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At least 19 records

Tropospheric chemical models

The differences in atmospheric composition over the globe and the short- and long-term variations in this composition are the net effect of several atmospheric and biospheric processes: biospheric emissions, atmospheric circulation, atmospheric chemical transformations and finally deposition back to the surface. Accurate and realistic atmospheric chemistry and circulation models are essential to interpret the observed global distributions and trends of atmospheric species in terms of these underlying processes. Comparisons between model predictions and observations test current understanding of these processes and models used in conjunction with inverse methods allow deductions of the rates of these processes from the observations. With the planned inclusion of at least CO and CH4 observations on the Earth Observing System (EOS) satellites, together with the large global data set expected from in situ observations under the International Global Atmospheric Chemistry (IGAC) Project, the further development of global three-dimensional high-resolution atmospheric chemistry and circulation models in order to interpret this new data is a high-priority endeavor.

Prinn, R. G.↗

Geographic information system for fusion and analysis of high-resolution remote sensing and ground data

We seek to combine high-resolution remotely sensed data with models and ground truth measurements, in the context of a Geographical Information System (GIS), integrated with specialized image processing software. We will use this integrated system to analyze the data from two Case Studies, one at a boreal forest site, the other a tropical forest site. We will assess the information content of the different components of the data, determine the optimum data combinations to study biogeophysical changes in the forest, assess the best way to visualize the results, and validate the models for the forest response to different radar wavelengths/polarizations. During the 1990's, unprecedented amounts of high-resolution images from space of the Earth's surface will become available to the applications scientist from the LANDSAT/TM series, European and Japanese ERS-1 satellites, RADARSAT and SIR-C missions. When the Earth Observation Systems (EOS) program is operational, the amount of data available for a particular site can only increase. The interdisciplinary scientist, seeking to use data from various sensors to study his site of interest, may be faced with massive difficulties in manipulating such large data sets, assessing their information content, determining the optimum combinations of data to study a particular parameter, visualizing his results and validating his model of the surface. The techniques to deal with these problems are also needed to support the analysis of data from NASA's current program of Multi-sensor Airborne Campaigns, which will also generate large volumes of data. In the Case Studies outlined in this proposal, we will have somewhat unique data sets. For the Bonanza Creek Experimental Forest (Case 1) calibrated DC-8 SAR (Synthetic Aperture Radar) data and extensive ground truth measurement are already at our disposal. The data set shows documented evidence to temporal change. The Belize Forest Experiment (Case 2) will produce calibrated DC-8 SAR and AVIRIS data, together with extensive measurements on the tropical rain forest itself. The extreme range of these sites, one an Arctic forest, the other a tropical rain forest, has been deliberately chosen to find common problems which can lead to generalized observations and unique problems with data which raise issues for the EOS System.

Freeman, Anthony↗

Geographic information system for fusion and analysis of high-resolution remote sensing and ground truth data

We seek to combine high-resolution remotely sensed data with models and ground truth measurements, in the context of a Geographical Information System, integrated with specialized image processing software. We will use this integrated system to analyze the data from two Case Studies, one at a bore Al forest site, the other a tropical forest site. We will assess the information content of the different components of the data, determine the optimum data combinations to study biogeophysical changes in the forest, assess the best way to visualize the results, and validate the models for the forest response to different radar wavelengths/polarizations. During the 1990's, unprecedented amounts of high-resolution images from space of the Earth's surface will become available to the applications scientist from the LANDSAT/TM series, European and Japanese ERS-1 satellites, RADARSAT and SIR-C missions. When the Earth Observation Systems (EOS) program is operational, the amount of data available for a particular site can only increase. The interdisciplinary scientist, seeking to use data from various sensors to study his site of interest, may be faced with massive difficulties in manipulating such large data sets, assessing their information content, determining the optimum combinations of data to study a particular parameter, visualizing his results and validating his model of the surface. The techniques to deal with these problems are also needed to support the analysis of data from NASA's current program of Multi-sensor Airborne Campaigns, which will also generate large volumes of data. In the Case Studies outlined in this proposal, we will have somewhat unique data sets. For the Bonanza Creek Experimental Forest (Case I) calibrated DC-8 SAR data and extensive ground truth measurement are already at our disposal. The data set shows documented evidence to temporal change. The Belize Forest Experiment (Case II) will produce calibrated DC-8 SAR and AVIRIS data, together with extensive measurements on the tropical rain forest itself. The extreme range of these sites, one an Arctic forest, the other a tropical rain forest, has been deliberately chosen to find common problems which can lead to generalized observations and unique problems with data which raise issues for the EOS System.

Freeman, Anthony↗

Global Weather Prediction and High-End Computing at NASA

We demonstrate current capabilities of the NASA finite-volume General Circulation Model an high-resolution global weather prediction, and discuss its development path in the foreseeable future. This model can be regarded as a prototype of a future NASA Earth modeling system intended to unify development activities cutting across various disciplines within the NASA Earth Science Enterprise.

Lin, Shian-Jiann↗

Growth-phase thinning of the near-Earth current sheet during the CDAW 6 substorm

The thinning of the near-Earth current sheet during the growth phase of the Coordinated Data Analysis Workshop (CDAW) 6 magnetospheric substorm is studied. The expansion onset of the substorm occurred at 1054 UT, March 22, 1979. During the growth phase, two spacecraft, International Sun Earth Explorer (ISEE) 1 and ISEE 2, were within the current sheet approximately 13 R(sub E) from the Earth and obtained simultaneous high-resolution magnetic data at two points in the current sheet. Plasma data were also provided by the ISEE spacecraft and solar wind data by IMP 8. To facilitate the analysis, the GSM magnetic field data are transformed to a 'neutral sheet coordinate system' in which the new x axis is parallel to the average magnetic field above and below the neutral sheet and the new y axis lies in the GSM equatorial plane. A model based on the assumption that the current sheet is a time-invariant structure fails to predict neutral sheet crossing times. Consequently, the Harris sheet model, which allows one to remove the restriction of time invariancy, is used instead. It is found that during the growth phase, a model parameter corresponding to the thickness of the current sheet decreased exponentially from about 5 R(sub E) to 1 R(sub E) with a time constant of about 14 min. In addition, the ISEE 1 and ISEE 2 neutral sheet crossings after expansion onset indicate that the neutral sheet was moving upward at 7 km/s relative to the spacecraft. Since both crossings occurred in approximately 80 s, the current sheet thickness is estimated to be about 500 km. These results demonstrate that the near-Earth current sheet undergoes dramatic thinning during the substorm growth phase and expansion onset.

Sanny, Jeff↗

The Science Behind the NASA/NOAA Electronic Theater 2002

Details of the science stories and scientific results behind the Etheater Earth Science Visualizations from the major remote sensing institutions around the country will be explained. The NASA Electronic Theater presents Earth science observations and visualizations in a historical perspective. Fly in from outer space to Temple Square and the University of Utah Campus. Go back to the early weather satellite images from the 1960s see them contrasted with the latest US/Europe/Japan global weather data. See the latest images and image sequences from NASA & NOAA missions like Terra, GOES, NOAA, TRMM, SeaWiFS, Landsat 7 visualized with state-of-the art tools. A similar retrospective of numerical weather models from the 1960s will be compared with the latest "year 2002" high-resolution models. See the inner workings of a powerful hurricane as it is sliced and dissected using the University of Wisconsin Vis-5D interactive visualization system. The largest super computers are now capable of realistic modeling of the global oceans. See ocean vortexes and currents that bring up the nutrients to feed phitoplankton and zooplankton as well as draw the crill fish, whales and fisherman. See the how the ocean blooms in response to these currents and El Nino/La Nina climate regimes. The Internet and networks have appeared while computers and visualizations have vastly improved over the last 40 years. These advances make it possible to present the broad scope and detailed structure of the huge new observed and simulated datasets in a compelling and instructive manner. New visualization tools allow us to interactively roam & zoom through massive global images larger than 40,000 x 20,000 pixels. Powerful movie players allow us to interactively roam, zoom & loop through 4000 x 4000 pixel bigger than HDTV movies of up to 5000 frames. New 3D tools allow highly interactive manipulation of detailed perspective views of many changing model quantities. See the 1m resolution before and after shots of lower Manhattan and the Pentagon after the September 11 disaster as well as shots of Afghanistan from the Space Imaging IKONOS as well as debris plume images from Terra MODIS and SPOT Image. Shown by the SGI-Octane Graphics-Supercomputer are visualizations of hurricanes Michelle 2001, Floyd, Mitch, Fran and Linda. Our visualizations of these storms have been featured on the covers of the National Geographic, Time, Newsweek and Popular Science. Highlights will be shown from the NASA's large collection of High Definition TV (HDTV) visualizations clips New visualizations of a Los Alamos global ocean model, and high-resolution results of a NASA/JPL Atlantic ocean basin model showing currents, and salinity features will be shown. El Nino/La Nina effects on sea surface temperature and sea surface height of the Pacific Ocean will also be shown. The SST simulations will be compared with GOES Gulf Stream animations and ocean productivity observations. Tours will be given of the entire Earth's land surface at 500 m resolution from recently composited Terra MODIS data, Visualizations will be shown from the Earth Science Etheater 2001 recently presented over the last years in New Zealand, Johannesburg, Tokyo, Paris, Munich, Sydney, Melbourne, Honolulu, Washington, New York City, Pasadena, UCAR/Boulder, and Penn State University. The presentation will use a 2-CPU SGI/CRAY Octane Super Graphics workstation with 4 GB RAM and terabyte disk array at 2048 x 768 resolution plus multimedia laptop with three high resolution projectors. Visualizations will also be featured from museum exhibits and presentations including: the Smithsonian Air & Space Museum in Washington, IMAX theater at the Maryland Science Center in Baltimore, the James Lovell Discovery World Science museum in Milwaukee, the American Museum of Natural History (NYC) Hayden Planetarium IMAX theater, etc. The Etheater is sponsored by NASA, NOAA and the American Meteorological Society. This presentation is brought to you by the University of Utah College of Mines and Earth Sciences and, the Utah Museum of Natural History.

Hasler, A. Fritz↗

High-Resolution Spectroscopic Database for the NASA Earth Observing System Program

The purpose of this project is to develop and enhance the HITRAN molecular spectroscopic database and associated software to support the observational programs of the Earth Observing System (EOS). In particular, the focus is on the EOS projects: the Atmospheric Infrared Sounder (AIRS), the High-Resolution Dynamics Limb Sounder (HIRDLS), Measurements of Pollution in the Troposphere (MOPITT), the Tropospheric Emission Spectrometer (TES), and the Stratospheric Aerosol and Gas Experiment (SAGE III). The data requirements of these programs in terms of spectroscopy are varied, but usually call for additional spectral parameters or improvements to existing molecular bands. In addition, cross-section data for heavier molecular species must be expanded and made amenable to modeling in remote sensing. The effort in the project also includes developing software and distribution to make access, manipulation, and use of HITRAN functional to the EOS program.

Rothman, Laurence S.↗

High-Resolution Spectroscopic Database for the NASA Earth Observing System Program

The purpose of this project is to develop and enhance the HITRAN molecular spectroscopic database and associated software to support the observational programs of the Earth Observing System (EOS). In particular, the focus is on the EOS projects: the Atmospheric Infrared Sounder (AIRS), the High-Resolution Dynamics Limb Sounder (HIRDLS), Measurements of Pollution in the Troposphere (MOPITT), the Tropospheric Emission Spectrometer (TES), and the Stratospheric Aerosol and Gas Experiment (SAGE III). The HITRAN program is also involved in the Ozone Monitoring Experiment (OMI). The data requirements of these programs in terms of spectroscopy are varied with respect to constituents being observed, required remote-sensing parameters, and spectral coverage. A general requisite is for additional spectral parameters and improvements to existing molecular bands sufficient for the simulation of the observations leading to retrieval of the atmospheric state. In addition, cross-section data for heavier molecular species must be expanded and made amenable to modeling in remote sensing. The effort in the project also includes developing software and distribution to make access, manipulation, and use of HITRAN functional to the EOS program.

Rothman, Laurence↗

The Bermuda Bio-Optics Program (BBOP)

The Bermuda Bio-Optics Project (BBOP) is a collaborative effort between the Institute for Computational Earth System Science (ICESS) at the University of California at Santa Barbara (UCSB) and the Bermuda Biological Station for Research (BBSR). This research program is designed to characterize light availability and utilization in the Sargasso Sea, and to provide an optical link by which biogeochemical observations may be used to evaluate bio-optical models for pigment concentration, primary production, and sinking particle fluxes from satellite-based ocean color sensors. The BBOP time-series was initiated in 1992, and is carried out in conjunction with the US JGOFS Bermuda Atlantic Time-series Study (BATS) at the Bermuda Biological Station for Research. The BATS program itself has been observing biogeochemical processes (primary productivity, particle flux at and elemental cycles) in the mesotrophic waters of the Sargasso Sea since 1988. Closely affiliated with BBOP and BATS is a separate NASA-funded study of the spatial variability of biogeochemical processes in the Sargasso Sea using high-resolution Advanced Very High Resolution Radiometer (AVHRR) and Sea-Viewing Wide Field-of-view Sensor (SeaWiFS) data collected at Bermuda. The collaboration between BATS and BBOP measurements has resulted in a unique data set that addresses not only the SIMBIOS goals but also the broader issues of important factors controlling the carbon cycle.

Siegel, David A.↗

Russian-US Partnership to Study the 23-km-diameter El'gygtgyn Impact Crater, Northeast Russia

El'gygytgyn crater, located within Eastern Siberia, is a Pliocene-aged (3.6 Ma), well-preserved impact crater with a rim diameter of roughly 23 km. The target rocks are a coherent assemblage of crystalline rocks ranging from andesite to basalt. At the time of impact the region was forested and the Arctic Ocean was nearly ice-free. A 15-km lake fills the center of the feature and water depths are approximately 175 m. Evidence of shock metamorphism, -- including coesite, fused mineral glasses, and planar deformation features in quartz -- has been reported. This feature is one of the youngest and best preserved complex craters on Earth. Because of its remote Arctic setting, however, El gygytgyn crater remains poorly investigated. The objectives of this three-year project are to establish and maintain a research partnership between scientists from Russia and the United States interested in the El gygytgyn crater. The principal institutions in the U.S. will be the Geophysical Institute, University of Alaska Fairbanks and the University of Massachusetts Amherst. The principal institution in Russia will be the North East Interdisciplinary Scientific Research Institute (NEISRI), which is the Far-East Branch of the Russian Academy of Science. Three science tasks are identified for the exchange program: (1) Evaluate impactite samples collected during previous field excursions for evidence of and level of shock deformation. (2) Build a high-resolution digital elevation model for the crater and its surroundings using interferometric synthetic aperture radar techniques on JERS-1, ERS-1, ERS-2, and/or RadarSat range-doppler data. (3) Gather all existing surface data available from Russian and U.S. institutions (DEM, remote sensing image data, field-based lithological and sample maps, and existing geophysical data) and assemble into a Geographic Information Systems database.

Sharpton, Virgil L.↗

High-resolution observations of the isotopic composition of carbon and silicon in the galactic cosmic rays

High resolution satellite observations of the galactic cosmic rays (approximately 100-300 MeV/amu) have yielded determinations of near-earth isotopic compositions, which are presented: (C-13)/(C-12) = 0.070 + or - 0.006; (Si-29)/(Si-28) = 0.109(+0.024, -0.014); and (Si-30)/(Si-28) = 0.084(+0.020, -0.014). Using a standard propagation model, source values greater than solar are derived for each of these ratios. The (C-13) excess may be the result of cross section uncertainties, but the (Si-29) and (Si-30) appear to reflect real differences between the galactic cosmic-ray source and the solar system.

Wiedenbeck, M. E.↗

AVIRIS calibration and application in coastal oceanic environments

The Airborne Visible-Infrared Imaging Spectrometer (AVIRIS) is a test-bed for future spacecraft sensors such as the High-Resolution Imaging Spectrometer and the Moderate-Resolution Imaging Spectrometers planned for the Earth Observing System. To use this sensor for ocean applications, S/N was increased by spatial averaging of images. Post-flight recalibration was accomplished by measuring in situ the water-leaving radiance at flight time, modeling its transmission to the aircraft, and adding modeled atmospheric radiance to that value. The preflight calibration curve was then adjusted until aircraft and modeled total radiance values matched. Water-leaving radiance values from the recalibrated AVIRIS imagery were consistent with in situ data supporting the validity of the approach. Imagery of the absorption coefficient at 415 nm and backscattering coefficient at 671 nm were used to depict the dissolved and particulate constituents of the Tampa Bay plume during late, ebb-tidal conditions.

Carder, Kendall L.↗

AVIRIS calibration and application in coastal oceanic environments

The Airborne Visible-Infrared Imaging Spectrometer (AVIRIS) is a test-bed for future spacecraft sensors such as the High-Resolution Imaging Spectrometer and the Moderate-Resolution Imaging Spectrometers planned for the Earth Observing System. To use this sensor for ocean applications, S/N was increased by spatial averaging of images. Post-flight recalibration was accomplished using in situ the water-leaving radiance measured at flight time, modeling radiance transmission to the aircraft, and adding modeled atmospheric radiance to that value. The preflight calibration curve was then adjusted until aircraft and modeled total radiance values matched. Water-leaving radiance values from the recalibrated AVIRIS imagery were consistent with in situ data supporting the validity of the approach. Imagery of the absorption coefficient at 415 nm and backscattering coefficient at 671 nm were used to depict the dissolved and particulate constituents of an ebb-tidal esturance plume on the East coast of Florida.

Carder, Kendall L.↗

Clouds and the Earth's Radiant Energy System (CERES) Algorithm Theoretical Basis Document: Cloud Analyses and Determination of Improved Top of Atmosphere Fluxes (Subsystem 4) - Volume 3

The theoretical bases for the Release 1 algorithms that will be used to process satellite data for investigation of the Clouds and Earth's Radiant Energy System (CERES) are described. The architecture for software implementation of the methodologies is outlined. Volume 3 details the advanced CERES methods for performing scene identification and inverting each CERES scanner radiance to a top-of-the-atmosphere (TOA) flux. CERES determines cloud fraction, height, phase, effective particle size, layering, and thickness from high-resolution, multispectral imager data. CERES derives cloud properties for each pixel of the Tropical Rainfall Measuring Mission (TRMM) visible and infrared scanner and the Earth Observing System (EOS) moderate-resolution imaging spectroradiometer. Cloud properties for each imager pixel are convolved with the CERES footprint point spread function to produce average cloud properties for each CERES scanner radiance. The mean cloud properties are used to determine an angular distribution model (ADM) to convert each CERES radiance to a TOA flux. The TOA fluxes are used in simple parameterization to derive surface radiative fluxes. This state-of-the-art cloud-radiation product will be used to substantially improve our understanding of the complex relationship between clouds and the radiation budget of the Earth-atmosphere system.

Source record↗

Global Single and Multiple Cloud Classification with a Fuzzy Logic Expert System

An unresolved problem in remote sensing concerns the analysis of satellite imagery containing both single and multiple cloud layers. While cloud parameterizations are very important both in global climate models and in studies of the Earth's radiation budget, most cloud retrieval schemes, such as the bispectral method used by the International Satellite Cloud Climatology Project (ISCCP), have no way of determining whether overlapping cloud layers exist in any group of satellite pixels. Coakley (1983) used a spatial coherence method to determine whether a region contained more than one cloud layer. Baum et al. (1995) developed a scheme for detection and analysis of daytime multiple cloud layers using merged AVHRR (Advanced Very High Resolution Radiometer) and HIRS (High-resolution Infrared Radiometer Sounder) data collected during the First ISCCP Regional Experiment (FIRE) Cirrus 2 field campaign. Baum et al. (1995) explored the use of a cloud classification technique based on AVHRR data. This study examines the feasibility of applying the cloud classifier to global satellite imagery.

Welch, Ronald M.↗

Remote Sensing of Volcanic Clouds: Sulfur Gases and Plume Top Topography

New absorption line parameters for H2S were published and submitted to the Gestion et Etude des Informations Spectroscopiques Atmospheriques (GEISA) and high resolution transmission molecular absorption (HITRAN) databases. These new absorption line parameters will make it possible to use observations from the future Tropospheric Emission Spectrometer (TES) instrument [Earth Observing System (EOS) Chemistry Mission (CHEM) platform] to make more accurate H2S measurements if it observes an H2S-rich volcanic cloud. H2S is the second most abundant volcanic sulfur gas, and like SO2, it also converts to H2SO4 aerosols and can have a climate impact. A paper on the Moderate-resolution Imaging-Spectroradiometer (MODIS) SO2 alert is being revised. New aspects in the revision include verification of the SO2 alert during the EOS mission; factors affecting SO2 detection at thermal infrared, ultraviolet, and microwave wavelengths; radiative transfer tests; more description of satellite instruments; and thermal surface alert installed for MODIS. Her research involves the use of remote sensing to generate maps of plume top altitude. This parameter is important for models of volcanic eruption, aircraft hazards, and climate impact. The topographic shape of the top surface of a volcanic plume can provide information necessary to understand the physics controlling the injection and dispersal of a volcanic plume in the atmosphere. Glaze et al. describe the application of a photoclinometric technique to volcanic plumes. The software algorithm has been improved to account for more general plume and illumination geometries and for easily extracting position information directly from Advanced Very High-Resolution Radiometer (AVHRR) level 1B data. Testing of the algorithm has focused on acquiring AVHRR data for a variety of volcanic plumes in an effort to identify problems with the software as well as model sensitivities. The plumes chosen were erupted from volcanoes at a variety of latitudes, at different times of day, and in different seasons. Another important issue that is being investigated is the importance of plume opacity. A diagram illustrates the method for deriving phi, the angle a wind-blown plume makes with the horizontal, in the direction perpendicular to the remote sensing scan. A figure shows a sample output of the algorithm, a wire mesh map of plume top topography. Additional information is contained in the original.

Crisp, Joy A.↗

Outgassing of Flown and Unflown MIR Solar Cells

A solar panel array with more than ten years space exposure was removed from the Mir core module in November 1997, and an eight panel section was returned to Earth in January 1998. Several solar cells were removed from panel eight of the returned array and placed in a high vacuum system with a residual gas analyzer (200 amu mass spectrometer) and a cold finger. Similar unflown solar cells of the same vintage were later obtained from Energia. Several of the unflown cells were also placed in the vacuum system and outgassed residues were collected on the LN2 cold finger. Almost 3 mg of outgassed residue was collected -from a string of three unflown solar cells over a period of 94 hours under vacuum. The collected residue was weighed with a microbalance, and then the residue was analyzed by FTIR spectroscopy, and by gas chromatograph-mass spectroscopy. About 25 outgassed constituents were separated by the gas chromatograph, and a high-resolution mass spectrum was obtained of each constituent. Molecular identifications have been made for the constituents. The constituents are primarily cyclic siloxanes, and several of the constituents are isomers of the same molecule. Most of the outgassed constituents have a molecular mass of about 500 amu. Almost one mg of residue was extracted from one sq cm of coverglass/adhesive from a flown solar cell by soaking in isopropyl alcohol for 30 minutes. The gas chromatograph separated about 20 constituents. The constituents are mostly cyclic siloxanes with linear branches, hydrocarbons, and phthalates. The typical molecular mass is about 600 amu. These identifications of specific outgassing molecules have resulted in a more complete understanding of the SiO(x) contamination on the Mir solar cell coverglasses, and on the MEEP experiment trays and optical specimens during the Shuttle-Mir Phase One flight experiment program. Adjusted outgassing rates based on the data reported here, and/or measured outgassing rates and specific molecular identifications of ISS hardware samples are needed to input into model predictions of induced environment effects of the ISS.

Harvey, Gale A.↗

Angular Distribution Models for Top-of-Atmosphere Radiative Flux Estimation from the Clouds and the Earth's Radiant Energy System Instrument on the Tropical Rainfall Measuring Mission Satellite: Methodology - Part 1

Clouds and the Earth s Radiant Energy System (CERES) investigates the critical role that clouds and aerosols play in modulating the radiative energy flow within the Earth-atmosphere system. CERES builds upon the foundation laid by previous missions, such as the Earth Radiation Budget Experiment, to provide highly accurate top-of-atmosphere (TOA) radiative fluxes together with coincident cloud and aerosol properties inferred from high-resolution imager measurements. This paper describes the method used to construct empirical angular distribution models (ADMs) for estimating shortwave, longwave, and window TOA radiative fluxes from CERES radiance measurements on board the Tropical Rainfall Measuring Mission satellite. To construct the ADMs, multiangle CERES measurements are combined with coincident high-resolution Visible Infrared Scanner measurements and meteorological parameters from the European Centre for Medium-Range Weather Forecasts data assimilation product. The ADMs are stratified by scene types defined by parameters that have a strong influence on the angular dependence of Earth's radiation field at the TOA. Examples of how the new CERES ADMs depend upon the imager-based parameters are provided together with comparisons with existing models.

Loeb, N. G.↗