Linear drift and periodic variations observed in long time series of polar motion

 Two long time series were analysed: the C01 series of the International Earth Rotation Service and the pole series obtained by re-analysis of the classical astronomical observations using the HIPPARCOS reference frame. The linear drift of the pole was determined to be 3.31 ± 0.05 milliarcseconds/year towards 76.1 ± 0.80° west longitude. For the least-squares fit the a priori correlations between simultaneous pole coordinates x _p , y _p were taken into account, and the weighting function was calculated by estimating empirical variance components. The decadal variations of the pole path were investigated by Fourier and wavelet analysis. Using sliding windows, the periods and amplitudes of the Chandler wobble and annual wobble were determined. Typical periods in the variable Chandler wobble and annual wobble parameters were obtained from wavelet analyses. Received: 21 January 2000 / Accepted: 28 August 2000     

Chandler摆动的双频现象用于拟合极移确定项的研究

极移中Chandler摆动出现的双频现象,一直以来为许多学者所关注。推导了基于Chandler摆动双频的极移确定项模型,并采用该模型对极移确定项进行了拟合。与仅采用单频进行确定项拟合的对比表明,利用双频能取得更理想的结果。     

Comparison of polar motion with oceanic and atmospheric angular momentum time series for 2-day to Chandler periods

During a 4-year period starting in July 1996 and using intervals ranging from 3 days to 4 years, four precise polar motion (PM) series have been compared to excitation by atmospheric angular momentum (AAM) augmented with oceanic angular momentum (OAM) data. The first three series (C03, C04 and Bulletin A) are multi-technique combinations generated by the International Earth Rotation and Reference Systems Service (IERS) and the fourth combined series (IGS00P02) is produced by the International GPS Service (IGS) using only GPS data. The IGS PM compared the best with the combined excitations of atmosphere and oceans (AAM+OAM) at all intervals, showing high overall correlation of 0.8–0.9. Even for the interval of only three days, the IGS PM gave a significant correlation of about 0.6. Moreover, during the interval of February 1999 – July 2000, which should be representative of the current precision of the IGS PM, a significant correlation (>0.4) extended to periods as short as 2.2 days and 2.5 days for the x_p and y_p PM components, respectively. When using the IERS Bulletin B (C04) PM and an interval of almost 6 years, starting in November 1994, the combined OAM+AAM accounted for practically all the annual, semi-annual and Chandler wobble (CW) PM signals. When only AAM was used, either the US National Centers for Environment Prediction reanalysis data, which were used throughout this study, or the Japanese Meteorological Agency data, two large and well-resolved amplitude peaks of about 0.1 mas/day, remained at the retrograde annual and CW periods.     

A study of gravity variations caused by polar motion using superconducting gravimeter data from the GGP network

Long-term continuous gravity observations, recorded at five superconducting gravimeter (SG) stations in the Global Geodynamic Project (GGP) network, as well as data on orientation variations in the Earths rotation axis (i.e. polar motion), have been used to investigate the characteristics of gravity variations on the Earths surface caused by polar motion. All the SG gravity data sets were pre-processed using identical techniques to remove the luni-solar gravity tides, the long-term trends of the instrumental drift, and the effects of atmospheric pressure. The analysis indicates that the spectral peaks, related to the Chandler and annual wobbles, were identified in both the power and product spectral density estimates. The magnitude of gravity variations, as well as the gravimetric amplitude factor associated with the Chandler wobble, changed significantly at different SG stations and during different observation periods. However, when all the SG observations at these five sites were combined, the gravimetric parameters of the Chandler wobble were retrieved accurately: 1.1613 ± 0.0737 for the amplitude factor and –1°.30 ± 1°.33 for the phase difference. The value of the estimated amplitude factor is in agreement with that predicted theoretically for the zonal tides of an elastic Earth model.     

用极移数据直接测算钱德勒摆动Q值

运用已经发展起来的共振激发和参数共振模型,在频率调制的基础上,对IERS极移数据测算出钱德勒摆动的Q值,得到平均值为63,并以每百年0.8的速率在增大。这一结果与Q的滞弹性PREM模型理论值69十分接近,表明共振激发模型和参数共振模型完全与钱德勒摆动滞弹理论相容。     

Chandler摆动轨迹的非线性螺旋线拟合及机制的研究

依照非线性动力学原理,从摆动的不稳定性出发,推出Chandler摆动的非线性动力学螺旋运动轨迹模型。给出Chandler摆动的非线性动力学螺旋轨迹解法,由IERS实测数据中的Chandler摆动位移坐标值,可以得到每两个数据间的螺线插值参数。这对于以往的线性插值的折线拟合是一个改进,也为Chandler摆动的螺旋运动轨迹给出了理论解释。计算得到,Chandler摆动平均每年螺旋的螺距有6.75mas。     

对钱德勒参数进行时变修正的CLS+AR模型在极移预测中的应用

根据LS模型参数中钱德勒项的时变性质,提出了基于钱德勒参数时变修正的CLS模型,并用CLS+AR对极移进行预测。实验结果表明,CLS+AR模型在极移预测精度上较LS+AR模型有较大改善。     

三轴地球Chandler晃动的振幅-频率调制机制

研究了三轴地球的自由晃动,给出了Euler动力学方程的椭圆函数解和Euler/Chandler周期。研究表明,三轴性使得极移轨迹变为短、长半轴分别与主惯性轴A、B平行的椭圆,同时使得极移和自转速率产生耦合效应,导致Chandler晃动的振幅-频率调制机制。根据IERS数据还得出了地极正以3.93 mas/a的速率向77.98°W方向漂移的结论。     

Modeling and forecast of the polar motion excitation functions for short-term polar motion prediction

Short-term forecast of the polar motion is considered by introducing a prediction model for the excitation function that drives the polar motion dynamics. The excitation function model consists of a slowly varying trend, periodic modes with annual and several sub-annual frequencies (down to the 13.6-day fortnightly tidal period), and a transient decay function with a time constant of 1.5 days. Each periodic mode is stochastically specified using a second-order auto-regression process, allowing its frequency, phase, and amplitude to vary in time within a statistical tolerance. The model is used to time-extrapolate the excitation function series, which is then used to generate a polar motion forecast dynamically. The skills of this forecast method are evaluated by comparison to the C-04 polar motion series. Over the lead-time horizon of four months, the proposed method has performed equally well to some of the state-of-art polar motion prediction methods, none of which specifically features forecasting of the excitation function. The annual mode in the ₂ component is energetically the most dominant periodicity. The modes with longer periods, annual and semi-annual in particular, are found to contribute more significantly to forecast accuracy than those with shorter periods.     

Polar motion modeling,analysis, and prediction with time dependent harmonic coefficients

A time dependent amplitude model was proposed for the analysis and prediction of polar motion time series. The formulation was implemented to analyze part of the new combined solution, EOP (IERS) C 04, daily polar motion time series of 14 years length using a statistical model with first order autoregressive disturbances. A new solution approach, where the serial correlations of the disturbances are eliminated by sequentially differencing the measurements, was used to estimate the model parameters using weighted least squares. The new model parsimoniously represents the 14-year time series with 0.5 mas rms fit, close to the reported 0.1 mas observed pole position precisions for the x and y components. The model can also predict 6 months into the future with less than 4 mas rms prediction error for both polar motion components, and down to sub mas for one-step ahead prediction as validated using a set of daily time series data that are not used in the estimation. This study is dedicated to the memory of Prof. Urho Uotila (1923–2006) whose teaching of “Adjustment Computations” over the years influenced so much, so many of us who had the privilege of being his students.     

New Solution for the Earth’s Free Wobble and Its Geophysical Implications

In this paper, the theory of the free wobble of the triaxial Earth is developed and new conclusions are drawn: the Euler period should be actually expressed by the first kind of complete elliptic integral; the trace of the free polar motion is elliptic and the orientations of its semi-minor and major axes are approximately parallel to the Earth’s principal axes A and B, respectively. In addition, the present theory shows that there is a mechanism of frequency-amplitude modulation in the Chandler wobble, whi...     

Parameter variability of the observed periodic oscillations of polar motion with smaller amplitudes

Compared to the Chandler and annual wobbles, the higher-frequency components of polar motion (PM) have substantially smaller amplitudes. Therefore, their study has had to wait until higher-quality time series with high temporal resolution, as measured by space geodetic techniques, have become available. Based on the combined Earth orientation series SPACE99 computed by the Jet Propulsion Laboratory (JPL) from 1976 to 2000 at daily intervals, the periodic PM terms, in particular at the quasi-biennial, 300-day, semi-Chandler, semi-annual, 4-month, 90-day, 2-month and 1.5-month periods, have been separated by band-pass filtering and it has been found that the persistence of oscillations becomes less with increasing frequency. In order to quantify and better describe the parameter variability of these PM components over time, the radii, direction angles and period lengths were computed from the periodic terms filtered out from the time series. The results clearly show the characteristics and time evolution of the periodic PM components. The largest elliptic oscillation is the semi-annual wobble with a maximum semi-major axis of up to 13 mas (milliarc seconds). The other wobbles are smaller. They have maximum semi-major axes of between 3 and 8 mas. If the oscillations have period lengths of 4 months and less, then they are elapsed not only progradly, but also retrogradly. AcknowledgementsThis paper was presented at the 27th General Assembly of the European Geophysical Society in Nice, France, 22–26 April 2002. Thanks go to Kevin Fleming for his linguistic advice. The author would also like to thank Barbara Koaczek for suggesting some valuable improvements.     

Excitation of non-atmospheric polar motion by the migration of the Pacific Warm Pool

Changes in the annual variation of the Earths polar motion are found to be largely caused by the variation of the atmospheric angular momentum (AAM). Recent simulation results of oceanic general circulation models further suggest global oceanic effects on the annual polar motion in addition to the atmosphere. In comparison with previous model studies of global oceanic effects, this research particularly singles out a large-scale ocean anomaly and investigates its effect on the annual polar motion, determined from satellite observations of the movement of the Western Pacific Warm Pool (WPWP). Although the scale of the warm pool is much smaller than that of the solid Earth, analysis of the non-atmospheric polar motion excitation has shown that the WPWP contributes non-negligibly to the annual polar motion. The analysis consists of over 30 years of WPWP data (1970–2000) and shows values of polar motion excitation for the x-component of (2.5 mas, –79°) and for the y-component of (0.6 mas, 173°). Comparison of this result with the total geodetic non-atmospheric polar motion excitation of (10.3 mas, 59°) for the x-component and (10.6 mas, 62°) for the y-component shows the significance of the WPWP. Changes in the Earths polar motion have attracted significant attention, not only because it is an important geodetic issue, but also because it has significant value as a global measure of variations within the hydrosphere, atmosphere, cryosphere, and solid Earth, and hence global changes.Tel: 86–21–64386191 Fax: 86–21–64384618Acknowledgments. The authors are grateful to Dr. R. Gross (JPL) and two anonymous reviewers for providing invaluable comments. They also thank Dr. J.L. Chen (CSR) for helpful discussions. Y. Zhou, D. Zheng and X. Liao were supported by the National Natural Science Foundation of China (10273018, 10133010) and Key Project of Chinese Academy of Sciences (KJCX2-SW-T1). X-H. Yan was supported by the National Aeronautics and Space Administration (NASA) through Grant NAG5–12745, and by the National Science Foundation (NSF) through the Presidential Faculty Fellow award to X-H. Yan (OCE-9453499). W.T. Liu was supported by the NASA Physical Oceanography Program.     

Temporal variations of the polar moment of inertia and the second-degree geopotential

In order to study the geodynamic behaviour of the Earth over short (elastic Earth) and long (almost perfectly liquid Earth) geological periodic variations, the changes of the moment of inertia are decomposed into two parts: the first, described by a volume integral, explains the effect of the density variations, while the second gives the impact of the surface variations using a surface integral. It is shown that both components have physical significance, but their contribution is different in case of short (lunisolar) and long (connected to secular despinning) periods.     

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.     

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.     

相对海平面变化时段选择效应分析

验潮站观测的海面高度数据是监测海平面变化以及确定平均海面的重要基础观测信息,利用滑动时段法和时段累积法对验潮站不同观测时段相对海平面变化速率的差异进行了分析,讨论了时段选择效应对计算相对海平面变化的影响,并利用美国东海岸验潮站观测数据对分析结果进行了补充实验.实验结果表明,不同观测时段相对海平面变化速率差异最大可达27...     

An improved empirical model for the effect of long-period ocean tides on polar motion

Because the tide-raising potential is symmetric about the Earth’s polar axis it can excite polar motion only by acting upon non-axisymmetric features of the Earth like the oceans. In fact, after removing atmospheric and non-tidal oceanic effects, polar motion excitation observations show a strong fortnightly tidal signal that is not completely explained by existing dynamical and empirical ocean tide models. So a new empirical model for the effect of the termensual (Mtm and mtm), fortnightly (Mf and mf), and monthly (Mm) tides on polar motion is derived here by fitting periodic terms at these tidal frequencies to polar motion excitation observations that span 2 January 1980 to 8 September 2006 and from which atmospheric and non-tidal oceanic effects have been removed. While this new empirical tide model can fully explain the observed fortnightly polar motion excitation signal during this time interval it would still be desirable to have a model for the effect of long-period ocean tides on polar motion that is determined from a dynamical ocean tide model and that is therefore independent of polar motion observations.     

低轨道卫星重复周期的设计方法及其对重力场反演的影响

研究低轨卫星重复周期的设计原理,给出相应的计算公式。基于此对不同轨道高度卫星的重复周期进行数值仿真,并利用动力学方法分析不同重复周期轨道星下点轨迹的空间采样对重力场反演精度的影响。结果表明,卫星的重复周期与其轨道高度的变化并不成线性关系,并且在顾及重力场时间分辨率的情况下,长重复周期能够提高卫星地面轨迹的空间采样,为重力场解算提供较好的条件。