A three dimensional model of thermospheric dynamics. 3 - Planetary waves
Generation and propagation of tidal waves in three dimensional spherical model of thermospheric dynamics
Mayr, H. G.↗
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The effects of mantle and anelasticity on nutations, earth tides, and tidal variations in rotation rate
The paper models the effects of mantle anelasticity on luni-solar nutations, on tidal deformation, on tidal variations in rotation rate, and on the eigenfrequency of the free core nutation. The results can be used to invert observations to solve for the anelastic contributions to the shear and bulk moduli of the upper and lower mantle. Specific anelastic models are used to numerically estimate the effects of anelasticity on these geodetic observables. The nutation estimates are compared with observational results. Among the conclusions: (1) mantle anelasticity is likely to be the most important source of damping for the free core nutation; (2) present VLBI nutation results are, in principle, accurate enough to usefully bound anelasticity at diurnal periods. But the discrepancy between the VLBI observed nutations and the 1984 IAU nutation model cannot be explained by anelasticity and is not yet well enough understood to allow anelasticity to be determined from the data.
Wahr, John↗
Theoretical aspects of tidal and planetary wave propagation at thermospheric heights
A simple semiquantitative model is presented which allows analytic solutions of tidal and planetary wave propagation at thermospheric heights. This model is based on perturbation approximation and mode separation. The effects of viscosity and heat conduction are parameterized by Rayleigh friction and Newtonian cooling. Because of this simplicity, one gains a clear physical insight into basic features of atmospheric wave propagation. In particular, we discuss the meridional structures of pressure and horizontal wind (the solutions of Laplace's equation) and their modification due to dissipative effects at thermospheric heights. Furthermore, we solve the equations governing the height structure of the wave modes and arrive at a very simple asymptotic solution valid in the upper part of the thermosphere. That 'system transfer function' of the thermosphere allows one to estimate immediately the reaction of the thermospheric wave mode parameters such as pressure, temperature, and winds to an external heat source of arbitrary temporal and spatial distribution. Finally, the diffusion effects of the minor constituents due to the global wind circulation are discussed, and some results of numerical calculations are presented.
Volland, H.↗
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.↗
On Lateral Viscosity Contrast in the Mantle and the Rheology of Low-Frequency Geodynamics
Mantle-wide heterogeneity is largely controlled by deeply penetrating thermal convective currents. These thermal currents are likely to produce significant lateral variation in rheology, and this can profoundly influence overall material behaviour. How thermally related lateral viscosity variations impact models of glacio-isostatic and tidal deformation is largely unknown. An important step towards model improvement is to quantify, or bound, the actual viscosity variations that characterize the mantle. Simple scaling of viscosity to shear-wave velocity fluctuations yields map-views of long- wavelength viscosity variation. These give a general quantitative description and aid in estimating the depth dependence of rheological heterogeneity throughout the mantle. The upper mantle is probably characterized by two to four orders of magnitude variation (peak-to-peak). Discrepant time-scales for rebounding Holocene shorelines of Hudson Bay and southern Iceland are consistent with this characterization. Results are given in terms of a local average viscosity ratio, (Delta)eta(bar)(sub i), of volumetric concentration, phi(sub i). For the upper mantle deeper than 340 km the following reasonable limits are estimated for (delta)eta(bar) approx. equal 10(exp -2): 0.01 less than or equal to phi less than or equal to 0.15. A spectrum of ratios (Delta)eta(bar)(sub i) less than 0.1 at concentration level eta(sub i) approx. equal 10(exp -6) - 10(exp -1) in the lower mantle implies a spectrum of shorter time-scale deformational response modes for second-degree spherical harmonic deformations of the Earth. Although highly uncertain, this spectrum of spatial variation allows a purely Maxwellian viscoelastic rheology simultaneously to explain all solid tidal dispersion phenomena and long-term rebound-related mantle viscosity. Composite theory of multiphase viscoelastic media is used to demonstrate this effect.
Ivins, Erik R.↗
Remote Sensing-Driven Hydrodynamic Modeling in Data-Scarce Regions: Integrating ICESat-2, Sentinel-2, SWOT and Re-analysis Models for Coastal Monitoring
Hydrodynamic models in coastal and estuarine systems are typically constrained by sparse bathymetry, boundary, and validation data, especially in regions where field campaigns are costly or impractical. Here we develop and test a fully satellite-driven framework for hydrodynamic modeling in South Africa’s Langebaan Lagoon without using any local in situ measurements. Bathymetry is derived by training multispectral Sentinel-2 reflectance against ICESat-2 ATL24 photon-derived depths using an XGBoost model optimized with Bayesian search. The final satellite-derived bathymetry reproduces independent ATL24 points with RMSE = 0.45 m and R 2 = 0.97. This bathymetry was used in a depth-averaged Delft3D Flexible Mesh model driven at the open boundary by TPXO tidal harmonics and by ERA5 winds. We validate modeled water surface elevation against 16 SWOT low-rate (250 m, unsmoothed) passes in 2023. SWOT–model comparisons yield an overall RMSE of 0.11 m and R 2 = 0.61, with typical point differences <0.10 m (∼7% of the 1.5 m tidal range), and showed consistent spatial gradients in water level from the offshore boundary, through Saldanha Bay, and into the lagoon. At the offshore boundary, TPXO and SWOT sea surface heights agree closely (R 2 = 0.86). A simple phase adjustment of ∼26,min between TPXO and SWOT lowers the RMSE from 0.18,m to 0.11,m, showing that phase offset accounts for some of the discrepancy, with additional errors likely linked to non-tidal signals. Our results demonstrate that combining passive optical, photon-counting LiDAR, radar interferometry, and global tidal/atmospheric models enables robust, transferrable hydrodynamic modeling in data-scarce coastal systems, offering a cost-effective pathway for monitoring.
ICESat-2↗
Evaluation of Atmospheric Loading and Improved Troposphere Modelling
Forward modeling of non-tidal atmospheric loading displacements at geodetic tracking stations have not routinely been included in Doppler Orbitography and Radiopositionning Integrated by Satellite (DORIS) or Satellite Laser Ranging (SLR) station analyses for either POD applications or reference frame determination. The displacements which are computed from 6-hourly models such as the ECMWF and can amount to 3-10 mm in the east, north and up components depending on the tracking station locations. We evaluate the application of atmospheric loading in a number ways using the NASA GSFC GEODYN software: First we assess the impact on SLR & DORIS-determined orbits such as Jason-2, where we evaluate the impact on the tracking data RMS of fit and how the total orbits are changed with the application of this correction. Preliminary results show an RMS radial change of 0.5 mm for Jason-2 over 54 cycles and a total change in the Z-centering of the orbit of 3 mm peak-to-peak over one year. We also evaluate the effects on other DORIS-satellites such as Cryosat-2, Envisat and the SPOT satellites. In the second step, we produce two SINEX time series based on data from available DORIS satellites and assess the differences in WRMS, scale and Helmert translation parameters. Troposphere refraction is obviously an important correction for radiometric data types such as DORIS. We evaluate recent improvements in DORIS processing at GSFC including the application of the Vienna Mapping Function (VMF1) grids with a-priori hydrostatic (VZHDs) and wet (VZWDs) zenith delays. We reduce the gridded VZHD at the stations height using pressure and temperature derived from GPT (strategy 1) and Saastamoinen. We discuss the validation of the VMF1 implementation and its application to the Jason-2 POD processing, compared to corrections using the Niell mapping function and the GMF. Using one year of data, we also assess the impact of the new troposphere corrections on the DORIS-only solutions, most importantly on the scale of the weekly solutions.
Zelensky, Nikita P.↗
Tidal frequency estimation for closed basins
A method was developed for determining the fundamental tidal frequencies for closed basins of water, by means of an eigenvalue analysis. The mathematical model employed, was the Laplace tidal equations.
Eades, J. B., Jr.↗
Water resources planning for rivers draining into mobile bay
A hydrodynamic model describing water movement and tidal elevation is formulated, computed, and used to provide basic data about water quality in natural systems. The hydrodynamic model is based on two-dimensional, unsteady flow equations. The water mass is considered to be reasonably mixed such that integration (averaging) in the depth direction is a valid restriction. Convective acceleration, the Coriolis force, wind and bottom interactions are included as contributing terms in the momentum equations. The solution of the equations is applied to Mobile Bay, and used to investigate the influence that river discharge rate, wind direction and speed, and tidal condition have on water circulation and holdup within the bay. Storm surge conditions, oil spill transport, artificial island construction, dredging, and areas subject to flooding are other topics which could be investigated using the mathematical modeling approach.
Ng, S.↗
Probing the tides in interacting galaxy pairs
Detailed spectroscopic and imaging observations of colliding elliptical galaxies revealed unmistakable diagnostic signatures of the tidal interactions. It is possible to compare both the distorted luminosity distributions and the disturbed internal rotation profiles with numerical simulations in order to model the strength of the tidal gravitational field acting within a given pair of galaxies. Using the best-fit numerical model, one can then measure directly the mass of a specific interacting binary system. This technique applies to individual pairs and therefore complements the classical methods of measuring the masses of galaxy pairs in well-defined statistical samples. The 'personalized' modeling of galaxy pairs also permits the derivation of each binary's orbit, spatial orientation, and interaction timescale. Similarly, one can probe the tides in less-detailed observations of disturbed galaxies in order to estimate some of the physical parameters for larger samples of interacting galaxy pairs. These parameters are useful inputs to the more universal problems of (1) the galaxy merger rate, (2) the strength and duration of the driving forces behind tidally stimulated phenomena (e.g., starbursts and maybe quasi steller objects), and (3) the identification of long-lived signatures of interaction/merger events.
Borne, Kirk D.↗
Tidal Friction in the Earth-Moon System and Laplace Planes: Darwin Redux
The dynamical evolution of the Earth-Moon system due to tidal friction is treated here. George H. Darwin used Laplace planes (also called proper planes) in his study of tidal evolution. The Laplace plane approach is adapted here to the formalisms of W.M. Kaula and P. Goldreich. Like Darwin, the approach assumes a three-body problem: Earth, Moon, and Sun, where the Moon and Sun are point-masses. The tidal potential is written in terms of the Laplace plane angles. The resulting secular equations of motion can be easily integrated numerically assuming the Moon is in a circular orbit about the Earth and the Earth is in a circular orbit about the Sun. For Earth-Moon distances greater than ∼10 Earth radii, the Earth's approximate tidal response can be characterized with a single parameter, which is a ratio: a Love number times the sine of a lag angle divided by another such product. For low parameter values it can be shown that Darwin's low-viscosity molten Earth, M. Ross's and G. Schubert's model of an Earth near melting, and Goldreich's equal tidal lag angles must all give similar histories. For higher parameter values, as perhaps has been the case at times with the ocean tides, the Earth's obliquity may have decreased slightly instead of increased once the Moon's orbit evolved further than 50 Earth radii from the Earth, with possible implications for climate. This is contrast to the other tidal friction models mentioned, which have the obliquity always increasing with time. As for the Moon, its orbit is presently tilted to its Laplace plane by 5.2deg. The equations do not allow the Moon to evolve out of its Laplace plane by tidal friction alone, so that if it was originally in its Laplace plane, the tilt arose with the addition of other mechanisms, such as resonance passages.
Darwin Redux↗
A three-dimensional model of thermosphere dynamics. I - Heat input and eigenfunctions. II - Tidal waves. III - Planetary waves.
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Volland, H.↗
Occultation of Epsilon Geminorum by Mars. III - Temperature structure of the Martian upper atmosphere
High-quality photoelectric observations of the April 8, 1976, occultation of Epsilon Gem by Mars are analyzed which were obtained at five different observatories. Temperature profiles are derived by numerical inversion of the star's light curves and found to be in mutual agreement. This is taken as evidence for the presence of strong atmospheric waves in the Martial upper atmosphere between number densities of 10 to the 13th and 10 to the 15th per cu cm. It is estimated that the vertical wavelength is about 20 km, the horizontal wavelength is greater than 600 km, and the peak-to-peak wave amplitude is approximately 40 K. The results are shown to be qualitatively consistent with Zurek's (1976) model of thermally driven tidal modes. No compelling evidence for turbulence effects is found in the occultation data.
French, R. G.↗
Modelling the pole tide and its effect on the earth's rotation
The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, both analytical and numerical models for the pole tide are constructed. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.
Carton, J. A.↗
The derivation of sub-canopy surface terrain models of coastal forests using synthetic aperture radar
Radar data acquired by the Shuttle Imaging Radar-B mission covering a portion of the Mouths of the Ganges forests were used to create a terrain model for use in determining tidal flow and eventual nutrient transport from the forest to the marine habitat. Results show that good digital topographic terrain models of wet coastal forests can be generated using multiple sets of L-band SAR and ancillary tide elevation data. The dominance of the interaction phenomenon in the radar backscatter of flooded forests can be used to create sub-canopy inundation maps which when merged with tide surface data can be used to generate reasonable topographic models. Ideally models could be improved by using multiple sets of data at a constant incidence angle over the total tide range. The optimal angle for the SAR depends upon the characteristics of the forest. The range of 46 to 57 deg seems applicable to the 12.5 m tall closed canopy in this example. Such models can be an extremely valuable tool for studying and mapping the mangal ecosystem.
Imhoff, M. L.↗
Effects of Long Period Ocean Tides on the Earth's Rotation
The spectra of polar motion excitation functions exhibit enhanced power in the fortnightly tidal band. This enhanced power is attributed to ocean tidal excitation. Ocean tide models predict polar motion excitation effects that differ with each other, and with observations, by factors as large as 2-3. There is a need for inproved models for the effect of long-period ocean tides on Earth's rotation.
oceans tides Earth's rotation↗
Along-Orbit Analysis of GRACE Follow-On Inter-Satellite Laser Ranging Measurements for Sub-Monthly Surface Mass Variations
We examined the sensitivity of GRACE Follow-On (GRACE-FO) laser ranging interferometer (LRI) measurements to sub-monthly time-variable gravity (TVG) signals caused by transient, high-frequency mass changes in the Earth system. GRACE-FO LRI provides complementary inter-satellite ranging measurements with higher precision over a wider range of frequencies than the baseline K-band microwave ranging system. The common approach for studying mass variation relies on the inverted TVG or mascon solutions over a period of, for example, one month or 10 days which are adversely affected by temporal aliasing and/or smoothing. In this article, we present the alternative along-orbit analysis methodology in terms of line-of-sight gravity difference (LGD) to fully exploit the higher precision LRI measurements for examination of sub-monthly mass changes. The discrepancy between “instantaneous” LGD LRI observations and monthly mean LGD (from Level-2 data) at satellite altitude indicates the sub-monthly gravitational variability not captured by monthly-mean solutions. In conjunction with the satellite ocean altimetry observations, high frequency non-tidal atmosphere and ocean models, and hydrology models, we show that the LGD LRI observations detect the high-frequency oceanic mass variability in the Argentine Basin and the Gulf of Carpentaria, and sub-monthly variations in surface (river) water in the Amazon Basin. We demonstrate the benefits gained from repeat ground track analysis of GRACE-FO LRI data in the case of the Amazon surface water flow. The along-orbit analysis methodology based on LGD LRI time series presented here is especially suitable for quantifying temporal and spatial evolution of extreme, rapidly changing mass variations.
Khosro Ghobadi-Far↗
The rings of Uranus - Nature and origin
Effects of a resonance between a set of ring particles and individual satellites are considered. It is suggested that the resonances are 1:1 for the rings of Uranus and that each ring must contain an as-yet unseen satellite. A model is proposed in which the rings of Uranus were caused by small satellites that entered the Roche zone due to tidal drag. According to this model, the satellites gradually lost material from their surfaces in this zone, the particles left a satellite with relatively low speeds and must have entered orbits similar to that of the satellite, and the gravitational force of the satellite compelled these particles to remain in a narrow sharply defined ring.
Dermott, S. F.↗