SEARCH · Search NASA

Results for “dynamic inference”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15

All sources NASA NTRS DOE OSTI

DOE OSTI2023

The Role of Atmospheric Noise in Decadal SST Variability

Abstract A substantial role for atmospheric noise in simulations of decadal internal variability of SST is demonstrated by a comparison of a multicentury climate model control and a corresponding interactive ensemble (IE) simulation. The IE is designed to reduce atmospheric noise in the heat flux, wind stress, and freshwater flux at the air–sea interface. This comparison suggests that nearly all SST variability on decadal time scales is forced by internal atmospheric variability. The results are examined to determine the relative roles of atmospheric surface heat flux noise and ocean dynamics in the decadal volume-averaged heat budget of the upper ocean. The regional heat budgets in two regions, the South Pacific and the midlatitude North Atlantic, show the net atmospheric surface heat flux to be approximately in equilibrium with the ocean dynamics forcing. The IE and control results are used in the equilibrium heat budget approximation to infer the atmospheric heat flux response to SST, as well as the time series of the control atmospheric noise surface heat flux and ocean dynamics forcings for several regions. The South Pacific region SST is found to be primarily forced by the atmospheric noise surface heat flux and the North Atlantic region SST is forced by the ocean dynamics. Similar strengths for the atmospheric heat flux noise and ocean dynamics forcing, with an interdecadal atmospheric heat flux noise time scale and a centennial ocean dynamics time scale, are found for an Atlantic multidecadal variability region SST.

Meteorology & Atmospheric Sciences↗

DOE OSTI2023

Neutrino-driven Winds in Three-dimensional Core-collapse Supernova Simulations

Abstract In this paper, we analyze the neutrino-driven winds that emerge in 12 unprecedentedly long-duration 3D core-collapse supernova simulations done using the code F ornax . The 12 models cover progenitors with zero-age main-sequence mass between 9 and 60 solar masses. In all our models, we see transonic outflows that are at least 2 times as fast as the surrounding ejecta and that originate generically from a proto−neutron star surface atmosphere that is turbulent and rotating. We find that winds are common features of 3D simulations, even if there is anisotropic early infall. We find that the basic dynamical properties of 3D winds behave qualitatively similarly to those inferred in the past using simpler 1D models, but that the shape of the emergent wind can be deformed, very aspherical, and channeled by its environment. The thermal properties of winds for less massive progenitors very approximately recapitulate the 1D stationary solutions, while for more massive progenitors they deviate significantly owing to aspherical accretion. The Y e temporal evolution in winds is stochastic, and there can be some neutron-rich phases. Though no strong r -process is seen in any model, a weak r -process can be produced, and isotopes up to 90 Zr are synthesized in some models. Finally, we find that there is at most a few percent of a solar mass in the integrated wind component, while the energy carried by the wind itself can be as much as 10%–20% of the total explosion energy.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

3D multi-system Bayesian calibration with energy conservation to study rapidity-dependent dynamics of nuclear collisions

Considerable information about the early-stage dynamics of heavy ion collisions is encoded in the rapidity dependence of measurements. To leverage the large amount of experimental data, we perform a systematic analysis using three-dimensional hydrodynamic simulations of multiple collision systems — large and small, symmetric and asymmetric. Specifically, we perform fully 3D multi-stage hydrodynamic simulations initialized by a parameterized model for rapidity-dependent energy deposition, which we calibrate on the hadron multiplicity and anisotropic flow coefficients. We utilize Bayesian inference to constrain properties of the early- and late-time dynamics of the system, and highlight the impact of enforcing global energy conservation in our 3D model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRSDate not supplied

Wind Tunnel to Full Scale Mapping of Winds and Loads for Launch-Vehicle Ground Wind Loads

A launch vehicle ground-wind-loads program was conducted at the NASA Langley Transonic Dynamics Tunnel. The objectives were to quantify key aerodynamic and structural characteristics that impact the occurrence of large wind-induced oscillations of a launch vehicle when exposed to ground winds prior to launch. Of particular interest is the dynamic response of a launch vehicle when a von Kármán vortex street forms in the wake of the vehicle resulting in quasiperiodic lift and drag forces.Vehicle response to these quasiperiodic forces can become quite large when the frequency of vortex shedding nears that of a lowly-damped structural mode thereby exciting a resonant response. The study of ground-wind-loads presents unique challenges to quantify significant characteristics of the approaching wind and to relate the wind-tunnel acquired static, dynamic, and gravitational loads to full-scale vehicles. This paper will explain the correlation process between model-scale and full-scale wind characteristics and resulting structural loads. Characterization of the wind at a launch site requires knowledge of the vehicle dynamics and the anemometer performance. Vehicle dynamics dictate the frequency range of interest in characterization of the atmospheric turbulence, and in defining the required data window-length to model dynamic oscillation build-up during wind-gust analysis. Knowledge of the anemometer performance is required to infer peak wind magnitudes since most anemometers cannot directly measure instantaneous peak values. Following proper wind-speed correlation, static and dynamic wind-tunnel loads must be converted to full-scale equivalent values to derive design and operational guidance. In addition to the direct computation of full-scale equivalent loads using relevant scaling parameters, the corrections applied to dynamic loads accounting for differences in structural damping will also be discussed. Furthermore, a phenomenon that manifests in many slender and flexible launch vehicles is a load magnification due to gravity resulting from mass offset under deflection. A method for scaling this contribution from model-scale to full-scale is presented. Finally, a comparison of wind-tunnel derived loads using the described methodologies to launch vehicle measured loads is presented.

ground wind loads↗

NASA NTRSDate not supplied

Wind-Tunnel to Full-Scale Mapping of Winds and Loads for Launch-Vehicle Ground Wind Loads

A launch vehicle ground-wind-loads program was conducted at the NASA Langley Transonic Dynamics Tunnel. The objectives were to quantify key aerodynamic and structural characteristics that impact the occurrence of large wind-induced oscillations of a launch vehicle when exposed to ground winds prior to launch. Of particular interest is the dynamic response of a launch vehicle when a von Kármán vortex street forms in the wake of the vehicle resulting in quasiperiodic lift and drag forces. Vehicle response to these quasiperiodic forces can become quite large when the frequency of vortex shedding nears that of a lowly-damped structural mode thereby exciting a resonant response. The study of ground-wind-loads presents unique challenges to quantify significant characteristics of the approaching wind and to relate the wind-tunnel acquired static, dynamic, and gravitational loads to full-scale vehicles. This paper will explain the correlation process between model-scale and full-scale wind characteristics and resulting structural loads. Characterization of the wind at a launch site requires knowledge of the vehicle dynamics and the anemometer performance. Vehicle dynamics dictate the frequency range of interest in characterization of the atmospheric turbulence, and in defining the required data window-length to model dynamic oscillation build-up during wind-gust analysis. Knowledge of the anemometer performance is required to infer peak wind magnitudes since most anemometers cannot directly measure instantaneous peak values. Following proper wind-speed correlation, static and dynamic wind-tunnel loads must be converted to full-scale equivalent values to derive design and operational guidance. In addition to the direct computation of full-scale equivalent loads using relevant scaling parameters, the corrections applied to dynamic loads accounting for differences in structural damping will also be discussed. Furthermore, a phenomenon that manifests in many slender and flexible launch vehicles is a load magnification due to gravity resulting from mass offset under deflection. A method for scaling this contribution from model-scale to full-scale is presented. Finally, a comparison of wind-tunnel derived loads using the described methodologies to launch vehicle measured loads is presented.

Ground wind loads↗

NASA NTRS1973

A first look at atmospheric dynamics and temperature variations on Titan.

Pollack (1973) has used a radiative equilibrium model to match radiometric data for Titan and infers the atmospheric mass, composition, opacity, and gross vertical thermal structure. These results are used to estimate the atmospheric temperature variations by means of scaling analysis, taking into account dynamics both for a baroclinic wave regime and for an axially symmetric circulation regime. Horizontal temperature variations of the atmosphere and surface are found to be very small, and the circulation is found to be weak and probably axially symmetric. The small temperature variations appear to preclude the storage of volatiles in polar caps, so that the present atmospheric methane content may be due to a balance between outgassing and photodissociation.

Leovy, C. B.↗

DOE OSTI2021

Modeling protein structures from predicted contacts with modern molecular dynamics potentials: accuracy, sensitivity, and refinement

Protein structure prediction has become increasingly popular and successful in recent years. An essential step for fragment-free, template-free methods is the generation of a final three-dimensional protein model from a set of predicted amino acid contacts that are often described by interresidue pairwise atomic distances. Here we explore the use of modern, open-source molecular dynamics (MD) engines, which have been continually developed over the last three decades with all-atom Hamiltonians to model biomolecular structure and dynamics, to generate accurate protein structures starting from a set of inferred pairwise distances. Additionally, the ability of MD empirical physical potentials to correct inaccuracies in the predicted geometries is tested. We rigorously characterize the effect of modeling parameters on results, the effect of different amounts of error in the predicted distances on the final structures, and test the ability of post-processing analysis to sort the best models out of a set of statistical replicas. We find that with exact distances and with noisy distances, the method can produce excellent structural models, and that the molecular dynamics force field seems to help correct errors in distance predictions, resisting the effects of applied noise.

Davidson, Russ↗

DOE OSTI2022

A Differentiable Hydrology Approach for Modeling With Time-Varying Parameters

In the analysis of observational data with mathematical models, it is often desirable to let one or more model parameters vary with time to account for changing environmental conditions or to offer more flexibility. A standard approach for dynamic models is to allow for the number of parameters to grow as a function of time, leading to a high-dimensional inference problem for long data records. We propose using Hamiltonian Monte Carlo, a gradient-based Markov chain Monte Carlo (MCMC) method, to perform Bayesian inference for time-varying parameters (TVP) in hydrology models. As derivatives of model error functions with regard to parameters are not available in closed form, we implemented the GR4J rainfall-runoff models in Theano/PyMC3, and Jax/NumPyro, allowing for the application of automatic differentiation techniques. A simulation experiment assessing the viability of these methods for recovering underlying temporal variation in parameters indicates that a discrete Gaussian random walk-based prior appears to be best suited across a range of scenarios while the continuous-time Gaussian process compares relatively poorly. In an analysis of 20 years of daily real-world streamflow records from the Model Parameter Estimation Experiment (MOPEX) hydrology data set with increasing data sparsity and at multiple temporal resolutions, we find that TVP inference with gradient-based MCMC is a flexible and reliable approach for analyzing hydrology models with dynamic parameter sets.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Extracellular DNA Alters Detection of Subtle Bacterial Responses to Soil Rewetting

Microbial communities are often characterized using DNA-based sequencing, but these approaches also capture extracellular DNA (exDNA) released from dead cells, potentially altering inference about microbial responses to environmental change. This may be especially important during pulse disturbances, such as soil drying–rewetting, which can increase microbial mortality and transient necromass pools. We assessed whether exDNA altered inference about bacterial responses to drying–rewetting (an 80 mm simulated rainfall event following a 28-day drought) in conventionally tilled corn and perennial switchgrass soils. We quantified bacterial abundance (16 S rRNA gene copies), alpha diversity, and community composition in paired soil samples with exDNA included (+ exDNA) and in samples treated with propidium monoazide (PMAxx) to reduce amplification of exDNA (− exDNA). At our level of replication (n = 4), PMAxx treatment did not significantly alter overall temporal response patterns (i.e., no significant main effect of DNA treatment or DNA × time interaction). However, PMAxx treatment increased sensitivity to detect some pairwise temporal changes in bacterial abundance and community composition in corn soils following rewetting. exDNA pools were proportionally highest immediately after rewetting in corn soils, suggesting transient extracellular DNA may contribute to masking during disturbance recovery. In contrast, PMAxx treatment had comparatively small effects in switchgrass soils, which exhibited weaker temporal responses overall. Inclusion of exDNA also changed which taxa appeared most responsive to rewetting. Together, our results suggest that exDNA does not uniformly bias soil microbial inference, but may reduce detectability of subtle disturbance-driven shifts in certain soils. Future studies should advance knowledge of microbial turnover and necromass dynamics, particularly using multiple complementary methods, to help predict when exDNA is most likely to influence ecological inference.

drying-rewetting↗

DOE OSTI2026

BMINN: Learning chemical potentials and parameters from voltage data for multi-phase battery modeling

Free-energy landscapes and chemical potentials govern the dynamics of phase transitions, transport, and stability in functional materials, yet they remain experimentally inaccessible under realistic operating conditions. Here we introduce a Bayesian model-integrated neural network (BMINN) that embeds physics-based formulations of non-autonomous partial differential-algebraic equations into probabilistic learning. This approach reconstructs hidden thermodynamics directly from macroscopic current-voltage data, providing quantitative access to metastable states, staging transitions, and energy barriers without synchrotron probes. Demonstrated on lithium-graphite electrodes, BMINN recovers full Gibbs free-energy landscapes with fidelity validated against operando X-ray diffraction. The framework generalizes across dynamical regimes, enabling accurate voltage prediction, internal state estimation, and inference of governing parameters. Beyond batteries, BMINN exemplifies a broadly applicable strategy for learning missing physics in multiphase, non-equilibrium systems, offering a new pathway to uncover hidden thermodynamic functions across condensed matter and materials physics.

25 ENERGY STORAGE↗

DOE OSTI2023

Neglecting Model Parametric Uncertainty Can Drastically Underestimate Flood Risks

Abstract Floods drive dynamic and deeply uncertain risks for people and infrastructures. Uncertainty characterization is a crucial step in improving the predictive understanding of multi‐sector dynamics and the design of risk‐management strategies. Current approaches to estimate flood hazards often sample only a relatively small subset of the known unknowns, for example, the uncertainties surrounding the model parameters. This approach neglects the impacts of key uncertainties on hazards and system dynamics. Here we mainstream a recently developed method for Bayesian inference to calibrate a computationally expensive distributed hydrologic model. We compare three different calibration approaches: (a) stepwise line search, (b) precalibration or screening, and (c) the Fast Model Calibrations (FaMoS) approach. FaMoS deploys a particle‐based approach that takes advantage of the massive parallelization afforded by modern high‐performance computing systems. We quantify how neglecting parametric uncertainty and data discrepancy can drastically underestimate extreme flood events and risks. Precalibration improves prediction skill score over a stepwise line search. The Bayesian calibration improves the uncertainty characterization of model parameters and flood risk projections.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Deep Koopman operators for causal discovery

Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. Thus, applying these methods to study causal dynamics in real-world systems, such as the Earth, is a major challenge. Addressing this shortcoming, we leverage deep learning and a Koopman operator-theoretic formalism to present a class of causal discovery algorithms. Kausal uses deep Koopman operator methods to approximate nonlinear dynamics in a linearized vector space in which traditional causal inference methods such as Granger causality can be more easily applied. Our idealized experiments demonstrate Kausal’s superior ability in discovering and characterizing causal signals compared to existing deep learning and non-deep learning state-of-the-art approaches. Finally, the successful identification of major El Niño and La Niña events in observations showcases Kausal’s skill to handle real-world applications.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Wall conditioning effects of boron powder injection in KSTAR with a tungsten divertor

Boron powder dropped into KSTAR plasmas decreased the radiated power, core electron density, and Z eff , indicating that the ablated and redeposited boron powder helped to condition the plasma-facing surfaces. Visible line emission of oxygen and tungsten were also reduced by 50% (80%) with boron injection into H-mode (L-mode) discharges that used the new KSTAR tungsten monoblock lower divertor. Dynamic particle balance analysis found a negligible difference in the inferred wall pumping rate during the steady portion of the discharges. It is inferred that the observed conditioning effects were principally caused by a reduction in intrinsic impurities as opposed to a reduction in wall recycling. These results are in qualitative agreement with low-Z injected powder experiments across many fusion devices, confirming the utility of low-Z powder injection as a real-time wall conditioning tool.

boron powder injection↗

DOE OSTI2024

Intra- and inter-subtype HIV diversity between 1994 and 2018 in southern Uganda: a longitudinal population-based study

There is limited data on human immunodeficiency virus (HIV) evolutionary trends in African populations. We evaluated changes in HIV viral diversity and genetic divergence in southern Uganda over a 24-year period spanning the introduction and scale-up of HIV prevention and treatment programs using HIV sequence and survey data from the Rakai Community Cohort Study, an open longitudinal population-based HIV surveillance cohort. Gag (p24) and env (gp41) HIV data were generated from people living with HIV (PLHIV) in 31 inland semi-urban trading and agrarian communities (1994–2018) and four hyperendemic Lake Victoria fishing communities (2011–2018) under continuous surveillance. HIV subtype was assigned using the Recombination Identification Program with phylogenetic confirmation. Inter-subtype diversity was evaluated using the Shannon diversity index, and intra-subtype diversity with the nucleotide diversity and pairwise TN93 genetic distance. Genetic divergence was measured using root-to-tip distance and pairwise TN93 genetic distance analyses. Demographic history of HIV was inferred using a coalescent-based Bayesian Skygrid model. Evolutionary dynamics were assessed among demographic and behavioral population subgroups, including by migration status. 9931 HIV sequences were available from 4999 PLHIV, including 3060 and 1939 persons residing in inland and fishing communities, respectively. In inland communities, subtype A1 viruses proportionately increased from 14.3% in 1995 to 25.9% in 2017 (P < .001), while those of subtype D declined from 73.2% in 1995 to 28.2% in 2017 (P < .001). The proportion of viruses classified as recombinants significantly increased by nearly four-fold from 12.2% in 1995 to 44.8% in 2017. Inter-subtype HIV diversity has generally increased. While intra-subtype p24 genetic diversity and divergence leveled off after 2014, intra-subtype gp41 diversity, effective population size, and divergence increased through 2017. Intra- and inter-subtype viral diversity increased across all demographic and behavioral population subgroups, including among individuals with no recent migration history or extra-community sexual partners. This study provides insights into population-level HIV evolutionary dynamics following the scale-up of HIV prevention and treatment programs. Continued molecular surveillance may provide a better understanding of the dynamics driving population HIV evolution and yield important insights for epidemic control and vaccine development.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Understanding protein-complex assembly through grand canonical maximum entropy modeling

Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are far more protein complexes that are yet to be solved because of their dynamic associations with one another. Nevertheless, it is possible to infer these protein complexes through a physical model. However, it is often not clear to physicists what kind of data from biology is necessary for such a modeling endeavor. Here, we aim to model these clusters of coarse-grained protein assemblies from multiple subunits through the constraints of interactions among the subunits and the chemical potential of each subunit. We obtained the constraints on the interactions among subunits from the known protein structures. We inferred the chemical potential that dictates the particle number distribution of each protein subunit from the knowledge of protein abundance from experimental data. Guided by the maximum entropy principle, we formulated an inverse statistical mechanical method to infer the distribution of particle numbers from the data of protein abundance as chemical potentials for a grand canonical multicomponent mixture. Using grand canonical Monte Carlo simulations, we captured a distribution of high-order clusters in a protein complex of succinate dehydrogenase with four known subunits. The complexity of hierarchical clusters varies with the relative protein abundance of each subunit in distinctive cell types such as lung, heart, and brain. When the crowding content increases, we observed that crowding stabilizes emergent clusters that do not exist in dilute conditions. We, therefore, proposed a testable hypothesis that the hierarchical complexity of protein clusters on a molecular scale is a plausible biomarker of predicting the phenotypes of a cell.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Root responses to elevated CO 2 , warming and irrigation in a semi-arid grassland: Integrating biomass, length and life span in a 5-year field experiment

Plant roots mediate the impacts of environmental change on ecosystems, yet knowledge of root responses to environmental change is limited because few experiments evaluate multiple environmental factors and their interactions. Inferences about root functions are also limited because root length dynamics are rarely measured. Using a 5-year experiment in a mixed-grass prairie, we report the responses of root biomass, length and life span to elevated carbon dioxide (CO 2 ), warming, elevated CO 2 and warming combined, and irrigation. Root biomass was quantified using soil cores and root length dynamics were assessed using minirhizotrons. By comparing root dynamics with published results for soil resources and above-ground productivity, we provide mechanistic insights into how climate change might impact grassland ecosystems. In the upper soil layer, 0–15 cm depth, both irrigation and elevated CO 2 alone increased total root length by twofold, but irrigation decreased root biomass and elevated CO 2 had only small positive effects on root biomass. The large positive effects of irrigation and elevated CO 2 alone on total root length were due to increases in both root length production and root life span. The increased total root length and life span under irrigation and elevated CO 2 coincided with apparent shifts from water limitation of plant growth to nitrogen limitation. Warming alone had minimal effects on root biomass, length and life span in this shallow soil layer. Warming and elevated CO 2 combined increased root biomass and total root length by c. 25%, but total root length in this treatment was lower than expected if the effects of CO 2 and warming alone were additive. Treatment effects on total root length and root life span varied with soil depth and root diameter. Synthesis. Sub-additive effects of CO 2 and warming suggest studies of elevated CO 2 alone might overestimate the future capacity of grassland root systems to acquire resources. In this mixed-grass prairie, elevated CO 2 with warming stimulated total root length and root life span in deeper soils, likely enhancing plant access to more stable pools of growth-limiting resources, including water and phosphorus. Therefore, these root responses help explain previous observations of higher, and more stable, above-ground productivity in these projected climate conditions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

A New Field Instrument for Leaf Volatiles Reveals an Unexpected Vertical Profile of Isoprenoid Emission Capacities in a Tropical Forest

Both plant physiology and atmospheric chemistry are substantially altered by the emission of volatile isoprenoids (VI), such as isoprene and monoterpenes, from plant leaves. Yet, since gaining scientific attention in the 1950’s, empirical research on leaf VI has been largely confined to laboratory experiments and atmospheric observations. Here, we introduce a new field instrument designed to bridge the scales from leaf to atmosphere, by enabling precision VI detection in real time from plants in their natural ecological setting. With a field campaign in the Brazilian Amazon, we reveal an unexpected distribution of leaf emission capacities (EC) across the vertical axis of the forest canopy, with EC peaking in the mid-canopy instead of the sun-exposed canopy surface, and moderately high emissions occurring in understory specialist species. Compared to the simple interpretation that VI protect leaves from heat stress at the hot canopy surface, our results encourage a more nuanced view of the adaptive role of VI in plants. We infer that forest emissions to the atmosphere depend on the dynamic microenvironments imposed by canopy structure, and not simply on canopy surface conditions. We provide a new emissions inventory from 52 tropical tree species, revealing moderate consistency in EC within taxonomic groups. We highlight priorities in leaf volatiles research that require field-portable detection systems. Our self-contained, portable instrument provides real-time detection and live measurement feedback with precision and detection limits better than 0.5 nmol VI m -2 leaf s -1 . We call the instrument ‘PORCO’ based on the gas detection method: photoionization of organic compounds. We provide a thorough validation of PORCO and demonstrate its capacity to detect ecologically driven variation in leaf emission rates and thus accelerate a nascent field of science: the ecology and ecophysiology of plant volatiles.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1986

The rotation period of Uranus

On 24 January 1986 the spacecraft Voyager 2 transversed the innermost magnetosphere of the planet Uranus, coming as close as 4.2 Uranus radii to the planet. It is pointed out that the magnetic field data provide a direct measure of the rotation period of the planet's interior, where the field is generated. Two period determinations are reported. A combination of the obtained values provides a weighted mean value of P = 17.24 + or - 0.01 h. It is concluded that the 17.24-h rotation period has important consequences for studies of atmospheric dynamics and the internal structure and composition of Uranus. Thus, inferences regarding the internal structure can be drawn from the relationship between the observed planetary oblateness, rotation period, and gravitational moment.

Desch, M. D.↗