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Exploring Alternate Parameterizations for Snowfall with Validation from Satellite and Terrestrial Radars

Increases in computational resources have allowed operational forecast centers to pursue experimental, high resolution simulations that resolve the microphysical characteristics of clouds and precipitation. These experiments are motivated by a desire to improve the representation of weather and climate, but will also benefit current and future satellite campaigns, which often use forecast model output to guide the retrieval process. Aircraft, surface and radar data from the Canadian CloudSat/CALIPSO Validation Project are used to check the validity of size distribution and density characteristics for snowfall simulated by the NASA Goddard six-class, single-moment bulk water microphysics scheme, currently available within the Weather Research and Forecast (WRF) Model. Widespread snowfall developed across the region on January 22, 2007, forced by the passing of a midlatitude cyclone, and was observed by the dual-polarimetric, C-band radar King City, Ontario, as well as the NASA 94 GHz CloudSat Cloud Profiling Radar. Combined, these data sets provide key metrics for validating model output: estimates of size distribution parameters fit to the inverse-exponential equations prescribed within the model, bulk density and crystal habit characteristics sampled by the aircraft, and representation of size characteristics as inferred by the radar reflectivity at C- and W-band. Specified constants for distribution intercept and density differ significantly from observations throughout much of the cloud depth. Alternate parameterizations are explored, using column-integrated values of vapor excess to avoid problems encountered with temperature-based parameterizations in an environment where inversions and isothermal layers are present. Simulation of CloudSat reflectivity is performed by adopting the discrete-dipole parameterizations and databases provided in literature, and demonstrate an improved capability in simulating radar reflectivity at W-band versus Mie scattering assumptions.

Molthan, Andrew L.↗

Exploring Alternative Parameterizations for Snowfall with Validation from Satellite and Terrestrial Radars

Increases in computational resources have allowed operational forecast centers to pursue experimental, high resolution simulations that resolve the microphysical characteristics of clouds and precipitation. These experiments are motivated by a desire to improve the representation of weather and climate, but will also benefit current and future satellite campaigns, which often use forecast model output to guide the retrieval process. The combination of reliable cloud microphysics and radar reflectivity may constrain radiative transfer models used in satellite simulators during future missions, including EarthCARE and the NASA Global Precipitation Measurement. Aircraft, surface and radar data from the Canadian CloudSat/CALIPSO Validation Project are used to check the validity of size distribution and density characteristics for snowfall simulated by the NASA Goddard six-class, single moment bulk water microphysics scheme, currently available within the Weather Research and Forecast (WRF) Model. Widespread snowfall developed across the region on January 22, 2007, forced by the passing of a mid latitude cyclone, and was observed by the dual-polarimetric, C-band radar King City, Ontario, as well as the NASA 94 GHz CloudSat Cloud Profiling Radar. Combined, these data sets provide key metrics for validating model output: estimates of size distribution parameters fit to the inverse-exponential equations prescribed within the model, bulk density and crystal habit characteristics sampled by the aircraft, and representation of size characteristics as inferred by the radar reflectivity at C- and W-band. Specified constants for distribution intercept and density differ significantly from observations throughout much of the cloud depth. Alternate parameterizations are explored, using column-integrated values of vapor excess to avoid problems encountered with temperature-based parameterizations in an environment where inversions and isothermal layers are present. Simulation of CloudSat reflectivity is performed by adopting the discrete-dipole parameterizations and databases provided in literature, and demonstrate an improved capability in simulating radar reflectivity at W-band versus Mie scattering assumptions.

Molthan, Andrew L.↗

The Super Tuesday Outbreak: Forecast Sensitivities to Single-Moment Microphysics Schemes

Forecast precipitation and radar characteristics are used by operational centers to guide the issuance of advisory products. As operational numerical weather prediction is performed at increasingly finer spatial resolution, convective precipitation traditionally represented by sub-grid scale parameterization schemes is now being determined explicitly through single- or multi-moment bulk water microphysics routines. Gains in forecasting skill are expected through improved simulation of clouds and their microphysical processes. High resolution model grids and advanced parameterizations are now available through steady increases in computer resources. As with any parameterization, their reliability must be measured through performance metrics, with errors noted and targeted for improvement. Furthermore, the use of these schemes within an operational framework requires an understanding of limitations and an estimate of biases so that forecasters and model development teams can be aware of potential errors. The National Severe Storms Laboratory (NSSL) Spring Experiments have produced daily, high resolution forecasts used to evaluate forecast skill among an ensemble with varied physical parameterizations and data assimilation techniques. In this research, high resolution forecasts of the 5-6 February 2008 Super Tuesday Outbreak are replicated using the NSSL configuration in order to evaluate two components of simulated convection on a large domain: sensitivities of quantitative precipitation forecasts to assumptions within a single-moment bulk water microphysics scheme, and to determine if these schemes accurately depict the reflectivity characteristics of well-simulated, organized, cold frontal convection. As radar returns are sensitive to the amount of hydrometeor mass and the distribution of mass among variably sized targets, radar comparisons may guide potential improvements to a single-moment scheme. In addition, object-based verification metrics are evaluated for their utility in gauging model performance and QPF variability.

Molthan, Andrew L.↗

For Spacious Skies: Self-Separation with "Autonomous Flight Rules" in US Domestic Airspace

Autonomous Flight Rules (AFR) are proposed as a new set of operating regulations in which aircraft navigate on tracks of their choice while self-separating from traffic and weather. AFR would exist alongside Instrument and Visual Flight Rules (IFR and VFR) as one of three available flight options for any appropriately trained and qualified operator with the necessary certified equipment. Historically, ground-based separation services evolved by necessity as aircraft began operating in the clouds and were unable to see each other. Today, technologies for global precision navigation, emerging airborne surveillance, and onboard computing enable traffic conflict management to be fully integrated with navigation procedures onboard the aircraft. By self-separating, aircraft can operate with more flexibility and fewer flight restrictions than are required when using ground-based separation. The AFR concept proposes a practical means in which self-separating aircraft could share the same airspace as IFR and VFR aircraft without disrupting the ongoing processes of Air Traffic Control. The paper discusses the context and motivation for implementing self-separation in US domestic airspace. It presents a historical perspective on separation, the proposed way forward in AFR, the rationale behind mixed operations, and the expected benefits of AFR for the airspace user community.

Wing, David J.↗

NASA Tech Briefs, July 2011

Topics covered include: 1) Collaborative Clustering for Sensor Networks; 2) Teleoperated Marsupial Mobile Sensor Platform Pair for Telepresence Insertion Into Challenging Structures; 3) Automated Verification of Spatial Resolution in Remotely Sensed Imagery; 4) Electrical Connector Mechanical Seating Sensor; 5) In Situ Aerosol Detector; 6) Multi-Parameter Aerosol Scattering Sensor; 7) MOSFET Switching Circuit Protects Shape Memory Alloy Actuators; 8) Optimized FPGA Implementation of Multi-Rate FIR Filters Through Thread Decomposition; 9) Circuit for Communication Over Power Lines; 10) High-Efficiency Ka-Band Waveguide Two-Way Asymmetric Power Combiner; 11) 10-100 Gbps Offload NIC for WAN, NLR, and Grid Computing; 12) Pulsed Laser System to Simulate Effects of Cosmic Rays in Semiconductor Devices; 13) Flight Planning in the Cloud; 14) MPS Editor; 15) Object-Oriented Multi Disciplinary Design, Analysis, and Optimization Tool; 16) Cryogenic-Compatible Winchester Connector Mount and Retaining System for Composite Tubes; 17) Development of Position-Sensitive Magnetic Calorimeters for X-Ray Astronomy; 18) Planar Rotary Piezoelectric Motor Using Ultrasonic Horns; 19) Self-Rupturing Hermetic Valve; 20) Explosive Bolt Dual-Initiated from One Side; 21) Dampers for Stationary Labyrinth Seals; 22) Two-Arm Flexible Thermal Strap; 23) Carbon Dioxide Removal via Passive Thermal Approaches; 24) Polymer Electrolyte-Based Ambient Temperature Oxygen Microsensors for Environmental Monitoring; 25) Pressure Shell Approach to Integrated Environmental Protection; 26) Image Quality Indicator for Infrared Inspections; 27) Micro-Slit Collimators for X-Ray/Gamma-Ray Imaging; 28) Scatterometer-Calibrated Stability Verification Method; 29) Test Port for Fiber-Optic-Coupled Laser Altimeter; 30) Phase Retrieval System for Assessing Diamond Turning and Optical Surface Defects; 31) Laser Oscillator Incorporating a Wedged Polarization Rotator and a Porro Prism as Cavity Mirror; 32) Generic, Extensible, Configurable Push-Pull Framework for Large-Scale Science Missions; 33) Dynamic Loads Generation for Multi-Point Vibration Excitation Problems; 34) Optimal Control via Self-Generated Stochasticity; 35) Space-Time Localization of Plasma Turbulence Using Multiple Spacecraft Radio Links; 36) Surface Contact Model for Comets and Asteroids; 37) Dust Mitigation Vehicle; 38) Optical Coating Performance for Heat Reflectors of the JWST-ISIM Electronic Component; 39) SpaceCube Demonstration Platform; 40) Aperture Mask for Unambiguous Parity Determination in Long Wavelength Imagers; 41) Spaceflight Ka-Band High-Rate Radiation-Hard Modulator; 42) Enabling Disabled Persons to Gain Access to Digital Media; 43) Cytometer on a Chip; 44) Principles, Techniques, and Applications of Tissue Microfluidics; and 45) Two-Stage Winch for Kites and Tethered Balloons or Blimps.

Source record↗

CME Flux Rope and Shock Identifications and Locations: Comparison of White Light Data, Graduated Cylindrical Shell Model, and MHD Simulations

Coronal mass ejections (CMEs) are major transient phenomena in the solar corona that are observed with ground-based and spacecraft-based coronagraphs in white light or with in situ measurements by spacecraft. CMEs transport mass and momentum and often drive shocks. In order to derive the CME and shock trajectories with high precision, we apply the graduated cylindrical shell (GCS) model to fit a flux rope to the CME directed toward STEREO A after about 19:00 UT on 29 November 2013 and check the quality of the heliocentric distance-time evaluations by carrying out a three-dimensional magnetohydrodynamic (MHD) simulation of the same CME with the Block Adaptive Tree Solar-Wind Roe Upwind Scheme (BATS-R-US) code. Heliocentric distances of the CME and shock leading edges are determined from the simulated white light images and magnetic field strength data. We find very good agreement between the predicted and observed heliocentric distances, showing that the GCS model and the BATS-R-US simulation approach work very well and are consistent. In order to assess the validity of CME and shock identification criteria in coronagraph images, we also compute synthetic white light images of the CME and shock. We find that the outer edge of a cloud-like illuminated area in the observed and predicted images in fact coincides with the leading edge of the CME flux rope and that the outer edge of a faint illuminated band in front of the CME leading edge coincides with the CME-driven shock front.

Schmidt, J. M.↗

Comparison of Key Absorption and Optical Properties Between Pure and Transported Anthropogenic Dust over East and Central Asia

Asian dust particulate is one of the primary aerosol constituents in the Earth-atmosphere system that exerts profound influences on environmental quality, human health, the marine biogeochemical cycle, and Earth's climate. To date, the absorptive capacity of dust aerosol generated from the Asian desert region is still an open question. In this article, we compile columnar key absorption and optical properties of mineral dust over East and Central Asian areas by utilizing the multiyear quality-assured datasets observed at 13 sites of the Aerosol Robotic Network (AERONET). We identify two types of Asian dust according to threshold criteria from previously published literature. (1) The particles with high aerosol optical depth at 440 nm (AOD(440) > or = 0.4) and a low Angstrom wavelength exponent at 440-870 nm (alpha < 0.2) are defined as Pure Dust (PDU), which decreases disturbance of other non-dust aerosols and keeps high accuracy of pure Asian dust. (2) The particles with AOD(440) > or = 0.4 and 0.2 < alpha < 0.6 are designated as Transported Anthropogenic Dust (TDU), which is mainly dominated by dust aerosol and might mix with other anthropogenic aerosol types. Our results reveal that the primary components of high AOD days are predominantly dust over East and Central Asian regions, even if their variations rely on different sources, distance from the source, emission mechanisms, and meteorological characteristics. The overall mean and standard deviation of single-scattering albedo, asymmetry factor, real part and imaginary part of complex refractive index at 550 nm for Asian PDU are 0.935 +/- 0.014, 0.742 +/- 0.008, 1.526 +/- 0.029, and 0.00226 +/- 0.00056, respectively, while corresponding values are 0.921 +/- 0.021, 0.723 +/- 0.009, 1.521 +/- 0.025, and 0.00364 +/- 0.0014 for Asian TDU. Aerosol shortwave direct radiative effects at the top of the atmosphere (TOA), at the surface (SFC), and in the atmospheric layer (ATM) for Asian PDU (alpha < 0.2) and TDU (0.2 < alpha < 0.6) computed in this study, are a factor of 2 smaller than the results of Optical Properties of Aerosols and Clouds (OPAC) mineral-accumulated (mineral-acc.) and mineral-transported (mineral-tran.) modes. Therefore, we are convinced that our results hold promise for updating and improving accuracies of Asian dust characteristics in present-day remote sensing applications and regional or global climate models.

Bi, Jianrong↗

Use of Machine Learning to Reduce Uncertainties in Particle Number Concentration and Aerosol Indirect Radiative Forcing Predicted by Climate Models

The radiative forcing of anthropogenic aerosols associated with aerosol–cloud interactions (RF(sub aci)) remains the largest source of uncertainty in climate prediction. The calculation of particle number concentration (PNC), one of the critical parameters affecting RF(sub aci), is generally simplified in climate models. Here we employ outputs from long-term (30-years) simulations of a global size-resolved (sectional) aerosol microphysics model and a machine-learning tool to develop a Random Forest Regression Model (RFRM) for PNC. We have implemented the PNC RFRM in GISS-ModelE2.1 with a mass-based One-Moment Aerosol module, which is one of CMIP6 models. Compared to the default setting, the GISS-ModelE2.1 simulation based on RFRM reduces the changes of cloud droplet number concentration associated with anthropogenic emissions, and decreases the RF(sub aci) from −1.46 W⋅m(exp −2) to −1.11 W⋅m(exp −2). This work highlights a promising approach based on machine learning to reduce uncertainties of climate models in predicting PNC and RF(sub aci) without compromising their computing efficiency.

Radiative forcing↗

Heating rates in tropical anvils

The interaction of infrared and solar radiation with tropical cirrus anvils is addressed. Optical properties of the anvils are inferred from satellite observations and from high-altitude aircraft measurements. An infrared multiple-scattering model is used to compute heating rates in tropical anvils. Layer-average heating rates in 2 km thick anvils were found to be on the order of 20 to 30 K/day. The difference between heating rates at cloud bottom and cloud top ranges from 30 to 200 K/day, leading to convective instability in the anvil. The calculations are most sensitive to the assumed ice water content, but also are affected by the vertical distribution of ice water content and by the anvil thickness. Solar heating in anvils is shown to be less important than infrared heating but not negligible. The dynamical implications of the computed heating rates are also explored and it is concluded that the heating may have important consequences for upward mass transport in the tropics. The potential impact of tropical cirrus on the tropical energy balance and cloud forcing are discussed.

Ackerman, Thomas P.↗

DeepLynx Ecosystem 2025

Poor data integration and governance continue to plague complex engineering projects, resulting in missed cost, schedule, and performance targets. Departments operate in isolated systems with manual data exchange, creating fragmented information that compounds errors and leads to significant delays and cost overruns. The DeepLynx ecosystem addresses these challenges through an open-source, modular data management platform that transforms fragmented project data into an integrated digital thread. Built on a federated microservice architecture, the ecosystem comprises seven specialized tools centered around DeepLynx Nexus, a unified data catalog with hierarchical organization and graph-based navigation capabilities. The ecosystem includes: DeepLynx Stream for real-time timeseries data ingestion from industrial sources; DeepLynx Ingest for governed data uploads with formal review workflows; DeepLynx Lattice for ontology-based entity and relationship extraction; DeepLynx Run for workflow orchestration and secure AI/ML compute; DeepLynx Visualize for 3D digital twin visualization; and DeepLynx Insight for AI-assisted document analysis with traceable, grounded responses. Deployable in cloud, on-premise, or hybrid environments using containerized Docker applications and Helm charts, the DeepLynx ecosystem provides flexible infrastructure that adapts to organizational requirements. By consolidating project data into a unified data lake with role-based access controls and OAuth2 authentication, DeepLynx enables digital thread and digital twin capabilities that improve decision-making, reduce risk, and support complex engineering workflows throughout the project lifecycle.

42 - ENGINEERING↗

tobac v1.5: introducing fast 3D tracking, splits and mergers, and other enhancements for identifying and analysing meteorological phenomena

There is a continuously increasing need for reliable feature detection and tracking tools based on objective analysis principles for use with meteorological data. Many tools have been developed over the previous 2 decades that attempt to address this need but most have limitations on the type of data they can be used with, feature computational and/or memory expenses that make them unwieldy with larger datasets, or require some form of data reduction prior to use that limits the tool's utility. The Tracking and Object-Based Analysis of Clouds (tobac) Python package is a modular, open-source tool that improves on the overall generality and utility of past tools. A number of scientific improvements (three spatial dimensions, splits and mergers of features, an internal spectral filtering tool) and procedural enhancements (increased computational efficiency, internal regridding of data, and treatments for periodic boundary conditions) have been included in tobac as a part of the tobac v1.5 update. These improvements have made tobac one of the most robust, powerful, and flexible identification and tracking tools in our field to date and expand its potential use in other fields. Future plans for tobac v2 are also discussed.

54 ENVIRONMENTAL SCIENCES↗

NASA Earthdata Cloud

Briefing is to highlight an overview of the NASA Earthdate Cloud with more specific details on the "Governance of Cloud Accounts", "Shared Services", Cloud ADA controls, in scope of this AWS public sector session.

Computer Operations and Hardware↗

First results from Goddard High-Resolution Spectrograph - C I, S I, and CO toward Xi Persei and the physical conditions in diffuse clouds

Observations made by the Goddard High Resolution Spectrograph of the cool, neutral interstellar gas in the line of sight to Xi Per are reported. Heliocentric velocities and equivalent widths were measured for absorption lines of C I and S I. Synthetic spectra were computed and fitted to the observed CO(2-0) and (3-0) bands in the A IPi - X 1Sigma(+) system. Derived populations of the C I ground-state fine-structure levels and the CO ground-state rotational levels were used to derive densities of two of the three, and possibly four, detected cloud components. The velocity component displaying the strongest C I absorption reveals extraordinarily high pressure.

Smith, Andrew M.↗

CFD Simulation of Liquid Rocket Engine Injectors

Detailed design issues associated with liquid rocket engine injectors and combustion chamber operation require CFD methodology which simulates highly three-dimensional, turbulent, vaporizing, and combusting flows. The primary utility of such simulations involves predicting multi-dimensional effects caused by specific injector configurations. SECA, Inc. and Engineering Sciences, Inc. have been developing appropriate computational methodology for NASA/MSFC for the past decade. CFD tools and computers have improved dramatically during this time period; however, the physical submodels used in these analyses must still remain relatively simple in order to produce useful results. Simulations of clustered coaxial and impinger injector elements for hydrogen and hydrocarbon fuels, which account for real fluid properties, is the immediate goal of this research. The spray combustion codes are based on the FDNS CFD code' and are structured to represent homogeneous and heterogeneous spray combustion. The homogeneous spray model treats the flow as a continuum of multi-phase, multicomponent fluids which move without thermal or velocity lags between the phases. Two heterogeneous models were developed: (1) a volume-of-fluid (VOF) model which represents the liquid core of coaxial or impinger jets and their atomization and vaporization, and (2) a Blob model which represents the injected streams as a cloud of droplets the size of the injector orifice which subsequently exhibit particle interaction, vaporization, and combustion. All of these spray models are computationally intensive, but this is unavoidable to accurately account for the complex physics and combustion which is to be predicted, Work is currently in progress to parallelize these codes to improve their computational efficiency. These spray combustion codes were used to simulate the three test cases which are the subject of the 2nd International Workshop on-Rocket Combustion Modeling. Such test cases are considered by these investigators to be very valuable for code validation because combustion kinetics, turbulence models and atomization models based on low pressure experiments of hydrogen air combustion do not adequately verify analytical or CFD submodels which are necessary to simulate rocket engine combustion. We wish to emphasize that the simulations which we prepared for this meeting are meant to test the accuracy of the approximations used in our general purpose spray combustion models, rather than represent a definitive analysis of each of the experiments which were conducted. Our goal is to accurately predict local temperatures and mixture ratios in rocket engines; hence predicting individual experiments is used only for code validation. To replace the conventional JANNAF standard axisymmetric finite-rate (TDK) computer code 2 for performance prediction with CFD cases, such codes must posses two features. Firstly, they must be as easy to use and of comparable run times for conventional performance predictions. Secondly, they must provide more detailed predictions of the flowfields near the injector face. Specifically, they must accurately predict the convective mixing of injected liquid propellants in terms of the injector element configurations.

Farmer, Richard↗

Simulation and Interpretation of the Genesis of Tropical Storm Gert (2005) as Part of the NASA Tropical Cloud Systems and Processes Experiment

Several hypotheses have been put forward for the how tropical cyclones (tropical storms and hurricanes in the Atlantic) first develop circulation at the surface, a key event that needs to occur before a storm can begin to draw energy from the warm ocean. One hypothesis suggests that the surface circulation forms from a "top-down" approach in which a storm s rotating circulation begins at middle levels of the atmosphere and builds down to the surface through processes related to light "stratiform" (horizontally extensive) precipitation. Another hypothesis suggests a bottom-up approach in which deep thunderstorm towers (convection) play the major role in spinning up the flow at the surface. These "hot towers" form in the area of the mid-level circulation and strongly concentrate this rotation at low levels within their updrafts. Merger of several of these hot towers then intensifies the surface circulation to the point in which a storm forms. This paper examines computer simulations of Tropical Storm Gert (2005), which formed in the Gulf of Mexico during the National Aeronautics and Space Administration s (NASA) Tropical Cloud Systems and Processes (TCSP) Experiment, to investigate the development of low-level circulation and, in particular, whether stratiform or hot tower processes were responsible for the storm s formation. Data from NASA satellites and from aircraft were used to show that the model did a good job of reproducing the formation and evolution of Gert. The simulation shows that a mix of both stratiform and convective rainfall occurred within Gert. While the stratiform rainfall clearly acted to increase rotation at middle levels, the diverging outflow beneath the stratiform rain worked against spinning up the low-level winds. The hot towers appeared to dominate the low-level flow, producing intense rotation within their cores and often being associated with significant pressure falls at the surface. Over time, many of these hot towers merged, with each merger adding to the rotation of the storm and the pressure falls at the surface. This process continued to increase the strength of the storm until the storm made landfall on the east coast of Mexico. These results support the bottom-up hypothesis for development.

Braun, Scott A.↗

Space Debris Symposium (A6.) Measurements and Space Surveillance (1.): Measurements of the Small Particle Debris Cloud from the 11 January, 2007 Chinese Anti-satellite Test

On January 11, 2007, the Chinese military conducted a test of an anti-satellite (ASAT) system, destroying their own Fengyun-1C spacecraft with an interceptor missile. The resulting hypervelocity collision created an unprecedented number of tracked debris - more than 2500 objects. These objects represent only those large enough for the US Space Surveillance Network (SSN) to track - typically objects larger than about 5-10 cm in diameter. There are expected to be even more debris objects at sizes too small to be seen and tracked by the SSN. Because of the altitude of the target satellite (865 x 845 km orbit), many of the debris are expected to have long orbital lifetimes and contribute to the orbital debris environment for decades to come. In the days and weeks following the ASAT test, NASA was able to use Lincoln Laboratory s Haystack radar on several occasions to observe portions of the ASAT debris cloud. Haystack has the capability of detecting objects down to less than one centimeter in diameter, and a large number of centimeter-sized particles corresponding to the ASAT cloud were clearly seen in the data. While Haystack cannot track these objects, the statistical sampling procedures NASA uses can give an accurate statistical picture of the characteristics of the debris from a breakup event. For years computer models based on data from ground hypervelocity collision tests (e.g., the SOCIT test) and orbital collision experiments (e.g., the P-78 and Delta-180 on-orbit collisions) have been used to predict the extent and characteristics of such hypervelocity collision debris clouds, but until now there have not been good ways to verify these models in the centimeter size regime. It is believed that unplanned collisions of objects in space similar to ASAT tests will drive the long-term future evolution of the debris environment in near-Earth space. Therefore, the Chinese ASAT test provides an excellent opportunity to test the models used to predict the future debris environment. For this study, Haystack detection events are compared to model predictions to test the model assumptions, including debris size distribution, velocity distribution, and assumptions about momentum transfer between the target and interceptor. In this paper we will present the results of these and other measurements on the size and extent of collisional breakup debris clouds.

Matney, Mark J.↗