Long-term prediction of polar motion using a combined SSA and ARMA model

To meet the need for real-time and high-accuracy predictions of polar motion (PM), the singular spectrum analysis (SSA) and the autoregressive moving average (ARMA) model are combined for short- and long-term PM prediction. According to the SSA results for PM and the SSA prediction algorithm, the principal components of PM were predicted by SSA, and the remaining components were predicted by the ARMA model. In applying this proposed method, multiple sets of PM predictions were made with lead times of two years, based on an IERS 08 C04 series. The observations and predictions of the principal components correlated well, and the SSA \(+\) ARMA model effectively predicted the PM. For 360-day lead time predictions, the root-mean-square errors (RMSEs) of PMx and PMy were 20.67 and 20.42 mas, respectively, which were less than the 24.46 and 24.78 mas predicted by IERS Bulletin A. The RMSEs of PMx and PMy in the 720-day lead time predictions were 28.61 and 27.95 mas, respectively.     

1990—2015年极移和日长周期性变化的小波分析

采用由国际地球自转及参考服务组织(IERS)提供的1990—2015年的EOP 08C04序列,分别利用小波变换和最小二乘法对极移(PM)和日长(LOD)的周期性变化进行了研究。小波分析结果表明,PM和LOD都存在明显的季节性和年际变化,但是,无法区分周年变化和钱德勒变化,可能是因为两者的频率太接近。在最小二乘意义上,对PM和LOD的趋势变化和周期变化进行了解算,结果发现LOD具有明显的半年和周年变化,同时探测了PM的半年和周年变化。1990—2015年间,LOD的趋势变化率为(-0.066 7±0.001 6)ms/a,PM在X和Y方向的趋势变化率分别为(2.898 0±0.131 0)mas/a和(0.957 0±0.152 0)mas/a,说明北极点相对地壳向18.3°E的方向移动。此外,对PM的X分量、PM的Y分量以及LOD两两之间进行了交叉小波变换,对三者之间的相关性进行了分析。     

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.     

The common short periodic oscillations in the Earth's rate of rotation,atmospheric angular momentum and solar activity

In order to find short periodic oscillations in the Earth's rate of rotation, atmospheric angular momentum, solar activity the Maximum Entropy Spectral Analysis — MESA (Burg, 1967) has been applied. The MESA with moving autoregressive order has been introduced in order to detect more accurately periods of very weak short periodic variations. Oscillations with periods of about 75, 50, 27 and 18 days have been found in length of day — LOD, from which tidal oscillations were removed up to 35 days — LODR computed by the Center for Space Research — CSR from Lageos Laser Ranging data, in the axial component of atmospheric angular momentum — ₃ determined by the U.S. National Meteorological Center — NMC and in the geomagnetic activity represented by the geomagnetic index —A _p (Lincoln, 1967). These oscillations computed by Ormsby band pass filter (Ormsby, 1961) are in a very good phase agreement in the case of oscillations with periods of 50 and 18 days in these 3 series. The MESA of the cross covariance estimations between LODR- ₃, ₃-A _p,A _p-LODR, LODR-FLUX, ₃-FLUX, andA _p-FLUX has confirmed the existence of common oscillations with periods of 70, 50, 27 and 18 days. This indicates a possible relationship between solar activity and the short periodic exchange of angular momentum between the atmosphere and the solid Earth.     

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.     

地表质量负载对格陵兰岛区域GPS站点坐标时序特征的影响

选取ITRF2008框架下格陵兰岛区域12个GPS站2013年1月-2016年12月期间的日解坐标时间序列作为研究对象,并利用极大似然估计分析地表质量负载改正前后各站点的噪声特性、速度场及周期项振幅。结果表明：站点最优噪声模型主要为白噪声+幂律噪声与白噪声+闪烁噪声,地表质量负载形变修正GPS坐标时序后,明显增加U方向闪烁噪声的成分,平均降低其速度约0.36 mm/a,对水平方向影响较小;同时分别降低高程方向44.1%、14.2%的1 a项、0.5 a项振幅,相反,却增加了水平方向的周期项振幅。     

利用GNSS数据分析大港验潮站地壳沉降

青岛大港验潮站的地壳沉降关系到该站平均海平面的绝对变化,因而也就关系到我国高程基准面的变化。本文利用青岛GNSS基准站约10年的观测数据对该站的地壳沉降变化进行分析。首先将青岛GNSS基准站纳入由50个国际IGS站和43个国内陆态网络基准站组成的全球网中,进行单日松弛解和单日约束解解算,获得该站坐标时间序列。然后对该站垂向坐标时间序列进行分析,利用粗差探测、偏差探测、趋势项分析、频谱分析等方法对粗差、偏差、趋势项和周期项进行探测、分析,并通过时间序列模型估计获得时间序列中的周期项振幅和偏差估值。分析表明青岛GNSS基准站垂直方向近一段时间未发现存在显著性的地壳沉降变化,但受到比较明显的周年和半周年周期变化影响。结合青岛大港验潮站验潮数据分析结果得出结论:青岛大港验潮站平均海平面的绝对上升速率是1.62mm/a。     

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.     

基于小波变换的CORS高程坐标时序周期性分析与降噪方法研究

以香港连续运行参考站（CORS）网中的6个CORS的高程坐标时间序列数据为研究对象,利用小波多分辨分析从时频的角度来探测坐标时序中存在的周期性变化与非线性运动趋势,并采用小波变换阈值的方法对坐标时序进行降噪处理,根据不同的降噪质量评价指标来对比降噪效果．结果表明:高程坐标时序中存在极为明显的年周期与半年周期变化的特征,通过小波降噪可以有效地减弱或消除原始时序中的噪声信息,获得更接近理论分析的坐标时间序列．      

华北区域GNSS基准站高程时间序列的非线性变化分析

基于陆态网络全球卫星导航系统（GNSS）观测成果,采用功率谱分析法和最小二乘方法,以华北地区为例,研究了区域基准站高程时间序列的非线性变化特征,并分析了不同环境负载的影响.结果表明,GNSS基准站高程方向存在显著的周年和半年周期特征,且周年特征要显著于半周年特征.位于不同地区的基准站的振幅和相位存在差异,华北平原南部地区的周年振幅要大于北部地区,整体上华北地区周年变化在秋季时节振幅达到最大.不同环境负载效应对华北GNSS高程位移的影响不一致,利用三种环境负载修正GNSS序列后,水文负载的修正效果最好,非潮汐大气负载次之,非潮汐海洋负载修正结果不理想.      

联合区域叠加滤波法与小波变换去除GPS站坐标时间序列噪声

GPS站坐标时间序列中存在的周期性与非周期性误差严重影响了对测站运动特征的分析及其非线性变化的物理机制解释。因此,为削弱噪声的影响,本文首先利用区域叠加滤波法去除了南加利福尼亚地区16个测站时间序列的共模误差,以此削弱时间序列中存在的包括周年和半周年误差在内的周期性误差。为去除滤波后残留的噪声,对滤波后的信号进行静态离散小波变换,提取了周期为半周年以上的信号。结果表明,联合区域叠加滤波法与小波变换对GPS站坐标时间序列进行处理,既能够削弱周期性误差对信号的影响,又能较好地提取测站的非线性运动信号。     

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.     

Continental hydrology loading observed by VLBI measurements

Variations in continental water storage lead to loading deformation of the crust with typical peak-to-peak variations at very long baseline interferometry (VLBI) sites of 3–15 mm in the vertical component and 1–2 mm in the horizontal component. The hydrology signal at VLBI sites has annual and semi-annual components and clear interannual variations. We have calculated the hydrology loading series using mass loading distributions derived from the global land data assimilation system (GLDAS) hydrology model and alternatively from a global grid of equal-area gravity recovery and climate experiment (GRACE) mascons. In the analysis of the two weekly VLBI 24-h R1 and R4 network sessions from 2003 to 2010 the baseline length repeatabilities are reduced in 79 % (80 %) of baselines when GLDAS (GRACE) loading corrections are applied. Site vertical coordinate repeatabilities are reduced in about 80 % of the sites when either GLDAS or GRACE loading is used. In the horizontal components, reduction occurs in 70–80 % of the sites. Estimates of the annual site vertical amplitudes were reduced for 16 out of 18 sites if either loading series was applied. We estimated loading admittance factors for each site and found that the average admittances were 1.01 \(\pm \) 0.05 for GRACE and 1.39 \(\pm \) 0.07 for GLDAS. The standard deviations of the GRACE admittances and GLDAS admittances were 0.31 and 0.68, respectively. For sites that have been observed in a set of sufficiently temporally dense daily sessions, the average correlation between VLBI vertical monthly averaged series and GLDAS or GRACE loading series was 0.47 and 0.43, respectively.     

联合小波和方差分量估计方法分析中国IGS测站时间序列变化特征

利用小波谱分析了中国区域IGS（International GNSS Service）站坐标时间序列中周期信号成分及其随时间的变化,根据小波谱中小波系数的能量在时域上的变化对时间序列进行分段,然后采用方差-协方差验后估计法分析了白噪声+闪烁噪声组合模型下测站在不同时间段的运动特征及变化规律。结果表明,中国区域的IGS站运动特征在不同时间段内是变化的,其中URUM站垂直速度变化大于4 mm,BJFS以及CHAN站水平速度变化大于2 mm,其余站速度变化均在2 mm以内;周年、半周年信号的振幅也均有差异,其中BJFS站垂直分量周年振幅变化最大,超过5 mm;此外,强度较弱的其他周期项存在于分段时间序列中,但其对速度、周期振幅以及噪声分量估计结果影响较小;对时间序列进行分段估计,所得的参数不同,其相差程度可反映出不同时间段内的板块运动等地球物理因素变化的差异。     

热膨胀效应对GNSS基准站垂向位移非线性变化的影响

天线观测墩及基岩的热膨胀效应会造成GNSS基准站坐标时间序列高程方向的非线性变化。本文提出了一种计算热膨胀效应导致的基准站垂向位移的改进方法:首先利用基岩热膨胀模型和基准站地表温度数据,分别计算热膨胀效应对基准站天线观测墩和基岩的影响量;其次,利用最小二乘拟合方法,同时估计模型中周期项的周期、振幅、相位等信息,而已有方法仅估计振幅与相位信息;最后,基于改进的模型,分析了基准站垂向位移的周期性特征变化。本文利用该方法分析了有代表性的9个IGS基准站的数据。结果表明:基岩热膨胀和天线观测墩热效应能造成测站垂直方向位移变化;在分析的基准站中,最大影响分别可达0.57mm和1.85mm;热膨胀效应造成的GNSS基准站垂直方向位移时间序列具有周年和半周年周期特性,分别可以解释测站U方向坐标时间序列季节性变化的11.2%和3.3%,影响大小随测站纬度的增加而增加,且半周年影响明显小于周年影响;同时,部分测站发现了其他小周期的影响(约51d)。此外,基于该方法,选取了全球107个IGS站,计算了热膨胀造成的各测站垂向位移周年振幅及其相位,结果显示周年振幅最大可达3.3mm,其大小和测站纬度具有比较明显的相关性。     

Monitoring Earth orientation using space-geodetic techniques: state-of-the-art and prospective

Earth orientation parameters (EOPs) provide the transformation between the International Terrestrial Reference Frame (ITRF) and the International Celestial Reference Frame (ICRF). The different EOP series computed at the Earth Orientation Centre at the Paris Observatory are obtained from the combination of individual EOP series derived from the various space-geodetic techniques. These individual EOP series contain systematic errors, generally limited to biases and drifts, which introduce inconsistencies between EOPs and the terrestrial and celestial frames. The objectives of this paper are first to present the various combined EOP solutions made available at the EOP Centre for the different users, and second to present analyses concerning the long-term consistency of the EOP system with respect to both terrestrial and celestial reference frames. It appears that the present accuracy in the EOP combined IERS C04 series, which is at the level of 200 as for pole components and 20 s for UT1, does not match its internal precision, respectively 100 as and 5 s, because of propagation errors in the realization of the two reference frames. Rigorous combination methods based on a simultaneous estimation of station coordinates and EOPs, which are now being implemented within the International Earth Rotation Service (IERS), are likely to solve this problem in the future.     

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.     

Accuracy of mean earth ellipsoid based on Doppler,laser and altimeter observations

The error in the mean earth ellipsoid computer on the basis of Doppler or laser observations of artificial earth satellites or radar altimeter observations of the ocean surface from a satellite depends upon instrument precision, on uncertainties in the specification of the earth's gravity field at both long and short wave lengths, on uncertainties in the origin of the coordinate system, on modeling errors in ionospheric (except laser) and tropospheric refraction, and, for altimetry, on oceanographic effects. The magnitude of the uncertainty in the computed ellipsoid will vary depending on the size of these errors and on the number and distribution of observation stations. Review of computations based on various data sets indicates that differences in the computed ellipsoids are consistent with those expected due to the various error sources and that the best fitting ellipsoid has a semi-major axis of6378136±2 m.     

Forecasting sea level anomalies from TOPEX/Poseidon and Jason-1 satellite altimetry

This paper aims at the prediction of both global mean sea level anomalies (SLAs) and gridded SLA data in the east equatorial Pacific obtained from TOPEX/Poseidon and Jason-1 altimetric measurements. The first prediction technique (denoted as LS) is based on the extrapolation of a polynomial-harmonic deterministic least-squares model describing a linear trend, annual and semi-annual oscillations. The second prediction method (denoted as LS + AR) is a combination of the extrapolation of a polynomial-harmonic model with the autoregressive forecast of LS residuals. In the case of forecasting global mean SLA data, both techniques allow one to compute the predictions of comparable accuracy (root mean square error for 1-month in the future is of 0.5 cm). In the case of predicting gridded SLA data, the LS + AR prediction method gains significantly better prediction accuracy than the accuracy obtained by the LS technique during El Niño 1997/1998, La Niña 1998/1999 and during normal conditions.