Earth Rotation Observations Research Articles

Reconciling past changes in Earth's rotation with 20th century global sea-level rise: Resolving Munk's enigma.

In 2002, Munk defined an important enigma of 20th century global mean sea-level (GMSL) rise that has yet to be resolved. First, he listed three canonical observations related to Earth's rotation [(i) the slowing of Earth's rotation rate over the last three millennia inferred from ancient eclipse observations, and changes in the (ii) amplitude and (iii) orientation of Earth's rotation vector over the last century estimated from geodetic and astronomic measurements] and argued that they could all be fit by a model of ongoing glacial isostatic adjustment (GIA) associated with the last ice age. Second, he demonstrated that prevailing estimates of the 20th century GMSL rise (~1.5 to 2.0 mm/year), after correction for the maximum signal from ocean thermal expansion, implied mass flux from ice sheets and glaciers at a level that would grossly misfit the residual GIA-corrected observations of Earth's rotation. We demonstrate that the combination of lower estimates of the 20th century GMSL rise (up to 1990) improved modeling of the GIA process and that the correction of the eclipse record for a signal due to angular momentum exchange between the fluid outer core and the mantle reconciles all three Earth rotation observations. This resolution adds confidence to recent estimates of individual contributions to 20th century sea-level change and to projections of GMSL rise to the end of the 21st century based on them.

Impact of self‐attraction and loading on Earth rotation

AbstractThe impact of self‐attraction and loading (SAL) on Earth rotation has not been previously considered except at annual timescales. We estimate Earth rotation excitations using models of atmospheric, oceanic, and land hydrology surface mass variations and investigate the importance of including SAL over monthly to interannual timescales. We assess SAL effects in comparison with simple mass balance effects where net mass exchanged with the atmosphere and land is distributed uniformly over the global ocean. For oceanic polar motion excitations, SAL impacts are important even though mass balance impact is minor except at the annual period. This is true of global (atmosphere + land + ocean) polar motion excitations as well, although the SAL impacts are smaller. When estimating length‐of‐day excitations, mass balance effects have a dominant impact, particularly for oceanic excitation. Although SAL can have a significant impact on estimated Earth rotation excitations, its consideration generally did not improve comparisons with geodetic observations. This result may change in the future as surface mass models and Earth rotation observations improve.

Agreement between Earth's rotation and mass displacement as detected by GRACE

The progress in GRACE data processing should improve the estimation of low degree spherical harmonics which are expected to agree better with Earth's rotation observations. The polar motion and length-of-day excitations determined from the spherical harmonics of the GRGS latest release (RL02) are explored and compared to the previous release (RL01). The RL02 gives best fit of the observed annual variations than RL01 and geophysical models do. However, the observed residual signal obtained after removing annual and semiannual oscillations is still better explained by the geophysical models even if RL02 estimates are improved at these frequencies scales. Linear trends are also estimated over study period (2003–2008). The linear trends of χ1 based on GRACE RL01/02 and EOP are similar but they are very different for χ2. Further studies with longer time series of GRACE and future gravimetric missions could help better interpret the long term variations and the effects of ice sheet mass loss or post glacial rebound. Concerning LOD variations, GRACE/LAGEOS mass displacement information brings better agreement with EOP observations, compared to the pressure term estimated by models, however the RL02 has not shown significant improvement.

Ensemble Kalman-Filtering of Earth rotation observations with a global ocean model

We study the changes in ocean angular momentum which lead to changes in the Earth's rotation. The focus lies on the consistency of model, model-forcing and observations. To check this consistency an ensemble-based Kalman-Filter approach was applied to ocean angular momentum time series which we derived from Earth rotation observations. The filter propagates a reduced rank error-covariance matrix with an optimal ensemble. This way, a complex system like the utilized global ocean circulation model can be assimilated with 32 ensemble members only. The Kalman-Filter improved the ocean-model's trajectory with respect to the observations, i.e., the observed ocean angular momentum was better reproduced by our model. A subsequent analysis of the changes which were induced by the filter revealed that the utilized atmospheric forcing is insufficient. When the filter is not entitled to change the forcing fields no improvement in the model trajectory was possible.

Assimilation of Earth rotation parameters into a global ocean model: excitation of polar motion

Abstract. The oceanic contribution to Earth rotation anomalies can be manifold. Possible causes are a change of total ocean mass, changes in current speed or location and changes in mass distribution. To derive the governing physical mechanisms of oceanic Earth rotation excitation we assimilate Earth rotation observations with a global circulation ocean model. Before assimilation, observations of length of day and polar motion were transformed into estimates of ocean angular momentum. By using the adjoint 4D-VAR assimilation method we were able to reproduce these estimated time series. Although length of day was assimilated simultaneously the analysis in this paper focuses on the oceanic polar motion generation. Our results show that changes in mass distribution and currents contribute to oceanic polar motion generation. Both contributions are highly correlated and show similar amplitudes. The changes in the model done by the assimilation procedure could be related to changes in the atmospheric forcing. Since for geometrical reasons the change of total ocean mass does not project on polar motion, we conclude that the polar motion is mainly generated by a geostrophic response to atmospheric momentum forcing. In geostrophic currents mass displacement and current speed entail each other. This way the large similarity of mass and current generated ocean angular momentum can be explained.

Spin, Wobble, and Nutation

Observing and Understanding Earth Rotation: A Joint GGOS/IAU Science Workshop; Shanghai, China, 25–28 October 2010; The Earth rotates about its axis once a day, but it does not do so uniformly. Instead, the rate of rotation fluctuates by as much as a millisecond a day, the Earth wobbles as it rotates because the Earth's mass is not balanced about its rotation axis, and the Earth's rotation axis precesses and nutates in space. These variations in the Earth's rotation are caused by processes acting within the interior of the Earth such as glacial isostatic adjustment and core‐mantle interaction torques, by processes acting at the surface of the Earth such as fluctuations in the transport of mass within the atmosphere and oceans, and by processes acting external to the Earth such as torques due to the gravitational attraction of the Sun, the Moon, and the planets. These and other aspects of the Earth's rotation were discussed at a recent workshop in China that attracted 90 participants from 12 countries. The workshop was jointly organized by the Global Geodetic Observing System (GGOS) of the International Association of Geodesy and Commission 19 (Rotation of the Earth) of the International Astronomical Union (IAU). The objectives of the workshop were to (1) assess our ability to observe the Earth's time‐varying rotation, (2) assess our understanding of the causes of the observed variations, (3) assess the consistency of Earth rotation observations with global gravity and shape observations, and (4) explore methods of combining rotation, gravity, and shape observations to gain greater understanding of the processes causing them to change on both the Earth and other planets, like Mars.

Assimilation of Earth rotation parameters into a global ocean model: length of day excitation

Changes in the oceanic current system and in the oceanic mass distribution alter, together with other processes, the state of the Earth’s rotation. This state is characterized by the length of day (LOD) and the tilt of the pole-to-pole axis. The aim of our study was to derive the respective governing physical mechanisms in the ocean. Therefore, Earth rotation observations were assimilated into a global circulation model of the ocean. Although assimilation is a well-established tool in climate science, the assimilation of Earth rotation observations into a global ocean model was done here for the first time. Prior to the assimilation, the Earth rotation observations were projected onto the angular momentum of the ocean. Non-oceanic contributions were removed. The result of the subsequent assimilation procedure is a time varying ocean model state that reproduces the projected Earth rotation observations well. This solution was studied to understand the oceanic generation of Earth rotation deviations and to identify governing physical mechanisms. This paper focuses on LOD anomalies although polar motion was assimilated simultaneously. Our results indicate that changes in the oceanic LOD excitation are mostly attributed to changes in total ocean mass. Changes in the spatial distribution of ocean mass turned out to have a minor contribution to the LOD deviations. The same applies to changes in the current system.

Rotational evaluation of a long-period spherical harmonic ocean tide model

By exchanging angular momentum with the solid earth, tidal variations in ocean currents and sea level cause the rotation of the solid earth to change. Observations of earth rotation variations can therefore be used to evaluate ocean tide models. The rotational predictions of a spherical harmonic ocean tide model that is not constrained by any type of data are compared here to the predictions of numerical ocean tide models and to earth rotation observations from which atmospheric and non-tidal oceanic effects have been removed. The spherical harmonic ocean tide model is shown to account for the observed variations at the fortnightly tidal period in polar motion excitation but not in length-of-day. Overall, its long-period polar motion excitation predictions fit the observed tidal signals better than do the predictions of the numerical ocean tide models studied here. It may be possible to improve its agreement with length-of-day observations by tuning certain model parameters, as was done to obtain the close agreement reported here between the modeled and observed polar motion excitation; alternatively, the discrepancy in length-of-day may point to the need to revise current models of mantle anelasticity and/or models of the oceanic response to atmospheric pressure variations.

Lining up the Ducks

CLIMATE SCIENCE Tide gauge and satellite measurements indicate that global mean sea level has increased by 1.5 to 2.0 mm/year during the 20th century. A significant fraction of this increase is ascribed to glacial melting caused by warming, with the remainder due to thermal expansion of the oceans. Because glacial melting redistributes Earth's mass from high latitudes, where water is stored as ice, to lower latitudes, any appreciable melting should change the planet's rate of rotation, as when a spinning figure skater extends her arms, and the orientation of the rotational vector, which should move as mass shifts. However, the simultaneous agreement in the movement of the rotational pole, the historical observations of ancient eclipses (which allow trends in the length of day to be computed), and space-based gravity measurements (which reflect mass redistributions) has seemingly precluded any major amount of ice melting during the past hundred years. Mitrovica et al. challenge that view with a new theory of rotational stability that involves reformulating how the shape of Earth has responded to glacial melting. In this way, they show how the full suite of Earth rotation and geodetic observations can be reconciled with those of glacial melting and associated sea level rise. — HJS Earth Planet. Sci. Lett. 243 , 390 (2006).

Reanalysis of ancient eclipse, astronomic and geodetic data: A possible route to resolving the enigma of global sea-level rise

Predictions of the Earth's response to the ice age appear to simultaneously reconcile a set of astronomical, geodetic and ancient eclipse observations related to changes in rotation, thus ruling out ice melting as a major contributor to 20th century sea-level rise. We demonstrate that the reconciliation disappears when an improved theory of rotational stability is applied. Furthermore, our reanalysis of longer satellite records renders previous estimates of the secular change in rotation rate suspect. The updated ice-age predictions and observations permit an anomalous 20th century ice flux of ∼1 mm/yr equivalent sea-level rise. Thus, the full suite of Earth rotation observations are consistent with a connection between climatic warming and recent melting of ice reservoirs.

The CEP and Geophysical Interpretation of Modern Earth Rotation Observations

AbstractThe definition of the Celestial Ephemeris Pole (CEP) which is the pole of reference for precession and nutation, should be revised taking into account recent advances in observation and theory. This paper reviews the current realization of the CEP and discusses possible extensions of both the conceptual definition and the realization of the CEP. Attention is focused on the corresponding connections between the Earth orientation parameters describing rotational variations and the related excitation parameters expressing dynamics of the geophysical fluids.

Glacial isostatic adjustment and Earth rotation: Refined constraints on the viscosity of the deepest mantle

We explore the extent to which two properties of Earth's present‐day rotational state may be applied to constrain the viscosity of the lower regions of the lower mantle. The analysis builds upon recent advances in understanding the radial resolving power of the relative sea level data of postglacial rebound which have demonstrated anew that no significant increase of viscosity across the 660‐km seismic discontinuity appears to be allowed by these data. Such observations do not constrain the viscosity of the mantle below about 1400 km depth, however, and here we estimate the average viscosity in this deepest region by invoking observations of the present‐day rate and direction of polar wander and the present‐day magnitude of the nontidal acceleration of the rate of planetary rotation. Since the rotational response to the glaciation cycle depends only upon the degree 2 spherical harmonic components of the induced deformation, this response is expected to provide the most specific sampling possible of deep mantle properties. Our analysis is based upon the use of glacial excitation functions calculated from complete gravitationally self‐consistent solutions of the sea level equation for the most recent refinement of the history of ice sheet thickness variations across the last glacial‐interglacial transition, namely, the ICE‐4G model. This analysis shows that when Earth rotation observations are combined with relative sea level constraints, the viscosity of the deepest mantle is required to be ∼1 order of magnitude higher than the viscosity of the upper part of the lower mantle. Such significant elevation of viscosity in the lowermost region of the lower mantle is also in accord with recent inferences based upon analysis of the nonhydrostatic geoid. The analyses presented herein therefore suffice to effect a reconciliation between the requirements of these distinct geophysical observations.

Antennacluster-Antennacluster VLBI for Study of the Core-Mantle Coupling

Search for evidences of the dissipative core-mantle coupling is probably the most interesting subject for VLBI Earth rotation observations in view of physical informations to be obtained about the core-mantle boundary region. It is shown that the VLBI detected out-of-phase component of the retrograde annual nutation term is most likely to be a manifestation of the dissipative coupling because the coupling coefficient required to explain the observed out-of-phase component is just in the same order of magnitude as the one associated with the decade fluctuations in the rotation rate of the Earth, which are commonly attributed to the dissipative core-mantle coupling. Several observational tests are proposed to clarify the mechanism and frequency characteristics of the coupling. Researches along this direction require accuracy and time resolution of the VLBI observations beyond their present-day level. It is shown that a VLBI system of new design, 'antennacluster-antennacluster VLBI system', will be able to realize the high performance required.

Further considerations on combining earth rotation observations from different space geodetic systems

Additional results are presented concerning a study that consider improvements over present Earth Rotation Parameter (ERP) determination methods by directly combining observations from various space geodetic systems in one adjustment. Earlier results are extended, showing that in addition to slight improvements in accuracy substantial (a factor of three or more) improvements in precision and significant reductions in correlations between various parameters can be obtained (by combining Lunar Laser Ranging (LLR), Satellite Laser Ranging (SLR) to Lageos, and Very Long Baseline Interferometry (VLBI) data in one adjustment) as compared to results from individual systems. Smaller improvements are also seen over the weighted means of the individual system results. Although data transmission would not be significantly reduced, negligible additional computer time would be required if (standardized) normal equations were available from individual solutions. Suggestions for future work and implications for the new International Earth Rotation Service (IERS) are also presented.

Analyses of the solid earth and ocean tidal perturbations on the orbits of the Geos 1 and Geos 2 satellites

The luni-solar tidal perturbations in the inclination of the GEOS-I and GEOS-II satellite orbits were analyzed for the solid Earth and ocean tide conditions. Precision reduced camera and TRANET Doppler observations spanning periods of over 600 days for each satellite were used to derive mean orbital elements. Perturbations due to the earth's gravity field, solar radiation pressure, and atmospheric drag were modelled, and the resulting inclination residuals were analyzed for tidal effects. The amplitudes of the observed total tidal effects were about 1.2 arc seconds (36 meters) in the inclination of GEOS-I and 4.5 arc seconds (135 meters) for GEOS-II. The solid earth tides were then modelled using earth tide measurements, earth rotation observations, and seismic data. The resulting inclination residuals were analyzed for ocean tide parameters. The derived parameters consist of one second degree coefficient and an accompanying phase angle in a spherical harmonic expansion of the ocean tidal potential for each tidal constituent. The results are presented.