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The Earth does not rotate uniformly. Not only does its rate of rotation vary, but it wobbles as it rotates. These variations in the Earth's rotation, which occur on all observable timescales from subdaily to decadal and longer, are caused by a wide variety of processes, from external tidal forces to surficial processes involving the atmosphere, oceans, and hydrosphere to internal processes acting both at the core-mantle boundary as well as within the solid body of the Earth. In this chapter, the equations governing small variations in the Earth's rotation are derived, the techniques used to measure the variations are described, and the processes causing the variations are discussed.

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... As a dynamic system, the Earth is affected by some internal dynamic processes, external mass transport and the gravitational attraction of the Sun, Moon and planets; hence, the Earth's rotation is changing (Gross, 1993(Gross, , 2015. The instantaneous position of the Earth's rotation vector is described by the three components (m1, m2, m3), where m1 and m2 describe polar motion (PM) (m1+im2), and m3 describes variations in the rotation rate (directly proportional to changes in the length of day (LOD)) (Wahr, 1985). ...

... The instantaneous position of the Earth's rotation vector is described by the three components (m1, m2, m3), where m1 and m2 describe polar motion (PM) (m1+im2), and m3 describes variations in the rotation rate (directly proportional to changes in the length of day (LOD)) (Wahr, 1985). The decadal variations in the Earth's rotation have been studied since the 1960s, but the cause of those variations is currently unknown (see Gross (2015) for a review). Recently, two interdecadal periodic signals, an ~5.9yr oscillation (referred to as SYO) and an ~8.5yr oscillation (referred to as EYO), have been identified in the Earth's rotation variations. ...

... In addition to Liu et al. (2007) using NTFT to restore the Chandler wobble from the PM, NTFT has also been used to restore the normal modes of the Earth's free oscillations (e.g., Duan and Huang, 2019). Unlike the Chandler wobble, which has uncertain time-varying amplitudes in the time domain (Gross, 2015), the normal modes of the Earth's free oscillations are stable cosine oscillations with fixed attenuations. Hence, here, we use the NTFT+curve fitting process to restore the 0S0 mode as an example and compare the obtained results with those of previous studies. ...

To accurately restore interdecadal oscillations from the length of day variation ({\Delta}LOD) and the polar motion (PM), we propose a normal time-frequency transform (NTFT) combing with curve fitting scheme. Compared with the NTFT, the combined NTFT with a boundary extreme point mirror-image-symmetric extension (BEPME) process, and singular spectrum analysis (SSA) in some simulated tests, the superiority and reliability of this new scheme have been confirmed; and we further verified the validity of it in a mature case analysis from the Earth's free oscillation modes 0S0 and 1S0. After then, we use it to restore the ~5.9yr oscillation (referred to as SYO) and ~8.5yr oscillation (referred to as EYO) from the {\Delta}LOD and the PM records. Our results reconfirm that the SYO and EYO in the {\Delta}LOD (and PM) have no stable damping trend (which is different from results in some previous studies), and for the first time, we find that the SYOs (and EYOs) contained in the {\Delta}LOD and the PM show very good consistency. Such consistency demonstrates that the SYOs/EYOs in the {\Delta}LOD and the PM must come from the same source. As the external excitation sources of the Earth rotation contain no such oscillations, we suggest that core motions are possible sources.

... The free mode due to the torque-free rotational equations of motion is called the free wobble or Chandler wobble (CW). If the pole is excited, it can be observed in polar motion, which has been known and measured for the Earth for over 100 years (e.g., Gross, 2015;Moritz & Mueller, 1988;Wahr, 1988). The Earth's polar motion is mostly a combination of the CW (3-to 6-m variable amplitude) with a period of 14 months and annual 12-month forced polar motion (3 m), resulting from seasonal atmospheric pressure changes (Merriam, 1982;Wahr, 1983). ...

... The rigid-body period is significantly less than the observed value of 206.9 days. For Earth, the rigid-body prediction is 305 days, and the observed Chandler period is 433.0 ± 1.1 days (Gross, 2015), an even larger increase due to a larger Love number k 2 (mostly due to the Earth being elastic and more massive than Mars) and a smaller secular Love number k 0 (also called fluid Love number) that enters in the denominator in the expression of the Chandler period. The modeled CW period P CW for a triaxial elastic body with a liquid core is given by (e.g., Zharkov & Gudkova, 2009, equation 8) ...

... Mars' CW will damp out quickly (~60 years; unless there is an excitation, which for Earth is mostly thought to be related to atmospheric, oceanic, and hydrologic processes (Gross, 2000(Gross, , 2015. For Mars, the excitation is related to the seasonal mass exchange between the Mars polar caps, and mostly driven by atmospheric pressure changes especially near the one-third Mars year frequency , which is close to the Chandler frequency. ...

For the first time for any planetary body other than the Earth, the free wobble of the pole called the Chandler wobble has been detected for Mars with a period of 206.9 ± 0.5 days and amplitude of 10 cm from radio tracking observations of Mars Odyssey, Mars Reconnaissance Orbiter (MRO), and Mars Global Surveyor (MGS), in order of decreasing sensitivity. The motion of the rotation pole location on the surface of Mars, or polar motion, is observed using two different approaches: (1) joint global estimates of Mars' orientation and its gravity field and (2) time series solutions of C21 and S21. For Mars interior models, the Chandler wobble period is combined with other measurements including the moments of inertia from our estimated precession rate ψ̇=−7603.9±1.3mas/year and tidal Love number k2 = 0.169 ± 0.006. The Chandler wobble period constrains the rheology of the Martian mantle and in particular its long‐term frequency dependence.

... November 2021) with a Chandler period of 433 days. Geodetic equatorial, χ 1 and χ 2 , excitation functions are computed using the Liouville algorithm (e.g., [24]): ...

... The factors 0.684 and 1.608 account for the yielding of the solid Earth to surface mass loading and the effect of core decoupling, respectively. Numerical values for these factors are taken from [24]. In this study, different equatorial EAMFs computed from different sources are used to describe the geophysical excitation functions of PM and assess the ability of these models to explain full interannual signals in geodetic observations. ...

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.

... If these are driven by mass redistribution, they capture the changing orientation of the rotation vector as it tracks the changing moment of inertia tensor of the planet. The latter are directly connected to the global gravity field of degree 2, order 1 (e.g., Gross 2015). ...

... Polar motion offers an additional way to monitor large-scale global mass redistributions with a possible contribution from the core. The decadal polar motion is of the order of 10-25 milliarcsec (mas) (e.g., Gross 2015). Since the early 2000s, when satellite gravity observations have allowed to monitor the planetary scale changes in terrestrial water storage more accurately, the latter have been shown to account for most of the non-steady drift in polar motion (e.g., Adhikari and Ivins 2016). ...

Fluid motion within the Earth’s liquid outer core leads to internal mass redistribution. This occurs through the advection of density anomalies within the volume of the liquid core and by deformation of the solid boundaries of the mantle and inner core which feature density contrasts. It also occurs through torques acting on the inner core reorienting its non-spherical shape. These in situ mass changes lead to global gravity variations, and global deformations (inducing additional gravity variations) occur in order to maintain the mechanical equilibrium of the whole Earth. Changes in Earth’s rotation vector (and thus of the global centrifugal potential) induced by core flows are an additional source of global deformations and associated gravity changes originating from core dynamics. Here, we review how each of these different core processes operates, how gravity changes and ground deformations from each could be reconstructed, as well as ways to estimate their amplitudes. Based on our current understanding of core dynamics, we show that, at spherical harmonic degree 2, core processes contribute to gravity variations and ground deformations that are approximately a factor 10 smaller than those observed and caused by dynamical processes within the fluid layers at the Earth’s surface. The larger the harmonic degree, the smaller is the contribution from the core. Extracting a signal of core origin requires the accurate removal of all contributions from surface processes, which remains a challenge.
Article Highlights
Dynamical processes in Earth's fluid core lead to global gravity variations and surface ground deformations
We review how these processes operate, how signals of core origin can be reconstructed and estimate their amplitudes
Core signals are a factor 10 smaller than the observed signals; extracting a signal of core origin remains a challenge

... Polar motion (PM), movement of Earth's rotational axis relative to the crust, is a geophysical phenomenon excited by relative motion and mass redistribution within the Earth system. Sources include the atmosphere, hydrosphere, cryosphere and solid Earth (Gross 2007). PM observations and prediction (from geophysical data and models) provide a unique integrated view of Earth system changes. ...

... PM observations show an evident Chandler wobble, the Eulerian free wobble with about 14-month period. Annual and interannual PM variations are forced by relative motion of winds and ocean currents and mass redistribution of air and water (Gross 2007). Markowitz (1961) found quasi-periodic multi-decadal oscillations (Markowitz wobble) in PM, but their origin was unknown. ...

A long-term drift in polar motion (PM) has been observed for more than a century, and Glacial Isostatic Adjustment (GIA) has been understood as an important cause. However, observed PM includes contributions from other sources, including contemporary climate change and perhaps others associated with Earth’s interior dynamics. It has been difficult to separate these effects, because there is considerable scatter among GIA models concerning predicted PM rates. Here we develop a new method to estimate GIA PM using data from the GRACE mission. Changes in GRACE degree 2, order 1 spherical harmonic coefficients are due both to GIA and contemporary surface mass load changes. We estimate the surface mass load contribution to degree 2, order 1 coefficients using GRACE data, relying on higher-degree GRACE coefficients that are dominantly affected by surface loads. Then the GIA PM trend is obtained from the difference between observed PM trend (which includes effects from GIA and surface mass loads) and the estimated PM trend mostly associated with surface mass loads. A previous estimate of the GIA PM trend from PM observations for the period 1900–1978 is toward 79.90° W at a speed of 3.53 mas/year (10.91 cm/year). Our new estimate for the GIA trend is in a direction of 61.77° W at a speed of 2.18 mas/year (6.74 cm/year), similar to the observed PM trend during the early twentieth century. This is consistent with the view that the early twentieth-century trend was dominated by GIA and that more recently there is an increasing contribution from contemporary surface mass load redistribution associated with climate change. Our GIA PM also agrees with the linear mean pole during 1900–2017. Contributions from other solid Earth process such as mantle convection would also produce a linear trend in PM and could be included in our GIA estimate.

... The fluctuation characteristics and excitations of the intradecadal changes in the length-of-day variation (∆LOD) were thought to be related to the secular variations in the core geomagnetic field and hence help to constrain the magnetic field strength in the core as well as to understand the mechanism driving the Earth's core-mantle interactions (e.g., Mound and Buffett, 2006;Gross, 2015). Two periodic signals have been detected from the ΔLOD in the intradecadal period band (i.e., the 5-10yr period band), an approximately six year oscillation (SYO) (e.g., Liao and Greiner-Mai, 1999;Holme and de Viron, 2013) and an approximately 8.5yr oscillation (EYO) (Ding 2019; Duan and Huang, 2020a). ...

... Note that the AAM/OAM/HAM effects are the main Earth external excitation sources of the Earth's rotation (Gross, 2015). All those four datasets have been pre-processed (the same pre-processes can be found in Ding (2019) ...

The intradecadal fluctuations in the length-of-day variation (∆LOD) are considered likely to play an important role in core motions. Two intradecadal oscillations, with ~5.9yr and ~8.5yr periods (referred to as SYO and EYO, respectively), have been detected in previous studies. However, whether the SYO and the EYO have exhibited stable damping trends since 1962 and whether geomagnetic jerks are possible excitation sources for the SYO/EYO are still debated. In this study, based on different methods and different ∆LOD records with different time spans, we showed robust evidence to prove that the SYO and the EYO have had no stable damping trends since 1962. We also found that there may be a ~7.6yr signal, but given that its average amplitude is too small, further confirmations are needed in the future. After confirming that the jerks have no special consistency with the peaks/valleys of the EYO/SYO, we further used a deconvolution process and confirmed that the geomagnetic jerks seem to be related to sudden changes in the SYO/EYO time series and their excitation series. Thus we finally suggest that jerks are possible excitation sources of the SYO/EYO. After using a deconvolution process, we estimate that the period P and quality factor Q of the SYO and the EYO are [P=5.85±0.06yr, Q≥180] and [P=8.45±0.17yr, Q≥350], respectively.

... The relative motion represents wind, current and mass redistribution including, for example, groundwater depletion, glacier mass loss, and sea level rise. 19 Polar motion data provides integrated implication of the change of the whole Earth system. In order to understand causes of polar motion, various methods predicting Earth Orientation Parameters (EOP) have been conducted. ...

... Chandler wobble associated with Earth's free oscillation 19,24 is apparent in EOP, and thus it is necessary to correct the wobble to accurately measure the Earth's rotation variation. The Chandler wobble is the dominant EOP component at the Chandler frequency (0.843 cycles/year % 14 months) and can be removed by applying a digital¯lter in the frequency domain: ...

An accurate analysis of the polar motion variation is essential to understand the global change of the environment and predict useful information about short-term and long-term change in climate. Observation of polar motion excitation using multiple measurements including Very-Long-Baseline-Interferometry (VLBI) provides highly accurate measurement of polar motion variation. The observed polar motion excitation has been modeled with multiple geophysical models, but the discrepancies between observations and models still exist. In this paper, we propose two approaches for detecting the discrepancy of the polar motion excitation: topological data analysis (TDA) and convolutional neural network (CNN) analysis. Our methods clearly show that the observed polar motion has a different topological structure from the model data, and there are time periods that the model fails to represent the polar motion. Numerical results indicate that the proposed methods show promise for applications to polar motion signal analysis.

... Ruch bieguna ziemskiego definiuje się jako zmianę położenia osi obrotu w bryle Ziemi względem jej powierzchni, który określa się współrzędnymi x p , y p bieguna ziemskiego. Parametry EOP są wyznaczane od końca XIX wieku i od tamtej pory nastąpił znaczny wzrost dokładności ich wyznaczania, w szczególności od momentu wprowadzenia do ich obserwacji satelitarnych technik pomiarowych [16]. ...

... Oba modele opracowywane są w NASA JPL (NASA Jet Propulsion Laboratory) i stanowią również oficjalny produkt GGFC Special Bureau for the Ocean ( [37]). Model ECCO składa się z 46 poziomów o wysokości od 10 metrów przy powierzchni oceanów do 400 metrów na ich dnie i jest stymulowany przez model oceaniczny NCEP/NCAR ( [15], [16]). Model kf080 obejmuje pomiary altymetryczne wysokości powierzchni oceanów oraz dane pozyskane z pomiarów batytermograficznych (XBT data -expendable bathythermograph data). ...

Przeprowadzone analizy zmian geodezyjnej – rezydualnej funkcji pobudzenia ruchu
bieguna ziemskiego, wyznaczonej na podstawie najnowszych modeli AAM i OAM
oraz porównania z hydrologiczną funkcją pobudzenia wyznaczoną z modelu
LSDM (Land Surface Discharge Model) oraz na podstawie danych z satelitarnej
grawimetrycznej misji GRACE, mają na celu pokazanie różnic pomiędzy różnymi
funkcjami GAO oraz ich zgodność z hydrologią lądową (HAM). Głównym
celem tych badań jest określenie kryterium, które uzasadnia użycie jednej kombinacji
rezydualnej funkcji pobudzenia ruchu bieguna ziemskiego GAO, zgodnej
ze zmianami funkcji HAM będącej odzwierciedleniem zmian rzeczywistego
ekwiwalentnego słupa wody TWS. Realizacja tego kryterium będzie opierała się
na wyznaczeniu poziomu szumu każdej z rozpatrywanych rezydualnych funkcji
pobudzenia przy użyciu tzw. „three – cornered hat method” oraz wyznaczeniu
tzw. kombinowanej funkcji GAO przy założeniu, że poziom szumu nowo wyznaczonej
kombinowanej funkcji jest minimalny. Oczekujemy, że zgodność tak
wyznaczonej funkcji GAO z hydrosferą lądową zwiększy się w zakresie rozpatrywanych
oscylacji niesezonowych.

... Mass redistribution and its movement within the Earth system excite rotational changes, mainly at seasonal or shorter timescales. The importance of Atmospheric Angular Momentum (AAM) and Oceanic Angular Momentum (OAM) signals for polar motion excitation at seasonal timescales is well known (Gross et al., 2003;Brzezinski et al., 2005;Gross, 2007) as both the atmosphere and the ocean have spatial patterns, which contribute to polar motion excitation (Nastula et al., 2003). The atmosphere (including pressure and mass changes) exhibits a high level of mobility. ...

... The consideration of the global mass balance effects is a crucial point in the geophysical interpretations of polar motion and length of the day variations (Chen et al. 2005;Gross, 2007;Brzezinski et al., 2009). ...

Changes in Terrestrial Water Storage (TWS) due to seasonal changes in soil moisture, ice and snow loading and melting influence the Earth's inertia tensor. Quantitative assessment of hydrological effects of polar motion remain unclear because of the lack of the observations and differences between various atmospheric and ocean models. Here, we compare the effects of several hydrological excitation functions computed as the difference between the excitation function of polar motion GAM (Geodetic Angular Momentum) and join atmospheric plus oceanic excitation functions, called geodetic residuals. Geodetic residuals are computed for different Atmospheric Angular Momentum (AAM) and Oceanic Angular Momentum (OAM) models and are analyzed and compared with the hydrological excitation function determined from the Land Surface Discharge Model. They are analyzed on decadal, interannual, seasonal and non-seasonal time scales. The equatorial components of χ1 and χ2 were decomposed into prograde and retrograde time series by applying Complex Fourier Transform Models. The agreement between hydrological geodetic residuals and excitation functions was validated using Taylor diagrams. This shows that agreement is highly dependent on AAM and OAM models. Errors in these models affect the resulting geodetic residuals and have a big impact on the Earth's angular momentum budget.

... The advantages of this approach include the use of highly accurate neural networks and the possibility to include physical information. As polar motion components can be considered to follow Ordinary Differential Equations (ODEs, Chin et al. [2004]; Gross [2007]), the Neural ODEs method can be applied. ...

This paper introduces a new learning algorithm for accurate, physically driven time series prediction. The fundamental assumption behind the method is that the phenomena follow Ordinary Differential Equations. We investigate the general case where the time series follows an ODE of degree m∈N $m\in \mathbb{N}$. The resulting method is a learning algorithm based on the finite differences between the values of time series. We present the application of the method in the field of geodesy for polar motion prediction, the main objective of the present paper. We show that in this application, the linear form of the method is sufficient and offers competitive predictive performance. We present a baseline solution, in which we use historical polar motion time series from 1976 to predict up to the year 2020. The prediction horizon in this case is short‐term (up to 10 days into the future). In addition, we compare the prediction accuracy in the short‐term horizon with the results of the best performing model in the first Earth Orientation Prediction Comparison Campaign. On average, a 53% improvement in prediction performance is achieved. In further analyses, we compare the prediction accuracy for both short‐term and long‐term against the results of state‐of‐the‐art methods, namely Multichannel Singular Spectrum Analysis, and a combination of Singular Spectrum Analysis and Copula sampling. We show that the proposed method in this paper can outperform the mentioned two methods in both short and long‐term horizons, with an average improvement of the prediction performance of 54% and 52%, respectively.

... PM changes are mostly composed of two counterclockwise wobbles at periods of 433 days (Chandler wobble) and 365 days (annual wobble). Annual and interannual PM variations are forced by the relative motion of winds and ocean currents and the mass redistribution of air and water (Gross 2007(Gross , 2015. The major part of PM changes are explained by the atmosphere (both winds and surface pressure) (e.g. ...

Polar motion (PM) is an essential parameter needed to transform coordinates between celestial and terrestrial reference frames, thus playing a crucial role in precise positioning and navigation. The role of hydrological signals in PM excitation is not yet fully understood, which is largely because of the lack of agreement between estimates of hydrological angular momentum (HAM) computed from different data sources. In this study, we used data obtained from the latest, sixth phase of the Coupled Model Intercomparison Project (CMIP6) to assess the impact of the continental hydrosphere on PM excitation. To do so, we exploited soil moisture and snow water variables obtained from historical simulations of CMIP6 to estimate climate-based HAM. The HAM series were computed, then we analysed their variability in terms of trends, seasonal and non-seasonal oscillations. An important part of this study is the validation of HAM estimates based on comparison with the hydrological signal in geodetically observed PM excitation (geodetic residuals, GAO). In addition, HAM series based on climate models were compared with those determined from global gravimetric data provided by the Gravity Recovery and Climate Experiment (GRACE) mission, and from the Land Surface Discharge Model (LSDM). This study also aimed to identify the most appropriate CMIP6 models for interpretation of PM variations. Overall, the correspondence between GAO and HAM received from CMIP6 was lower than the previously obtained consistency with GRACE results, and the level of agreement was dependent on the oscillation considered and the model used. However, it may be possible to identify several CMIP6 models from among the almost 100 available that provides a HAM series more compatible with GAO than HAM from GRACE or LSDM, especially in annual oscillations. The GISS-E2-1-G_historical_r10i1p1f1 model was found to provide the highest consistency with GAO for annual prograde amplitudes, GFDL-CM4_historical_r1i1p1f1 for annual retrograde amplitudes, BCC-ESM1_historical_r3i1p1f1 for the annual prograde phase, and MIROC-ES2L_historical_r2i1p1f2 for the annual retrograde phase. Because of their length, the CMIP6 data allow for analysis of the past and future changes in HAM from 1850 to 2100, which is of particular importance in the exploration of the impact of climate change on PM excitation.
Graphical Abstract

... These independently determined low-degree SH coefficients offer important validations of GRACE/GRACE-FO gravity solutions at the longest wavelengths. The two degree-2 order-1 SH coefficients ( ΔC 2,1 and ΔS 2,1 ) are linearly related to polar motion (PM), the equatorial components of Earth rotational axis (Eubanks 1993;Gross 2007). Polar motion (PM) is regarded as one of (7) ...

Time-variable gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions have opened up a new avenue of opportunities for studying large-scale mass redistribution and transport in the Earth system. Over the past 19 years, GRACE/GRACE-FO time-variable gravity measurements have been widely used to study mass variations in different components of the Earth system, including the hydrosphere, ocean, cryosphere, and solid Earth, and significantly improved our understanding of long-term variability of the climate system. We carry out a comprehensive review of GRACE/GRACE-FO satellite gravimetry, time-variable gravity fields, data processing methods, and major applications in several different fields, including terrestrial water storage change, global ocean mass variation, ice sheets and glaciers mass balance, and deformation of the solid Earth. We discuss in detail several major challenges we need to face when using GRACE/GRACE-FO time-variable gravity measurements to study mass changes, and how we should address them. We also discuss the potential of satellite gravimetry in detecting gravitational changes that are believed to originate from the deep Earth. The extended record of GRACE/GRACE-FO gravity series, with expected continuous improvements in the coming years, will lead to a broader range of applications and improve our understanding of both climate change and the Earth system.

... The rotation period of the Earth is varying under the influence of external torques and internal exchanges of angular momentum [e.g. Gross, 2015]. Assuming geostrophic core flow motion, Jault et al. [1988] show a good correlation between such flows and LOD decadal variations. ...

Direct measurements of the geomagnetic field being only available over the historical period (from 1590 to today), global reconstructions beyond that time therefore resort to indirect measurements provided by paleo- and archeomagnetism. In this respect, archeomagnetism can provide particularly well dated data. This thesis aims at analyzing the geomagnetic field intensity variations provided by archeomagnetism over multi-decadal to centennial timescales, from two different but complementary aspects. A first study focuses on the acquisition of archeointensity data in central Asia and their consequences on the knowledge of regional and global geomagnetic field variations. In particular, global geomagnetic field models over the historical period based on direct mea-surements solely need additional constraints to overcome the absence of direct intensitymeasurements before ~1840. Two options have been proposed: either to linearly extrapolate backward the behavior of the axial dipole moment observed since 1840, as in the gufm1 model, or to rely on a global archeointensity dataset. In this study, a regional approach is used, based on new archeointensity data obtained from Bukhara for the historical period. This city is of particular interest owing to its outstanding, well-preserved historical center and the archives just as well preserved providing precise dating constraints on the buildings sampled for this study. The baked clay bricks fragments are analysed using the Triaxe experimental protocol. The obtained intensity variations curve shows a rapid decrease from 1600 to ~1750 followed by an increase until the early 19th. This evolution is in good agreement with other Triaxe data acquired in western Europe and western Russia. These three Triaxe datasets are used to recalibrate the axial dipole moment from the gufm1 model. The resulting evolution is non-linear, with a minimum amplitude during the second half of the 18th century. Although the results presented in this study need to be confirmed by further data acquisition worldwide, it nonetheless illustrates that archeointensity data can provide constraints on the geomagnetic intensity evolution over multi-decadal to centennial timescales at both regional and global scales.The second study focuses on intensity variations inferred from archeomagnetic data, from a theoretical standpoint. Recently, extreme archeointensity events lasting only a few decades, termed geomagnetic spikes, have been proposed in the Near-East during the first millennium BC. They are associated with variations rates up to several μT/yr, while today’s maximum is of order ~0.1 μT/yr. Magnetic flux expulsion at the core’s surface has been proposed to explain such extreme events, but this process has not yet been studied in detail. In this study, a 2D kinematic model of magnetic flux expulsion is implemented, controlled by a single parameter: the magnetic Reynolds number Rm, the ratio of magnetic diffusion to advection times. This model allows for the monitoring of initially horizontal magnetic field lines, advected by a fixed flow pattern constituted by two counter-rotating eddies. As the magnetic field lines are distorted and folded by the flow, the magnetic flux is progressively expelled towards the domain’s boundaries. If the boundary separates the conducting fluid from an insulating medium, the magnetic flux can diffuse through it. To follow the flux expulsion through the insulating boundary, the vertical component of the magnetic field is monitored during the system evolution. The characteristic rise time is found to scale as Rm0.15, while the maximum instantaneous variation rate scales as Rm0.45. These scaling laws are then extrapolated at the Earth’s surface. The results show that geomagnetic spikes cannot be generated by flux expulsion. However, other intensity peaks of durations longer than one century and associated with much lower variation rates would be compatible with flux expulsion events.

... We infer that the unmodelled OPTL deformation of standard solution may be partly absorbed by other estimated parameters during the GPS data processing. Moreover, annual and Chandler terms of polar motion have time-varying amplitude and phase (Gross 2007), and the induced peak-to-peak amplitude of OPTL deformation ranging from 2014 to 2018 are relatively small in Section 2.1 (shown in Fig. 2). ...

The changes in the centrifugal force induced by polar motion perturbs 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 modeling, subdaily polar motion can introduce annual variations in OPTL with the small magnitudes in micrometers. The new secular pole model can cause OPTL vertical velocity difference up to 0.03 mm/yr compared with the mean pole model of International Earth Rotation and Reference System Service (IERS) Conventions (2010). The OPTL deformation are dominated by the annual (∼365.25 days) and Chandler (∼ 433 days) 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 (RMS) of OPTL induced GPS daily displacements can reach submillimeter 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 (GGOS) requirements for the future terrestrial reference frame at millimeter level.

... Observed EOP excitations include mass and motion term contributions, and the mass term excitations can be linearly related to degree-2 gravitational changes ΔC 21 and ΔS 21 as (Eubanks 1993;Gross 2007Gross , 2015, in which mass i , i = 1,2 are mass term excitations of observed PM X and Y. M (5.972 × 10 24 kg) and R (6371 km) are mass and mean radius of the Earth, C and A (C-A = 2.61 × 10 35 kg·m 2 ) the two principal inertia moments of the Earth (Eubanks 1993). k' 2 is the degree-2 load Love (1) ...

We carry out a comprehensive analysis and assessment of degree-2 gravitational changes ΔC21, and ΔS21, estimated using the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GFO), satellite laser ranging (SLR), Earth Orientation Parameters (EOP), and geophysical models over the period April 2002–February 2020. The four independent estimates of ΔC21 and ΔS21 variations agree well over a broad band of frequencies. The GRACE/GFO Release 6 (RL06) solutions show major improvements over the previous RL05 solutions at both seasonal and intra-seasonal time scales, when compared with EOP and SLR estimates. Among the four independent estimates, highest correlation coefficients and smallest RMS residuals are found between GRACE/GFO and EOP estimates of ΔC21 and ΔS21 variations. GRACE/GFO and EOP ΔC21 and ΔS21 estimates exhibit slightly different trends, which are related to the implementation and interpretation of the pole tide correction in GRACE/GFO data processing. This study provides an important early validation of GFO ΔC21 and ΔS21 solutions, especially the new pole tide correction applied in GRACE/GFO RL06 solutions using independent estimates.

... On seven instances, we observed Venus on consecutive days and measured variations ranging between 2 and 17 ppm with a weighted average value of 9 ± 5 ppm (1σ), suggesting a spin rate of change as large as dω/dt ∼ 3.1 × 10 −17 rad s −2 and corresponding torques T = Cdω/dt ∼ 1.9 × 10 21 N m. The LOD variations observed at Venus are 3 orders of magnitude larger than on Earth, where core-mantle interactions can change the LOD by ∼4 ms (46 ppb) on ∼20-year timescales [40]. The torques responsible for the LOD variations on Earth are ...

Fundamental properties of the planet Venus, such as its internal mass distribution and variations in length of day, have remained unknown. We used Earth-based observations of radar speckles tied to the rotation of Venus obtained in 2006-2020 to measure its spin axis orientation, spin precession rate, moment of inertia, and length-of-day variations. Venus is tilted by 2.6392 $\pm$ 0.0008 degrees ($1\sigma$) with respect to its orbital plane. The spin axis precesses at a rate of 44.58 $\pm$ 3.3 arcseconds per year, which gives a normalized moment of inertia of 0.337 $\pm$ 0.024 and yields a rough estimate of the size of the core. The average sidereal day on Venus is currently 243.0226 $\pm$ 0.0013 Earth days ($1\sigma$). The spin period of the solid planet exhibits variations of 61 ppm ($\sim$20 minutes) with a possible diurnal or semidiurnal forcing. The length-of-day variations imply that changes in atmospheric angular momentum of at least $\sim$4% are transferred to the solid planet.

... Итоговые значения вычисленных нами по формулам (9)-(11) координат геоцентра с учетом и без учета эффекта обратного барометра Массовые члены возмущающих функций атмосферы согласно [Gross, 2007] имеют вид: ...

... The associated global-scale angular momentum, coming both from a nearglobal rotation of the ocean or a global-scale mass redistribution, is expected to leave its signature in the Earth's rotation 6,7 . The Earth's rotation is not constant, and presents uctuations in a broad range of frequencies 8,9 . Most of those signals come from the variability in the angular momentum of the Earth's core and the atmosphere 8 . ...

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 (MJO), over the tropical interface between the Indian Ocean and the Pacific Ocean (popularly known as Maritime Continent) generate significant basin-wide intraseasonal barotropic sea level variability in the tropical Indian Ocean. Here we show, using an ocean general circulation 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 MJO in a few days. We also explain how this near-global-scale MJO-induced oceanic phenomenon is the first signature from a climate mode that can be isolated into the Earth polar axis motion, in particular during the strong see-saw of early 2013.

... The gold standard in this regard is the very long baseline interferometry (VLBI) technique [10]. Although accessible in principle, the VLBI measurement technique is not directly linked to the rotational axis of Earth, but to a network of widely spaced radio telescope positions [11]. With the help of modeled nutation and polar motion, the instantaneous orientation of the Earth rotation axis relative to the body of Earth can be inferred. ...

Absolute rotation rate sensing with extreme sensitivity requires a combination of several large scale gyroscopes in order to obtain the full vector of rotation. We report on the construction and operation of a four-component, tetrahedral laser gyroscope array as large as a five story building and situated in a near surface, underground laboratory. It is demonstrated that reconstruction of the full Earth rotation vector can be achieved with sub-arcsecond resolution over more than six weeks.

... Decadal variations in the Earth's length-of-day (LOD) have long been associated with dynamics in the liquid outer core (Munk & MacDonald 1960;Hide 1966;Jault et al. 1988;Gross 2015). More specifically, a pronounced variation on a period of roughly six years cannot be explained by atmospheric, oceanic and tidal forces, which are responsible for LOD variations on shorter timescales (Abarca del Rio et al. 2000;Holme & de Viron 2013). ...

We investigate the pressure torque between the fluid core and the solid mantle arising from magnetohydrodynamic modes in a rapidly rotating planetary core. A two-dimensional reduced model of the core fluid dynamics is developed to account for the non-spherical core-mantle boundary. The simplification of such a quasi-geostrophic model rests on the assumption of invariance of the equatorial components of the fluid velocity along the rotation axis. We use this model to investigate and quantify the axial torques of linear modes, focusing on the torsional Alfvén modes (TM) in an ellipsoid. We verify that the periods of these modes do not depend on the rotation frequency. Furthermore, they possess angular momentum resulting in a net pressure torque acting on the mantle. This torque scales linearly with the equatorial ellipticity. We estimate that for the TM calculated here topographic coupling to the mantle is too weak to account for the variations in the Earth’s length-of-day.

... Decadal variations in the Earth's length-of-day (LOD) have long been associated with dynamics in the liquid outer core (Munk & MacDonald 1960;Hide 1966;Jault et al. 1988;Gross 2015). More specifically, a pronounced variation on a period of roughly six years cannot be explained by atmospheric, oceanic and tidal forces, which are responsible for LOD variations on shorter time scales (Abarca del Rio et al. 2000;Holme & de Viron 2013). ...

We investigate the pressure torque between the fluid core and the solid mantle arising from magnetohydrodynamic modes in a rapidly rotating planetary core. A two-dimensional reduced model of the core fluid dynamics is developed to account for the non-spherical core-mantle boundary. The simplification of such a quasi-geostrophic model rests on the assumption of invariance of the equatorial components of the fluid velocity along the rotation axis. We use this model to investigate and quantify the axial torques of linear modes, focusing on the torsional Alfv\'en modes (TM) in an ellipsoid. We verify that the periods of these modes do not depend on the rotation frequency. Furthermore, they possess angular momentum resulting in a net pressure torque acting on the mantle. This torque scales linearly with the equatorial ellipticity. We estimate that for the TM calculated here topographic coupling to the mantle is too weak to account for the variations in the Earth's length-of-day.

... These changes are due to (i) external tidal torques by the Moon and Sun (referred to as the astronomical variations), and (ii) internal interactions of the solid Earth with other (fluid) components of the Earth system (referred to as the geophysical variations). Observed changes in the Earth's rotation have long been used to understand the dynamical processes in the Earth (e.g., [1]; for a recent review see, e.g., [2]). In this paper, we focus on the polar motion, the rotation axis orientation variation relative to the terrestrial reference frame, that is arising from electromagnetic interactions in the form of angular momentum exchanges between the convective fluid outer core and the solid mantle. ...

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. Keywords: Polar motion, Electromagnetic core-mantle coupling, Geomagnetic field, Geodynamo

... Core-mantle coupling is also affected by stratification. Transfer of angular momentum across the CMB is commonly invoked to explain changes in LOD over periods of several decades (Gross, 2015). Possible mechanisms include topographic (Hide, 1969;Moffatt, 1977), electromagnetic (Bullard et al., 1950;Rochester, 1962) and gravitational (Jault et al., 1988;Buffett, 1996) torques. ...

Fluctuations in the length of day (LOD) over periods of several decades are commonly attributed to exchanges of angular momentum between the mantle and the core. However, the forces that enable this exchange are less certain. Suggestions include the influence of pressure on boundary topography, electromagnetic forces associated with conducting material in the boundary region and gravitational forces due to mass anomalies in the mantle and the core. Each of these suggestions has strengths and weaknesses. Here we propose a new coupling mechanism that relies on the presence of stable stratification at the top of the core. Steady flow of the core over boundary topography promotes radial motion, but buoyancy forces due to stratification oppose this motion. Steep vertical gradients develop in the resulting fluid velocity, causing horizontal electromagnetic forces in the presence of a radial magnetic field. The associated pressure field exerts a net horizontal force on the boundary. We quantify this hybrid mechanism using a local Cartesian approximation of the core-mantle boundary and show that the resulting stresses are sufficient to account for the observed changes in LOD. A representative solution has 52 m of topography with a wavelength of 100 km. We specify the fluid stratification using a buoyancy frequency that is comparable to the rotation rate and adopt a radial magnetic field based on geodetic constraints. The average tangential stress is 0.027 N m-2 for a background flow of V̄=0.5 mm s-1. Weak variations in the stress with velocity (i.e. V¯1/2) introduce nonlinearities into the angular momentum balance, which may generate diagnostic features in LOD observations.

... Considering angular momentum conservation, any mass redistribution on the Earth excites Earth rotation variations (Chao and Ray 1997). Changes in polar motion and LOD are excited by two mechanisms: (1) mass redistribution, changing the inertia tensor DI, usually referred to as mass term; (2) motion relative to the rotating reference frame changing the relative angular momentum h, usually referred to as motion term (Gross 2007;Munk and MacDonald 1960). The mass term is represented by the tidal heights of the ocean surface, the motion term arises from oceanic currents. ...

Recent improvements in the development of VLBI (very long baseline interferometry) and other space geodetic techniques such as the global navigation satellite systems (GNSS) require very precise a-priori information of short-period (daily and sub-daily) Earth rotation variations. One significant contribution to Earth rotation is caused by the diurnal and semi-diurnal ocean tides. Within this work, we developed a new model for the shortperiod ocean tidal variations in Earth rotation, where the ocean tidal angular momentum model and the Earth rotation variation have been setup jointly. Besides the model of the short-period variation of the Earth’s rotation parameters (ERP), based on the empirical ocean tide model EOT11a, we developed also ERP models, that are based on the hydrodynamic ocean tide models FES2012 and HAMTIDE. Furthermore, we have assessed the effect of uncertainties in the elastic Earth model on the resulting ERP models. Our proposed alternative ERP model to the IERS 2010 conventional model considers the elastic model PREM and 260 partial tides. The choice of the ocean tide model and the determination of the tidal velocities have been identified as the main uncertainties. However, in the VLBI analysis all models perform on the same level of accuracy. From these findings, we conclude that the models presented here, which are based on a reexamined theoretical description and long-term satellite altimetry observation only, are an alternative for the IERS conventional model but do not improve the geodetic results.

... Considering angular momentum conservation, any mass redistribution on the Earth excites Earth rotation variations (Chao and Ray 1997). Changes in polar motion and LOD are excited by two mechanisms: (1) mass redistribution, changing the inertia tensor DI, usually referred to as mass term; (2) motion relative to the rotating reference frame changing the relative angular momentum h, usually referred to as motion term (Gross 2007;Munk and MacDonald 1960). The mass term is represented by the tidal heights of the ocean surface, the motion term arises from oceanic currents. ...

Recent improvements in the development of VLBI (very long baseline interferometry) and other space geodetic techniques such as the global navigation satellite systems (GNSS) require very precise a-priori information of short-period (daily and sub-daily) Earth rotation variations. One significant contribution to Earth rotation is caused by the diurnal and semi-diurnal ocean tides. Within this work, we developed a new model for the short-period ocean tidal variations in Earth rotation, where the ocean tidal angular momentum model and the Earth rotation variation have been setup jointly. Besides the model of the short-period variation of the Earth’s rotation parameters (ERP), based on the empirical ocean tide model EOT11a, we developed also ERP models, that are based on the hydrodynamic ocean tide models FES2012 and HAMTIDE. Furthermore, we have assessed the effect of uncertainties in the elastic Earth model on the resulting ERP models. Our proposed alternative ERP model to the IERS 2010 conventional model considers the elastic model PREM and 260 partial tides. The choice of the ocean tide model and the determination of the tidal velocities have been identified as the main uncertainties. However, in the VLBI analysis all models perform on the same level of accuracy. From these findings, we conclude that the models presented here, which are based on a re-examined theoretical description and long-term satellite altimetry observation only, are an alternative for the IERS conventional model but do not improve the geodetic results.

... Numerous studies show that annual and semi-annual changes in the speed of the zonal westerly winds are responsible for most of the variations that are seen in the annual and semi-annual component of the Earth's length-of-day (LOD) [27][28][29][30][31][32]. The close correspondence between these two phenomena comes about because the total angular momentum of the Earth/Atmosphere system is effectively conserved over semi-annual to annual time scales [33]. ...

Lunar ephemeris data is used to find the times when the Perigee of the lunar orbit points directly toward or away from the Sun, at times when the Earth is located at one of its solstices or equinoxes, for the period from 1993 to 2528 A.D. The precision of these lunar alignments is expressed in the form of a lunar alignment index (ϕ). When a plot is
made of ϕ, in a frame-of-reference that is fixed with respect to the Perihelion of the Earth’s orbit, distinct periodicities are seen at 28.75, 31.0, 88.5 (Gleissberg Cycle), 148.25, and 208.0 years (de Vries Cycle). The full significance of the 208.0-year repetition pattern in ϕ only becomes apparent when these periodicities are compared to those observed in the spectra for two proxy time series. The first is the amplitude spectrum of the maximum daytime temperatures (Tm) on the Southern Colorado Plateau for the period from 266 BC to 1997 AD. The second is the Fourier spectrum of the solar modulation potential (ϕm) over the last 9400 years. A comparison between these three spectra shows that of the nine most prominent periods seen in ϕ, eight have matching peaks in the spectrum of ϕm, and seven have matching peaks in the spectrum of Tm. This strongly supports the contention that all three of these phenomena are related to one another. A heuristic Luni-Solar climate model is developed in order to explain the connections between ϕ, Tm and ϕm.

... The shorter period harmonic peaked at p = 1.1 years can be recognised in the first, second and fourth temperature PCs, and in the PC 2-4 associated with the ozone and wind IA variations. It is worth pointing out that this spectral component is close to the period of Chandler wobble found to lie at about 1.2 years and considered the main harmonic of the polar motion (Gross, 2007). QBO is another strongly presented harmonic, identified here as p = 2.4 years (or p = 2.2 years in some of the cases), which component was reported in previous studies (Sitnov, 1996 and2004;Lee et al., 2010;WMO, 2014;Petkov, 2015;Sofieva et al., 2017), while the periods between 1.4 years and QBO could be considered a result of interaction between QBO and the annual cycles (Baldwin et al., 2001). ...

The vertical features of the variations in the atmospheric ozone density, temperature and wind velocity observed at Ny-Ålesund, Svalbard were studied by applying the principal component analysis to the ozonesounding data collected during the 1992 – 2016 period. Two data sets corresponding to intra-seasonal (IS) variations, which are composed by harmonics with lower than 1 year periods and inter-annual (IA) variations, characterised by larger periods, were extracted and analysed separately. The IS variations in all the three parameters were found to be composed mainly by harmonics typical for the Madden-Julian Oscillation (from 30- to 60-day periods) and, while the first four principal components (PCs) associated with the temperature and wind contributed about 90% to the IS variations, the ozone IS oscillations appeared to be a higher dimensional object for which the first 15 PCs presented almost the same extent of contribution. The IA variations in the three parameters were consisted of harmonics that correspond to widely registered over the globe Quasi-Biennial, El Niño-Southern, North Atlantic and Arctic Oscillations respectively, and the IA variations turned out to be negligible below the tropopause that characterises the Svalbard troposphere as comparatively closed system with respect to the long-period global variations. The behaviour of the first and second PCs associated with IS ozone variations in the time of particular events, like the strong ozone depletion over Arctic in the spring 2011 and solar eclipses was discussed and the changes in the amplitude-frequency features of these PCs were assumed as signs of the atmosphere response to the considered phenomena.

On seanonal timescale, the variation of Earth rotation is mainly regulated by angular momentum exchanges between the solid Earth and the fluidal atmosphere, ocean and hydrosphere. In the 2nd EOP PCC, we developed Dill2019’s method for polar motion prediction, using piecewise autoagressive parameters. The maximum prediction errors within 90 days are 36 and 16 mas for polar motion x and y components, respectively. Compared with Bulletin A, the mean absolute error of polar motion y prediction is improved by 20% in all timescale, and with a maximum improvement of 49% on the 5th day. Whereas, for polar motion x, the performance is slightly better (2% - 8%) within 30 days but worse (−7%~ −19%) within 30~90 days. We found that the prediction accuracy is very sensitive to the quality of the angular momentum data. For example, on average, the prediction of polar motion y is around 2 times better than polar motion x. In addition, we found the accuracy of 30-90 days prediction is dramatically decreased in the year 2020. We suspect that such deterioration might be due to the pandemic of coronavirus COVID-19, which suppressed global airline activities by more than 60%, then result in a lose of air-borne meteorological data, which are important for weather forecast.

The uplift of the Tianshan and Pamir Mountains/Areas are caused by active intracontinental tectonic movements. The dynamic mechanism is controversial and has aroused great interest among scholars. In this study, we investigate the present three‐dimensional (3‐D) crustal deformation in the Tianshan and Pamir areas from multi‐geodetic observations from 2002 to 2021. The continuous water deficit throughout Tianshan and Pamir locates mainly in glacier‐covered areas, at a total rate of −0.8 cm w.e./yr, inducing spatial surface uplifting at rates of ∼0.2–0.5 mm/yr. These Global Positioning System (GPS)‐derived velocities in the vertical deformation of the Tianshan and Pamir were corrected based on surface elastic loading models and the Gravity Recovery and Climate Experiment Follow‐On (GRACE/GFO)‐inferred hydrological loading deformation, and interpolated using the GPS imaging method for a higher 3‐D crustal deformation spatial resolution. In conclusion, surface hydrology is one of the driven factors affecting the regional vertical velocity field observed by GPS. The kinematic crustal shortening and vertical tectonic uplift are integrated within different blocks, which illustrate the contemporary dynamics throughout the Tianshan and Pamir. The relevant spatial characteristics between the 3‐D crustal deformation and dynamic tomography along the Tianshan indicate that the relatively weaker lithosphere beneath the central Tianshan is subject to strong compression, which induces the present‐day crustal uplift.

This study re-estimates the anelasticity parameters of the martian mantle on the basis of both of the recent tidal and rotational parameters and also the latest internal structure models obtained from the in-situ seismic experiment. This study considers the geodetically-derived tidal Love number, global quality factor, and Chandler wobble period, together with the seismologically-derived interior models based on the geophysical and geodynamical inversions. On the assumption of simple power-law rheology, a grid search restricts the ranges of the anelasticity parameters, namely, the frequency exponent (α=0.22±0.13) and local quality factor normalization (Q0=76±9). The combination of the tidal and rotational parameters with the seismic models constrains the frequency exponent effectively.

This paper reviews current knowledge about the Earth’s core and the overlying deep mantle in terms of structure, chemical and mineralogical compositions, physical properties, and dynamics, using information from seismology, geophysics, and geochemistry. High-pressure experimental techniques that can help to interpret and understand observations of these properties and compositions in the deep interior are summarized. The paper also examines the consequences of core flows on global observations such as variations in Earth’s rotation and orientation or variations in the Earth’s magnetic field. Processes currently active at the core-mantle boundary and the various coupling mechanisms between the core and the mantle are discussed, together with some evidence from magnetic field observations.

Earth angular momentum forecasts are naturally accompanied by forecast errors that typically grow with increasing forecast length. In contrast to this behavior, we have detected large quasi-periodic deviations between atmospheric angular momentum wind term forecasts and their subsequently available analysis. The respective errors are not random and have some hard to define yet clearly visible characteristics which may help to separate them from the true forecast information. These kinds of problems, which should be automated but involve some adaptation and decision-making in the process, are most suitable for machine learning methods. Consequently, we propose and apply a neural network to the task of removing the detected artificial forecast errors. We found, that a cascading forward neural network model performed best in this problem. A total error reduction with respect to the unaltered forecasts amounts to about 30% integrated over a 6 day forecast period. Integrated over the initial 3 day forecast period, in which the largest artificial errors are present, the improvements amount to about 50%. After the application of the neural network, the remaining error distribution shows the expected growth with forecast length. However, a 24 hourly modulation and an initial baseline error of 2*10−8 became evident that were hidden before under the larger forecast error.

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.

Global geophysical networks provide powerful databases to infer globally coherent signals, and array processing techniques are useful for inferring them. In this study, we comprehensively analyze seven spherical harmonic-based array processing techniques: spherical harmonic stacking (SHS) as well as its gridded form (SHS_GT) and grid-interval weighted forms (SHS_GK1, SHS_GK2); matrix SHS (MSHS); multi-station experiment (MSE); and optimal sequence estimation (OSE). We first use more specific synthetic tests to evaluate the pros and cons of these techniques, and estimate bias in solutions caused by the station distributions. These methods are applied to four global observation networks, the Global Geodynamics Project (GGP) Network, the Global Seismographic Network (GSN), the Global Geomagnetic (GGM) Network and the Global GNSS Network. For the first time, we restored a much cleaner sequence for one singlet of the 0S2 mode based on the GGP network, and restored similar result for one singlet of the 3S1 mode based on the GSN network. We further isolate different Ylm-related tidal signals from the GGM network for the first time. Moreover, based on global GNSS observations, we estimate the Love number h21=0.6243(±7e−4)−0.01(±6e−3)i at the Chandler Wobble (CW) frequency with OSE/MSHS (The accuracy of the estimate is an order of magnitude higher than the previous results), and further obtain the corresponding lower-mantle anelasticity (fr(ω)=−29.5±0.9, fi(ω)=12.0±7.2). Our findings confirm that OSE and MSHS methods can more accurately obtain the complex amplitude of any Ylm-related signal, which is not possible with other methods (and we do obtain more precise results than previous studies upon using them); besides, we also confirm that OSE and MSHS methods can greatly reduce the interference of other signals to the target signals. Hence, we believe the results obtained from the OSE/MSHS will helpful for obtaining reasonable geophysical explanations.

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. Intense winds over the Maritime Continent associated with the Madden-Julian Oscillation lead to a large-scale redistribution of oceanic mass in the Indo-Pacific basins, and have a noticeable impact on the Earth’s angular momentum.

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.

Fundamental properties of the planet Venus, such as its internal mass distribution and variations in length of day, have remained unknown. We used Earth-based observations of radar speckles tied to the rotation of Venus obtained in 2006–2020 to measure its spin axis orientation, spin precession rate, moment of inertia and length-of-day variations. Venus is tilted by 2.6392 ± 0.0008 deg (1σ) with respect to its orbital plane. The spin axis precesses at a rate of 44.58 ± 3.3 arcsec per year (1σ), which gives a normalized moment of inertia of 0.337 ± 0.024 and yields a rough estimate of the size of the core. The average sidereal day on Venus in the 2006–2020 interval is 243.0226 ± 0.0013 Earth days (1σ). The spin period of the solid planet exhibits variations of 61 ppm (~20 min) with a possible diurnal or semidiurnal forcing. The length-of-day variations imply that changes in atmospheric angular momentum of at least ~4% are transferred to the solid planet.

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.

Different Earth orientation parameter (EOP) time series are publicly available that typically arise from the combination of individual space geodetic technique solutions. The applied processing strategies and choices lead to systematically differing signal and noise characteristics particularly at the shortest periods between 2 and 8 days. We investigate the consequences of typical choices by introducing new experimental EOP solutions obtained from combinations at either normal equation level processed by Deutsches Geodätisches Forschungsinstitut at the Technical University of Munich (DGFI‐TUM) and Federal Agency for Cartography and Geodesy (BKG), or observation level processed by European Space Agency (ESA). All those experiments contribute to an effort initiated by ESA to develop an independent capacity for routine EOP processing and prediction in Europe. Results are benchmarked against geophysical model‐based effective angular momentum functions processed by Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences (ESMGFZ). We find, that a multitechnique combination at normal equation level that explicitly aligns a priori station coordinates to the ITRF2014 frequently outperforms the current International Earth Rotation and Reference Systems Service (IERS) standard solution 14C04. A multi‐Global Navigation Satellite System (GNSS)‐only solution already provides very competitive accuracies for the equatorial components. Quite similar results are also obtained from a short combination at observation level experiment using multi‐GNSS solutions and SLR from Sentinel‐3A and Sentinel‐3B to realize space links. For ΔUT1, however, very long baseline interferometry (VLBI) information is known to be critically important so that experiments combining only GNSS and possibly SLR at observation level perform worse than combinations of all techniques at normal equation level. The low noise floor and smooth spectra obtained from the multi‐GNSS solution nevertheless illustrates the potential of this most rigorous combination approach so that further efforts to include in particular VLBI are strongly recommended.

By transforming a 1D second‐order linear oscillator into a 2D first‐order polar motion differential equation, it can be shown that the finite smoothness (i.e., the presence of jump in finite order derivatives) of the applied Newtonian forcing constitutes the sufficient and necessary condition for instantaneous excitation of free eigen‐mode. This condition can be met by forcing functions originated from turbulent and multiphase fluid motions. Sub‐macroscopic transition time associated with astatic elastic deformation limits the physical smoothness of the applied forcing for the Earth's polar motion. Eigen‐modes can also be excited by an infinitely smooth forcing that has a finite domain of non‐zero values. The eigen‐period serves as a macroscopic timescale to characterize the inertia of a linear oscillator. If a zero mean irregular forcing of finite smoothness exhibits a high degree of randomness and the timescale is much shorter than the eigen‐period, then for negligible damping the eigen‐waveform will increase in proportion to the squareroot of time, while the waveform distortion is statistically a constant. As a result, the pattern of distinctive eigen‐oscillation will dominate the forced solution for longer enough duration.

The intradecadal fluctuations in the length-of-day variation (∆LOD) are considered likely to play an important role in core motions. Two intradecadal oscillations, with ~5.9-year and ~8.5-year periods (referred to as SYO and EYO, respectively), have been detected in previous studies. However, whether the SYO and the EYO have had stable damping trends since 1962 and whether geomagnetic jerks are possible excitation sources for the SYO and the EYO are still debated. In this study, based on the same simulation test, the same ∆LOD record and the same method used in previous studies, combined with the classic filter method and much longer ∆LOD record, we show robust evidence to prove that the SYO and the EYO have no stable damping trends since 1962, and we confirm that there is also exists an ~7.6yr signal. After showing that the SYO has a relationship with jerks similar to that proposed in a previous study for the EYO, we suggest that the SYO and EYO may be related to geomagnetic jerks. However, there is no robust evidence to show that jerks are possible excitation sources of the SYO or EYO, and neither the SYO nor the EYO can be used independently to effectively predict geomagnetic jerks.
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[!!! [Notes: This is a draft we have uploaded to arXiv.org (there is a mistake in that abstract, we will modify soon). In this study, we find a ~7.6yr signal in the ∆LOD for the first time, and we confirm that the ~5.9 year and ~8.5 year in the ∆LOD have no stable damping trends but time-varying amplitudes. If we accecpt that the 5.9yr and 8.5yr signal in the ∆LOD have damping trend, a residaul spectral peak will be found around ~7yr, and if we suppose it corresponds to a periodic signal, we obtain a 7yr signal which has stable increasing amplitudes (based on same methods used in previous study). But those three damping signals cannot represent the orignal signals in the ∆LOD]!!!!!!].

Polar motion (PM) has a close relation to the Earth’s structure and composition, seasonal changes of the atmosphere and oceans, storage of waters, etc. As one of the four major space geodetic techniques, doppler orbitography and radiopositioning integrated by satellite (DORIS) is a mature technique that can monitor PM through precise ground station positioning. There are few articles that have analyzed the PM series derived by the DORIS solution in detail. The aim of this research was to assess the PM time-series based on the DORIS solution, to better capture the time-series. In this paper, Fourier fast transform (FFT) and singular spectrum analysis (SSA) were applied to analyze the 25 years of PM time-series solved by DORIS observation from January 1993 to January 2018, then accurately separate the trend terms and periodic signals, and finally precisely reconstruct the main components. To evaluate the PM time-series derived from DORIS, they were compared with those obtained from EOP 14 C04 (IAU2000). The results showed that the RMSs of the differences in PM between them were 1.594 mas and 1.465 mas in the X and Y directions, respectively. Spectrum analysis using FFT showed that the period of annual wobble was 0.998 years and that of the Chandler wobble was 1.181 years. During the SSA process, after singular value decomposition (SVD), the time-series was reconstructed using the eigenvalues and corresponding eigenvectors, and the results indicated that the trend term, annual wobble, and Chandler wobble components were accurately decomposed and reconstructed, and the component reconstruction results had a precision of 3.858 and 2.387 mas in the X and Y directions, respectively. In addition, the tests also gave reasonable explanations of the phenomena of peaks of differences between the PM parameters derived from DORIS and EOP 14 C04, trend terms, the Chandler wobble, and other signals detected by the SSA and FFT. This research will help the assessment and explanation of PM time-series and will offer a good method for the prediction of pole shifts.

Abstract 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. 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.

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.

In the absence of external torques, the earth system is a closed system and its angular momentum is conserved. The atmospheric angular momentum (AAM) exchange with the solid/liquid earth is achieved by friction and mountain torques. The variations of the AAM and torques are important indicators of global climate change. Using the NCEP/NCAR reanalysis data for 1948–2015, the long-term variations of the AAM and torques are analyzed. A weak positive AAM trend is detected, but an examination of the AAM budget shows that on annual to decadal scales, the signals of the AAM and total torque are inconsistent. During the study period, the total torque was mostly negative and had a decreasing trend, suggesting a decrease of the AAM. To check this inconsistency, we analyze the time series of the length-of-day anomalies, ΔLOD. It is found that ΔLOD is weakly correlated with the AAM, while the derivative of the earth’s core-induced ΔLOD is strongly correlated with the torque. If this is correct, then a core-induced climate change can indeed happen.

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 consistencywith 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 C20 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 μs level; (5) the level of residual LOD variations after removing models or model combinations is remarkably invariant with respect to LOD periods between ~2 months and ~3 yr, being 12-14 μs for the best original models and 7-12 μs for our combinations; (6) while differences between the IERS 14C04 and the JPL SPACE 2015 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 presentoverwhelming advantages.

Abstract The new Release-06 (RL06) Gravity Recovery and Climate Experiment (GRACE) gravity field solutions are evaluated by converting them into equatorial effective angular momentum functions (so-called excitation functions) for polar motion and comparing these to respective time series based on space-geodetic observations (geodetic excitation). The same is performed for the older RL05 solutions using identical processing. Maps of equivalent water heights derived from both releases show that the signal-to-noise ratio is significantly improved in RL06. The derived polar motion excitation functions from RL05 and RL06 differ by about 15$$\%$$ % . An analysis of the contributions of different Earth subsystems revealed that the release update mainly influenced the hydrological (12$$\%$$ % ) and oceanic excitations (17$$\%$$ % ), but it has a relatively small impact on the cryospheric excitations related to Antarctica (4$$\%$$ % ) and Greenland (1$$\%$$ % ). The RL06 data from different GRACE processing centers are more consistent among each other than the previous RL05 data. Comparisons of the GRACE-based excitation functions with the geodetic and model-based oceanic excitations show that the latest release update improved the agreement by about 2 to 15 percentage points.

Kinetic energy from the Earth's internal state, both from potential tectonic activity and from its rotational velocity, may not be easily harnessed, yet it yields enough interesting variability that it could provide many clues to understanding related geophysical processes, such as the variability in climate. This chapter describes models of length of day, the Chandler wobble, and earthquake distributions.

The real-time estimation of polar motion (PM) is needed for the navigation of Earth satellite and interplanetary spacecraft. However, it is impossible to have real-time information due to the complexity of the measurement model and data processing. Various prediction methods have been developed. However, the accuracy of PM prediction is still not satisfactory even for a few days in the future. Therefore, new techniques or a combination of the existing methods need to be investigated for improving the accuracy of the predicted PM. There is a well-introduced method called Copula, and we want to combine it with singular spectrum analysis (SSA) method for PM prediction. In this study, first, we model the predominant trend of PM time series using SSA. Then, the difference between PM time series and its SSA estimation is modeled using Copula-based analysis. Multiple sets of PM predictions which range between 1 and 365 days have been performed based on an IERS 08 C04 time series to assess the capability of our hybrid model. Our results illustrate that the proposed method can efficiently predict PM. The improvement in PM prediction accuracy up to 365 days in the future is found to be around 40% on average and up to 65 and 46% in terms of success rate for the
PM
x
and
PM
y
, respectively.

An improved model of Earth's gravitational field, GEM-T3, has been developed from a combination of satellite tracking, satellite altimeter, and surface gravimetric data. GEM-T3 provides a significant improvement in the modeling of the gravity field at half wavelengths of 400 km and longer. This model, complete to degree and order 50, yields more accurate satellite orbits and an improved geoid representation than previous Goddard Earth Models. GEM-T3 uses altimeter data from GEOS 3 (1975–1976), Seasat (1978) and Geosat (1986–1987). Tracking information used in the solution includes more than 1300 arcs of data encompassing 31 different satellites. The recovery of the long-wavelength components of the solution relies mostly on highly precise satellite laser ranging (SLR) data, but also includes TRANET Doppier, optical, and satellite-to-satellite tracking acquired between the ATS 6 and GEOS 3 satellites. The main advances over GEM-T2 (beyond the inclusion of altimeter and surface gravity information which is essential for the resolution of the shorter wavelength geoid) are some improved tracking data analysis approaches and additional SLR data. Although the use of altimeter data has greatly enhanced the modeling of the ocean geoid between 65°N and 60°S latitudes in GEM-T3, the lack of accurate detailed surface gravimetry leaves poor geoid resolution over many continental regions of great tectonic interest (e.g., Himalayas, Andes). Estimates of polar motion, tracking station coordinates, and long-wavelength ocean tidal terms were also made (accounting for 6330 parameters). GEM-T3 has undergone error calibration using a technique based on subset solutions to produce reliable error estimates. The calibration is based on the condition that the expected mean square deviation of a subset gravity solution from the full set values is predicted by the solutions' error covariances. Data weights are iteratively adjusted until this condition for the error calibration is satisfied. In addition, gravity field tests were performed on strong satellite data sets withheld from the solution (thereby ensuring their independence). In these tests, the performance of the subset models on the withheld observations is compared to error projections based on their calibrated error covariances. These results demonstrate that orbit accuracy projections are reliable for new satellites which were not included in GEM-T3.

It is possible to infer general properties of fluid flow in the core, but there is a large class of flows that fit even perfect data. This class can be reduced in size by making simplifying hypotheses about the flow and electrical conductivity of fluid in the core. For a hypothesis to be reasonable it must be possible to test it against observation; if the test proves favourable the hypothesis is adopted. Three such hypotheses are suggested here: the familiar one of perfect electrical conductivity, and two new ones, those of purely toroidal motion, and steady motion. The first two make it possible to find one component of core flow everywhere. In principle the third hypothesis allows both components to be found. A map of one component for the period 1959-74 shows significant north-south flow over Indonesia and rapid motion in a swath running from beneath North America, across Africa and down to the southern Indian Ocean. With longer-term data it may be possible to find both components of the flow.

Four scenarios of present day Antarctic ice sheet mass change are developed from comprehensive reviews of the available glaciological and oceanographic evidence. The gridded scenarios predict widely varying contributions to secular sea level change ranging from −1.1 to 0.45 mm/yr, and predict polar motion and time-varying low-degree gravitational coefficients that differ significantly from earlier estimates. A reasonably linear relationship between the rate of sea level change from Antarctica A and the predicted Antarctic is found for the four scenarios. This linearity permits a series of forward models to be constructed that incorporate the effects of ice mass changes in Antarctica, Greenland, and distributed smaller glaciers, as well as postglacial rebound (assuming the ICE-3G deglaciation history), with the goal of obtaining optimum reconciliation between observed constraints on and sea level rise . Numerous viable combinations of lower mantle viscosity and hydrologie sources are found that satisfy “observed” in the range of 1 to 2–2.5 mm/yr and observed for degrees 2, 3, and 4. In contrast, rates of global sea level rise above 2.5 mm/yr are inconsistent with available observations. The successful composite models feature a pair of lower mantle viscosity solutions arising from the sensitivity of to glacial rebound. The paired values are well separated at mm/yr, but move closer together as is. increased, and, in fact, merge around =2-2.5 mm/yr, revealing an intimate relation between and preferred lower mantle viscosity. This general pattern is quite robust and persists for different solutions, for variations in source assumptions, and for different styles of lower mantle viscosity stratification. Tighter constraints for l > 2 may allow some viscosity stratification schemes and source assumptions to be excluded in the future. For a given total observed , the sea level rise from Antarctica A is tightly constrained and ranges from 0 to + 1 mm/yr (corresponding to an ablating ice sheet) as estimates of are raised from 1 to 2.5 mm/yr. However, when the degree 3 zonal harmonic constraint is removed, the solutions show little sensitivity to Antarctic mass balance, emphasizing the need for a well determined odd-degree secular zonal harmonic for determining polar ice mass balance.

If the methods of observation are changed it is most important that there should be some period of overlap so that possible systematic differences can be determined.

Satellite laser ranging (SLR) to LAGEOS acquired during the period 1978-1988 has been analyzed to yield estimates of tectonic motion for 22 laser tracking stations situated on seven major plates. The analysis is based on the precise modeling of the orbit dynamics of LAGEOS and includes the determination of other geodynamic and nonconservative force model parameters involved in the orbit determination problem at the centimeter level. Site velocities were recovered from station positions determined each calendar quarter using a network adjustment procedure which maintains the reference frame. -from Authors

In this paper we investigate contributions of the equatorial components of the regional Effective Atmospheric Angular Momentum (EAAM) excitation functions to both the geodetically determined polar motion excitation and to the global EAAM excitation function variations in the spectral range between 10 and 150 days. The regional EAAM excitation functions in 192 geographic sectors are computed from the Japanese Meteorological Agency’s Global Objective Analysis data for the period from 1988 to 1995. We compute the coherence of these functions with the polar motion and with the global EAAM excitation functions. The results show that, in the case without the inverted barometric corrections to the pressure term, most of the contributions come from the South Pacific, North Atlantic and North Pacific regions where variations of the atmospheric pressure and wind are largest. However, the addition of the inverted barometric corrections results in the dominant contribution of Eurasia and North America to the regional EAAM excitation functions spectra. The distribution of the maxima of the coherence between the global and the regional EAAM excitation functions shows coincidence with that of the centers of atmospheric circulation. The prograde component of the coherence seems to be connected with atmospheric variations over both oceans and lands, while the retrograde one is with those over oceans.

The annual and semiannual residuals derived in the axial angular momentum budget of the solid Earth-atmosphere system reflect significant signals. They must be caused by further excitation sources. Since, in particular, the contribution for the wind term from the atmospheric layer between the 10 and 0.3 hPa levels to the seasonal variations in length of day (LOD) is still missing, it is necessary to extend the top level into the upper stratosphere up to 0.3 hPa. Under the conservation of the total angular momentum of the entire Earth, variations in the oceanic angular momentum (OAM) and the hydrological angular momentum (HAM) are further significant excitation sources at seasonal time scales. Focusing on other contributions to the Earth's axial angular momentum budget, the following data are used in this study: axial atmospheric angular momentum (AAM) data derived for the 10-0.3 hPa layer from 1991 to 1997 for computing the missing wind effects; axial OAM functions as generated by oceanic general circulation models (GCMs), namely for the ECHAM3 and the MICOM models, available from 1975 to 1994 and from 1992 to 1994, respectively, for computing the oceanic contributions to LOD changes, and, concerning the HAM variations, the seasonal estimates of the hydrological contribution as derived by Chao and O'Connor [(1988) Geophys J 94: 263-270]. Using vector representation, it is shown that the vectors achieve a close balance in the global axial angular momentum budget within the estimated uncertainties of the momentum quantities on seasonal time scales.

Angular momentum is a fundamental conserved property of dynamic systems. Applying the principle of conservation of angular momentum to the Earth allows the causes of the observed changes in the rotation of the solid Earth to be investigated. After reviewing the application of this principle to the study of observed changes in the Earth’s rotation, it is used to investigate the influence of the atmosphere and oceans on the Earth’s rotation during 1985–1995. Although atmospheric winds are the dominate process causing the Earth’s rate of rotation to change on time scales of a few days to a few years, the redistribution of mass within the atmosphere and oceans is shown to be important in causing polar motion on these time scales.

A 50-year time series of ocean angular momentum (OAM) is used to estimate the oceanic contribution to the excitation of the Chandler wobble. Our estimate of the oceanic excitation power, 18 mas2/cpy, is in good agreement with the residual excitation derived from a simultaneous use of polar motion and atmospheric angular momentum data, 21 mas2/cpy. Direct comparison of the OAM series and the inferred non-atmospheric excitation yields lower correlation and lower coherence at the Chandler frequency than in the study of Brzeziński and Nastula (2001) based on the shorter OAM series of Ponte et al. (1998). Differences in coherence levels are partly related to significant differences found in the two OAM series, indicating substantial dependence of OAM results on model and data assimilation procedures.

Recently, Gross (2000) demonstrated that the Chandler wobble may be excited by a combination of oceanic and atmospheric processes during 1985–1996 using observational records and a general ocean circulation model. Aoyama and Naito (2001) suggest that the atmospheric wind and pressure variations by themselves maintain a major part of the observed Chandler wobble during the period 1983–1998. A coupled climate system model provides a synthetic climate record with temporal and spatial coverage not attainable with historical observational data, allowing for the evaluation of climate excitation of polar motion at longer timescales (such as the 30-year Markowitz wobble) and over a longer period. The U.S. Department of Energy’s Parallel Climate Model (PCM) has simulated the climate for 1870–1999 using historical atmospheric conditions. The ten historical simulations have been produced by varying the length of the spin-up. We present results of polar motion excitation from PCM oceanic, atmospheric, and hydrologie processes.

If the Euler-Liouville Equation describing rigid body rotation, (adapted to include Earth deformation and dissipation) is valid, then the Chandler Wobble can be described by two parameters, a resonant period P and a dissipation quality factor Q. Both parameters command great geophysical interest as global measures of Earth's physical properties, including elasticity, anelasticity, shape, and distribution of mass. P and Q may be estimated from observed polar motion by various methods, but historically the most useful has been maximum likelihood, an approach introduced by Harold Jeffreys in 1940. At that time the sources of Chandler Wobble excitation were unknown. That is, only the output (polar motion) of the presumably randomly excited resonant Earth was observed. Maximum likelihood estimates of P and Q are those corresponding to a minimum variance excitation, if the excitation behaves like Gaussian white noise. Jeffreys' approach remains useful because excitation sources are not fully known. However, reasonable estimates of polar motion excitation are now available from data-assimilating global numerical models of the atmosphere, oceans, and hydrologic cycle. It is reasonable to expect that superior estimates of P and Q may be obtained if we make use of additional information from these climate models.

The variations in the Earth’s rotation take place in different time scales reaching from geological periods down to days. Modern observation techniques as satellite measurements and Very Long Baseline Interferometry (VLBI) measure with increasing accuracy and resolution short-term variations in the range of seasonal cycles to tidal periods. Essential for the seasonal variations is the solar radiation and its cycle.

The output of a coupled climate system model provides a synthetic climate record with temporal and spatial coverage not attainable with observational data, allowing evaluation of climatic excitation of polar motion on timescales of months to decades. Analysis of the geodetically inferred Chandler excitation power shows that it has fluctuated by up to 90% since 1900 and that it has characteristics representative of a stationary Gaussian process. Our model-predicted climate excitation of the Chandler wobble also exhibits variable power comparable to the observed. Ocean currents and bottom pressure shifts acting together can alone drive the 14-month wobble. The same is true of the excitation generated by the combined effects of barometric pressure and winds. The oceanic and atmospheric contributions are this large because of a relatively high degree of constructive interference between seafloor pressure and currents and between atmospheric pressure and winds. In contrast, excitation by the redistribution of water on land appears largely insignificant. Not surprisingly, the full climate effect is even more capable of driving the wobble than the effects of the oceans or atmosphere alone are. Our match to the observed annual excitation is also improved, by about 17%, over previous estimates made with historical climate data. Efforts to explain the 30-year Markowitz wobble meet with less success. Even so, at periods ranging from months to decades, excitation generated by a model of a coupled climate system makes a close approximation to the amplitude of what is geodetically observed.

The zonal response coefficient kappa is studied, and some improvements in its determination are made. First, the reprocessing of the Bureau International de l'Heure data with the 1980 International Astronomical Union nutation series is found to result in improved estimates of kappa . Second, a time series of the angular momentum of the atmosphere is found to have power in the tidal bands, and it is demonstrated that removing the atmospheric influence from the rotation data leads to better estimates of kappa . The frequency dependence of kappa due to finite dissipation in the earth is computed, and the observations are subsequently shown to limit the allowable models of dissipation. Finally, dynamic ocean tide models are studied, and it is concluded that the rotation data cannot distinguish between these and an equilibrium tide.

The westward drift of the non-dipole part of the earth's magnetic field and of its secular variation is investigated for the period 1907-45 and the uncertainty of the results discussed. It is found that a real drift exists having an angular velocity which is independent of latitude. For the non-dipole field the rate of drift is 0.18$\pm $0.015 $ ^{\circ} $ /year, that for the secular variation is 0.32$\pm $0.067 $ ^{\circ} $ /year. The results are confirmed by a study of harmonic analyses made between 1829 and 1945. The drift is explained as a consequence of the dynamo theory of the origin of the earth's field. This theory required the outer part of the core to rotate less rapidly than the inner part. As a result of electromagnetic forces the solid mantle of the earth is coupled to the core as a whole, and the outer part of the core therefore travels westward relative to the mantle, carrying the minor features of the field with it.

We explored the atmospheric contribution to the excitation of Chandler wobble (CW), which has spanned about 11 years beginning, from September 1983. The atmospheric angular momentum (AAM) function presented by the Japan Meteorological Agency (JMA) and the wobble data set (SPACE93) are employed. We devised a wobble domain method of analysis which enables us to quantify the narrow band power of AAM. The AAM-induced wobble closely resembles the observed wobble, and wind contribution turns out to dominate over atmospheric pressure contribution in the vicinity of the Chandler frequency. When only pressure contribution is taken into account, it is insufficient, as shown in previous studies.

Exchanges of angular momentum between the core and the mantle responsible of the so-called decade variations in the length of the day (l.o.d.) are reexamined. It is proposed that, for the relevant time constants, the changes in the core angular momentum are carried by cylindrical annuli rigidly rotating around the Earth's rotation axis. Then the possible coupling mechanisms are discussed. A mechanism is presented which can reduce this torque down to values compatible with l.o.d. data. -from Authors

The time-scale of the variation in the length of the day is comparable to, or shorter than, the electromagnetic decay time, τη, of the mantle. This suggests that an electromagnetic theory for the origin of these fluctuations should not only depend on the electromechanical coupling time, τI, introduced by ROCHESTER (1960), but also on τη. It is shown that, when τI is small compared with τη, the fluctuation time for perturbations in the angular velocity of the mantle is of order τc=τI2/3τη1/3, and not τη. The possibility that τI is not large compared with τη for the case of the Earth is considered. Also, by means of a simple shellular model of the core, the rôle of Alfvén waves in modifying the coupling of core to mantle is discussed. The relationship of this theory with that of BRAGINSKII (1970) is briefly noted. A new account is given of mantle induction which, although only valid at small magnetic Reynolds numbers (based on the conductivity of the mantle), is sufficiently general to permit the coupling of the mantle to an arbitrary slow motion on the core surface to be treated.

Applies the theory developed in Paper 1 (above), which includes the solid inner core explicitly in the dynamical equations, to obtain the eigenfrequencies and other characteristics of the Earth's nutational normal modes as well as the amplitudes of forced nutations at various tidal frequencies, for two commonly used Earth models, 1066A and the Preliminary Reference Earth Model (PREM). Also evaluates various procedures for taking account of known deviations of the Earth from models, notably in the dynamical ellipticity e, for which the two models yield values which are over 1% smaller than the value e* deduced from the precession constant. -from Authors

Astronomically-determined irregular fluctuations in the Earth's rotation
vector on decadal time scales can be used to estimate the fluctuating
torque on the lower surface of the Earth's mantle produced by
magnetohydrodynamic flow in the underlying liquid metallic core. A
method has been proposed for testing the hypothesis that the torque is
due primarily to fluctuating dynamic pressure forces acting on irregular
topographic features of the core-mantle boundary and also on the
equatorial bulge. The method exploits (a) geostrophically-constrained
models of fluid motions in the upper reaches of the core based on
geomagnetic secular variation data, and (b) patterns of the topography
of the CMB based on the mantle flow models constrained by data from
seismic tomography, determinations of long wave-length anomalies of the
Earth's gravitational field and other geophysical and geodetic data.
According to the present study, the magnitude of the axial component of
the torque implied by determinations of irregular changes in the length
of the day is compatible with models of the Earth's deep interior
characterized by the presence of irregular CMB topography of effective
"height" no more than about 0.5 km (about 6% of the equatorial bulge)
and strong horizontal variations in the properties of the D″ layer
at the base of the mantle. The investigation is now being extended to
cover a wider range of epochs and also the case of polar motion on
decadal time scales produced by fluctuations in the equatorial
components of the torque.

Fluctuations in the Earth's rotation rate on the seasonal and
subseasonal time frame are dominated by atmospheric forcing, as evinced
by the strong correlation between sub-annual variations in length-of-day
(LOD) and atmospheric angular momentum (AAM). The role of the atmosphere
in forcing interannual LOD fluctuations is examined here through
comparisons with AAM and Southern Oscillation Index (SOI) time series.
Spectral studies of both the LOD and the SOI indicate a strong
bimodality in the interannual band; significant variability is centered
at 4.2 years, associated with the "traditional" Southern Oscillation
[hereafter referred to as the low frequency (LF) component]; also seen
is a distinct quasi-biennial (OB) component, centered at 2.3 years. The
LF component is present in the global AMM series; however, a significant
QB component is lacking in the AMM, which contains the tropospheric but
not the full stratospheric contribution. Atmospheric winds integrated up
to the 1 mb level play the dominant role in these variations, accounting
for up to 89% of the LOD variation in a case study of the 1982-83 El
Niño. The stratosphere is an important contributor, as it
accounts for as much as an additional 20% in the LOD variance explained
relative to the winds below 100 mb. A comparison between interannual AMM
variations from the National Meteorological Center and European Centre
for Medium-Range Forecasts analyses integrated up to 50mb implies that
"noise" in the AAM data may explain a sizable portion of the LOD
residual. Additional sources of discrepancy include systematic AAM error
and a possible oceanic contribution.
Comparison studies between interannual LOD variations and a Modified
Southern Oscillation Index (MSOI) indicate the largest correlations with
LOD lagging by one to three months, consistent with the growth and
development of an El Niño event. Examining LOD series back to
1880, we observe high correlation between LOD and the MSOI from about
1930 to the present, indicating that LOD can be used as a proxy index
for interannual variations in global wind systems after 1930.

We focus on a regional analysis of equatorial components of the effective atmospheric angular momentum (EAAM) functions that measure the excitation of polar motion. These functions are computed from National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP/NCAR) reanalysis data both globally and in 108 geographic sectors for the period 1968–1997. We investigate the relationship between the regional sector EAAM and the global functions responsible for polar motion excitation. We examine two excitation terms in parallel, with and without the inverted barometer (IB) approximation, which adjusts the atmosphere to account for an isostatic equilibrium response of the ocean to overlying pressure. In the case of pressure terms without IB the largest contributions to the equatorial components of polar motion excitation functions originate in the South Pacific, North Atlantic, and North Pacific regions. Applying the IB correction results in the dominance of Eurasia and North America instead, with nearly all Southern Hemisphere contributions disappearing. When comparing the regional functions to their global sum, such fluctuations are mainly coherent with variations over northern midlatitude land areas. In some sectors, oscillations in these functions tend to occur broadly across two frequency bands: 25–75 and 75–125 days in both prograde and retrograde directions, corresponding to counterclockwise and clockwise polar motion, respectively. Other sectors contain more continuous spectral bands, which are centered at ∼70 days. Coherence and cross-spectral analyses lead us to identify a region over Eurasia that contributes importantly to exciting polar motion; we also note an eastwardly propagating signal toward this region in these excitation terms.

The International Laser Ranging Service (ILRS) was established in September 1998 as a service within the IAG to support programs in geodetic, geophysical, and lunar research activities and to provide data products to the International Earth Rotation Service (IERS) in support of its prime objectives. Now in operation for 5 years, the ILRS develops: (1) the standards and specifications necessary for product consistency and (2) the priorities and tracking strategies required to maximize network efficiency. The service collects, merges, analyzes, archives and distributes satellite and lunar laser ranging data to satisfy a variety of scientific, engineering, and operational needs and encourages the application of new technologies to enhance the quality, quantity, and cost effectiveness of its data products. The ILRS works with: (1) the global network to improve station performance; (2) new satellite missions in the design and building of retroreflector targets to maximize data quality and quantity and (3) science programs to optimize scientific data yield. The ILRS Central Bureau maintains a comprehensive web site as the primary vehicle for the distribution of information within the ILRS community. The site, which can be accessed at: http://ilrs.gsfc.nasa.gov is also available at mirrored sites at the Communications Research Laboratory (CRL) in Tokyo and the European Data Center (EDC) in Munich.

Results of a 100-year run of the Hadley Centre general circulation model
are used to compute monthly values of the three components of
atmospheric torque on the Earth and of the associated atmospheric
angular momentum series. All these results are compared with equivalent
ones from the National Center for Environmental Prediction/National
Center for Atmospheric Research reanalyses for the overlap period since
1948. We find some important differences; consequently, our results
should be taken as an order of magnitude of the effect. We also compute
the effect of the atmosphere on length of day (LOD) and polar motion by
the use of both the torque and the angular momentum approaches. We find
comparable amplitude with both torque and angular momentum for the polar
motion; the axial torque, however, related to LOD, appears to be
unphysical. The excitation of long-period LOD variation is in phase with
the observed variation but much smaller. The low-frequency polar motion
is only coherent with the observation at certain particular periods.

The role played by dierent core processes in the changes in the Earth's rotation is assessed and fully dynamical models of the torsional Alfvén waves inside the uid core are reviewed. These waves, rst studied by Braginsky (1970), consist of geostrophic circulation. They have decadal periods and yield time changes in core angular momentum. They arise from small departures from an hypothetical quasistatic state, where the total action of the Lorentz force on the geostrophic cylinders cancels out. They cause torques acting on the mantle. Simple models of the torsional waves that rely only on zonal averages of the magnetic eld have incor-porated electromagnetic coupling to the mantle. They, however, need some correction. In addition, only a kinematic approach of the topo-graphic coupling, caused by nonaxial symmetry of the uid cavity, has been successfully attempted to date. Taking into account uncertainties in the height of the coremantle topography and in the electrical conduc-tivity of the deep mantle, it turns out that, in the present state of core modelling, the pressure, gravity and electromagnetic torques acting on the mantle may all produce decade changes in the length of the day with a magnitude comparable to the observations.

The present-day perturbations of the Earth's rotation are sensitive to
the glacial isostatic adjustment (GIA) arising from the Late Pleistocene
glacial cycles and also to the recent mass balance of polar ice caps. In
this study, we evaluate the polar wander and the change of degree-two
harmonic of the Earth's geopotential , proportional to the rotation
rate, for four Late Pleistocene ice models. We examine these
perturbations as a function of lower- and upper-mantle viscosities and
lithospheric thickness and rheology (elastic or viscoelastic), in which
a compressible Earth model with elasticity and density given by the
seismological model PREM is used. By considering the observations and
predictions including the GIA process arising from the Late Pleistocene
ice and recent mass balance of polar ice caps, we discuss the recent
mass balance of the Antarctic and Greenland ice sheets. We also examine
the effects of internal processes and the melting of mountain glaciers,
although this work is only preliminary. The results shown below seem to
be supported even if these effects are included. Two solutions are
obtained for source areas of the recent Antarctic melting. We denote an
equivalent sea level (ESL) rise (mm yr-1)) from the Greenland
and Antarctic ice sheets as and , respectively, being positive for
melting and negative for growth. One, solution s1, is a solution
satisfying the relationship , and the other, solution s2, generally
satisfies the relationship and . In most cases, the magnitude of for
solution s2 is larger than that for solution s1. The melting area of the
Antarctic ice sheet for solution s1 roughly corresponds to the Weddell
Sea region, approximately located on the symmetric part of Greenland to
the Equator. The area for solution s2 is located on the symmetric part
of Greenland to the centre of the Earth. In both solutions, therefore,
the polar wander direction caused by the mass imbalance of each ice
sheet is in an opposite direction. The reason for this is that the
observed polar wander direction is nearly identical to the prediction
from the GIA process for the Late Pleistocene ice models. However, it is
difficult to independently examine which solution is better. If we
consider a recent ESL rise of ~0.6 mm yr-1 from the Greenland
ice sheet, then a similar ESL rise of 0.5-1.0 mm yr-1 is also
suggested for the Antarctic ice sheet around the Weddell Sea region.
This solution also suggests the lower-mantle viscosity to be
~1022 Pa s.

This paper describes two phases of research concerning effects of the
oceans on Earth's rotation. First, based on a spherical harmonic theory
developed over the past several years, the tide height and currents
corresponding to 32 tidal constituents have been determined, and their
effects on polar motion and the length of day computed. These effects
are derived from "static" Liouville equations, which include static
mantle and ocean responses to, and frequency-independent fluid core
decoupling from, the rotational perturbations initially excited.
Short-period tidal perturbations of rotation are found to be dominated
by the effects of currents; but the largest perturbations—and the
ones most detectable—are those produced by long-period tides.
Second, the Lionville theory is modified to allow for a full dynamic
oceanic response and for frequency-dependent core decoupling, effects
which are potentially very important at short periods. Preliminary
results from the new theory suggest, however, that it may not be
necessary to include a dynamic oceanic response to rotation.

THE El Niño Southern Oscillation (ENSO), a climate fluctuation
that recurs on a 2-7-yr timescale, is associated with persistent
large-scale fluctuations in the dynamical behaviour of the global
atmosphere-ocean system1. Here we present a study of the
latitudinal redistribution of angular momentum within the atmosphere
from 1976 to 1991. We observe slow, global-scale coherent poleward
propagation of atmospheric angular-momentum fluctuations on interannual
timescales. These originate in equatorial regions, where they lead the
main atmospheric anomalies of the ENSO cycle by nearly two years; they
penetrate to latitudes higher than 60° in both hemispheres, where
they lag behind the ENSO cycle by about four years. We can also
distinguish the bimodality of the ENSO phenomenon, with a low-frequency
component centred at a period close to 4.2 years and a high-frequency
component centred near 2.4 years. Each of the two components has a
distinct latitudinal propagation pattern. In the period studied, strong
El Niño and related La Niña climatic events occur when
these components add constructively.