Polar Motion Research Articles

A Comparative Study of Interannual Oscillation Models for Determining Geophysical Polar Motion Excitations

Similar to seasonal and intraseasonal variations in polar motion (PM), interannual variations are also largely caused by changes in the angular momentum of the Earth’s geophysical fluid layers composed of the atmosphere, the oceans, and in-land hydrologic flows (AOH). Not only are inland freshwater systems crucial for interannual PM fluctuations, but so are atmospheric surface pressures and winds, oceanic currents, and ocean bottom pressures. However, the relationship between observed geodetic PM excitations and hydro-atmospheric models has not yet been determined. This is due to defects in geophysical models and the partial knowledge of atmosphere–ocean coupling and hydrological processes. Therefore, this study provides an analysis of the fluctuations of PM excitations for equatorial geophysical components χ1 and χ2 at interannual time scales. The geophysical excitations were determined from different sources, including atmospheric, ocean models, Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On data, as well as from the Land Surface Discharge Model. The Multi Singular Spectrum Analysis method was applied to retain interannual variations in χ1 and χ2 components. None of the considered mass and motion terms studied for the different atmospheric and ocean models were found to have a negligible effect on interannual PM. These variables, derived from different Atmospheric Angular Momentum (AAM) and Oceanic Angular Momentum (OAM) models, differ from each other. Adding hydrologic considerations to the coupling of AAM and OAM excitations was found to provide benefits for achieving more consistent interannual geodetic budgets, but none of the AOH combinations fully explained the total observed PM excitations.

First Evidence of Correlation Between Evapotranspiration and Gravity at a Daily Time Scale From Two Vertically Spaced Superconducting Gravimeters

AbstractEstimating evapotranspiration (ET) is a primary challenge in modern hydrology. Hydrogravimetry is an integrative approach providing highly precise continuous measurement of gravity acceleration. However, large‐scale effects (e.g., tides, polar motion, atmospheric loading) limit the fine time‐scale interpretation of the gravity data and processing leads to residual signal noise. To circumvent this limitation, we exploited the difference between two superconducting gravimeters (SGs) vertically spaced by 512 m. The gravity difference allows to remove common large‐scale effects. Daily variation of the gravity difference is significantly correlated with daily evapotranspiration as estimated using the water balance model SimpKcET (p‐value = 4.10−10). However, this approach is effective only during rain‐free periods. In the future, comparison with direct ET measurements (e.g., eddy‐covariance, scintillometer) may confirm and strengthen our interpretation. Improved hydrogravimetric data processing could extend the proposed approach to other experimental sites equipped with a single SG.

Towards Understanding the Interconnection between Celestial Pole Motion and Earth's Magnetic Field Using Space Geodetic Techniques.

The understanding of forced temporal variations in celestial pole motion (CPM) could bring us significantly closer to meeting the accuracy goals pursued by the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG), i.e., 1 mm accuracy and 0.1 mm/year stability on global scales in terms of the Earth orientation parameters. Besides astronomical forcing, CPM excitation depends on the processes in the fluid core and the core–mantle boundary. The same processes are responsible for the variations in the geomagnetic field (GMF). Several investigations were conducted during the last decade to find a possible interconnection of GMF changes with the length of day (LOD) variations. However, less attention was paid to the interdependence of the GMF changes and the CPM variations. This study uses the celestial pole offsets (CPO) time series obtained from very long baseline interferometry (VLBI) observations and data such as spherical harmonic coefficients, geomagnetic jerk, and magnetic field dipole moment from a state-of-the-art geomagnetic field model to explore the correlation between them. In this study, we use wavelet coherence analysis to compute the correspondence between the two non-stationary time series in the time–frequency domain. Our preliminary results reveal interesting common features in the CPM and GMF variations, which show the potential to improve the understanding of the GMF’s contribution to the Earth’s rotation. Special attention is given to the corresponding signal between FCN and GMF and potential time lags between geomagnetic jerks and rotational variations.

Application of singular spectrum analysis and multilayer perceptron in the mid-long-term polar motion prediction

Long-term prediction parameters of polar motion (PM) with high precision have an important significance in understanding Earth geophysical processes in the future. The multilayer perceptron (MLP) is introduced into PM prediction and we try for the first time to combine MLP with autoregressive moving average model (ARMA) and singular spectrum analysis (SSA) for the mid-long-term prediction of PM. The principal components of PM were extracted and predicted by SSA first. Then, the combined MLP and ARMA were used to predict the residual term. The PM predictions were obtained by adding the principal components and the residual predictions. Applying this proposed method, 157 500-day and 12 5-year lead time predictions of PM were made based on IERS 14 C04 product. The results showed that the proposed method performed well in the mid-long-term period of PM predictions, which was superior to IERS Bulletin A.

Correction of precession-nutation and polar motion in analytical solutions of satellite equations of motion

In the analytical solutions of satellite equations of motion, the precession-nutation and polar motion (PNPM) effects are usually not considered. For the first-order orbit theory, the magnitude of these effects is small enough to be neglected; however, it might be a different case for a higher order solution, which could possibly be applied in precise orbit prediction or determination in the near future. To clarify the influence of PNPM acting on the Keplerian elements of near-Earth satellite orbits in analytical theory, this paper gives both theoretical and numerical analysis of these effects based on Gaussian equations of motion. From the analysis, the impact of PNPM can be divided into two parts. The first part is a rotational error on the perturbing force vector since the force vector is converted into a coordinate system without considering PNPM; the other part is caused by the error of the satellite coordinates computed in the Earth-Centered Earth-Fixed (ECEF) or True-of-Date (TOD) coordinate system when the PNPM effects are neglected. More importantly, an easy-to-use semi-analytical correction procedure is proposed. It can be applied to the Keplerian elements directly without having to derive again the solutions. With this method, the error caused by neglecting the PNPM can be well corrected.

Ratchet transport of self-propelled chimeras in an asymmetric periodic structure

We studied the rectified transport of underdamped particles subject to phase lag in an asymmetric periodic structure. When the inertia effect is considered, it is possible to observe reversals of the average velocity with small self-propelled force, whereas particles always move in the positive direction with large self-propelled force. The introduction of phase lag leads particles to follow circular orbits and suppress the polar motion. In addition, this can adjust the direction of particle motion. There exists an optimal value of polar interaction strength at which the rectification is maximal. These results open the way for many application processes, such as spatial sorting of particles mixture and separation based on their physical properties.

Resonant self-force effects in extreme-mass-ratio binaries: A scalar model

Extreme-mass ratio inspirals (EMRIs), compact binaries with small mass ratios $\epsilon\ll 1$, will be important sources for low-frequency gravitational wave detectors. Almost all EMRIs will evolve through important transient orbital $r\theta$ resonances, which will enhance or diminish their gravitational wave flux, thereby affecting the phase evolution of the waveforms at $O(\epsilon^{1/2})$ relative to leading order. While modeling the local gravitational self-force (GSF) during resonances is essential for generating accurate EMRI waveforms, so far the full GSF has not been calculated for an $r\theta$-resonant orbit owing to computational demands of the problem. As a first step we employ a simpler model, calculating the scalar self-force (SSF) along $r\theta$-resonant geodesics in Kerr spacetime. We demonstrate two ways of calculating the $r\theta$-resonant SSF (and likely GSF), with one method leaving the radial and polar motions initially independent as if the geodesic is nonresonant. We illustrate results by calculating the SSF along geodesics defined by three $r\theta$-resonant ratios (1:3, 1:2, 2:3). We show how the SSF and averaged evolution of the orbital constants vary with the initial phase at which an EMRI enters resonance. We then use our SSF data to test a previously proposed integrability conjecture, which argues that conservative effects vanish at adiabatic order during resonances. We find prominent contributions from the conservative SSF to the secular evolution of the Carter constant, $\langle \dot{\mathcal{Q}}\rangle$, but these nonvanishing contributions are on the order of, or less than, the estimated uncertainties of our self-force results. The uncertainties come from residual, incomplete removal of the singular field in the regularization process. Higher order regularization parameters, once available, will allow definitive tests of the integrability conjecture.

Polyphony of Short-Term Climatic Variations

It is widely accepted to believe that humanity is mainly responsible for the worldwide temperature growth during the period of instrumental meteorological observations. This paper aims to demonstrate that it is not so simple. Using a wavelet analysis on the example of the time series of the global mean near-surface air temperature created at the American National Climate Data Center (NCDC), some complex structures of inter-annual to multidecadal global mean temperature variations were discovered. The origin of which seems to be better attributable to the Chandler wobble in the Earth’s Pole motion, the Luni-Solar nutation, and the solar activity cycles. Each of these external forces is individually known to climatologists. However, it is demonstrated for the first time that responses of the climate system to these external forces in their integrity form a kind of polyphony superimposed on a general warming trend. Certainly, the general warming trend as such remains to be unconsidered. However, its role is not very essential in the timescale of a few decades. Therefore, it is this polyphony that will determine climate evolution in the nearest future, i.e., during the time most important for humanity currently.

Modeling ocean-induced rapid Earth rotation variations: an update

We revisit the problem of modeling the ocean’s contribution to rapid, non-tidal Earth rotation variations at periods of 2–120 days. Estimates of oceanic angular momentum (OAM, 2007–2011) are drawn from a suite of established circulation models and new numerical simulations, whose finest configuration is on a ^circ grid. We show that the OAM product by the Earth System Modeling Group at GeoForschungsZentrum Potsdam has spurious short period variance in its equatorial motion terms, rendering the series a poor choice for describing oceanic signals in polar motion on time scales of less than sim 2 weeks. Accounting for OAM in rotation budgets from other models typically reduces the variance of atmosphere-corrected geodetic excitation by sim 54% for deconvolved polar motion and by sim 60% for length-of-day. Use of OAM from the ^circ model does provide for an additional reduction in residual variance such that the combined oceanic–atmospheric effect explains as much as 84% of the polar motion excitation at periods < 120 days. Employing statistical analysis and bottom pressure changes from daily Gravity Recovery and Climate Experiment solutions, we highlight the tendency of ocean models run at a 1^circ grid spacing to misrepresent topographically constrained dynamics in some deep basins of the Southern Ocean, which has adverse effects on OAM estimates taken along the 90^circ meridian. Higher model resolution thus emerges as a sensible target for improving the oceanic component in broader efforts of Earth system modeling for geodetic purposes.

Phospholipids in Motion: High-Resolution 31P NMR Field Cycling Studies.

Diverse phospholipid motions are key to membrane function but can be quite difficult to untangle and quantify. High-resolution field cycling 31P NMR spin-lattice relaxometry, where the sample is excited at high field, shuttled in the magnet bore for low-field relaxation, then shuttled back to high field for readout of the residual magnetization, provides data on phospholipid dynamics and structure. This information is encoded in the field dependence of the 31P spin-lattice relaxation rate (R1). In the field range from 11.74 down to 0.003 T, three dipolar nuclear magnetic relaxation dispersions (NMRDs) and one due to 31P chemical shift anisotropy contribute to R1 of phospholipids. Extraction of correlation times and maximum relaxation amplitudes for these NMRDs provides (1) lateral diffusion constants for different phospholipids in the same bilayer, (2) estimates of how additives alter the motion of the phospholipid about its long axis, and (3) an average 31P-1H angle with respect to the bilayer normal, which reveals that polar headgroup motion is not restricted on a microsecond timescale. Relative motions within a phospholipid are also provided by comparing 31P NMRD profiles for specifically deuterated molecules as well as 13C and 1H field dependence profiles to that of 31P. Although this work has dealt exclusively with phospholipids in small unilamellar vesicles, these same NMRDs can be measured for phospholipids in micelles and nanodisks, making this technique useful for monitoring lipid behavior in a variety of structures and assessing how additives alter specific lipid motions.

The Contribution of a Newly Unraveled 64 Years Common Oscillation on the Estimate of Present‐Day Global Mean Sea Level Rise

AbstractThe multidecadal fluctuations in sea level changes play an important role in the exact quantification of present‐day global mean sea level (GMSL) rise and its acceleration. Here, we use an array processing technique (optimal sequence estimation) to analyze 44 global tide gauge (TG) sea‐level records with identical January 1933–December 2019 data spans. The results reveal for the first time a common 64.0 ± 3 years periodic oscillation with a spherical harmonic Y21 spatial pattern. Based on the estimated equivalent “excitation” amplitude (A = 47.7 ± 2 mm) and phase (φ = −0.406 rad), we constructed a global model for this 64 years sea‐level fluctuation. The complex amplitudes of the extracted ∼64 years fluctuation from 94 TG records with different data spans, and of two GMSL time series are consistent with the corresponding results predicted by the constructed model using the stacking results using 44 TGs. We find that the 64 years oscillation has significant contributions on the estimate of reconstructed GMSL trend: it contributed about 24% to the sea‐level trend during 1993–2014 and cause a relative deceleration during 2024–2055; while it contributes slightly to the satellite‐based GMSL trend estimates during 1993–2020. We confirm that this 64 years signal is not originated from the Earth's polar motion; however, it has good consistency with the Earth's magnetic field dipole changes, and with the ∼65 years oscillation in the ΔLOD, which suggests that this 64 years signal could come from core motions. We believe our results unravel a new understanding of the mechanisms of GMSL's long‐term fluctuations within the Earth system.

Analysis and prediction of polar motion using MSSA method

Polar motion is the movement of the Earth's rotational axis relative to its crust, reflecting the influence of the material exchange and mass redistribution of each layer of the Earth on the Earth's rotation axis. To better analyze the temporally varying characteristics of polar motion, multi-channel singular spectrum analysis (MSSA) was used to analyze the EOP 14 C04 series released by the International Earth Rotation and Reference System Service (IERS) from 1962 to 2020, and the amplitude of the Chandler wobbles were found to fluctuate between 20 and 200 mas and decrease significantly over the last 20 years. The amplitude of annual oscillation fluctuated between 60 and 120 mas, and the long-term trend was 3.72 mas/year, moving towards N56.79 °W. To improve prediction of polar motion, the MSSA method combining linear model and autoregressive moving average model was used to predict polar motion with ahead 1 year, repeatedly. Comparing to predictions of IERS Bulletin A, the results show that the proposed method can effectively predict polar motion, and the improvement rates of polar motion prediction for 365 days into the future were approximately 50% on average.

Madden-Julian oscillation winds excite an intraseasonal see-saw of ocean mass that affects Earth\u2019s polar motion

Strong large-scale winds can relay their energy to the ocean bottom and elicit an almost immediate intraseasonal barotropic (depth independent) response in the ocean. The intense winds associated with the Madden-Julian Oscillation over the Maritime Continent generate significant intraseasonal basin-wide barotropic sea level variability in the tropical Indian Ocean. Here we show, using a numerical model and a network of in-situ bottom pressure recorders, that the concerted barotropic response of the Indian and the Pacific Ocean to these winds leads to an intraseasonal see-saw of oceanic mass in the Indo-Pacific basin. This global-scale mass shift is unexpectedly fast, as we show that the mass field of the entire Indo-Pacific basin is dynamically adjusted to Madden-Julian Oscillation in a few days. We find this large-scale ocean see-saw, induced by the Madden-Julian Oscillation, has a detectable influence on the Earth’s polar axis motion, in particular during the strong see-saw of early 2013.

Einstein’s Equation of motion for exterior test particles with spherical mass distribution having varied field, time and radial distance; Golden metric tensors approach.

Golden metric tensors exterior to hypothetical distribution of mass whose field varies with time and radial distance have been used to construct the coefficient of affine connections that invariably was used to obtained the Einstein’s equations of motion for test particles of non-zero rest masses. The expression for the variation of time on a clock moving in this gravitational field was derived using the time equation of motion. The test particles in this field under the condition of pure polar motion have an inverse square dependence velocity which depends on radial distance. Our result indicates that despite using the golden metric tensor, the inverse square dependence of the velocity on radial distance has not been changed.

Optimal VLBI baseline geometry for UT1-UTC Intensive observations

One of the main tasks of Very Long Baseline Interferometry (VLBI) is the rapid determination of the highly variable Earth’s rotation expressed through the difference between Universal Time UT1 and Coordinated Universal Time UTC (dUT1). For this reason, dedicated one hour, single baseline sessions, called “Intensives”, are observed on a daily basis. Thus far, the optimal geometry of Intensive sessions was understood to include a long east–west extension of the baseline to ensure a dUT1 estimation with highest accuracy. In this publication, we prove that long east–west baselines are the best choice only for certain lengths and orientations. In this respect, optimal orientations may even require significant inclination of the baseline with respect to the equatorial plane. The basis of these findings is a simulation study with subsequent investigations in the partial derivatives of the observed group delays tau with respect to dUT1 partial tau /partial dUT1. Almost 3000 baselines between artificial stations located on a regular 10 times 10 degree grid are investigated to derive a global and generally valid picture about the best length and orientation of Intensive baselines. Our results reveal that especially equatorial baselines or baselines with a center close to the equatorial plane are not suited for Intensives although they provide a good east–west extension. This is explained by the narrow right ascension band of visible sources and the resulting lack of variety in the partial derivatives. Moreover, it is shown that north–south baselines are also capable of determining dUT1 with reasonable accuracy, given that the baseline orientation is significantly different from the Earth rotation axis. However, great care must be taken to provide accurate polar motion a priori information for these baselines. Finally, we provide a better metric to assess the suitability of Intensive baselines based on the effective spread of partial tau /partial dUT1.

The ocean pole tide loading and its effect on GPS position time-series

SUMMARY The changes in the centrifugal force induced by polar motion perturb the ocean, causing an ocean pole tide. The induced displacements due to the ocean pole tide, namely ocean pole tide loading (OPTL), previously ignored, raises the concerns in the GPS data processing with the increasing accuracy of Global Position System (GPS) technique. Though the amplitude of this effect is small, it is worth to demonstrate the magnitude and its impact on GPS solutions of the processing choices for correcting it from observations or onto estimated coordinates. For OPTL modelling, subdaily polar motion can introduce annual variations in OPTL with the small magnitudes in micrometres. The new secular pole model can cause OPTL vertical velocity difference up to 0.03 mm yr−1 compared with the mean pole model of International Earth Rotation and Reference System Service Conventions (2010). The OPTL deformation is dominated by the annual (∼365.25 d) and Chandler (∼433 d) periods, and the largest peak-to-peak variations can reach 0.70, 0.84 and 2.38 mm for East, North and Up components, respectively. We then investigate the effects of OPTL correction on GPS daily positions of 133 stations from 2014 to 2018. The root mean square of OPTL induced GPS daily displacements can reach submillimetre level. In most cases, a posteriori OPTL correction with daily averaged values applied onto the coordinates is acceptable considering the small deviation between the solution removing OPTL from coordinates and the solution correcting OPTL from observations. However, this does not hold when GPS coordinates have been aligned to a secular reference frame, as the annual/Chandler variations of OPTL would be biased. When reference frame alignment is required, either OPTL correction at observation level or a posteriori OPTL correction before reference frame alignment is recommended. Furthermore, we have demonstrated that the effects of OPTL on the annual variations of GPS position time-series can reach as much as 0.4 mm in the verticals. It has limited effect on the linear velocity and reduction of the residuals scatter (annual variations excluded), within Global Geodetic Observing System requirements for the future terrestrial reference frame at millimetre level.

Kriging-based prediction of the Earth’s pole coordinates

Abstract Coordinates of the Earth’s pole represent two out of five Earth orientation parameters describing Earth’s rotation. They are necessary in transformation between celestial reference frame and terrestrial reference frame and what goes further in precise positioning and navigation, applications in astronomy, communication with outer space objects. Complexity of measuring techniques and data processing involved in the pole coordinates determination make it impossible to obtain them in real-time mode, hence a prediction problem of the polar motion emerges. In this study, geostatistical prediction methods, i. e., simple and ordinary kriging are applied. Millions of predictions have been performed to draw reasonable conclusions on prediction capabilities of applied kriging variants. The study is intended in ultra-short-term prediction (up to 15 days into the future) using the IERS EOP 14 C04 (IAU2000A) and IERS EOP 05 C04 (IAU2000A) series as a reference. Mean absolute prediction errors (for days 1–15) with respect to IERS 14 C04 are ranging 0.66–5.25 mas for PMx and 0.47–3.59 mas for PMy. On the other hand, for IERS 05 C04 the values are 0.60–4.95 mas and 0.44–3.29 mas for PMx and PMy; respectively. The results indicate competitiveness of the introduced methods with existing ones.

Distribution of electromagnetic energy density in a dispersive and dissipative metamaterial

The distribution of electromagnetic energy density in a dispersive and dissipative metamaterial consisting of arrays of wires and split-ring resonators is obtained, using a simple approach. We show energy stored in the system can be regarded to consist of energy density of electric and magnetic fields plus energy density terms related to response of the medium. To derive energy density formulas of the medium, we compare equations of motion of polarization and magnetization of the system with corresponding differential equations of appropriate RLC circuits.

Jurassic fast polar shift rejected by a new high-quality paleomagnetic pole from southwest Greenland

A selective compilation of paleomagnetic data from North America indicates that a vast amount of rapid polar motion occurred in Late Jurassic time. The over 30° polar shift that accumulated during a relatively short time interval (~160–145 Ma) suggests an episode of fast true polar wander (TPW) and was referred to as the Jurassic “monster polar shift” by some workers. However, this rapid TPW event is not supported by paleomagnetic data on a global scale. Here, we scrutinize the Jurassic apparent polar wander path (APWP) by virtue of a new paleomagnetic and 40Ar/39Ar geochronology study of Mesozoic coast-parallel dykes exposed in southwest Greenland. Combined with existing geochronological data, our results show that the dykes were emplaced during a prolonged period centered at 147.6 ± 3.4 Ma (2σ). A primary nature of the characteristic remanent magnetization is supported by multiple positive baked contact tests and a reversal test. The paleomagnetic pole calculated from 40 site-mean paleomagnetic directions is located at Plat = 69.3°S, Plong = 5.0°E (A95 = 4.6°), or at Plat = 73.9°S and Plong = 0.4°E when reconstructed to North America. Our new high-quality paleomagnetic pole and an updated global APWP do not support the fast Jurassic polar shift but instead indicate steady polar motion with moderate rates of about 0.7°/Myr. The new pole effectively reduces the mismatch between the APWPs for Laurentia and Europe. Our critical reassessment of the monster polar shift indicates that it may be an artifact of paleomagnetic and geochronological data that were previously used to argue for its existence.

Resonant self-force effects in extreme-mass-ratio binaries: A scalar model

Extreme-mass-ratio inspirals (EMRIs), compact binaries with small mass-ratios $\epsilon\ll 1$, will be important sources for low-frequency gravitational wave detectors. Almost all EMRIs will evolve through important transient orbital $r\theta$-resonances, which will enhance or diminish their gravitational wave flux, thereby affecting the phase evolution of the waveforms at $O(\epsilon^{1/2})$ relative to leading order. While modeling the local gravitational self-force (GSF) during resonances is essential for generating accurate EMRI waveforms, so far the full GSF has not been calculated for an $r\theta$-resonant orbit owing to computational demands of the problem. As a first step we employ a simpler model, calculating the scalar self-force (SSF) along $r\theta$-resonant geodesics in Kerr spacetime. We demonstrate two ways of calculating the $r\theta$-resonant SSF (and likely GSF), with one method leaving the radial and polar motions initially independent as if the geodesic is non-resonant. We illustrate results by calculating the SSF along geodesics defined by three $r\theta$-resonant ratios (1:3, 1:2, 2:3). We show how the SSF and averaged evolution of the orbital constants vary with the initial phase at which an EMRI enters resonance. We then use our SSF data to test a previously-proposed integrability conjecture, which argues that conservative effects vanish at adiabatic order during resonances. We find prominent contributions from the conservative SSF to the secular evolution of the Carter constant, $\langle \dot{\mathcal{Q}}\rangle$, but these non-vanishing contributions are on the order of, or less than, the estimated uncertainties of our self-force results. The uncertainties come from residual, incomplete removal of the singular field in the regularization process. Higher order regularization parameters, once available, will allow definitive tests of the integrability conjecture.