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Physical Oceanography in the Solar System and Beyond

A key controller of a planet’s rotational evolution, and hence habitability, is tidal dissipation, which on Earth occurs primarily in the oceans. As the discovery of habitable exoplanets is a primary objective of exoplanet research, it is imperative that we understand how “exo-oceans” behave. Despite this importance, little research has investigated the physical oceanography of worlds other than Earth. This oversight has occurred even though the Earth science community has studied tidal flows in Earth’s oceans for over a century and developed sophisticated models that exquisitely match satellite altimetry data, e.g. Here, we present a) models of tidal effects on exoplanets to motivate the problem, b) the application of a physical oceanography model to a putative ancient Venus ocean, and c) the application of that model to an ensemble of “alternative Earths” with a range of continental configurations and seafloor properties. We find that oceanic tidal dissipation can span 5 orders of magnitude, revealing that simulating exo-oceans with Earth science tools will provide fundamental insight into exoplanet evolution and habitability

Physical Oceanography↗
DOE OSTI2023

Development of an Unmanned Mobile Current Turbine Platform: Preprint

The design and development of a prototype unmanned mobile floating platform, equipped with a custom low-flow marine current turbine for autonomously seeking and harnessing tidal/coastal currents is described. The platform is an unmanned surface vehicle in the form of a catamaran with two electric outboard motors and capabilities for autonomous navigation. An undershot water wheel, aided by a custom flow concentrator, has been selected as the basic design for the marine current turbine, which is mounted on the stern of the unmanned surface vehicle platform. The concept of operation is that the platform would navigate to a designated marine current resource, autonomously anchor at the location, align itself in the current and deploy the current turbine using a custom cable-lift deployment mechanism. As the turbine harnesses the local current, an onboard power-take-off device converts the harnessed mechanical energy to electricity which is stored in onboard batteries. Considerations of deployment in tidal and coastal waters required obtaining the necessary environmental permits for conducting in-water testing; developing required mitigation measures in protecting local wildlife and their habitats; and identifying potential in-water test sites and surveying them for their suitability in terms of the current resource, bottom type, water depth, and local boat traffic. The design and development of the turbine and the results of initial in-water testing are discussed. The potential for scaling up the system for extended capacity is presented.

ENGINEERING,TIDAL AND WAVE POWER↗
DOE OSTI2020

Baroclinic Residual Circulation and Mass Transport Due to Internal Tides

Baroclinic (BC) tidal residual circulation due to internal tides is investigated around islands over a shallow ridge using a numerical ocean model. Internal tides enhance vertical mixing over shallow slopes, leading to horizontal density gradients that drive BC residual circulation along the main thermocline. For a strongly stratified summer case, the vertical diffusivity estimated by the Mellor and Yamada turbulence closure model exceeds 1 × 10 -2 m 2 s -1 , and the velocity of BC residual circulations reaches 0.2 m s -1 . The magnitude of BC residual circulation is larger than that of barotropic residual tidal circulation, implying that BC residual circulation due to internal tides plays an important role in coastal ocean circulation. Furthermore, BC residual flow accounts for an equal percentage (5%) of the total tidal kinetic energy as the barotropic residual flow under summer stratification conditions. Results from a coupled sediment resuspension and transport model show the growth of intermediate nepheloid layers formed by strong bottom shear stress and BC residual flow. The residual component contributes largely (23% of the total in summer) to the total suspended sediment flux. Seasonal variability is explored, with weaker winter stratification leading to reduced mixing, and thus weaker BC residual circulation and sediment flux. Lastly, the magnitude of the BC residual circulation is also shown to be proportional to the square of the tidal amplitude.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Mixing of the Connecticut River Plume During Ambient Flood Tides: Spatial Heterogeneity and Contributions of Bottom–Generated and Interfacial Mixing

The Connecticut River plume is influenced by energetic ambient tides in the Long Island Sound receiving waters. The objectives of this modeling study are (a) characterizing the spatial heterogeneity of turbulent buoyancy fluxes, (b) partitioning turbulent buoyancy fluxes into bottom-generated and interfacial shear contributions, and (c) quantifying contributions to plume-integrated mixing within the tidal plume. The plume formed during ambient flood tides under low river discharge, spring tides, and no winds is analyzed. Turbulent buoyancy fluxes (B) and depth-integrated B through the plume (Bd) are characterized by pronounced spatial heterogeneity. Strong mixing (Bd ~ 10 –5 -10 –4 m 3 /s 3 ) occurs near the mouth, in the nearfield plume turning region, over shoals, and nearshore shallow areas. Low to moderate mixing (Bd ~ 10 –8 -10 –6 m 3 /s 3 ) occupies half the plume. Buoyancy fluxes are first partitioned based on the depth of the shear stress minimum between plume-generated and bottom-generated shear maxima. Four other tested partitioning methods are based on open channel flow and stratified shear flow parameterizations. Interfacial and bottom-generated shear contribute to different areas of intense and moderate mixing. All methods indicate a significant plume mixing role for bottom-generated mixing, but interfacial mixing is a bigger contributor. Plume-integrated total and interfacial mixing peak at max ambient flood and the timing of peak bottom-generated mixing varies among partitioning methods. Two-thirds of the mixing occurs in concentrated intense mixing areas. A parameter space with the ambient tidal Froude number and plume thickness to depth ratio as axes indicates many tidally modulated plumes are moderately to dominantly influenced by bottom-generated tidal mixing.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Ultra-deep imaging of NGC 1052-DF2 and NGC 1052-DF4 to unravel their origins

A number of scenarios have been proposed to explain the low velocity dispersion (and hence possible absence of dark matter) of the low surface brightness galaxies NGC 1052-DF2 and NGC 1052-DF4. Most of the proposed mechanisms are based on the removal of dark matter via the interaction of these galaxies with other objects. A common feature of these processes is the prediction of very faint tidal tails, which should be revealed by deep imaging (μ g > 30 mag arcsec −2 ). Using ultra-deep images obtained with the Gemini telescopes, about 1 mag deeper than previously published data, we analyzed the possible presence of tidal tails in both galaxies. We confirm the presence of tidal tails in NGC 1052-DF4, but see no evidence for tidal effects in NGC 1052-DF2, down to surface brightnesses ofμ g = 30.9 mag arcsec −2 . We therefore conclude that while the absence of dark matter in NGC 1052-DF4 could be attributed to the removal of dark matter by gravitational interactions, in the case of NGC 1052-DF2 this explanation seems less plausible, and therefore other possibilities such as an incorrect distance measurement or that the system may be rotating could alleviate the dark matter problem.

Astronomy & Astrophysics↗
DOE OSTI2022

On the physical size of the Milky Way globular cluster NGC 7089 (M2)

ABSTRACT We study the outer regions of the Milky Way globular cluster NGC 7089 based on new Dark Energy Camera observations. The resulting background-cleaned stellar density profile reveals the existence of an extended envelope. We confirm previous results that cluster stars are found out up to ∼1° from the cluster’s centre, which is nearly three times the value of the most robust tidal radii estimations. We also used results from direct N-body simulations in order to compare with the observations. We found a fairly good agreement between the observed and numerically generated stellar density profiles. Because of the existence of gaps and substructures along globular cluster tidal tails, we closely examined the structure of the outer cluster region beyond the Jacobi radius. We extended the analysis to a sample of 35 globular clusters, 20 of them with observed tidal tails. We found that if the stellar density profile follows a power law ∝ r−α, the α slope correlates with the globular cluster present mass, in the sense that, the more massive the globular cluster, the smaller the α value. This trend is not found in globular clusters without observed tidal tails. The origin of such a phenomenon could be related, among other reasons, to the proposed so-called potential escapers or to the formation of globular clusters within dark matter minihaloes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

SDSS-IV MaNGA: the role of the environment in AGN triggering

ABSTRACT The large- and small-scale environments around optically-selected AGN host galaxies and a control sample of non-active galaxies in the MaNGA survey have been investigated in order to evaluate the importance of the environment in AGN triggering. Using the MaNGA integral field spectroscopy, we quantify non-circular motions of the ionized gas and detect an excess of radial gas motions in AGN hosts relative to control galaxies, not associated to AGN feedback and are most likely the result of tidal interactions, possibly associated with the triggering of the AGN. We find that the large-scale environments are similar for the AGN hosts and control galaxies in our sample and are biased towards lower large-scale densities and group virial masses, suggestive that the large-scale environment properties is only relevant to the AGN phenomenon in an indirect way, in the form, e.g. of the morphology-density relation. The small-scale environment, as measured by the frequency and luminosity of close neighbours, was also found to be similar for AGN and control galaxies. However, we find a correlation between the intensity of the non-circular gas motions in AGN hosts and the strength of the tidal field, while the control sample does not present such correlation. Also, AGN hosts with the most intense radial gas motions present larger tidal fields than their control galaxies. These findings indicate that at least a fraction of the AGN hosts in our sample have been triggered by tidal interactions with nearby galaxies.

Rembold, Sandro B.↗
DOE OSTI2020

Relativistic hybrid stars with sequential first-order phase transitions and heavy-baryon envelopes

We compute the mass, radius and tidal deformability of stars containing phase transitions from hadronic to quark phase(s). These quantities are computed for three types of hadronic envelopes: purely nuclear, hyperonic, and Δ-resonance--hyperon admixed matter. We consider either a single first-order phase transition to a quark phase with a maximally stiff equation of state (EOS) or two sequential first-order phase transitions mimicking a transition from hadronic to a quark matter phase followed by a second phase transition to another quark phase. We explore the parameter space which produces low-mass twin and triplet configurations where equal-mass stars have substantially different radii and tidal deformabilities. We demonstrate that while for purely hadronic stiff EOS the obtained maximum mass is inconsistent with the upper limit on this quantity placed by GW170817, the inclusion of the hyperonic and Δ-resonance degrees of freedom, as well as the deconfinement phase transition at sufficiently low density, produces a configuration of stars consistent with this limit. The obtained hybrid star configurations are in the mass range relevant for the interpretation of the GW170817 event. We compare our results for the tidal deformability with the limits inferred from GW170817 showing that the onset of non-nucleonic phases, such as Δ-resonance--hyperon admixed phase and/or the quark phase(s), are favored by this data if the nuclear EOS is stiff. Also, we show that low-mass twins and especially triplets proliferate the number of combinations of possible types of stars that can undergo a merger event, the maximal number being six in the case of triplets. The prospects for uncovering the first-order phase transition(s) to and in quark matter via measurements of tidal deformabilities in merger events are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Photometric redshifts and intrinsic alignments: Degeneracies and biases in the 3 × 2 pt analysis

We present a systematic study of cosmological parameter bias in weak lensing and large-scale structure analyses for upcoming imaging surveys induced by the interplay of intrinsic alignments (IA) and photometric redshift (photo-z) model misspecification error. We first examine the degeneracies between the parameters of the tidal alignment–tidal torquing (TATT) model for IA and of a photo-z model including a mean shift ( Δ z ¯ ) and variance ( σ z ) for each tomographic bin of lenses and sources, under a variety of underlying true IA behaviors. We identify strong degeneracies between: (1) the redshift scaling of the tidal alignment amplitude and the mean shift and variances of source bins, (2) the redshift scaling of the tidal torquing amplitude and the variance of the lowest- z source bin, and (3) the IA source density weighting and the mean shift and variance of several source bins. We then use this information to guide our exploration of the level of cosmological parameter bias which can be induced given incorrect modeling of IA, photo-z, or both. We find that marginalizing over all the parameters of TATT is generally sufficient to preclude cosmological parameter bias in the scenarios we consider. However, this does not necessarily mean that IA and photo-z parameters are themselves unbiased, nor does it mean that the best-fit model is a good fit to the data. We also find scenarios where the inferred parameters produce χ d . o . f . 2 values indicative of a good fit but cosmological parameter bias is significant, particularly when the IA source density weighting parameter is not marginalized over. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Model simulations of Plum Island Ecosystems LTER low marsh site using ELM-PFLOTRAN

Model simulations using the E3SM Land Model (ELM) coupled to the PFLOTRAN reactive transport model via the Alquimia interface. The simulations were conducted for a tidal salt marsh at the Plum Island Ecosystems LTER near Rowley, Massachusetts, USA. Model simulations were forced using site-specific tidal cycles and salinity, and the simulations used a biogeochemical reaction network including aerobic decomposition, sulfate reduction, iron reduction, and methanogenesis. Model outputs include simulated carbon stocks, carbon dioxide and methane fluxes, and porewater concentrations of key solutes related to sulfur, iron, and carbon cycling. The model simulations included a saline simulation (with tidal sulfate inputs), a fresh simulation (with low salinity and low sulfate inputs), and a saline simulation with lower vegetation productivity to represent the effect of salinity on vegetation. These simulations were conducted to demonstrate that a new model framework incorporating subsurface redox and biogeochemical interactions into a land surface model could reproduce measured surface greenhouse gas fluxes and biogeochemical dynamics in tidal marsh ecosystems, and to test whether including redox interactions in a land surface model would allow the model to resolve contrasts in biogeochemical cycling and greenhouse gas production between saline and freshwater wetlands.The data package includes gzipped tar archives (which can be expanded using standard tar and gzip utilities) of model outputs from three model configurations: saline subsurface and reduced vegetation productivity related to salinity; saline subsurface with vegetation productivity not reduced; and freshwater. Also included are code for the modified E3SM model, Alquimia interface, and PFLOTRAN reactive transport simulator in gzipped tar format; plain text parameter and configuration files; python code files for visualizing model output and defining model configurations; and model output, tide and salinity forcing, and configuration files in netCDF format. See the README.md file in the data package for a detailed description of all files contained in the package. All files are in netCDF (.nc), gzipped tar archive (.tar.gz or .tgz), or text (all other files).Updated: May 13, 2024. Model output, E3SM code, PFLOTRAN input files, and python codes for visualizing results were updated to reflect changes made for the manuscript revision. The updated archive reflects the code and model output from the final accepted manuscript. Changes included updated reaction parameters reflecting improved parameterization and additional comparisons with field measurements. E3SM code changes included better support for multiple grid cells and improved flow and transport parameterization.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Data-model files associated with the manuscript "Modeling the Effects of Wetland Restoration on Coastal Hydrology: A Case Study of Elkhorn Slough Watershed, California"

This package contains the data, simulation setups, notebooks and figures used in “Modeling the Effects of Wetland Restoration on Coastal Hydrology: A Case Study of Elkhorn Slough Watershed, California” (Xu et al., 2025). In this study, we selected Elkhorn Slough, a tidal estuary, in California, to investigate the impact of wetland restoration and sea level rise on coastal hydrology using the process-based coastal hydrologic model, Advanced Terrestrial Simulator (ATS), informed by site-specific data. We designed a novel modeling workflow for incorporating wetland restoration features into land cover and soil properties for the model parameterization. The validation results demonstrate a strong agreement between modeled and observed data. We studied the characteristics of coastal watershed hydrology, then focused on the surface water dynamics at two wetland sites within Elkhorn Slough, a reference site and a restored site. Our simulation results indicate that the restored site successfully maintains surface elevation, resulting in reduced surface inundation. We also examined the impact of wetland restoration under expected sea level rise over the next few decades. The low-lying Yampah Marsh, the reference site, is likely to be inundated due to future sea level rise when highest tides arrive; while a higher percentage of Hester Marsh, the restored site, would retain marsh vegetation in coming decades, regardless of tidal conditions. Our study provides important information for examining the outcome of restoration practices that include surface elevation in tidal wetlands under climate changes.Several files can be found from this data package.1. README.md: This file describes the title, journal, co-authors, abstract, repository structure and model version.2. Simulation_Setups.zip: The file contains the model configuration files (XML format) for ATS. 3. Notebooks.zip: The file contains the Jupyter notebooks for generating the pre- and post-restoration meshes and the meshes of future scenarios. 4. Figures.zip: The file contains the figures used in the manuscript.5. Data.zip: The file contains the data used to drive the model simulations, including watershed and wetlands boundaries, mesh files and references to additional datasets (e.g., meteorological forcing, tidal dataset, DEMs, land cover, soil properties). Also, it contains water level observations at the restored wetland.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Harvesting Subsea Water Motion to Provide Clean Electrical Power

This TEAMER project had three main objectives related to characterizing the performance of a vortex-induced vibration (VIV) marine energy harvesting device called the Whatever Input To Torsion (WITT). The first was to characterize the motion of the WITT device as it vibrates on top of a pipe in a natural tidal flow. The second was to measure how much electricity the WITT device generates when it is deployed on top of a pipe that is secured to the seabed with a lander. The third objective was to measure how much electricity the WITT device generates in the same configuration but with a longer pipe. This TEAMER project succeeded in satisfying the first objective by measuring the motion of the WITT device with an inertial measurement unit (IMU) mounted in the WITT housing. The motion was described by examining changes in the acceleration, pitch, roll, and yaw, and displacement. The frequency of the motion was characterized using spectral analysis. The TEAMER project succeeded in reaching the second objective by measuring the power produced by the WITT. It is reported here as the average and maximum power in hourly intervals. WITT Energy decided to not have us pursue the third objective of testing a longer pipe because the first test was unexpectedly successful at having the system vibrate at the target frequency. A longer pipe would have resulted in a decreased frequency and therefore not have been a useful test. Based on these findings, the decision was made to keep the same pipe length for both tests and improve on other aspects of the test structure that had failed during the first test. The key finding of this TEAMER project is that the WITT is capable of generating electricity in moderate flow speeds when it is in a housing that is attached to a 2.5 m pipe and secured to the seabed by a lander. This report contains the first power values for a VIV instrument that generates electricity from a pendulum swinging at the top of a long pipe. The experiment demonstrated that the vibration frequency of the device varied with the tidal current speed, which changed throughout a given tidal cycle. This meant that the desired peak frequency was not sustained for more than one hour. The success of this TEAMER test provides evidence that continued research in the area of electricity generation from VIV holds promise as a source of marine energy for offshore applications. Future tests should focus on refining the pipe length equations and improving the power take off system of the WITT power electronics. In addition, experiments aimed at expanded testing and evaluation (e.g. longer than one month) are needed to measure the power production at higher tidal current speeds and test the system's durability.

Branch, Ruth A. (ORCID:0000000202356719)↗
DOE OSTI2021

New Determination of Fundamental Properties of Palomar 5 Using Deep DESI Imaging Data

The legacy imaging surveys for the Dark Energy Spectroscopic Instrument project provides multiple-color photometric data, which are about 2 mag deeper than those from the SDSS. In this study, we redetermine the fundamental properties for an old halo globular cluster of Palomar 5 based on these new imaging data, including structure parameters, stellar population parameters, and luminosity and mass functions. These characteristics, together with its tidal tails, are key for dynamical studies of the cluster and constraining the mass model of the Milky Way. By fitting the King model to the radial surface density profile of Palomar 5, we derive the core radius of [[Formula]], tidal radius of [[Formula]], and concentration parameter of c = 0.78 ± 0.04. We apply a Bayesian analysis method to derive the stellar population properties and get an age of 11.508 ± 0.027 Gyr, metallicity of [Fe/H] = −1.798 ± 0.014, reddening of E(B − V) = 0.0552 ± 0.0005, and distance modulus of (m−M){sub 0} = 16.835±0.006. The main-sequence luminosity and mass functions for both the cluster center and tidal tails are investigated. The luminosity and mass functions at different distances from the cluster center suggest that there is obvious spatial mass segregation. Many faint low-mass stars have been evaporated at the cluster center, and the tidal tails are enhanced by low-mass stars. Both the concentration and relaxation times suggest that Palomar 5 is a totally relaxed system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Simulations of Interacting Binary Systems—Pathways to Radio-bright Gamma-Ray Burst Progenitors

Although the association of gamma-ray bursts (GRBs) with massive stellar death is on firm footing, the nature of the progenitor system and the key ingredients required for a massive star to produce a GRB remain open questions. Here, we investigate the evolution of a 15–25M ⊙ massive star with a 10–15M ⊙ black hole (BH) using Modules for Experiments in Stellar Astrophysics. We quantify companion-influenced angular-momentum evolution over a stellar lifetime for orbital periods where tides are significant, varying stellar and BH masses, initial stellar spin, and accretion and dynamo prescriptions while tracking mass loss and angular momentum. The final spin is set by tidal torques versus stellar winds. For binaries that initially avoid Roche-lobe overflow, tides can spin up the star, but a late-stage expansion can drive tidal stripping; associated mass and angular-momentum loss can suppress spin-up. We find that massive-star BH binaries at comparable mass ratios may be potential GRB progenitors for short orbital periods (∼20–5 × 10 2 days) and long orbital periods (∼2 × 10 3 –4 × 10 3 days), where our suite of lifetime simulations reveals a favored parameter space with negligible mass loss and enough spin angular momentum to power a GRB jet. For initially nonrotating stars, this provides a lower limit on the final spin above a threshold estimate consistent with forming a postcollapse BH mass of 5–10M ⊙ with a spin parameter ≥ 0.5. For initially rapidly rotating stars, tidal interactions may sustain high spin when mass loss is negligible because the binary is not tidally synchronized.

Hernandez, Angel [Univ. of Colorado, Boulder, CO (↗
NASA NTRS1974

Lunar seismicity, structure, and tectonics

Natural seismic events have been detected by the long-period seismometers at Apollo stations 16, 14, 15, and 12 at annual rates of 3300, 1700, 800, and 700, respectively, with peak activity at 13- to 14-day intervals. The data are used to describe magnitudes, source characteristics, and periodic features of lunar seismicity. In a present model, the rigid lithosphere overlies an asthenosphere of reduced rigidity in which present-day partial melting is probable. Tidal deformation presumably leads to critical stress concentrations at the base of the lithosphere, where moonquakes are found to occur. The striking tidal periodicities in the pattern of moonquake occurrence and energy release suggest that tidal energy is the dominant source of energy released as moonquakes. Thus, tidal energy is dissipated by moonquakes in the lithosphere and probably by inelastic processes in the asthenosphere.

Lammlein, D. R.↗
NASA NTRS1973

Investigation of the environmental change pattern of Japan

The author has identified the following significant results. ERTS-1 imagery clearly identifies the relationships between the status of erosion, effluent patterns affected by the coastal current, and the cultural construction activities. Simple photographic techniques can be used for detecting water mass distribution separately from cloud cover and also noise caused by reflected sunlight from wave surfaces. Polluted water does not diffuse continuously into the oceanic water, but forms masses in the water in the Kuroshio area. The polluted or turbid water in the area just north of the Tomogashima Channel, the south outlet of the Osaka Bay, shows that the northward tidal current runs in a clockwise eddy at the tidal period when the imagery was taken. Such an eddy-like pattern of tidal current had never been revealed by conventional oceanographic data. A front between an oceanic water mass and a polluted water mass runs in a NW-SE direction in the central part of the Osaka Bay. The patterns of turbid water discharged from the Kii River and Yoshino River show a northward tidal current in the North Kii Straits. The pattern of lighter turbid or polluted water located in the northwest region of the North Kii straits suggests the existence of a clockwise eddy in the straits.

Maruyasu, T.↗
NASA NTRS1976

Earth tides, volcanos and climatic change

The effect of variations in tidal stresses on the earth caused by the sun and moon on volcanic activity and climate is investigated. A statistically significant correlation is found between the derivatives of the envelopes of peak tidal stresses at high northern latitudes and the mean temperature of the Northern Hemisphere as reflected in oxygen isotope ratios in the Greenland ice cap. It is suggested that variations in tidal stresses cause changes in the amount of stratospheric dust produced by volcanic activity, which affects the thickness of the stratospheric dust veil and the atmospheric radiation balance. For a simple model, periodic variations in tidal stress account for 13% of the variance in the ice-core temperature record.

Roosen, R. G.↗
NASA NTRS1978

Open ocean tide modelling

Two trends evident in global tidal modelling since the first GEOP conference in 1972 are described. The first centers on the incorporation of terms for ocean loading and gravitational self attraction into Laplace's tidal equations. The second centers on a better understanding of the problem of near resonant modelling and the need for realistic maps of tidal elevation for use by geodesists and geophysicists. Although new models still show significant differences, especially in the South Atlantic, there are significant similarities in many of the world's oceans. This allows suggestions to be made for future locations for bottom pressure gauge measurements. Where available, estimates of M2 tidal dissipation from the new models are significantly lower than estimates from previous models.

Parke, M. E.↗