing leading edge, consistent with the experiment setup. These simulations resulted in a cost-competitive approach compared to DDES on RANS-type grids. Although the agreement between WMLES predictions of first and second order single point statistics with experimental measurements is promising, a fundamental shortcoming is noted in terms of an overshoot in streamwise momentum in corner regions of the wing-fuselage juncture. This excess momentum subsequently delays the onset of separation,thereby resulting in an underprediction in length of the separation bubble. Some quantitative sensitivity to numerical discretization is observed; lowering of numerical dissipation shows better agreement with the experiment.

T^3↗

Global-scale distribution of ozone in the remote troposphere from ATom and HIPPO airborne field missions

Ozone is a key constituent of the troposphere, where it drives photochemical processes, impacts air quality, and acts as a climate forcer. Large-scale in situ observations of ozone commensurate with the grid resolution of current Earth system models are necessary to validate model outputs and satellite retrievals. In this paper, we examine measurements from the Atmospheric Tomography (ATom; four deployments in 2016–2018) and the HIAPER Pole-to-Pole Observations (HIPPO; five deployments in 2009–2011) experiments, two global-scale airborne campaigns covering the Pacific and Atlantic basins. ATom and HIPPO represent the first global-scale, vertically resolved measurements of O3 distributions throughout the troposphere, with HIPPO sampling the atmosphere over the Pacific and ATom sampling both the Pacific and Atlantic. Given the relatively limited temporal resolution of these two campaigns, we first compare ATom and HIPPO ozone data to longer-term observational records to establish the representativeness of our dataset. We show that these two airborne campaigns captured on average 53 %, 54 %, and 38 % of the ozone variability in the marine boundary layer, free troposphere, and upper troposphere–lower stratosphere (UTLS), respectively, at nine well-established ozonesonde sites. Additionally, ATom captured the most frequent ozone concentrations measured by regular commercial aircraft flights in the northern Atlantic UTLS. We then use the repeated vertical profiles from these two campaigns to confirm and extend the existing knowledge of tropospheric ozone spatial and vertical distributions throughout the remote troposphere. We highlight a clear hemispheric gradient, with greater ozone in the Northern Hemisphere, consistent with greater precursor emissions and consistent with previous modeling and satellite studies. We also show that the ozone distribution below 8 km was similar in the extra-tropics of the Atlantic and Pacific basins, likely due to zonal circulation patterns. However, twice as much ozone was found in the tropical Atlantic as in the tropical Pacific, due to well-documented dynamical patterns transporting continental air masses over the Atlantic. Finally, we show that the seasonal variability of tropospheric ozone over the Pacific and the Atlantic basins is driven year-round by transported continental plumes and photochemistry, and the vertical distribution is driven by photochemistry and mixing with stratospheric air. This new dataset provides additional constraints for global climate and chemistry models to improve our understanding of both ozone production and loss processes in remote regions, as well as the influence of anthropogenic emissions on baseline ozone.

ATom, aircraft profiles, Atlantic pollution, ozone↗

Low and High Temperature Non-Thermonuclear Fusion Approaches to Energy Production

We are responding to the RFI points A1, A2 and A3. We appreciate the need for a high density, high power, environmentally-benign and carbon-neutral power system. Although fusion has been considered for over 70 years, the nearly intractable means of maintaining a hydrogen plasma at temperatures exceeding the center of the Sun increasingly delays not only commercialization but even the scientific breakeven point. As a recent JASON report notes, the world-wide energy grid is moving towards decentralization which is counter to the large tokamak fusion de-vices necessary given their underdense plasmas. NASA has spent several years understanding and developing Lattice Confinement Fusion as an alternative to thermonuclear fusion by exploring many means of loading and triggering fusion reactions in deuterated metal lattices. Triggering has run the gamut from bremsstrahlung-initiated photo-neutrons to the role of electron screening in assisting these reactions. Electron screening may be responsible for both nuclear effects in deuterium pumped metals as well as fast neutrons observed from electrolytically driven cathodes. Electron screened fusion rate enhancement has been observed by others, including the Lawrence Berkeley National Laboratory. NASA’s need for deep space power drove this research with a goal of a ten-year lifetime for a multi-kWe power system. Previous NASA studies have explored the use of fusion systems for nuclear thermal propulsion for manned spaceflight to the outer planets. Despite these designated uses, small-scale terrestrial power applications as well as medical isotope production are possible once scaling is achieved. ARPA-E can contribute to the Nation’s Green Energy mandates by funding research in this field that builds on condensed matter nuclear science findings by the US Navy and NASA.

L. P. Forsley↗

Enhanced Simulation Techniques in Predicting Sonic Boom Loudness Using CFD

This paper outlines advancements in predicting sonic boom loudness within the Launch, Ascent, and Vehicle Aerodynamics (LAVA) computational framework. Traditionally, a two step process consisting of a steady state computational fluid dynamics problem for near-field analysis and a far-field propagation solver for calculation of loudness metrics has been used. Improvements to this process made in this work include utilizing a high-order space marching method for mid-field computations, developing a novel output-based mesh adaptation method targeting error in near-field pressure sig-natures, and developing a robust scripting system using curvilinear grids to increase robustness and simplify the process of running large databases of simulation cases. These advancements are detailed and applied to the simulation of the X-59, presenting comparative cost and timing analyses between the prior two step workflow and the current three step procedure. We achieve increased accuracy and robustness for loudness predictions with at least a50%computational cost reduction.

CST↗

Materials for Power Transmission in Extreme Environments

NASA’s goal for a sustained human presence on the Moon and a future Lunar economy requires the development of novel power transmission materials for extreme environments. As an increasing number of public and private entities set their sights towards a future on the Moon, the demand for surface power will dramatically increase – potentially up to megawatt levels. A Lunar economy is envisioned to include a human habitat, manned and unmanned science exploration assets, excavation rovers and systems, and large-scale infrastructure construction such as solar arrays and power grids. A NASA trade study estimated that 1 to 3 km of power transmission lines (1 to 3 KV ac and dc) will be needed over time. Current high power and voltage SOA cables/wire can easily exceed 1 kg/m where mass is not as critical. Connectors, deployment spools and robots further increase the subsystem mass significantly increasing costs. On the other hand, advances in aeronautics provides path towards space missions. The operating environment on the Moon presents substantial risk to safe and reliable power transmission due to space weathering and degradation. These challenges include cosmic and UV radiation, extreme temperatures swings, the electrostatic Lunar exosphere, and the electrostatic and abrasive lunar regolith. The critical need for lightweight, safe and reliable power cables/wires materials is evident. In this presentation, the extreme high altitude and lunar environments and recent materials development from NASA Glenn Research Center’s High Voltage Materials team towards meeting NASA’s objectives and goals for aeronautics and space missions.

Cu/CNT conductors↗

The Viability of Trajectory Analysis for Diagnosing Dynamical and Chemical Influences on Ozone Concentrations in the UTLS

The viability of trajectory analysis for diagnosing the interplay between chemistry and dynamics is investigated by comparing ozone mixing ratios modelled using air-parcel pathways to values observed along flight tracks during ATTREX (Airborne Tropical TRopopause EXperiment). Trajectories are initiated at the locations of ozone observations and tracked backward in time to their sources at termini of backward trajectories. The modelled values of ozone utilize 3-dimensional analysis fields from WACCM (Whole Atmosphere Community Climate Model) (a chemical-climate model with dynamical fields nudged towards MERRA (Modern-Era Retrospective Analysis and Research Applications) reanalysis) and ERA-interim (product of ECMWF - the European Centre for Medium-Range Weather Forecasts) to determine source mixing ratios with chemical production and loss terms derived from the ozone chemistry used in WACCM. A statistical base of modelled ozone is constructed with 6 trajectory platforms (adiabatic, diabatic, and kinematic forced by ERA-interim and MERRA), two chemical models (WACCM chemistry and no chemistry), and 4 trajectory lengths (5, 10, 20, and 30 days). Linear regression is employed to separate systematic errors from random errors and to characterize the impact of source mixing ratios, path length, vertical motion, and chemistry on modelled ozone errors. Errors in the analysis ozone fields are large, if not dominant, contributors to model error. Random errors are particularly large for point-by-point comparisons, however averaging over 800 km (75 minutes) flight segments substantially reduces random error and exposes systematic errors. Of the two analysis ozone data sets, WACCM, which incorporates detailed chemistry, provides the smaller systematic errors while ERA-interim, which has crude chemistry but assimilates observational data, has the smaller random errors. Of the different trajectory platforms, adiabatic calculations produce the smaller random errors (irrespective of the use of chemistry) but both vertical motion and chemistry are required to optimally reduce systematic errors. These results suggest that meaningful analysis of dynamical and chemical interactions that control ozone mixing ratios are viable on spatial scales larger than a few reanalysis grid spaces, that errors in the analyzed ozone data sets are large but not prohibitively so, and that vertical velocities and heating rates from reanalysis data, while problematic, contain useful information [on the ozone concentrations in the UTLS (Upper Troposphere/Lower Stratosphere)].

ozone↗

Ionospheric calibration for single frequency altimeter measurements

This study is a preliminary analysis of the effectiveness (in terms of altimeter calibration accuracy) of various ionosphere models and the Global Positioning System (GPS) to calibrate single frequency altimeter height measurements for ionospheric path delay. In particular, the research focused on ingesting GPS Total Electron Content (TEC) data into the physical Parameterized Real-Time Ionospheric Specification Model (PRISM), which estimates the composition of the ionosphere using independent empirical and physical models and has the capability of adjusting to additional ionospheric measurements. Two types of GPS data were used to adjust the PRISM model: GPS receiver station data mapped from line-of-sight observations to the vertical at the point of interest and a grid map (generated at the Jet Propulsion Laboratory) of GPS derived TEC in a sun-fixed longitude frame. The adjusted PRISM TEC values, as well as predictions by the International Reference Ionosphere (IRI-90), a climatological (monthly mean) model of the ionosphere, were compared to TOPEX dual-frequency TEC measurements (considered as truth) for a number of TOPEX sub-satellite tracks. For a 13.6 GHz altimeter, a Total Electron Content (TEC) of 1 TECU 10(exp 16) electrons/sq m corresponds to approximately 0.218 centimeters of range delay. A maximum expected TEC (at solar maximum or during solar storms) of 10(exp 18) electrons/sq m will create 22 centimeters of range delay. Compared with the TOPEX data, the PRISM predictions were generally accurate within the TECU when the sub-satellite track of interest passed within 300 to 400 km of the GPS TEC data or when the track passed through a night-time ionosphere. If neither was the case, in particular if the track passed through a local noon ionosphere, the PRISM values differed by more than 10 TECU and by as much as 40 TECU. The IRI-90 model, with no current ability to unseat GPS data, predicted TEC to a slightly higher error of 12 TECU. The performance of PRISM is very promising for predicting TEC and will prove useful for calibrating single frequency altimeter height measurements for ionospheric path delay. When adjusted to the GPS line-of-sight data the PRISM URSI empirical model predicted TEC over a day's period to within a global error of 8.60 TECU rms during a nighttime ionosphere and 9.74 TECU rms during the day. When adjusted to the GPS derived TEC grid, the PRISM parametrized model predicted TEC to within an error of 8.47 TECU rms for a nighttime ionosphere and 12.83 TECU rms during the day. However, the grid cannot be considered globally due to the lack of sufficient numbers of GPS stations and large latitude gaps in GPS data. It is the opinion of the authors that using the PRISM model and adjusting to the global sun-fixed TEC grid regenerated with a localized weighted interpolation offers the best possibility of meeting the 10 TECU global rms (or 2 cm at 13.6 GHz) ionosphere range correction accuracy requirement of TOPEX/Poseidon and should be the subject of further study. However, it is clear that the anticipated requirement of 34 TECU global rms for TOPEX/Poseidon Follow-On (corresponding to the TOPEX/Poseidon performance) can not be met with any realizable combination of existing models and data assimilation schemes.

Schreiner, William S.↗

Information Power Grid Posters

This document is a summary of the accomplishments of the Information Power Grid (IPG). Grids are an emerging technology that provide seamless and uniform access to the geographically dispersed, computational, data storage, networking, instruments, and software resources needed for solving large-scale scientific and engineering problems. The goal of the NASA IPG is to use NASA's remotely located computing and data system resources to build distributed systems that can address problems that are too large or complex for a single site. The accomplishments outlined in this poster presentation are: access to distributed data, IPG heterogeneous computing, integration of large-scale computing node into distributed environment, remote access to high data rate instruments,and exploratory grid environment.

Vaziri, Arsi↗

Fuel optimal reorientation of axisymmetric spin-stabilized satellites

The fuel optimal spin axis reorientation problem for large and small maneuver times is solved using a new numerical technique. The approach, which employs the adaptive grid bisection search, is shown to be useful in determining the fuel optimal impulsive control strategy, particularly when rapid maneuvers are desired. For large enough maneuver times, the method produces the two-impulse reorientation maneuver. For even larger maneuver times, the existence of multiple optimal pulsing schemes is demonstrated.

Redmond, Jim↗

Multigrid calculation of three-dimensional viscous cascade flows

A three-dimensional code for viscous cascade flow prediction has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large-scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Arnone, A.↗

Developing Information Power Grid Based Algorithms and Software

This was an exploratory study to enhance our understanding of problems involved in developing large scale applications in a heterogeneous distributed environment. It is likely that the large scale applications of the future will be built by coupling specialized computational modules together. For example, efforts now exist to couple ocean and atmospheric prediction codes to simulate a more complete climate system. These two applications differ in many respects. They have different grids, the data is in different unit systems and the algorithms for inte,-rating in time are different. In addition the code for each application is likely to have been developed on different architectures and tend to have poor performance when run on an architecture for which the code was not designed, if it runs at all. Architectural differences may also induce differences in data representation which effect precision and convergence criteria as well as data transfer issues. In order to couple such dissimilar codes some form of translation must be present. This translation should be able to handle interpolation from one grid to another as well as construction of the correct data field in the correct units from available data. Even if a code is to be developed from scratch, a modular approach will likely be followed in that standard scientific packages will be used to do the more mundane tasks such as linear algebra or Fourier transform operations. This approach allows the developers to concentrate on their science rather than becoming experts in linear algebra or signal processing. Problems associated with this development approach include difficulties associated with data extraction and translation from one module to another, module performance on different nodal architectures, and others. In addition to these data and software issues there exists operational issues such as platform stability and resource management.

Dongarra, Jack↗

Large eddy simulation of homogeneous isotropic turbulence

This paper presents results from a comprehensive investigation of large-eddy simulations of homogeneous isotropic turbulence. Calculations have been made using grid meshes, a number of flowfield filters, and two simple subgrid scale turbulence models. Particular attention has been paid to the degree of isotropy and the ability of the approach to predict higher-order statistical quantities (skewness and flatness). Directions for needed improvement in the simulation approach are indicated, and a plea is made to experimenters to process their data in a way which will facilitate comparison with large eddy simulations.

Ferziger, J. H.↗

Evaluation of a Cloud Resolving Model Using TRMM Observations for Multiscale Modeling Applications

The climate change simulation community is moving toward use of global cloud resolving models (CRMs), however, current computational resources are not sufficient to run global CRMs over the hundreds of years necessary to produce climate change estimates. As an intermediate step between conventional general circulation models (GCMs) and global CRMs, many climate analysis centers are embedding a CRM in each grid cell of a conventional GCM. These Multiscale Modeling Frameworks (MMFs) represent a theoretical advance over the use of conventional GCM cloud and convection parameterizations, but have been shown to exhibit an overproduction of precipitation in the tropics during the northern hemisphere summer. In this study, simulations of clouds, precipitation, and radiation over the South China Sea using the CRM component of the NASA Goddard MMF are evaluated using retrievals derived from the instruments aboard the Tropical Rainfall Measuring Mission (TRMM) satellite platform for a 46-day time period that spans 5 May - 20 June 1998. The NASA Goddard Cumulus Ensemble (GCE) model is forced with observed largescale forcing derived from soundings taken during the intensive observing period of the South China Sea Monsoon Experiment. It is found that the GCE configuration used in the NASA Goddard MMF responds too vigorously to the imposed large-scale forcing, accumulating too much moisture and producing too much cloud cover during convective phases, and overdrying the atmosphere and suppressing clouds during monsoon break periods. Sensitivity experiments reveal that changes to ice cloud microphysical parameters have a relatively large effect on simulated clouds, precipitation, and radiation, while changes to grid spacing and domain length have little effect on simulation results. The results motivate a more detailed and quantitative exploration of the sources and magnitude of the uncertainty associated with specified cloud microphysical parameters in the CRM components of MMFs.

Posselt, Derek J.↗