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We analyzed the impacts of data span on trend estimates using Earth’s long-term polar motion time series, 1846-present, and using methodologies including singular spectrum analysis, and Panteleev’s filter to mitigate the time series containing transient signals. Our results show that the fluctuations of the mean rotational pole position, the Markowitz wobble, cannot be fully explained by the oceanic and atmospheric excitations. However, there exists plausible similarity with the variations of amplitudes of the Chandler wobble. To explain the abrupt deviation of the mean pole from the previous state after year 2000, we first compute Earth rotation excitations, using the temporal variations of the second-degree Stokes coefficients, C 21 , S 21 , estimated from GRACE, GRACE Follow-On and Satellite Laser Ranging (SLR), 2002–2021. We then compare their trend estimates with that of the Earth’s polar motion, and conclude that the drift of the pole is consistent with the climate-induced mass redistributions within the Earth system during the past two decades. However, the observed trend is not in exact agreement with the prediction values using contemporary glacial isostatic adjustment (GIA) process forward models. The analysis of the J 2 variations since 1976 from SLR and the corresponding length of day (LOD) changes, reveals a clear trend reversal around the year 2000. However, the observed J 2 variations can only explain ∼ 5 % of the long-term LOD changes. The remaining decadal signal in the LOD, usually accounted for by the angular momentum exchange at the core-mantle boundary, is observed to be anti-correlated with the Earth surface temperature anomaly. The geophysical explanation on these relationships remains elusive, and necessitates future studies.

International audience; Until now, the polar motion resonance (PMR) complex frequency has been determined in the seasonal and retrograde diurnal band of the polar motion. In this study, this resonance is studied in the prograde diurnal band, where polar motion is mainly composed of periodic terms caused by the diurnal oceanic tide. The resonance parameters (period and quality factor) are encompassed in the frequency transfer function between generating tidal potential and polar motion, and can be estimated accordingly. To this aim, we gather three published sets of prograde diurnal terms determined from Global Navigation Satellite System (GNSS) and Very Long Baseline Interferometry (VLBI), to which we append our own estimates based upon a processing of the VLBI delays over the period 1990-2020. Then, by fitting the PMR parameters so that the prograde diurnal terms match the corresponding components of the tide generating potential, we obtained a resonance period of about 401 d and an equivalent quality factor of -22, differing from those reigning in the seasonal band (PPMR ≍ 431 d; QPMR ≍ 56-255) and in the retrograde diurnal band (PPMR ≍ 380 d; QPMR ≍ -10). Our estimates confirm strikingly the theoretical prediction derived from the tidal ocean angular momentum derived from the FES 2014 ocean tide model.

SUMMARYThe rotational motions of the internal Earth layers induce resonances in the Earth nutations and tidal gravimetric response to external luni-solar gravitational forcings. The characterization of these resonances is a mean of investigating the deep Earth properties since their amplitudes and frequencies depend on a few fundamental geophysical parameters. In this work, we focus on the determination of the free core nutation and free inner core nutation periods and quality factors from the Bayesian inversion of VLBI and gravimetric data. We make a joint inversion of data from both techniques and show that, even if the results are only slightly different from the inversion of VLBI data alone, such approach may be valuable in the future if the accuracy of gravimetric data increases. We also briefly discuss the polar motion resonance, which is related to the Chandler Wobble as seen from the diurnal frequency band. Our overall estimates of the FCN period and quality factor, TFCN = (−430.2, −429.8) solar days and QFCN = (15 700, 16 700), respectively, are in good agreement with other studies, albeit slightly different for unclear reasons. Despite some concerns about the detection and characterization of the FICN, it seems that we could also successfully estimate its period, TFICN = (+600, +1300) solar days, and give a loose estimate of the upper bound on its quality factor.

SUMMARY The nutation harmonic terms are commonly determined from celestial pole offset series produced from very long baseline interferometry (VLBI) time delay analysis. This approach is called an indirect approach. As VLBI observations are treated independently for every session, this approach has some deficiencies such as a lack of consistency in the geometry of the session. To tackle this problem, we propose to directly estimate nutation terms from the whole set of VLBI time delays, hereafter referred as a direct approach, in which the nutation amplitudes are taken as global parameters. This approach allows us to reduce the correlations and the formal errors and gives significant discrepancies for the amplitude of some nutation terms. This paper is also dedicated to the determination of the Earth resonance parameters, named polar motion, free core nutation, and free inner core nutation. No statistically significant difference has been found between the estimates of resonance parameters based upon ‘direct’ and ‘indirect’ nutation terms. The inclusion of a complete atmospheric-oceanic non-tidal correction to the nutation amplitudes significantly affected the estimates of the free core nutation and the free inner core nutation resonant frequencies. Finally, we analyzed the frequency sensitivity of polar motion resonance and found that this resonance is mostly determined by the prograde nutation terms of period smaller than 386 d.

The Earth orientation parameters (EOP), the regular products of IERS Earth Orientation Centre, are computed at daily bases by combination of EOP solutions using different astro-geodetic techniques. At SYRTE we have developed a strategy of combination of the Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI) techniques at normal equation level using Dynamo software maintained by CNES (France). This approach allows to produce the EOP at the daily bases, which contains polar coordinates (x,y) and their rates (xr,yr), universal time UT1 and its rate LOD, and corrections from IAU2000A/2006 precession-nutation model (dX,dY), and in the same run station coordinates constituting the terrestrial frame (TRF). The recorded EOP solutions obtained from GNSS and VLBI combination at weekly bases is recently maintained by SYRTE.The strategy applied to consistently combine the IGS and IVS solutions provided in Sinex format over the time period 2000-2021 are presented and the resulting EOP, station positions (TRF) are analysed and evaluated, differences w.r.t. the individual solutions and the IERS time-series investigated.

The over four decades long record of Satellite Laser Ranging (SLR) observations to a variety of historical geodetic spherical satellites makes it possible to directly observe the long-term (seasonal to decadal time scales) displacement of the Earth’s mean axis of maximum inertia, namely its principal figure axis, with respect to the crust, through the determination of the degree-2 order-1 geopotential coefficients over the 34-year period 1984—2017.On the other hand, the pole coordinate time series (mainly from GPS and VLBI data), yield the motion of the rotation pole with even a greater accuracy.The time-dependent nature of the response of the Earth’s mantle to external forces, where it behaves either elastically on short time scales (seconds) or like a viscous fluid over geological time scales (millions of years), is poorly constrained at decadal periods. Here we propose to relate oscillations of the figure axis to those of the Earth’s rotation pole (through the Euler-Liouville equations) to study the mass-related excitation of polar motion and provide global constraints on the rheological properties of the deep Earth.

Since the beginning of the 20th century, the observation of the Earth rotation variations through astro-geodetic techniques enables to investigate the global rheological properties of the Earth, in particular, the resonance parameters of the free rotation modes reflect the solid Earth anelasticity, the ocean response to an external forcing, and the properties of the fluid inner core, eventually of the solid inner core. Better constraints on these resonance parameters can be obtained by confronting the observed terrestrial motion of the rotation pole (the so-called polar motion) - including nutation as a retrograde diurnal polar motion - to the modeled excitation producing it. The more precise the modeled excitation and the observed polar motion are, the better theEarth rheological properties will be determined. For now, the best precision is reached in thenutation band. So, the analysis has been first dedicated to a direct adjustment of the nutation componentsfrom VLBI delays, then the adjustment of the resonance parameters in the transfer function between the observed nutation terms and the corresponding rigid nutation terms that reflects the luni-solar forcing. The obtained resonance parameters confirms in particular the shortening of the polar motion resonance period of about 40 - 50 day in the retrograde diurnal band. Then, we show that the dynamical behavior of the oceans in the diurnal band is mostly responsible for that. We also predicted a supplementary change of the resonance parameters in the vicinityof the free core nutation resonance, as expected from the solid Earth response, and confirmed by the adjustment of these parameters through the nutation terms. In addition to the nutation band, we revisit the estimation of the polar motion resonance parameters in the seasonal band, dominated by the Chandler wobble, in light of the most recent global circulation models of the hydro-atmospheric layers. Finally, we extend the investigation of polar motion resonance to theprograde diurnal polar motion, where the excitations mostly result from the ocean tides. We obtain a resonance period of about 393 days, and confirmed by our prediction based on the ocean tidal models. These results allow us to impose constraints on the frequency dependence of the Love number k2 and the Love number oceanic ko, characterizing respectively the response of the solid Earth and the oceans to an external potential of degree 2.

The Earth Orientation Center of the International Earth Rotation and Reference Systems Service (IERS) has the task to provide the scientific community with the international reference time series of Earth orientation parameters (EOP), referred to as IERS EOP C04 or C04. These series result from a combination of operational EOP series derived from VLBI, GNSS, SLR, and DORIS. The C04 series were updated to provide EOP series consistent with the set of station coordinates of the ITRF 2014. The new C04, referred to as IERS EOP 14C04, is aligned onto the most recent versions of the conventional reference frames (ITRF 2014 and ICRF2). Additionally, the combination algorithm was revised to include an improved weighting of the intra-technique solutions. Over the period 2010–2015, differences to the IVS combination exhibit standard deviations of 40 $$\upmu $$ as for nutation and 10 $$\upmu $$ s for UT1. Differences to the IGS combination reveal a standard deviation of 30 $$\upmu $$ as for polar motion. The IERS EOP 14C04 was adopted by the IERS directing board as the IERS reference series by February 1, 2017.

The activities and some research progress of IAU Commission 19 (C19) - Rotation of the Earth - in the past triennial term (2012-2015) is reported in this paper, including the scientific session and business meeting of C19, as well as a business meeting of the IAU/IAG Joint Working Group of “Theory of Earth Rotation” (JWG_ThER) during the XXIX IAU General Assembly in Hawaii, USA. Three reports of JWG_ThER progress, IERS and IAG, eleven reports of national projects and individual institutions, a short summary of the history and heritage of C19, and an Overview of the status and outlook of new Commission A2 are also presented.

Observed polar motion consists of uniform circular motions at both positive (prograde) and negative (retrograde) frequencies. Generalized Euler–Liouville equations of Bizouard, taking into account Earth's triaxiality and asymmetry of the ocean tide, show that the corresponding retrograde and prograde circular excitations are coupled at any frequency. In this work, we reconstructed the polar motion excitation in the Chandler band (prograde and retrograde). Then we compared it with geophysical excitation, filtered out in the same way from the series of the Oceanic Angular Momentum (OAM) and Atmospheric Angular Momentum (AAM) for the period 1960–2000. The agreement was found to be better in the prograde band than in the retrograde one.

During the XXVIII IAU General Assembly in Beijing IAU Commission 19 - Rotation of the Earth - held a business meeting and a scientific meeting. The business meeting was held on Wednesday, 29 August 2012 during session 1 (08:30-10:00). It was attended by about 35 participants, and six reports were given. First the activities of IAU Commission 19 during the past triennium (2009–2012) were highlighted by the Commission president. Afterwards, the Commission secretary presented the results of the elections for the next triennium (2012–2015) and a list of new members of the Commission. The designated Commission president provided an outlook into the next triennium, before the representatives of the international bodies and services IAG (International Association of Geodesy), IVS (International VLBI Service for Geodesy and Astrometry), and IERS (International Earth Rotation and Reference Systems Service) gave reports about recent activities. A summary of the business meeting is given below in Section 2. The scientific meeting was held on Thursday, 20 August 2012 during sessions 1 and 2 (08:30-12:30). Eleven presentations were given, and about 40 participants attended the sessions. Summaries of the presentations are provided below in Section 3.

International audience; The influence of the continental water storage on the polar motion is not well known. Different models have been developed to evaluate these effects and compared to geodetic observations. However, previous studies have shown large discrepancies mainly attributed to the lack of global measurements of related hydrological parameters. Now, from the observations of the GRACE mission, we can estimate the polar motion excitation due to the global hydrology. Data processing of GRACE data is carried out by several centers of analysis, we focus on the new solution computed by the Groupe de Recherche de Géodésie Spatiale. At annual scales, excitations derived from GRACE data are in better agreement with geodetic observations than models estimates. The main contribution to the hydrological excitation comes from the monsoon climates regions where GRACE and models estimates are in a very good agreement. Still, the effect of the north high latitudes regions, where the principal areas of snow cover are found, cannot be neglected. At these regions, GRACE and models estimated contributions to polar motion excitations show significant discrepancies. Finally, GRACE-based excitations reveal the possible influence of water storage variations in exciting polar motion around the frequency of 3 cycles per year. 1. Introduction The excitation of polar motion is, to a large extent, related to the mass redistribution of geophysical fluids. The importance of atmospheric and oceanic angular momentum signals at monthly and seasonal periods is well known. The contribution of the continental hydrological signals, originating from land water, snow, and ice, is, however, less known. A number of previous studies have estimated hydrological excitation from climatological measurements, numerical climate models, and global hydrology models based upon the observed distribution of surface water, snow, ice, and soil moisture [15]. The hydrological part of polar motion excitation can also be obtained, as a residual series, by removing atmospheric and oceanic signals from the geodetic excitation of polar motion. The general conclusion of these studies is that the change in continental water storage plays a major role in the seasonal polar motion although the results of the hydrological models do not agree with each other and with observed polar motion [6, 7]. This is mainly due to the lack of global measurements of related hydrological parameters which are difficult to predict (like evaporation, run-off, groundwater, and snow/ice mass change). Other analyses show that hydrological signals seem

The rapid polar motion for periods below 20 days is revisited in light of the most recent and accurate geodetic and geophysical data. Although its amplitude is smaller than 2 mas, it is excited mostly by powerful atmospheric processes, as large as the seasonal ones. The residual amplitude, representing about 20% of the total excitation, stems from the oceans. Rapid polar motion has an irregular nature that is well explained by the combined influence of the atmosphere and the oceans. An overall spectrum reveals cycles principally at 20, 13.6 (fortnightly tidal period) and 10 days (corresponding to the normal atmospheric mode $${\Psi_3^1}$$ ), but this is only an averaged feature hiding its strong variability over seasonal time scales. This explains why it is so delicate to determine an empirical model of the tidal effect on polar motion. The variability in both amplitude and phase of the 13.6-day term is probably caused by a lunar barometric effect, modulated by some sub-seasonal thermal processes. The irregularities of the prominent cycles of the short-term polar motion are well explained by the atmospheric and oceanic excitations. The oceanic variability reinforces the atmospheric one, as they were triggered by the same agent, maybe seasonal and inter-annual thermal variations.

SUMMARY Tesseral coefficients C21 and S21 derived from Gravity Recovery and Climate Experiment (GRACE) observations allow to compute the mass term of the polar-motion excitation function. This independent estimation can improve the geophysical models and, in addition, determine the unmodelled phenomena. In this paper, we intend to validate the polar motion excitation derived from GRACE’s last release (GRACE Release 4) computed by different institutes: GeoForschungsZentrum (GFZ), Postdam, Germany; Center for Space Research (CSR), Austin, USA; Jet Propulsion Laboratory (JPL), Pasadena, USA, and the Groupe de Recherche en G´

We study the Chandler wobble (CW) of the pole from 1846 to 2017 extracted by the Panteleev filtering. The CW has period of 433 days, average amplitude of 0.13 milliarcseconds (mas) which is changing, and phase jump by in 1930-th. The CW amplitude strongly (almost to zero) decreases in 1930-th and 2010-th with the phase jump in 1930th. The envelope model contains 83- and 42-years quasi-periodicities. We think the first one can be represented by the 166-years changes of the envelope, crossing zero in 1930th. We reconstruct Chandler input excitation based on the Euler-Liouville equation. Its amplitude has ~ 20-years variations. We explain this based on simple model and prove, that they appear in consequence of 42-years modulation of CW. The excitation amplifies the amplitude of CW for ~ 20 years then damps it for another ~ 20 years. The analysis of the modulated CW signal in a sliding window demonstrates the specific effect, we called the "escargot effect", when instantaneous "virtual" retrograde component appears in the purely prograde (at long-time interval) signal. Chandler excitation envelope shape is similar to this instantaneous retrograde component, which reflects the changes of ellipticity of the approximation ellipse.

The interaction between the atmosphere and the underlying solid mantle is one of the most important sources of changes in all three components of the Earth's rotation vector on different time scales. In this paper the NCEP/NCAR reanalysis time series of four times daily atmospheric effective angular momentum (EAM) estimates is used to investigate some selected aspects of the atmospheric influence on Earth rotation. Emphasis is placed on the controversial features which were difficult or impossible to study using the operational EAM data, such as excitation of the free oscillations in polar motion, the Chandler wobble (CW) and the free core nutation (FCN), or the roles of diurnal and semidiurnal atmospheric tides and atmospheric normal modes in the rotational dynamics of the Earth.

International audience; A 29-year time-series of four-times-daily atmospheric effective angular momentum (EAM) estimates is used to study the atmospheric influence on nutation. The most important atmospheric contributions are found for the prograde annual (77 μas), retrograde annual (53 as), prograde semiannual (45 as), and for the constant offset of the pole (δψsinɛ0=−86 as, δɛ=77 as). Among them only the prograde semiannual component is driven mostly by the wind term of the EAM function, while in all other cases the pressure term is dominant. These are nonnegligible quantities which should be taken into account in the new theory of nutation. Comparison with the VLBI corrections to the IAU 1980 nutation model taking into account the ocean tide contribution yields good agreement for the prograde annual and semiannual nutations. We also investigated time variability of the atmospheric contribution to the nutation amplitudes by performing the sliding-window least-squares analysis of both the atmospheric excitation and VLBI nutation data. Almost all detected variations of atmospheric origin can be attributed to the pressure term, the biggest being the in-phase annual prograde component (about 30 as) and the retrograde one (as much as 100200 as). These variations, if physical, limit the precision of classical modeling of nutation to the level of 0.1 mas. Comparison with the VLBI data shows significant correlation for the retrograde annual nutation after 1989, while for the prograde annual term there is a high correlation in shape but the size of the atmospherically driven variations is about three times less than deduced from the VLBI data. This discrepancy in size can be attributed either to inaccuracy of the theoretical transfer function or the frequency-dependent ocean response to the pressure variations. Our comparison also yields a considerably better agreement with the VLBI nutation data when using the EAM function without the IB correction for ocean response, which indicates that this correction is not adequate for nearly diurnal variations.

Space geodetic techniques have different strengths and weaknesses for recovering geodetic parameters which makes their combination useful. However they may have some systematic behaviour which can be detected and removed at the observation level. In order to review the interest in combining techniques at this level, a Working Group was set up in the course of 2009 in the frame of the International Earth Rotation and Reference Systems Service (IERS). A major task of the WG COL is to study methods and advantages of combining space geodetic techniques (DORIS, GNSS, SLR, VLBI), searching for an optimal strategy to solve for geodetic parameters. The first action of the Working Group was to organize an inter-comparison benchmark campaign to serve as a test. The period chosen is from August 10 to August 30, 2008. It includes the intensive CONT08 VLBI period.

The Earth Orientation Center of the IERS, located at Paris Observatory, SYRTE, has the task to provide to the scientific community the international reference time series for the Earth Orientation Parameters (EOP), referred as ”IERS C04” (Combined 04), resulting from a combination of operational EOP series, each of them associated with a given geodetic technique. The procedure developed to derive the C04 solution was recently upgraded for several reasons: first we have implemented the new IAU2000 conventions; secondly it has been necessary to re-align the solution to improve its consistency with respect to the ITRF. Due to the separate determination of both celestial and terrestrial reference frames and EOP, there has been a slow degradation of the overall consistency and discrepancies at the level of 300 micro-arc-seconds were existing between the current IERS C04 and the ITRF realization. We have taken this opportunity to upgrade the numerical combination procedure; improvements concern in particular routines, tables dimensions, generalized double precisions. Using the combined polar motion solution associated with the newly release International Terrestrial Reference Frame 2005 (ITRF 2005), we produce a better solution including estimates of the errors of combined values. Individual EOP series have been reprocessed since 1984. Pole coordinates are now fully consistent with ITRF. The nutation offsets and UT1 are made consistent with the International Celestial Reference Frame (ICRF). The new C04 solution, referred as 05 C04, updated two times per week became the offcial C04 solution since October 2007.

International audience; The terrestrial motion of the Earth's rotation pole shows mainly two large oscillations: the Chandler and the annual wobbles driven by mass redistributions in surface geophysical fluids. These contributions interfere destructively every 6.4 years, slowing down the pole at that period of time. This is the case for the recent period from November 2005 till February 2006. Due to the high precision of Earth orientation data of these days and for the first time in the history of polar motion observation, very small structures of the motion are observed. We compared the observed polar motion with the contribution of atmosphere and oceans predicted from global atmospheric and oceanic analyses and models. We clearly see that centimeter level polar motion displacements during the 2005-2006 winter season are almost fully explained by major pressure events on the continents and on the ocean, especially a depression over Northern Europe in-phase with similar events over North America.

[1] Earth's precession and nutations are mainly generated by the luni-solar tidal torque. Diurnal retrograde variations in the atmospheric and oceanic angular momenta in an Earth-fixed reference system induce some additional nutation motions. Observed precession and nutations are derived from very long baseline interferometry (VLBI) data, assuming that the direction of the observed quasars are fixed in space. In this study, we consider the effects of two possible causes for explaining discrepancies between the observed nutations and those modeled in MHB2000 (model adopted by the International Astronomical Union): (1) the time variations in the atmospheric (and potentially oceanic) forcing of the nutations, of the free core nutation (FCN), and of the free inner core nutation (FICN), and (2) the possible contamination of VLBI-derived nutation amplitudes by apparent changes in the directions of the extragalactic radio sources. The robustness of MHB2000 is tested by perturbing some of the parameters and assessing the validity of the resulting nutation amplitudes against realistic estimations. We show that even allowing for large discrepancies related to atmospheric forcing, the ranges of the possible changes in the FCN and FICN periods and damping factors are small.

The Trouton and Noble experiment, which was initially performed (and fiascoed) in 1903, has only been questioned recently. When correctly performed, this very simple electrostatic aetherdrift experiment gives unambiguous positive results: a suspended, parallel-plate capacitor charged at high voltage by means of lateral feeding wires exhibits a stimulated torque and tends to line up its plates in the East-West direction. Other tests by means of vertical feeding wires exhibited continuous rotations. This new class of elementary EM phenomena is described in the present paper. As far as it relates to the state of motion of the vacuum, it is our understanding that: (i) it serves as the physical basis for another class of electrostatic phenomena involved in the generation of linear thrust and technically referred to as “Biefeld-Brown effect” drives; (ii) it might be of tremendous importance for implementing “future flight” propulsion systems; (iii) it might add a new dimension in space weather. The present paper aims at clarifying these concepts. We shall only present the exploratory side of a wider, proprietary research and development effort, so as to encourage the replication of Trouton-Noble’s experiment by academia and other members of the scientific and engineering community.

Nearly diurnal variations in the equatorial components of the atmospheric angular momentum are expected to excite minor but well measurable nutational motions of the earth’s pole. These motions include the free core nutation (FCN) of variable amplitude between 100 and 500 microarcseconds (µas), as well as a contribution to the amplitudes of some important constituents of the lunisolar nutation. We investigate this problem using a 29-years long homogeneous series of the 4-times daily EAM (effective angular momentum) estimates based on results of the common U.S. NCEP/NCAR reanalysis project. The most important atmospheric contributions are found for the following nutation constituents: prograde annual (77 µas), retrograde annual (53 µas), prograde semiannual (45 µas), and for the constant offset of the pole (dψ sin e0 = -86 µas, de = 77 µas); among them only the prograde semiannual component is driven mostly by the wind term of the EAM function while in all other cases the pressure term is dominating. Comparison with the VLBI corrections to the IAU 1980 nutation model and taking into account the ocean tide contribution, yields a good agreement for the prograde annual and semiannual nutations, that is our estimation receives an important observational confirmation. We also investigated time variability of the atmospheric contribution to the nutation amplitudes by performing the sliding window least squares analysis of both the atmospheric excitation and VLBI nutation data.

International audience; 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.

International audience; The purpose of this paper is to compute atmospheric torques on the Earth, including the oceans, with an emphasis on the equatorial components. This dynamic approach is an alternative method to the classical budget-based angular momentum method for viewing atmospheric effects on Earth's orientation in space. The expression of the total torque interaction between the atmosphere and the Earth is derived from the angular momentum balance equation. Such a torque is composed of three parts due to pressure, gravitation, and friction. Each of these torque components is evaluated numerically by a semi-analytical approach involving spherical harmonic approximations, and their orders of magnitude are intercompared. For the equatorial components the pressure and gravitational torques have far larger amplitudes than that of the friction torque; these two major torques have the same order of magnitude but opposite signs, and the value of the sum of the torques is shown to be close to the equatorial components of the atmospheric angular momentum time derivative s, as would be expected in a consistent model-based analysis system. The correlation between the two time series is shown to be very good at low frequency and decrease slowly with increasing frequency. The correlation is still significant (≥ 0.7) up to 0.5 cycle per day, but the correlation coefficient reduces to 0.5 at the diurnal frequency band, indicating the difficulty of calculating rapidly changing model-based torques within an atmospheric analysis system.