This paper presents a novel hybrid method named HW-EZ for short-to medium-term forecasting of ΔLOD and UT1-UTC up to 90 days ahead. This method relies on the LOD time series with zonal tidal signals removed, the adaptive Holt-Winters (HW) additive algorithm, and the effective angular momentum (EAM) functions derived from global atmospheric, oceanic, and land water models. The dominant ΔLOD variations are estimated using EAM and tides, while the remaining ones are modeled by HW-EZ with an 8-year sliding window. Numerical validation shows that HW-EZ reduces UT1-UTC mean absolute error (MAE) by 13.77%–67.55% relative to IERS Bulletin A over 1–30-day forecasts. Using 6-day EAM forecasts maintains nearly equivalent accuracy. Comparisons with the Second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC) confirm that HW-EZ outperforms the average of more than 50 international methods and is competitive with state-of-the-art schemes. The HW-EZ method achieves robust ultra-short-term performance with UT1-UTC MAE ≤0.158 ms for 1–6-day forecasts, making it suitable for real-time geodetic and navigation applications.

While numerous studies have been dedicated to the determination of Chandler wobble parameters, namely its period TCW and quality factor QCW, most of their results lack self-consistency. We proposed a rigorous approach to achieve self-consistent estimates of TCW and QCW using only geodetic excitations (χobs) derived from observed polar motion (PM) data in 2023 (denoted as CCRLL). However, a study published in 2025 (denoted as YF) criticized CCRLL's approach and argued that either TCW or QCW cannot be optimized without access to geophysical excitations (χgeo), relying on their misleading numerical simulations using real-valued PM transfer functions. Our present study has established theoretical relations between (TCW, QCW), degree-2 Love numbers and complex-valued transfer functions while proving that traditional Earth's rotation theories, employing real-valued transfer functions, are incapable of providing self-consistent estimates of TCW and QCW. This study also demonstrates that either χobs or χgeo can be used to invert for TCW and QCW, but χgeo must be recalculated using the complex transfer functions derived by this study and χobs-based estimates are more reliable. Thus, CCRLL's approach and results are validated while YF's arguments are refuted. Further, some updates and corrections to CCRLL's Love numbers and transfer functions are also presented.

While the geodetic excitation χ(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 derive χ(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 as χ(t) produced by the interactive webpage tool of the International Earth Rotation and Reference Systems Service (IERS). Numerical comparisons demonstrate that χ(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 MatLab function.

The period T CW and quality factor Q CW of the Chandler wobble (CW) as well as polar motion (PM) transfer functions are all determined by the Earth’s layered structure, mass distribution, elasticity, rheology and energy dissipation, via the Earth’s dynamic figure parameters and complex degree-2 Love numbers. However, most previous studies used geophysical excitations derived from real-valued PM transfer functions to invert for T CW and Q CW , thus leading to results that are not self-consistent. By separating the observed PM into the freely decaying CW and the excited PM, a traverse-based method is proposed to search values of T CW and Q CW that can fit both sides simultaneously, yielding the self-consistent estimates of T CW = 430.4 mean solar days and Q CW = 130. This implies the degree-2 tidal Love number k = 0.35011 − 0.00226i and load Love number k' = − 0.36090 + 0.00233i, and the PM transfer functions T NL = 1.80001 − 0.00692i (non-loading) and T L = 1.15040 − 0.00023i (loading) valid at the Chandler period.

The precision of the GNSS positioning depends on the accuracy and stability of the GNSS satellite orbits. Indeed, the analysis of the GNSS precise orbits determined by the IGS analysis centers shows different long-term behavior in the eccentricities and inclinations of GPS satellites, compared to GLONASS and Galileo satellites. This contribution focuses on analyzing sources of long-term dynamics in the GNSS orbits, particularly in the GPS orbits, and the influence of the constellation design. We investigate orbital resonances resulting from external accelerations such as lunisolar gravitation by semi-analytical simulations and compare the dynamical response of the four available constellations: GPS, Galileo, GLONASS, and BeiDou. Finally, we assess the impact of this different dynamical behavior on Precise Point Positioning (PPP).

Due to the conservation of global angular momentum, polar motion (PM) is dominated by global mass redistributions and relative motions in the atmosphere, oceans and land water at seasonal time scales. Thus, accurately measured PM data can be used to validate the general circulation models (GCMs) for the atmosphere, oceans and land water. This study aims to analyze geophysical excitations and observed excitations obtained from PM observations from both the harmonic and wavelet analysis perspectives, in order to refine our understanding of the geophysical excitation of PM. The geophysical excitations are derived from two sets of GCMs and a monthly gravity model combining satellite gravity data and some GCM outputs using the PM theory for an Earth model with frequency-dependent responses, while the observed excitation is obtained from the PM data using the frequency-domain Liouville’s equation. Our results show that wavelet analysis can reveal the time-varying nature of all excitations and identify when changes happen and how strong they are, while harmonic analysis can only show the average amplitudes and phases. In particular, the monthly gravity model can correct the mismodeled GCM outputs, while the Earth’s frequency-dependent responses provide us with a better understanding of atmosphere–ocean–land water–solid Earth interactions.

By taking into account the variable free polar motion (PM) known as the Chandler wobble (CW) and irregular forced PM excited by quasi-periodic changes in atmosphere, oceans and land water (described by the data of effective angular momenta EAM), we propose a short-term PM forecast method based on the Holt-Winters (HW) additive algorithm (termed as the HW-VCW method, with VCW denoting variable CW). In this method, the variable CW period is determined by minimizing the differences between PM observations and EAM-derived PM for every 8-year sliding timespan. Compared to the X- and Y-pole forecast errors (ΔPMX and ΔPMY) of the International Earth Rotation and Reference Systems Service (IERS) Bulletin A, our results derived from operational EAM can reduce ΔPMX by up to 38.4% and ΔPMY by up to 34.3% for forecasts ranging from 1 to 30 days. Further, we prove that using EAM forecast instead of operational EAM in the HW-VCW method can achieve similar accuracies.

Day-boundary orbit comparison is one of the criteria used to assess the performance of GNSS orbits. The overall statistics of orbit discontinuities such as RMS are usually computed to assess dynamical modeling and the processing configurations. Additional information about the systematic orbit errors is also accessible through their spectral content. A particular feature is the flicker or 1/f noise describing the low-frequency band, indicating time-correlated orbital errors. This type of noise is observed not only in the orbits but also in other GNSS-derived geodetic time series such as in station positions, Earth rotation parameters,... The sources explaining this feature, either from the GNSS orbit modeling or from unaccounted orbital perturbations, are not well understood. By computing simulated orbits, we look at possible causes in the orbit determination processing.

Crustal motion observations from Global Positioning System (GPS) networks have not yet been fully exploited in previous studies on glacial isostatic adjustment (GIA) and mantle rheology structure. In this study, we have isolated GIA signals from vertical velocity observations at rigorously selected (over 2,000) GPS stations from the Nevada Geodetic Laboratory (NGL) by removing the effects of atmospheric and oceanic loading, as well as changes in the contemporary glaciers. We have also attempted to include hydrological and sea-level loading corrections based on the most updated model products, but found them still not accurate enough for GIA-related studies. Therefore, we recommend the GPS-derived global GIA uplift rate dataset MIDAS-AO without hydrological and sea-level loading corrections applied. Under the constraints of MIDAS-AO uplift rates, we refined the VM5a viscosity model and obtained two revised viscosity profiles, VM5aR_AO1 and VM5aR_AO2, that differ by an extra layer in the transition zone of the latter profile. With respect to VM5a, VM5aR_AO1 indicates a slight increase of viscosity within the upper mantle, while VM5aR_AO2 favors a softer upper part of the upper mantle and a stiffer transition zone. Maps of the variations of model-dataset misfits show that our new viscosity profiles commonly recover a better fit for sites located at the Scandinavian Peninsula and south of the Hudson Bay.

Time-dependent loading deformations of the Earth’s surface, due to nontidal changes in the atmosphere, ocean, land water/ice, etc., contribute significantly to the seasonal and secular Global Positioning System (GPS) site displacements, especially for the up component. While loading deformations derived from general circulation model (GCM) outputs are usually used to correct loading signals in the GPS site displacements, this study aims to provide a loading correction model based on the multiple-data combined monthly gravity products LDCmgm90. We have adopted GPS measurements from 249 IGS reference frame stations and 3 different GCM-based loading models to test the reliability of the LDCmgm90 model. Compared to the GCM-based models, the LDCmgm90 loading correction is more effective in attenuating seasonal (especially annual) loading signals and can bring more significant improvements to most stations for both the data-trend-removed and the data-trend-retained cases. Thus, we have validated the LDCmgm90 model from the loading aspect and proved it to be a reliable loading-correction model for GPS displacements. The relatively better secular loading signals provided by the LDCmgm90 loading model may provide us a chance to study the long-term, nonloading signals in GPS data.

Abstract Like the seasonal and interannual variations in length‐of‐day (LOD), variations on intraseasonal timescales (periods shorter than 183 days) are also predominantly caused by changes in the angular momentum of the zonal winds. But the smaller intraseasonal LOD excitations from atmospheric surface pressure, oceanic currents, and the ocean bottom pressure are less clear. Here sliding window average filtering is applied to isolate intraseasonal signals from both geodetically observed LOD excitation (shorten to geodetic excitation for convenience) and atmospheric and oceanic LOD excitations. Based on careful comparison between these two‐excitation series, we find that during 1993–2018, atmospheric winds reduce the RMS of observed intraseasonal LOD series from 276.1 to 55.6 μs with a correlation coefficient of 0.9795. Including the effect of surface pressure changes with that of the winds reduced the RMS from 55.6 to 43.3 μs, and increased the correlation coefficient with the observations from 0.9795 to 0.9884. Additionally, including the effects of changes in oceanic currents and bottom pressure further reduced the RMS from 43.3 to 33.9 μs, and further increased the correlation coefficient from 0.9884 to 0.9931. Thus, although the impact of oceans is relatively minor, closer agreement with the observations in the intraseasonal frequency band is obtained when the effects of oceanic processes are added to that of atmospheric. The RMS values and correlation coefficients of ESMGFZ and MPIOM residual series are better than NCEP and ECCO in every component, indicating that NCEP model set is generally poorer than ESMGFZ in the intraseasonal band.

Abstract The El Niño–Southern Oscillation (ENSO) event has a long incubation process, during which the interannual variation of length‐of‐day (LOD) and the atmospheric angular momentum (AAM) series will be quickly affected due to the interaction between sea and air. Based on the comparisons between filtered interannual LOD variation, the AAM, the Oceanic Niño Index (ONI), and the Southern Oscillation Index (SOI) for the period of January 1953 and December 2013, the relationships among them and ENSO are studied. The results demonstrate that AAM changes and SOI/ONI series have similar waveform structures and trends. Interannual LOD variations, atmospheric LOD excitations, and ENSO indices such as the SOI and ONI are well correlated as a consequence of angular momentum conservation. AAMs can be accurately modeled at present, taking ESMGFZ as an example, its sampling interval can reach 3 hr, and can realize accurate prediction in the next 90 days. Consequently, AAM series also can be used as an index for ENSO events and has its own advantages compared with SOI/ONI.

It has been a standard practice for about 2 decades to compute global positioning system (GPS)‐based station velocity uncertainties using the apparent noise statistics of the non‐linear position residuals rather than assume white noise (WN) behavior. The latter choice would yield unrealistic velocity uncertainties. The most common noise types used are power‐law, usually close to flicker noise (FN), over most frequencies mixed with WN at the shortest periods. The complicating impact of offsets in the position time series, mostly caused by equipment changes or tectonic events, has not been fully appreciated. These are far less benign than recently suggested. In addition to contributing a pseudo‐random walk noise (RW) component to the velocity errors, estimating offset parameters changes the apparent noise color toward whiter. Spectral power is effectively drained by offsets at periods longer than roughly the mean span between them. This consequently favors a Gauss‐Markov process as the apparently preferred noise model and, importantly, obscures the presence of RW and long‐period Earth deformation in the series. Both effects can lead to potentially under‐estimated velocity uncertainties. The full value of decadal‐long GPS time series for geodynamical applications is thereby greatly eroded by recurring offsets, especially when they occur quasi‐regularly. In addition, contrary to common assumption, the noise color is generally not fixed with time, but clearly becomes whiter in more recent data. The origin of the colored noise and its whitening over time remain elusive.

Chameleonic: readily changing color or other attributes. Chameleon: a lizard that changes skin color to match what surrounds it so that it cannot be seen. The error spectrum of decadal long GPS position time series is typically represented by a combination of flicker (pink) noise at long periods and white noise at short periods. It is known that when fitting a linear trend to the series, part of the flicker noise at the longest observed period will be absorbed by the trend. Here, using real and synthetic GPS position series, we show how the error spectrum is even more altered by the position discontinuities that populate the series. The fitted position offsets at the discontinuity epochs absorb a significant portion of the power spectrum at periods longer than the separation between the discontinuity epochs. The resulting error spectrum is flattened at long periods and this implies that: * the estimated content of colored noise is biased low and can even apparently change its color towards whiter noise, i.e. the true noise color is not observable due to the discontinuities, * the red (random walk) noise , most probably present in the series in small quantity, becomes undetectable even if long series are used, * the pink (flicker) noise is not the best color noise to represent the error spectrum in long series containing discontinuities, * the colored noise content cannot be compared between series with different sets of discontinuities. These findings need to be considered when comparing the noise levels between series from different solutions, networks or monuments. In particular, and contrary to a recently published recommendation, station operators should make every effort to avoid adding new discontinuities into their station time series if reliable velocity estimates are expected.

AbstractAt timescales shorter than about 2~yr, non‐tidal length‐of‐day (LOD) variations are mainly excited by angular momentum exchanges between the atmospheric, oceanic and continental hydrological fluid envelopes and the underlying solid Earth. On decadal timescales, the dominant excitation sources of LOD variations are from core and mantle coupling. But the excitations of semi‐decadal (specifically 2~8 yr here) signals in length‐of‐day is less clear, and have been characterized by signals with a wide range of periods and varying amplitudes, including a peak at about 5~6 yr. Here sliding window average filtering is applied to isolate semi‐decadal signals from both geodetic technique observed LOD excitation (shorten to geodetic excitation for convenience) and atmospheric LOD excitations. Based on careful comparison between these two excitation series, we find that (1) the 5~6 yr oscillation in geodetic excitations is not periodically consistent; (2) there is a 5~yr oscillation in atmospheric excitation series, and atmosphere can explain all the semi‐decadal oscillation shorter than about 5~yr in geodetic LOD excitations; (3) contributions from atmosphere to 5~6 yr oscillation in LOD variations is small and cannot be clearly determined; (4) it appears that there are some modest long‐period (longer than 10 yr periods) signals in the atmospheric excitations, but these could be artifacts of the models. Then we compare those peaks/troughs epochs in the residual series between geodetic and atmospheric excitations (ROBS_ATM series for short) with the observed geomagnetic jerks, and find that all of the geomagnetic jerks can match one peaks/troughs in the ROBS_ATM series, and they occurred at the same time or within one year before these peaks/troughs. It implies that there is a common origin for the processes giving rise to geomagnetic jerks and the remaining 5~6 yr oscillation in the ROBS_ATM series.

Geophysical excitations of length-of-day (LOD) variations is of great significance in understanding changes in the Earth's spin rate and interactions between geophysical fluids and the solid Earth, as well as validating the reliability of atmospheric, oceanic and hydrological models. In this study seasonal excitations of LOD variation during 06.30,1987–06.30,2017 are investigated using both harmonic and inharmonic analyses. We examined the agreements between the IERS EOP 14 C04 ΔLOD series and that from the previous version EOP08C04, and analyzed contributions of atmospheric, oceanic, hydrological and sea level angular momenta to seasonal excitations of LOD variations on the bases of the ESMGFZ products. We found that the sea level angular momentum plays an important role in global mass conservation and can bring better agreements between the geophysical and geodetic excitations.

In addition to studies of sea level change and mantle rheology, reliable Glacial Isostatic Adjustment (GIA) models are necessary as a background model to correct the widely used Gravity Recovery and Climate Experiment (GRACE) monthly gravity solutions to determine subsecular, nonviscous variations. Based on spherical harmonic analyses, we developed a method using degree-dependent weighting to assimilate the Global Positioning System (GPS) derived crustal uplift rates into GIA model predictions, in which the good global pattern of GIA model predictions and better local resolution of GPS solutions are both retained. Some systematic errors in global GPS uplift rates were also corrected during the spherical harmonic analyses. Further, we used the refined GIA uplift rates to infer the GIA-induced rates of Stokes coefficients (complete to degree/order 120) relying on the accurate relationship between GIA vertical surface deformation and gravitational potential changes. The results show notable improvements relative to GIA model outputs, and may serve as a GIA-correction model for GRACE time-variable gravity data.

While the GRACE (Gravity Recovery and Climate Experiment) satellite mission is of great significance in understanding various branches of Earth sciences, the quality of GRACE monthly products can be unsatisfactory due to strong longitudinal stripe-pattern errors and other flaws. Based on corrected GRACE Mascon (mass concentration) gridded mass transport time series and updated LDCgam (Least Difference Combination global angular momenta) data, we present a new set of monthly gravity models called LDCmgm90, in the form of Stokes coefficients with order and degree both up to 90. The LDCgam inputs are developed by assimilating degree-2 Stokes coefficients from various versions of GRACE (including Mascon products) and SLR (Satellite Laser Ranging) monthly gravity data into combinations of outputs from various global atmospheric, oceanic, and hydrological circulation models, under the constraints of accurately measured Earth orientation parameters in the Least Difference Combination (LDC) scheme. Taking advantages of the relative strengths of the various input solutions, the LDCmgm90 is free of stripes and some other flaws of classical GRACE products.

At timescales shorter than about 2 yr, non-tidal length-of-day (LOD) variations are mainly excited by angular momentum exchanges between the atmospheric, oceanic and continental hydrological fluid envelopes and the underlying solid Earth. But, neither agreement among different geophysical models for the fluid dynamics nor consistency with geodetic observations of LOD has reached satisfactory levels. This is mainly ascribed to significant discrepancies and uncertainties in the theories and assumptions adopted by different modelling groups, in their numerical methods, and in the accuracy and coverage of global input data fields. Based on careful comparisons with more accurate geodetic measurements and satellite gravimetry products (from satellite laser ranging, SLR), observed LOD and C-20 geopotential time-series can provide strong constraints to evaluate or form combined geophysical models. In this study, wavelet decomposition is used to extract several narrow-band components to compare in addition to considering the total signals. We then make refinements to the least difference combination (LDC) method proposed by Chen et al., to form multimodel geophysical excitations. Two combination variants, called the weighted mean combination (WMC2 and WMC4), are also evaluated. All the multimodel methods attempt to extract the best-modelled frequency components from each geophysical model by relying on geodetic excitation and the C20 series as references. The comparative performances of the three combinations LDC, WMC2 and WMC4 and the original single models are determined. We find that (1) Estimating the Circulation and Climate of the Ocean and Max-Planck-Institute for Meteorology Ocean Model give a more reliable view of the ocean redistributions than the Ocean Model for Circulation and Tides used by European Centre for Medium-Range Weather Forecasts, especially for the annual component; (2) C20 series from SLR can provide a rigorous constraint for the total matter excitation of the geophysical fluids, especially for broad-band parts; (3) the Sea-Level Angular Momentum functions term, correcting for sea-level effects (global mass balance) put forward by the Earth System Modelling group at GFZ German Research Centre for Geosciences, can significantly improve the Hydrospheric Effective Angular Momentum functions matter terms; (4) the LDC/WMC combinations are much better than the original individual geophysical model excitations, reducing the magnitude of unexplained LOD excitations to roughly the 10 mu s level; (5) the level of residual LOD variations after removing models or model combinations is remarkably invariant with respect to LOD periods between similar to 2 months and similar to 3 yr, being 12-14 mu s for the best original models and 7-12 mu s for our combinations; (6) while differences between the IERS 14C04 and the JPL SPACE2015 geodetic LOD time-series are not negligible, errors in both series are still not large compared to the geophysical models (for periods > 2 months) so the impact on excitation studies is minimal except at semiannual periods and usually 14C04 compares better with excitation models. The improved geophysical models are recommended to replace the original ones as they present overwhelming advantages.