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At least 613 records · Page 34

Tracking capabilities of SPADs for laser ranging

The spatial sensitivity of Single-Photon Avalanche Diodes (SPADs) can be exploited in laser ranging measurements to finely tune the laser spot in the center of the detector sensitive area. We report the performance of a SPAD with l00 micron diameter. It features a time resolution better than 80 ps rms when operated 4V above V(b) at minus 30 C, and a spatial sensitivity better than 20 microns to radial displacements of the laser spot. New SPAD structures with auxiliary delay detectors are proposed. These improved devices could allow a two dimensional sensitivity, that could be employed for the design of pointing servos.

Zappa, F.↗

Advanced ground station architecture

This paper describes a new station architecture for NASA's Ground Network (GN). The architecture makes efficient use of emerging technologies to provide dramatic reductions in size, operational complexity, and operational and maintenance costs. The architecture, which is based on recent receiver work sponsored by the Office of Space Communications Advanced Systems Program, allows integration of both GN and Space Network (SN) modes of operation in the same electronics system. It is highly configurable through software and the use of charged coupled device (CCD) technology to provide a wide range of operating modes. Moreover, it affords modularity of features which are optional depending on the application. The resulting system incorporates advanced RF, digital, and remote control technology capable of introducing significant operational, performance, and cost benefits to a variety of NASA communications and tracking applications.

Zillig, David↗

Venus Gravity Handbook

This report documents the Venus gravity methods and results to date (model MGNP90LSAAP). It is called a handbook in that it contains many useful plots (such as geometry and orbit behavior) that are useful in evaluating the tracking data. We discuss the models that are used in processing the Doppler data and the estimation method for determining the gravity field. With Pioneer Venus Orbiter and Magellan tracking data, the Venus gravity field was determined complete to degree and order 90 with the use of the JPL Cray T3D Supercomputer. The gravity field shows unprecedented high correlation with topography and resolution of features to the 2OOkm resolution. In the procedure for solving the gravity field, other information is gained as well, and, for example, we discuss results for the Venus ephemeris, Love number, pole orientation of Venus, and atmospheric densities. Of significance is the Love number solution which indicates a liquid core for Venus. The ephemeris of Venus is determined to an accuracy of 0.02 mm/s (tens of meters in position), and the rotation period to 243.0194 +/- 0.0002 days.

Konopliv, Alexander S.↗

Evidence for Highly Inhomogeneous mm-Wave Sources During the Impulsive Flare of May 9, 1991

In this paper multiwavelength observations of an impulsive flare of May 9, 1991 are presented. This event was observed with the 48 GHz multibeam focal array used at the Itapetinga radio telescope, the microwave patrol telescopes at Bem and the BATSE high time resolution hard X-ray spectrometer on board CGRO. While spatially unresolved low sensitivity observations show two major impulsive peaks, the mm-wave observations with the ability of spatially high resolved tracking of the emission centroids suggest a primarily bipolar source configuration. For the first time two mm-wave sources with a spacing below the HPBW could be separated with the multibeam technique. The general features of the observations are explained as emission of partially trapped electrons. Furthermore we present evidence for highly inhomogeneous substructures within one of the two mm-wave sources for which the positional scatter of the emission center, within 2s, is less than 2".

Hermann, R.↗

High-Resolution Mapping of Lunar Crustal Magnetic Fields: Correlations with Albedo Markings of the Reiner Gamma Class

During the last eight months of the Lunar Prospector mission (December 1999-July 1999), the spacecraft was placed in a relatively low-altitude (15-30-km perapsis), near-polar orbit that allowed high-resolution mapping of crustal magnetic fields. We report here initial studies of the correlation of locally strong magnetic anomalies with unusual, swirl-like albedo markings of the Reiner Gamma class. Based on this correlation, which is known from earlier studies of Apollo subsatellite magnetometer data, it has been proposed that the swirls represent regions whose higher albedos have been preserved via deflection of the solar-wind ion bombardment by strong crustal fields. This model in turn depends on the hypothesis that solar-wind implanted H is at least one component of the process that optically matures exposed silicate surfaces in the inner solar system . Specifically, it is hypothesized that implanted H acts as an effective reducing agent to enhance the rate of production of nanophase metallic Fe particles from preexisting silicates during micrometeoroid impacts. According to the model, the curvilinear shapes of these albedo markings are caused, at least in part, by the geometry of ion deflections in a magnetic field. The improved resolution and coverage of the Prospector data allow more detailed mapping of the fields, especially on the lunar farside. This permits a more quantitative test of whether all albedo markings of this class are associated with strong local magnetic fields.Only if the latter condition is met can the solar-wind deflection hypothesis he valid. The basic procedure for mapping crustal magnetic fields using Lunar Prospector magnetometer data follows that developed for analysis of Apollo subsatellite magnetometer data. The specific mapping steps are (1) selection of mission time intervals suitable for mapping crustal fields; these are limited essentially either to times when the Moon is in a lobe of the geomagnetic tail or to times when the Moon is in the solar wind but the spacecraft is in the lunar wake; the data are transformed to a radial, east, and north coordinate system with measurements given as a function of spacecraft latitude, longitude, and altitude; (2) visual editing of individual orbit segments selected for minimal external field disturbances; (3) minimization of remaining low-frequency external fields for individual orbit data segments by quadratic detrending; and (4) two-dimensional filtering of individual orbit segments to produce a vector field map along the slightly curved surface defined by the spacecraft altitude; maps of the three field components (radial, east, and north), the field magnitude, and the spacecraft altitude are constructed. For data obtained at low to middle latitudes, the horizontal resolution of the field maps is limited by the orbit-track separation (about 30 km at the equator). Maps of the field magnitude have been constructed within limited selenographic regions based mainly on data acquired in March, April, and May of 1999. This was a time period when the orbit plane was nearly aligned with the Sun-Moon line so that field mapping was possible at times when the Moon was in the solar wind as well as when the Moon was in the geomagnetic tail. Most of the coverage is across the lunar farside. However, a shows an example of a field map produced from solar-wind wake data for a region including Reiner Gamm on western Oceanus Procellarum (location: 58.5W, 7.5N). The contour interval is 3 nT and the mean spacecraft altitude is 18 km to within the accuracy allowed by the resolution of the map (30 km or about 1 deg.); strong magnetic anomalies correlate closely with swirl locations. Individual orbit profiles (whose resolution along the orbit track is comparable to the spacecraft altitude of 18 km) also demonstrate a good correlation of field magnitude with surface albedo. In order to investigate the correlation of magnetic fields with the location of swirl features, we have reexamined available lunar imagery (Lunar Orbiter, Apollo, and Clementine) to identify and map swirl locations within regions where swirls have previously been mapped. In these images, swirls were distinguished from other high-albedo features such as crater rays by their curvilinear shapes and increased visibility in forward-scattered light. Digital maps of swirls identified by all available imagery were then superposed on maps of the field magnitude at the spacecraft altitude. Based upon analysis of these composite magnetic/geologic maps, we draw the preliminary conclusion that swirl features are associated with magnetic anomalies revealed by Lunar Prospector. Detailed maps of these swirl features are currently being constructed for the magnetically strong regions antipodal to the Imbrium, Serenitatis, and Crisium Basins. Additional information contained in the original,

Hood, L. L.↗

Atmospheric Transport During the Transport and Chemical Evolution over the Pacific TRACE-P Experiment

Atmospheric transport over the Pacific Basin is described during NASA's Transport and Chemical Evolution Over the Pacific Experiment (TRACE-P) that was conducted between February - April 2001. The mission included extensive chemical sampling from two aircraft based primarily in Hong Kong and Yokota Air Base, Japan. Meteorological conditions during TRACE-P changed rapidly due to the seasonal winter/spring transition and the decay of prolonged ENSO cold phase (La Nina) conditions. To document these changes, TRACE-P was divided into two halves, and mean flow patterns during each half are presented and discussed. Important circulation features are the semi-permanent Siberian anticyclone and transient middle latitude cyclones that form near eastern Asia and then move eastward over the northern Pacific. Five-day backward trajectories from the various flight tracks show that air sampled by the aircraft had been transported from a variety of locations. Some parcels remained over the tropical western North Pacific during the entire period, while other important origins were Southeast Asia, Africa, and central Asia. Patterns of satellite-derived precipitation and lightning are described. TRACE-P occurs during a neutral to weak La Nina period of relatively cold sea surface temperatures in the tropical Pacific. Compared to climatology, the TRACE-P period exhibits deep convection located west of its typical position; however, tropospheric flow patterns do not exhibit a strong La Nina signal. Circulation patterns during TRACE-P are found to be generally similar to those during NASA's PEM WEST-B mission that occurred in the same region during February - March 1994.

Fuelberg, Henry E.↗

An optimized index of human cardiovascular adaptation to simulated weightlessness

Prolonged exposure to weightlessness is known to produce a variety of cardiovascular changes, some of which may influence the astronaut's performance during a mission. In order to find a reliable indicator of cardiovascular adaptation to weightlessness, we analyzed data from nine male subjects after a 24-hour period of normal activity and after a period of simulated weightlessness produced by two hours in a launch position followed by 20 hours of 6 degrees head-down tilt plus pharmacologically induced diuresis (furosemide). Heart rate, arterial pressure, thoracic fluid index, and radial flow were analyzed. Autoregressive spectral estimation and decomposition were used to obtain the spectral components of each variable from the subjects in the supine position during pre- and post-simulated weightlessness. We found a significant decrease in heart rate power and an increase in thoracic fluid index power in the high frequency region (0.2-0.45 Hz) and significant increases in radial flow and arterial pressure powers in the low frequency region (<0.2 Hz) in response to simulated weightlessness. However, due to the variability among subjects, any single variable appeared limited as a dependable index of cardiovascular adaptation to weightlessness. The backward elimination algorithm was then used to select the best discriminatory features from these spectral components. Fisher's linear discriminant and Bayes' quadratic discriminant were used to combine the selected features to obtain an optimal index of adaptation to simulated weightlessness. Results showed that both techniques provided improved discriminant performance over any single variable and thus have the potential for use as an index to track adaptation and prescribe countermeasures to the effects of weightlessness.

NASA Discipline Number 14-10↗

Bird's Eye View - A 3-D Situational Awareness Tool for the Space Station

Even as space-qualified computer hardware lags well behind the latest home computers, the possibility of using high-fidelity interactive 3-D graphics for displaying important on board information has finally arrived, and is being used on board the International Space Station (ISS). With the quantity and complexity of space-flight telemetry, 3-D displays can greatly enhance the ability of users, both onboard and on the ground, to interpret data quickly and accurately. This is particularly true for data related to vehicle attitude, position, configuration, and relation to other objects on the ground or in-orbit Bird's Eye View (BEV) is a 3-D real-time application that provides a high degree of Situational Awareness for the crew. Its purpose is to instantly convey important motion-related parameters to the crew and mission controllers by presenting 3-D simulated camera views of the International Space Station (ISS) in its actual environment Driven by actual telemetry, and running on board, as well as on the ground, the user can visualize the Space Station relative to the Earth, Sun, stars, various reference frames, and selected targets, such as ground-sites or communication satellites. Since the actual ISS configuration (geometry) is also modeled accurately, everything from the alignment of the solar panels to the expected view from a selected window can be visualized accurately. A virtual representation of the Space Station in real time has many useful applications. By selecting different cameras, the crew or mission control can monitor the station's orientation in space, position over the Earth, transition from day to night, direction to the Sun, the view from a particular window, or the motion of the robotic arm. By viewing the vehicle attitude and solar panel orientations relative to the Sun, the power status of the ISS can be easily visualized and understood. Similarly, the thermal impacts of vehicle attitude can be analyzed and visually confirmed. Communication opportunities can be displayed, and line-of-sight blockage due to interference by the vehicle structure (or the Earth) can be seen easily. Additional features in BEV display targets on the ground and in-orbit, including cities, communication sites, landmarks, satellites, and special sites of scientific interest for Earth observation and photography. Any target can be selected and tracked. This gives the user a continual line-of-sight to the target of current interest, and real-time knowledge about its visibility. Similarly, the vehicle ground-track, and an option to show "visibility circles" around displayed ground sites, provide continuous insight regarding current and future visibility to any target BEV was designed with inputs from many disciplines in the flight control and operations community both at NASA and from the International Partners. As such, BEV is setting the standards for interactive 3-D graphics for spacecraft applications. One important contribution of BEV is a generic graphical interface for camera control that can be used for any 3-D applications. This interface has become part of the International Display and Graphics Standards for the 16-nation ISS partnership. Many other standards related to camera properties, and the display of 3-D data, also have been defined by BEV. Future enhancements to BEV will include capabilities related to simulating ahead of the current time. This will give the user tools for analyzing off-nominal and future scenarios, as well as for planning future operations.

Dershowitz, Adam↗

Seasonal Variation in Precipitation Patterns to the Global Ocean: An Analysis of the GPCP Version 2 Data Set

An analysis of temporal and spatial variation of oceanic precipitation was conducted on the GPCP version two data set. While the precipitation patterns observed are generally similar to the previous climatologies, new features and greater detail of global precipitation were revealed from out analysis of the GPCP data set. High precipitation waw observed in the inter-tropical convergence zone, the South Pacific convergence zone, and the storm tracks in the North Pacific and Atlantic Oceans. Low precipitation was observe in the Polar regions and in the subtropics of the East Pacific, East Atlantic, and the Southeast and Northwest Indian Ocean. The spatial coverage of these high and low precipitation regions changed thruough the year. A strong seasonal cycle or precipitation was observed for the Northern and the Southern Hemispheres and for each ocean basin. Global precipitation also varied significantly with both latitude and longitude, with a latitudinal maximum at 56 degrees South, 39 degrees South, 4 degrees South, 6 degrees North, 39 degrees North, and 56 degress North, and a longitudinal maxiumum over each ocean. The seasonal varying precipitation patterns are a foundation for evaluating the effect of wet deposition on ocean circulation, flux of chemical species, and its effect on marine ecosystems.

Miller, Richard↗

Architecting the Human Space Flight Program with Systems Modeling Language (SysML)

The next generation of missions in NASA's Human Space Flight program focuses on the development and deployment of highly complex systems (e.g., Orion Multi-Purpose Crew Vehicle, Space Launch System, 21st Century Ground System) that will enable astronauts to venture beyond low Earth orbit and explore the moon, near-Earth asteroids, and beyond. Architecting these highly complex system-of-systems requires formal systems engineering techniques for managing the evolution of the technical features in the information exchange domain (e.g., data exchanges, communication networks, ground software) and also, formal correlation of the technical architecture to stakeholders' programmatic concerns (e.g., budget, schedule, risk) and design development (e.g., assumptions, constraints, trades, tracking of unknowns). This paper will describe how the authors have applied System Modeling Language (SysML) to implement model-based systems engineering for managing the description of the End-to-End Information System (EEIS) architecture and associated development activities and ultimately enables stakeholders to understand, reason, and answer questions about the EEIS under design for proposed lunar Exploration Missions 1 and 2 (EM-1 and EM-2).

scheduling↗

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗

The Evolution of the Orbiting Sample Container for a Future Mars Sample Return

Although NASA has no specific plans at this time to return samples from Mars, the Program Formulation Office of the Mars Exploration Program sponsors ongoing mission concept studies, systems analyses, and technology investments which explore different strategies for the potential return of samples from Mars, consistent with the charter of the program and stated priorities of the science community. A critical component of such a campaign would be an Orbiting Sample container (OS), which would contain the Mars samples to be returned to Earth. This paper discusses the most recent efforts by the JPL’s Mars Formulation Office to mature an OS design planned for use on a potential Mars Sample Return (MSR) mission. Similar to the “Decadal Study Architecture” [1], the current MSR architecture envisions as a three-mission campaign with each mission serving a critical role towards returning Martian rock and atmospheric samples back to Earth. An OS would be a central piece of hardware in the proposed MSR architecture due to its interfaces to all the three missions of the potential campaign. Additionally, numerous stakeholders and subsystems such as science and planetary protection impose challenging requirements on the OS’s functions and capabilities. As a result, designing an OS that meets all the requirements is challenging and quite complex. The story of the OS’s evolution from black box concept thru to the current-and-still-maturing baseline design is the focus of this paper. From the OS’s launch off Earth aboard a Sample Retrieval Lander (SRL) through to return to Earth, the design and functional requirements generated by and for each stage of the OS’s mission are discussed. Then, with an understanding of what the OS would be required to do, a mapping of the main requirements to the design features of the current OS concept is explained. Many tests and analyses have been conducted to support and validate the current OS design. Results from test and analysis in the areas of aerothermal, impact dynamics, optical tracking, and radio electromagnetics are presented.

Spencer, David↗

Experimental Verification of Electric Drive Technologies Based on Artificial Intelligence Tools

A laboratory implementation of a fuzzy logic-tracking controller using a low cost Motorola MC68HC11E9 microprocessor is described in this report. The objective is to design the most optimal yet practical controller that can be implemented and marketed, and which gives respectable performance, even when the system loads, inertia and parameters are varying. A distinguishing feature of this work is the by-product goal of developing a marketable, simple, functional and low cost controller. Additionally, real-time nonlinearities are not ignored, and a mathematical model is not required. A number of components have been designed, built and tested individually, and in various combinations of hardware and software segments. These components have been integrated with a brushless motor to constitute the drive system. A microprocessor-based FLC is incorporated to provide robust speed and position control. Design objectives that are difficult to express mathematically can be easily incorporated in a fuzzy logic-based controller by linguistic information (in the form of fuzzy IF-THEN rules). The theory and design are tested in the laboratory using a hardware setup. Several test cases have been conducted to confirm the effectiveness of the proposed controller. The results indicate excellent tracking performance for both speed and position trajectories. For the purpose of comparison, a bang-bang controller has been tested. The fuzzy logic controller performs significantly better than the traditional bang-bang controller. The bang-bang controller has been shown to be relatively inaccurate and lacking in robustness. Description of the implementation hardware system is also given.

Rubaai, Ahmed↗

Lunar Observer Laser Altimeter observations for lunar base site selection

One of the critical datasets for optimal selection of future lunar landing sites is local- to regional-scale topography. Lunar base site selection will require such data for both engineering and scientific operations purposes. The Lunar Geoscience Orbiter or Lunar Observer is the ideal precursory science mission from which to obtain this required information. We suggest that a simple laser altimeter instrument could be employed to measure local-scale slopes, heights, and depths of lunar surface features important to lunar base planning and design. For this reason, we have designed and are currently constructing a breadboard of a Lunar Observer Laser Altimeter (LOLA) instrument capable of acquiring contiguous-footprint topographic profiles with both 30-m and 300-m along-track resolution. This instrument meets all the severe weight, power, size, and data rate limitations imposed by Observer-class spacecraft. In addition, LOLA would be capable of measuring the within-footprint vertical roughness of the lunar surface, and the 1.06-micron relative surface reflectivity at normal incidence. We have used airborne laser altimeter data for a few representative lunar analog landforms to simulate and analyze LOLA performance in a 100-km lunar orbit. We demonstrate that this system in its highest resolution mode (30-m diameter footprints) would quantify the topography of all but the very smallest lunar landforms. At its global mapping resolution (300-m diameter footprints), LOLA would establish the topographic context for lunar landing site selection by providing the basis for constructing a 1-2 km spatial resolution global, geodetic topographic grid that would contain a high density of observations (e.g., approximately 1000 observations per each 1 deg by 1 deg cell at the lunar equator). The high spatial and vertical resolution measurements made with a LOLA-class instrument on a precursory Lunar Observer would be highly synergistic with high-resolution imaging datasets, and will allow for direct quantification of critical slopes, heights, and depths of features visible in images of potential lunar base sites.

Garvin, James B.↗

A rationale for human operator pulsive control behavior

When performing tracking tasks which involve demanding controlled elements such as those with K/s-squared dynamics, the human operator often develops discrete or pulsive control outputs. A dual-loop model of the human operator is discussed, the dominant adaptive feature of which is the explicit appearance of an internal model of the manipulator-controlled element dynamics in an inner feedback loop. Using this model, a rationale for pulsive control behavior is offered which is based upon the assumption that the human attempts to reduce the computational burden associated with time integration of sensory inputs. It is shown that such time integration is a natural consequence of having an internal representation of the K/s-squared-controlled element dynamics in the dual-loop model. A digital simulation is discussed in which a modified form of the dual-loop model is shown to be capable of producing pulsive control behavior qualitively comparable to that obtained in experiment.

Hess, R. A.↗

Application of inertial instruments for DSN antenna pointing and tracking

The feasibility of using inertial instruments to determine the pointing attitude of the NASA Deep Space Network antennas is examined. The objective is to obtain 1 mdeg pointing knowledge in both blind pointing and tracking modes to facilitate operation of the Deep Space Network 70 m antennas at 32 GHz. A measurement system employing accelerometers, an inclinometer, and optical gyroscopes is proposed. The initial pointing attitude is established by determining the direction of the local gravity vector using the accelerometers and the inclinometer, and the Earth's spin axis using the gyroscopes. Pointing during long-term tracking is maintained by integrating the gyroscope rates and augmenting these measurements with knowledge of the local gravity vector. A minimum-variance estimator is used to combine measurements to obtain the antenna pointing attitude. A key feature of the algorithm is its ability to recalibrate accelerometer parameters during operation. A survey of available inertial instrument technologies is also given.

Eldred, D. B.↗

A 40th deg and order gravitational field model for Mars

Understanding the origin and evolution of major photographic features on Mars, such as the hemispheric dichotomy and Tharsis rise, will require improved resolution of that planet's gravitational and topographic fields. The highest resolution gravity model for Mars published to date was derived from Doppler tracking data from the Mariner 9 and Viking 1 and 2 spacecraft, and is of 18th degree and order. That field has a maximum spatial resolution of approx. 600 km, which is comparable to that of the best topographic model. The resolution of previous gravity models was limited not by data density, but rather by the computational resources available at the time. Because this restriction is no longer a limitation, the Viking and Mariner data sets were reanalyzed and a gravitational field was derived complete to the 40th degree and order with a corresponding maximum spatial resolution of 300 km where the data permit.

Zuber, M. T.↗