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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2

A Requirements-Driven Optimization Method for Acoustic Liners Using Analytic Derivatives

More than ever, there is flexibility and freedom in acoustic liner design. Subject to practical considerations, liner design variables may be manipulated to achieve a target attenuation spectrum. But characteristics of the ideal attenuation spectrum can be difficult to know. Many multidisciplinary system effects govern how engine noise sources contribute to community noise. Given a hardwall fan noise source to be suppressed, and using an analytical certification noise model to compute a community noise measure of merit, the optimal attenuation spectrum can be derived using multidisciplinary systems analysis methods. In a previous paper on this subject, a method deriving the ideal target attenuation spectrum that minimizes noise perceived by observers on the ground was described. A simple code-wrapping approach was used to evaluate a community noise objective function for an external optimizer. Gradients were evaluated using a finite difference formula. The subject of this paper is an application of analytic derivatives that supply precise gradients to an optimization process. Analytic derivatives improve the efficiency and accuracy of gradient-based optimization methods and allow consideration of more design variables. In addition, the benefit of variable impedance liners is explored using a multi-objective optimization.

Aircraft Noise↗

A Requirements-Driven Optimization Method for Acoustic Treatment Design

Acoustic treatment designers are able to attenuate specific noise sources inside turbofan engines. Subject to practical considerations, liner design variables may be manipulated to achieve a target attenuation spectrum. But, characteristics of the ideal attenuation spectrum can be difficult to know. Many multidisciplinary system effects govern how engine noise sources contribute to community noise. Given a hardwall fan noise source to be suppressed, and using an analytical certification noise model to compute a community noise measure of merit, the optimal attenuation spectrum can be derived using multidisciplinary systems analysis methods. The subject of this paper is an analytic method that derives the ideal target attenuation spectrum that minimizes noise perceived by observers on the ground. Software is developed and used to test and validate the method on a simple, notional source. With experience gained from minimizing noise of the simple source, the software is tested against a realistic hardwall fan source.

aircraft noise↗

Advanced subsonic transport approach noise: The relative contribution of airframe noise

With current engine technology, airframe noise is a contributing source for large commercial aircraft on approach, but not the major contributor. With the promise of much quieter jet engines with the planned new generation of high-by-pass turbofan engines, airframe noise has become a topic of interest in the advanced subsonic transport research program. The objective of this paper is to assess the contribution of airframe noise relative to the other aircraft noise sources on approach. The assessment will be made for a current technology large commercial transport aircraft and for an envisioned advanced technology aircraft. NASA's Aircraft Noise Prediction Program (ANOPP) will be used to make total aircraft noise predictions for these two aircraft types. Predicted noise levels and areas of noise contours will be used to determine the relative importance of the contributing approach noise sources. The actual set-up decks used to make the ANOPP runs for the two aircraft types are included in appendixes.

Willshire, William L., Jr.↗

Simulation of a Lunar Surface Base Power Distribution Network for the Constellation Lunar Surface Systems

The Lunar Surface Power Distribution Network Study team worked to define, breadboard, build and test an electrical power distribution system consistent with NASA's goal of providing electrical power to sustain life and power equipment used to explore the lunar surface. A testbed was set up to simulate the connection of different power sources and loads together to form a mini-grid and gain an understanding of how the power systems would interact. Within the power distribution scheme, each power source contributes to the grid in an independent manner without communication among the power sources and without a master-slave scenario. The grid consisted of four separate power sources and the accompanying power conditioning equipment. Overall system design and testing was performed. The tests were performed to observe the output and interaction of the different power sources as some sources are added and others are removed from the grid connection. The loads on the system were also varied from no load to maximum load to observe the power source interactions.

Mintz, Toby↗

Federated Giovanni: A Distributed Web Service for Analysis and Visualization of Remote Sensing Data

The Geospatial Interactive Online Visualization and Analysis Interface (Giovanni) is a popular tool for users of the Goddard Earth Sciences Data and Information Services Center (GES DISC) and has been in use for over a decade. It provides a wide variety of algorithms and visualizations to explore large remote sensing datasets without having to download the data and without having to write readers and visualizers for it. Giovanni is now being extended to enable its capabilities at other data centers within the Earth Observing System Data and Information System (EOSDIS). This Federated Giovanni will allow four other data centers to add and maintain their data within Giovanni on behalf of their user community. Those data centers are the Physical Oceanography Distributed Active Archive Center (PO.DAAC), MODIS Adaptive Processing System (MODAPS), Ocean Biology Processing Group (OBPG), and Land Processes Distributed Active Archive Center (LP DAAC). Three tiers are supported: Tier 1 (GES DISC-hosted) gives the remote data center a data management interface to add and maintain data, which are provided through the Giovanni instance at the GES DISC. Tier 2 packages Giovanni up as a virtual machine for distribution to and deployment by the other data centers. Data variables are shared among data centers by sharing documents from the Solr database that underpins Giovanni's data management capabilities. However, each data center maintains their own instance of Giovanni, exposing the variables of most interest to their user community. Tier 3 is a Shared Source model, in which the data centers cooperate to extend the infrastructure by contributing source code.

Giovanni↗

Air Pollution Scenario over Pakistan: Characterization and Ranking of Extremely Polluted Cities using Long-Term Concentrations of Aerosols and Trace Gases

Pakistan ranks third in the world in terms of mortality attributable to air pollution, with aerosol mass concentrations (PM2.5) consistently well above WHO (World Health Organization) air quality guidelines (AQG). However, regulation is dependent on a sparse network of air quality monitoring stations and insufficient ground data. This study utilizes long-term observations of aerosols and trace gases to characterize and rank the air pollution scenarios and pollution characteristics of 80 selected cities in Pakistan. Datasets used include (1) the Aqua and Terra (AquaTerra) MODIS (Moderate Resolution Imaging Spectroradiometer) Level 2 Collection 6.1 merged Dark Target and Deep Blue (DTB) aerosol optical depth (AOD) retrieval products; (2) the CAMS (Copernicus Atmosphere Monitoring Service) reanalysis PM1, PM2.5, and PM10 data; (3) the MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, Version 2) reanalysis PM2.5 data, (4) the OMI (Ozone Monitoring Instrument) tropospheric vertical column density (TVCD) of nitrogen dioxide (NO2), and VCD of sulfur dioxide (SO2) in the Planetary Boundary Layer (PBL), (5) the VIIRS (Visible Infrared Imaging Radiometer Suite) Nighttime Lights data, (6) MODIS Collection 6 Version 2 global monthly fire location data (MCD14ML), (7) population density, (8) MODIS Level 3 Collection 6 land cover types, (9) AERONET (AErosol RObotic NETwork) Version 3 Level 2.0 data, and (10) ground-based PM2.5 concentrations from air quality monitoring stations. Potential Source Contribution Function (PSCF) analyses were performed by integrating with ground-based PM2.5 concentrations and the NOAA (National Oceanic and Atmospheric Administration) HYSPLIT (Hybrid Single-Particle Lagrangian Integrated Trajectory) air parcel back trajectories to identify potential pollution source areas which are responsible for extreme air pollution in Pakistan. Results show that the ranking of the top polluted cities depends on the type of pollutant considered and the metric used. For example, Jhang, Multan, and Vehari were characterized as the top three polluted cities in Pakistan when considering AquaTerra DTB AOD products; for PM1, PM2.5, and PM10 Lahore, Gujranwala, and Okara were the top three; for tropospheric NO2 VCD Lahore, Rawalpindi, and Islamabad and for PBL SO2 VCD Lahore, Mirpur, and Gujranwala. The results demonstrate that Pakistan’s entire population has been exposed to high PM2.5 concentrations for many years, with a mean annual value of 54.7 μg/cu. m, over all Pakistan from 2003 to 2020. This value exceeds Pakistan’s National Environmental Quality Standards (Pak-NEQS, i.e., <15 μg/cu. m annual mean) for ambient air defined by the Pakistan Environmental Protection Agency (Pak-EPA) as well as the WHO Interim Target-1 (i.e., mean annual PM2.5 <35 μg/cu. m). The spatial analyses of the concentrations of aerosols and trace gases in terms of population density, nighttime lights, land cover types, and fire location data, and the PSCF analysis indicate that Pakistan’s air quality is strongly affected by anthropogenic sources inside of Pakistan, with contributions from surrounding countries. Statistically significant positive (increasing) trends in PM1, PM2.5, PM10, tropospheric NO2 VCD, and SO2 VCD were observed in ~89%, ~67%, ~48%, 91%, and ~88% of the Pakistani cities (80 cities), respectively. This comprehensive analysis of aerosol and trace gas levels, their characteristics in spatio-temporal domains, and their trends over Pakistan, is the first of its kind. Results will be helpful to the Ministry of Climate Change (Government of Pakistan), Pak-EPA, SUPARCO (Pakistan Space and Upper Atmosphere Research Commission), policymakers, and the local research community to mitigate air pollution and its effects on human health.

Muhammad Bilal↗

GPS Multipath Emulation using Software Generated Signals

Depending on the environment, multipath can be one of the largest error sources contributing to degradation in Global Navigation Satellite System (GNSS) (e.g., GPS) performance. Currently, open-source tools for simulating GPS signals are available and can be used in the testing and evaluation of GPS receiver equipment. These tools can generate GPS signals that, when used by a GPS receiver, result in computation of a position solution that was pre-determined at the time of signal generation. This work utilizes a custom version of the open-source GPS-SDR-SIM to produce emulated multipath GPS signals. A proof of concept was prototyped and demonstrated using this modified version of GPS-SDR-SIM to produce GPS as well as multipath signals. The generated data was processed using a software defined GPS receiver (GNSS-SDR) and it was found that the introduction of simulated multipath signals successfully produced the expected characteristics of a composite multipath signal in simulation.

GPS↗

GPS Multipath Emulation using Software Generated Signals

Depending on the environment, multipath can be one of the largest error sources contributing to degradation in Global Navigation Satellite System (GNSS) (e.g., GPS) performance. Currently, open-source tools for simulating GPS signals are available and can be used in the testing and evaluation of GPS receiver equipment. These tools can generate GPS signals that, when used by a GPS receiver, result in computation of a position solution that was pre-determined at the time of signal generation. This work utilizes a custom version of the open-source GPS-SDR-SIM to produce emulated multipath GPS signals. A proof of concept was prototyped and demonstrated using this modified version of GPS-SDR-SIM to produce GPS as well as multipath signals. The generated data was processed using a software defined GPS receiver (GNSS-SDR) and it was found that the introduction of simulated multipath signals successfully produced the expected characteristics of a composite multipath signal in simulation.

GPS↗

Linking Improvements in Sulfur Dioxide Emissions to Decreasing Sulfate Wet Deposition by Combining Satellite and Surface Observations with Trajectory Analysis

Sulfur dioxide (SO2), a criteria pollutant, and sulfate (SO42) deposition are major environmental concerns in the eastern U.S. and both have been on the decline for two decades. In this study, we use satellite column SO2 data from the Ozone Monitoring Instrument (OMI), and SO42 wet deposition data from the NADP (National Atmospheric Deposition Program) to investigate the temporal and spatial relationship between trends in SO2 emissions and the downward sulfate wet deposition over the eastern U.S. from 2005 to 2015. To establish the relationship between SO2 emission sources and receptor sites, we conducted a Potential Source Contribution Function (PSCF) analysis using HYSPLIT back trajectories for five selected Air Quality System (AQS) sites - (Hackney, OH, Akron, OH, South Fayette, PA, Wilmington, DE, and Beltsville, MD) - in close proximity to NADP sites with large downward SO42 trends since 2005. Back trajectories were run for three summers (JJA) and three winters (DJF) and used to generate seasonal climatology PSCFs for each site. The OMI SO2 and interpolated NADP sulfate deposition trends were normalized and overlapped with the PSCF, to identify the areas that had the highest contribution to the observed drop. The results suggest that emission reductions along the Ohio River Valley have led to decreases in sulfate deposition in eastern OH and western PA (Hackney, Akron and South Fayette). Farther to the east, emission reductions in southeast PA resulted in improvements in sulfate deposition at Wilmington, DE, while for Beltsville, reductions in both the Ohio River Valley and nearby favorably impacted sulfate deposition. For Beltsville, sources closer than 300km from the site contribute roughly 56% observed deposition trends in winter, and 82% in summer, reflecting seasonal changes in transport pattern as well as faster oxidation and washout of sulfur in summer. This suggests that emissions and wet deposition are linked through not only the location of sources relative to the observing sites, but also to photochemistry and the weather patterns characteristic to the region, as evidenced by a west to east shift in the contribution between winter and summer. The method developed here is applicable to other regions with significant trends such as China and India, and can be used to estimate the potential benefits of emission reduction in those areas.

Acid depostion↗

Stratospheric Aerosol and Gas Experiment (SAGE 3)

The proposed SAGE III instrument would be the principal source of data for global changes of stratospheric aerosols, stratospheric water vapor, and ozone profiles, and a contributing source of data for upper tropospheric water vapor, aerosols, and clouds. The ability to obtain such data has been demonstrated by the predecessor instrument, SAGE II, but SAGE III will be substantially more capable, as discussed below. The capabilities for monitoring the profiles of atmospheric constituents have been verified in detail, including ground-based validations, for aerosol, ozone, and water vapor. Indeed, because of its self-calibrating characteristics, SAGE II was an essential component of the international ozone trend assessments, and SAGE II is now proving to be invaluable in tracking the aerosols from Mt. Pinatubo. Although SAGE profiles generally terminate at the height of the first tropospheric cloud layer, it has been found that the measurements extend down to 3 km altitude more than 40 percent of the time at most latitudes. Thus, useful information can also be obtained on upper tropospheric aerosols, water vapor, and ozone.

Mccormick, M. P.↗

Correction to the luni-solar precession from very long baseline interferometry

The redetermination of the luni-solar precession is performed by using Very Long Baseline Interferometry (VLBI) catalogues of extragalactic radio sources containing positions at observation epochs which cover 9 years. The positions of the sources have been determined by the VLBI network of the Crustal Dynamics Project of NASA from measurements covering consecutive half year and one year intervals between 1981 and 1989. In the course of their reduction the International Astronomical Union (IAU) recommended precession terms were applied. On the assumption of an imperfection of the luni-solar precession it is expected that the positions of each source obtained at different epochs but uniformly reduced to the reference system J2000.0 exhibit an apparent proper motion. We attributed this motion tentatively to precession and solved for a correction of the luni-solar precession by making a least squares fit to the position differences between homonymous sources in the set of catalogues. The 18.6 yr terms of nutation entered the process as parameters the values of which were set by choice from the reservoir of recent determinations. Twenty-five sources contributed to the analysis with the effect that the annual and semi-annual catalogues contain 16 sources on the average. The analysis confirmed the slightly overestimated IAU value of the luni-solar precession yielding a mean correction of -3.59 +/- 1.14 mas/yr from the annual and -3.84 +/- 1.16 mas/yr from the semi-annual catalogues. We discuss these secular terms and their dependence on the adopted nutation terms.

Walter, H. G.↗

Permeable Surface Corrections for Ffowcs Williams and Hawkings Integrals

The acoustic prediction methodology discussed herein applies an acoustic analogy to calculate the sound generated by sources in an aerodynamic simulation. Sound is propagated from the computed flow field by integrating the Ffowcs Williams and Hawkings equation on a suitable control surface. Previous research suggests that, for some applications, the integration surface must be placed away from the solid surface to incorporate source contributions from within the flow volume. As such, the fluid mechanisms in the input flow field that contribute to the far-field noise are accounted for by their mathematical projection as a distribution of source terms on a permeable surface. The passage of nonacoustic disturbances through such an integration surface can result in significant error in an acoustic calculation. A correction for the error is derived in the frequency domain using a frozen gust assumption. The correction is found to work reasonably well in several test cases where the error is a small fraction of the actual radiated noise. However, satisfactory agreement has not been obtained between noise predictions using the solution from a three-dimensional, detached-eddy simulation of flow over a cylinder.

Lockard, David P.↗

Linking Improvements in Sulfur Dioxide Emissions to Decreasing Sulfate Wet Deposition By Combining Satellite and Surface Observations With Trajectory Analysis

Sulfur dioxide (SO2), a criteria pollutant, and sulfate (SO42−) deposition are major environmental concerns in the eastern U.S. and both have been on the decline for two decades. In this study, we use satellite column SO2 data from the Ozone Monitoring Instrument (OMI), and SO42− wet deposition data from the NADP (National Atmospheric Deposition Program) to investigate the temporal and spatial relationship between trends in SO2 emissions and the downward sulfate wet deposition over the eastern U.S. from 2005 to 2015. To establish the relationship between SO2 emission sources and receptor sites, we conducted a Potential Source Contribution Function (PSCF) analysis using HYSPLIT back trajectories for five selected Air Quality System (AQS) sites - (Hackney, OH, Akron, OH, South Fayette, PA, Wilmington, DE, and Beltsville, MD) - in close proximity to NADP sites with large downward SO42− trends since 2005. Back trajectories were run for three summers (JJA) and three winters (DJF) and used to generate seasonal climatology PSCFs for each site. The OMI SO2 and interpolated NADP sulfate deposition trends were normalized and overlapped with the PSCF, to identify the areas that had the highest contribution to the observed drop. The results suggest that emission reductions along the Ohio River Valley have led to decreases in sulfate deposition in eastern OH and western PA (Hackney, Akron and South Fayette). Farther to the east, emission reductions in southeast PA resulted in improvements in sulfate deposition at Wilmington, DE, while for Beltsville, reductions in both the Ohio River Valley and nearby favorably impacted sulfate deposition. For Beltsville, sources closer than 300 km from the site contribute roughly 56% observed deposition trends in winter, and 82% in summer, reflecting seasonal changes in transport pattern as well as faster oxidation and washout of sulfur in summer. This suggests that emissions and wet deposition are linked through not only the location of sources relative to the observing sites, but also to photochemistry and the weather patterns characteristic to the region, as evidenced by a west to east shift in the contribution between winter and summer. The method developed here is applicable to other regions with significant trends such as China and India, and can be used to estimate the potential benefits of emission reduction in those areas.

sulfur dioxide emissions↗

The HEAO A-2 experiment on the spatial and spectral structure of the X-ray sky /0.2-60 keV/

The HEAO A-2 experiment is described which is designed to observe the spectral and spatial structure of cosmic X-radiation over the entire sky with the minimum sensitivity and cross checks required to achieve a number of objectives. Developments in X-ray astronomy are discussed which are relevant to the experiment, including setting a lower limit on the number of discrete sources contributing to the background flux, determining the spatial dependence of the flux, observations of the spectral components of discrete sources, and the study of X-ray absorption by interstellar gas and the atmospheres of binary stars associated with pulsating X-ray sources. It is shown that systematics-free measurements will be made by making simultaneous observations of single sources with several detectors, by using two-layer detectors to eliminate the effects of electron contamination, and by incorporating magnets into low-energy detectors to minimize electron contamination.

Boldt, E.↗

Xenon Isotopic Analysis of Individual Intermediate Particles From the OSIRIS-REx Sample of Asteroid Bennu

The OSIRIS-REx mission sampled material from the B-type asteroid Bennu and delivered the sample to Earth on 24 September 2023. Here we present initial xenon isotopic analysis of individual intermediate particles of Bennu material collected by the OSIRIS-REx mission. Noble gases are key tracers of Solar System evolution. Xenon is particularly useful among the noble gases because its nine isotopes allow multiple contributing sources to be unambiguously identified. The sun, asteroids (as measured in meteorites), and comets (measured in the coma of comet 67P) have distinct xenon isotopic signatures reflecting different mixtures of nucleosynthetic components. In addition, 129 I, 238 U, and 244 Pu decay with different half-lives, producing characteristic xenon signatures. Exposure of samples containing light rare earth elements and barium to cosmic rays produces xenon from spallation and secondary neutron capture reaction. Noble gas analyses help address several of the driving hypotheses of the mission [9]. Particle-by-particle analysis can elucidate the diversity of material present and reveal distinct noble gas compositions, including the potential to detect presolar or cometary noble gas signatures on a small scale. The isotopic signature provides a fingerprint that can be used to constrain the sources of volatiles in planetary reservoirs and combined with other information (e.g. mineralogy and petrology of the material analyses) contributes to our understanding of the initial constituents, formation, and history of Bennu and its parent asteroid.

S A Crowther↗

Pre- and Post-perihelion Observations of C/2009 P1 (Garradd): Evidence for an Oxygen-rich Heritage?

We conducted pre- and post-perihelion observations of Comet C/2009 P1 (Garradd) on UT 2011 October 13 and 2012 January 8, at heliocentric distances of 1.83 and 1.57 AU, respectively, using the high-resolution infrared spectrometer (NIRSPEC) at the Keck II 10-m telescope on Mauna Kea, HI. Pre-perihelion, we obtained production rates for nine primary volatiles (native ices): H2O, CO, CH3OH, CH4, C2H6, HCN, C2H2, H2CO, and NH3. Post-perihelion, we obtained production rates for three of these (H2O, CH4, and HCN) and sensitive upper limits for three others (C2H2, H2CO, and NH3). CO was enriched and C2H2 was depleted, yet C2H6 and CH3OH were close to their currentmean values asmeasured in a dominant group of Oort cloud comets. This may indicate processing of its pre-cometary ices in a relatively oxygen-rich environment. Our measurements indicate consistent pre- and post-perihelion abundance ratios relative to H2O, suggesting we were measuring compositional homogeneity among measured species to the depths in the nucleus sampled. However, the overall gas production was lower post-perihelion despite its smaller heliocentric distance on January 8. This is qualitatively consistent with other studies of C/2009 P1, perhaps due to seasonal differences in the heating of one or more active regions on the nucleus. On October 13, the water profile showed a pronounced excess towards the Sun-facing hemisphere that was not seen in other molecules, including H2O on January 8, nor in the dust continuum. Inter-comparison of profiles from October 13 permitted us to quantify contributions due to release of H2O from the nucleus, and fromits release in the coma. This resulted in the latter source contributing 25-30% of the total observed water within our slit, which covered roughly +/-300 km by +/-4500 km from the nucleus. We attribute this excess H2O, which peaked at a mean projected distance of 1300-1500 km from the nucleus, to release from water-rich, relatively pure icy grains

Volatile composition↗

Evaluation of monthly rainfall estimates derived from the special sensor microwave/imager (SSM/I) over the tropical Pacific

Estimates of monthly rainfall have been computed over the tropical Pacific using passive microwave satellite observations from the special sensor microwave/imager (SSM/I) for the period from July 1987 through December 1990. These monthly estimates are calibrated using data from a network of Pacific atoll rain gauges in order to account for systematic biases and are then compared with several visible and infrared satellite-based rainfall estimation techniques for the purpose of evaluating the performance of the microwave-based estimates. Although several key differences among the various techniques are observed, the general features of the monthly rainfall time series agree very well. Finally, the significant error sources contributing to uncertainties in the monthly estimates are examined and an estimate of the total error is produced. The sampling error characteristics are investigated using data from two SSM/I sensors and a detailed analysis of the characteristics of the diurnal cycle of rainfall over the oceans and its contribution to sampling errors in the monthly SSM/I estimates is made using geosynchronous satellite data. Based on the analysis of the sampling and other error sources the total error was estimated to be of the order of 30 to 50% of the monthly rainfall for estimates averaged over 2.5 deg x 2.5 deg latitude/longitude boxes, with a contribution due to diurnal variability of the order of 10%.

Berg, Wesley↗

Gravity Degree-Depth Relationship Using Point Mass Spherical Harmonics

Relationships between the degree of a spherical harmonic model of the gravitational field of a body and the depth of a source expressed as a density contrast can be used to study the structure of features. Here, we show that the gravitational acceleration per spherical harmonic degree of a constant density source has an extremum that depends on the depth of the source. Using the spherical harmonics expansion for a point mass source, we use this to derive a degree-depth relationship. Our relationship resembles an earlier one derived by Bowin (1983), with substantial differences at the lower degrees. We also find that a recent relationship derived by Deng et al. (2022) over-estimates the source depth. The relationship that we derive relates spherical harmonic degree n to depth d for a planet of radius R according to d = (1 - e -1/n+1 )R, which simplifies to d = R/(n + 1) for high degrees. We support our new relationship with synthetic models of a density contrast in a planet. We also show how the differences between our relationship and that of Bowin (1983) affect band-filtered gravity, for example when inspecting the upper 100 km of the Moon. Using point masses in our modeling results in an approximate relationship where in reality sources can be deeper than estimated, since any source contributes to all spherical harmonic degrees. The use of the contribution per individual degree however provides an intuitive relationship between spherical harmonic degree and depth that can be used to place relative bounds on source depths or to determine the bounds on spherical harmonic expansions when band-filtering gravity field models.

Geopotential theory↗