Polar motion prediction using the combination of SSA and ARMA

High-precision polar motion(PM) prediction is of important significance in astronomy, geodesy, aviation,hydrographic mapping, interstellar navigation, and so on. SSA can effectively extract the trend and period terms of PM,in the process of achieving high-precision medium-and long-term polar motion prediction,it is necessary to solve the end effect problem and overfitting problem of SSA forecasting method;therefore, ARMA was applied to decreasethe end effect, and a suitable combination of reconstructed components was determined to avoid the high variance reaction of SSA overfitting. Based on the decomposition and reconstruction of the PM by SSA, the reconstructed components are determined to participate in the SSA iterative fitting model according to the variance contribution rate. The combination of the reconstructed components representing the polar motion period term and the trend term is determined according to the correlation analysis of the selected reconstructed components. After the above work, the principal component prediction sequence is obtained by fitting the period term and the trend term to convergence, respectively, and then, the SSA end effect is modified, and the residual term is predicted based on ARMA. The test results show that he prediction accuracy of SSA + ARMA at the front of the X and Y directions are improved by 96.90% and 97.53% compared with those of SSA, respectively,and the forecast accuracy of 365 days are improved by 37.93% and 19.53% in the X and Y directions compared with those of Bulletin A, respectively.

A new polar motion prediction method combined with the difference between polar motion series

After the first Earth Orientation Parameters Prediction Comparison Campaign(1 st EOP PCC),the traditional method using least-squares extrapolation and autoregressive(LS+AR)models was considered as one of the polar motion prediction methods with higher accuracy.The traditional method predicts individual polar motion series separately,which has a single input data and limited improvement in prediction accuracy.To address this problem,this paper proposes a new method for predicting polar motion by combining the difference between polar motion series.The X,Y,and Y-X series were predicted separately using LS+AR models.Then,the new forecast value of X series is obtained by combining the forecast value of Y series with that of Y-X series;the new forecast value of Y series is obtained by combining the forecast value of X series with that of Y-X series.The hindcast experimental comparison results from January 1,2011 to April 4,2021 show that the new method achieves a maximum improvement of 12.95%and 14.96%over the traditional method in the X and Y directions,respectively.The new method has obvious advantages compared with the differential method.This study tests the stability and superiority of the new method and provides a new idea for the research of polar motion prediction.

Improvement of the prediction accuracy of polar motion using empirical mode decomposition

Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode decomposition （EMD）, which is increasingly popular and has advantages over classical wavelet decomposition, can be used to remove short period variations from observed time series of pole co- ordinates. A hybrid model combing EMD and extreme learning machine （ELM）, where high frequency signals are removed and processed time series is then modeled and predicted, is summarized in this paper. The prediction performance of the hybrid model is compared with that of the ELM-only method created from original time series. The results show that the proposed hybrid model outperforms the pure ELM method for both short-term and long-term prediction of pole coordinates. The improvement of prediction accuracy up to 360 days in the future is found to be 24.91% and 26.79% on average in terms of mean absolute error （MAE） for the xp and yp components of pole coordinates, respectively.

IGS polar motion measurement accuracy

We elaborate an error budget for the long-term accuracy of IGS（International Global Navigation Satellite System Service） polar motion estimates, concluding that it is probably about 25-30 μas（1-sigma）overall, although it is not possible to quantify possible contributions（mainly annual） that might transfer directly from aliases of subdaily rotational tide errors. The leading sources are biases arising from the need to align daily, observed terrestrial frames, within which the pole coordinates are expressed and which are continuously deforming, to the secular, linear international reference frame. Such biases are largest over spans longer than about a year. Thanks to the very large number of IGS tracking stations, the formal covariance errors are much smaller,around 5 to 10 μas. Large networks also permit the systematic frame-related errors to be more effectively minimized but not eliminated. A number of periodic errors probably also influence polar motion results, mainly at annual, GPS（Global Positioning System） draconitic, and fortnightly periods, but their impact on the overall error budget is unlikely to be significant except possibly for annual tidal aliases. Nevertheless, caution should be exercised in interpreting geophysical excitations near any of the suspect periods.

Improved geophysical excitations constrained by polar motion observations and GRACE/SLR time-dependent gravity

At seasonal and intraseasonal time scales, polar motions are mainly excited by angular momentum fluctuations due to mass redistributions and relative motions in the atmosphere, oceans, and continental water, snow, and ice, which are usually provided by various global atmospheric, oceanic, and hydrological models（some with meteorological observations assimilated; e.g., NCEP, ECCO, ECMWF, OMCT and LSDM etc.）. Unfortunately, these model outputs are far from perfect and have notable discrepancies with respect to polar motion observations, due to non-uniform distributions of meteorological observatories,as well as theoretical approximations and non-global mass conservation in these models. In this study,the LDC（Least Difference Combination） method is adopted to obtain some improved atmospheric,oceanic, and hydrological/crospheric angular momentum（AAM, OAM and HAM/CAM, respectively）functions and excitation functions（termed as the LDCgsm solutions）. Various GRACE（Gravity Recovery and Climate Experiment） and SLR（Satellite Laser Ranging） geopotential data are adopted to correct the non-global mass conservation problem, while polar motion data are used as general constraints. The LDCgsm solutions can reveal not only periodic fluctuations but also secular trends in AAM, OAM and HAM/CAM, and are in better agreement with polar motion observations, reducing the unexplained excitation to the level of about 5.5 mas（standard derivation value; about 1/5-1/4 of those corresponding to the original model outputs）.

Excitation of Annual Polar Motion by the Pacific,Atlantic and Indian Oceans

The global oceans play important roles in exciting the annual polar motion besides the atmosphere. However, it is still unclear about how large the regional oceans contribute to the annual polar motion. We investigate systemically the contributions of the Pacific, Atlantic and Indian Oceans to the excitation of the annual polar motion, based on the output data of ocean current velocity field and ocean bottom pressure field from ＂Estimating the Circulation and Climate of the Ocean （ECCO）＂ ocean circulation model over the period 1993-2005. The result shows that due to its particular location and shape, the Atlantic Ocean makes a less significant contribution to the x-component of the annual polar motion excitation than the Pacific and Indian Oceans, while all these three oceans contribute to the y-component of the annual polar motion excitation to some extent.

Reassessment of electromagnetic core-mantle coupling and its implications to the Earth’s decadal polar motion

The observed Earth’s polar motion on decadal time scales has long been conjectured to be excited by the exchange of equatorial angular momentum between the solid mantle and the fluid outer core,via the mechanism of electromagnetic(EM)core-mantle coupling.However,past estimations of the EM coupling torque from surface geomagnetic observations is too weak to account for the observed decadal polar motion.Our recent estimations from numerical geodynamo simulations have shown the opposite.In this paper,we re-examine in detail the EM coupling mechanism and the properties of the magnetic field in the electrically conducting lower mantle(characterized by a thin D '-layer at the base of the mantle).Our simulations find that the toroidal field in the D'-layer from the induction and convection of the toroidal field in the outer core could be potentially much stronger than that from the advection of the poloidal field in the outer core.The former,however,cannot be inferred from geomagnetic observations at the Earth’s surface,and is missing in previous EM torque estimated from geomagnetic observations.Our deduction suggests further that this field could make the actual EM coupling torque sufficiently strong,at approximately 5×1019 Nm,to excite,and hence explain,the decadal polar motion to magnitude of approximately 10 mas.

EARTH ROTATION EQUATIONS CONTAINING BOTH NUTATION AND POLAR MOTION

The theory of Smith (1977,1980) is generalized to include both forced and free rotations by introducing an arbitrarily rotating nutation frame.The Eulerien equations are transformed to include the following unknowns:the angular velocity of the nutation frame with respect to the spatial frame,which represents the nutation,and the angles defining the orientation of the Earth with respect to the nutation frame,which represents the polar motion.Together with the definition of the nutation frame (as the definition of the nutation frame is arbitrary to some extent),one can solve simultaneously forced and free nutation and polar motion.As demonstrative examples,studies of nutation and polar motion are made by assuming the nutation axis to be the Earth’s figure axis,rotation axis and angular momentum axis respectively.And the case of the celestial ephemeris pole is also studied.

A new method for deriving broad-band polar motion geodetic excitations

While the geodetic excitationχ(t)of polar motion p(t)is essential to improve our understanding of global mass redistributions and relative motions with respect to the terrestrial frame,the widely adopted method to deriveχ(t)from p(t)has biases in both amplitude and phase responses.This study has developed a new simple but more accurate method based on the combination of the frequency-and time-domain Liouville's equation(FTLE).The FTLE method has been validated not only with 6-h sampled synthetic excitation series but also with daily and 6-h sampled polar motion measurements as well asχ(t)produced by the interactive webpage tool of the International Earth Rotation and Reference Systems Service(IERS).Numerical comparisons demonstrate thatχ(t)derived from the FTLE method has superior performances in both the time and frequency domains with respect to that obtained from the widely adopted method or the IERS webpage tool,provided that the input p(t)series has a length around or more than 25 years,which presents no practical limitations since the necessary polar motion data are readily available.The FTLE code is provided in the form of Mat Lab function.

Relationship between polar motion and key hydrological elements at multiple scales

Changes in the elements of the Earth system are closely related.Finding the key factors linked with hydrological changes is significant for in-depth analysis of hydrological changes.This study chooses polar motion,which is the movement of the Earth’s rotational axis relative to its crust,as a key factor in the investigation of the physical processes of its interaction with several hydrological elements.First,the statistical relationships between polar motion and multi-hydrological elements(i.e.,precipitation,evaporation,runoff,and terrestrial water storage)are investigated,using trend analysis,mutation analysis,cycle analysis,and correlation analysis methods,from basinal to global and from intra-annual to inter-annual scales.Second,their interactions are explored.The study quantifies the effect of hydrological changes on polar motion using the excitation function.It explores the effect of polar motion on hydrological changes based on the theory of equilibrium tides and atmospheric dynamics.The results show that they are significantly correlated and abruptly changed at a similar time.First,regional to global hydrological changes can significantly excite polar motion.From April 2002 to June 2020,the global terrestrial water storage decreased significantly(by approximately−4.68 mm yr^(−1)),which significantly drove polar motion towards the direction of the Greenwich Meridian(by approximately 4.32 mas yr^(−1)).Changes in regional terrestrial water storage also contributed significantly to directional changes in polar motion around 2005 and 2012.Second,polar motion can perturb the Earth’s centrifugal force system and generate equilibrium tides,and thus further cause changes in sea-level pressure,wind,and water vapor transport.Results show that polar motion-induced water vapor flux divergences correlate significantly with actual precipitation and terrestrial water storage changes in the Yangtze River and the Pearl River basins.Their correlations are also significant when trends are removed,and the polar motion-induced changes are 4 to 14 months earlier.This study further demonstrates the relationship between polar motion and hydrological changes and helps to understand the related factors of hydrological changes in other Earth systems.

THE COMPONENT OF 29.8 YEARS IN POLAR MOTION AND △ l. o.d. AND OSCILLATION OF EARTH'S INNER CORE

This paper deals with the components of pcriod of 29.8 yr in polar motion and △ I. o. d. The oscillation of inner core (OIC), as a most possible cause of them, is proposed. Parameters of oscillation are found and its effects on Earth’s mass center (EMC), distance of observatories to EMC, gravity and latitude are estimated.

Seasonal and inter-annual variations of length of day and polar motion observed by SLR in 1993―2006

A time series of length of the day (LOD) and polar motion (PM) were estimated from the range data measured by the satellite laser ranging technique (SLR) to LAGEOS 1/2 through 1993 to 2006. Com-pared with EOPC04 released by the International Earth Rotation and Reference Systems Service (IERS),the root mean squares errors for LOD,X and Y of PM are 0.0067 milliseconds (ms),0.18 milli-arc-sec-onds (mas) and 0.20 mas,respectively. Then the time series are analyzed with the wavelet transforma-tion and least squares method. Wavelet analysis shows that there are the obvious seasonal and inter-annual variations of LOD and PM,but the annual variation cannot be distinguished from the Chandler variation because these two frequencies are very close. The trends and periodic variations of LOD and PM are given in the least squares sense. LOD changes with the annual and semiannual periods. The annual and Chandler variations for PM are also detected,but the semiannual motion for PM is not found. The trend rate of the LOD change in 1993―2006 is ?0.18 ms per year,and the difference from the well-known 1.7 ms per century showed that the trend rate is diverse in different periods possibly. The trend rates of PM in the X and Y directions are 2.25 and 1.67 mas per year respectively,and the North Pole moves to 36.5°E relative to the crust,which is different from the direction of Greenland.

Atmospheric Excitation of Polar Motion

The polar motion excited by the fluctuation of global atmospheric angular momentum (AAM) is investigated. Based on the global AAM data, numerical results demonstrate that the fluctuation of AAM can excite the seasonal wobbles (e.g., the 18-month wobble) and the Chandler wobble, which agree well with previous studies. In addition, by filtering the dominant low frequency components, some distinct polar wobbles corresponding to some great diurnal and semi-diurnal atmospheric tides are found.

An analysis of the polar motion series from VLBI observations

From the reduction of 2893 globally distributed astrometric and geodetic VLBI sessions from August 1979 to the end of 1998, coordinates of 722 radio sources at J2000.0, coordinates and velocities of 128 stations at J1997.0 and about 20 years Earth Orientation Parameters were estimated. From the analysis of the resultant polar motion series, the following are demonstrated: ( i) During the VLBI data span the Markowitz wobble is not exhibited. (ii) The amplitudes of both annual and Chandler wobble show temporal variations, with the former being more obvious than the latter, (iii) Wavelet analysis shows that all the signals in the polar motion series are characterized by temporal variation in amplitudes. If we take any signal as strictly periodic, it is impossible to remove it completely from the polar motion series by least-squares fit because the hypothesis of a constant amplitude conflicts with VLBI measurements, (iv) By applying a filter, the secular polar motion was found to be (2.74 ± 0.01) mas/a

Excitation of annual polar motion by atmosphere and ocean

The quantitative result of annual polar motion excitation by the ocean is presented for the first time. The atmospheric excitation amounts to more than double of the oceanic excitation. The sum of atmospheric and oceanic excitations approximates more to the observed annual polar motion excitation, compared with atmospheric excitation only This suggests that the atmosphere and ocean are the main excitation sources of annual polar motion.

Indexing the relationship between polar motion and water mass change in a giant river basin

Previous studies on the relationship between polar motion and water mass change have mainly concentrated on the excitation of polar motion via global terrestrial water storage changes(TWSC). In view of the uneven distribution of global terrestrial water storage, the relationship between regional water mass change and polar motion needs to be further explored owing to the lack of documented results. In addition, given the uncertainty in the estimation of TWSC, it is required to develop appropriate indices to describe water mass change from different perspectives. The Amazon River basin(referred to Amazon hereafter), containing the world's largest river, located at around the 90°W longitude, is selected as the study area. Water vapor flux, precipitation, runoff and TWSC are selected as the indices of water mass changes to reveal the relationship between polar motion and water mass change in this giant basin. The Mann-Kendall(M-K) method, the accumulated anomaly analysis method and the curvature method are used to identify the abrupt change points; the least squares method is used to estimate the trends,and the Fast Fourier Transform(FFT) and the Ensemble Empirical Mode Decomposition(EEMD) are used to perform a periodic analysis, for all the above indices. It is shown that, of all the indices from 1948 to 2011, water vapor flux is the most closely related index to polar motion. In detail, precipitation and water vapor flux contain beat periods of polar motion; water vapor flux,precipitation and polar motion have a common M-K test abrupt change point(occurring in ca. 1968) at the 0.05 significance level; water vapor flux has a similar accumulated anomaly curve with that of polar motion; and water vapor flux is more highly correlated with polar motion than most other indexes. It is found, just like global TWSC, the χ2 component of the excitation via water vapor flux and water storage change in the Amazon follows that of observed polar motion; χ1 does not follow. However, the pattern in the Amazon that the χ2 component of the excitation by water follows that of observed polar motion is at a more significant level than in global. Finally, the new index termed Location of Vapor-based Inter Tropical Convergence Zone(LVITCZ) we proposed to describe the annual mean latitudinal location of water mass change shows a more close and visual relationship between water mass change and polar motion than other chosen indices do.

Polar Motion Excited by Atmosphere and Ocean in Multi-frequency Bands

This research aims to study the influences of the atmospheric and oceanic excitations on polar motion.Power spectrum density analyses show that the efficiencies of the atmospheric and oceanic excitations differ not only at different frequencies but also in the retrograde and prograde components,but the sum of atmospheric and oceanic excitations shows the best agreement with the observed excitation.

On seismic excitation of the polar motion

1 Studies of seismic excitation of the polar motion The earth’s rotation varies slightly with time. The 3-D earth rotation variation canbe conveniently separated into two components: i) the 1-D variation in the spin rate, oftenexpressed in terms of the length-of-day variation, ii) the 2-D variation in the rotational axisorientation, known as the polar motion as seen in the terrestrial referenee frame.

Polar motion and the North Atlantic Oscillation

THE motion of earth’s instantaneous rotation pole with respect to the earth crust or the mean pole of the epoch is briefly referred to as the polar motion.The polar motion is mainly charac-terized by the annual and Chandler polar motion.With data accumulation and promotion ofthe observation accuracy after the 1980s,people have extended researches of only annual

EQUATIONS OF MOTION AND BOUNDARY CONDITIONS OF INCREMENTAL RATE TYPE FOR POLAR CONTINUA

The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang.