Earth's Rotation Rate Research Articles

Earth rotation measurement with micromechanical yaw-rate gyro

The direct measurement of the Earth's rotation rate by means of a micromechanical yaw-rate gyroscope is difficult to achieve due to the considerable parameter variations of the current state-of-the-art sensors of this type. This paper outlines and applies a model of the external factors' effect on the sensor measurement via a method for their compensation through a mechanical change in the sensor's orientation. This allows the determination of a value such as the Earth's rotation rate, which is at the limit of the sensor's sensitivity and less than its short-term stability. A specialized information-measurement system has been developed for the implementation of the method. This system has been used for a number of measurements, presented in a graphical form. As a result, an average value of the Earth's rotation rate has been derived. This method is applicable for a subjective categorization and evaluation of micromechanical gyroscopes using a natural source of a very low angular speed.

Wavelet coherence analysis of Length-Of-Day variations and El Niño-Southern Oscillation

Abstract Wavelet coherence analysis is defined and used to analyze the relationships between Length-Of-Day (LOD) variations and El Nino-Southern Oscillation (ENSO) on interannual scales. Using the newest observation data, this study quantitatively shows time-scale-dependent correlations and phase shifts between LOD variations and the ENSO. Good no-lag correlations (larger than 0.8) can be found on 3.0–4.9-year scales, while either obvious phase-shifts or low correlations are found on the other interannual scales. Around 2.5-year (biennial), 3.5-year and 5.0-year scales (i.e. around the time scales of ENSO's significant modes), the LOD variations with respect to the ENSO lag in phase by 4–5 months, lead by 3 months and lag by 3–5 months, respectively. Thus, there are obvious time-scale-dependent correlations and phase-shifts between the Earth rotation rate variations and the ENSO even within interannual scales.

Effects of zonal deformations and the Earth's rotation rate variations on precession-nutation

Because of their importance in the accurate modeling of the Earth's orientation in space, some non-negligible predictable effects on precession-nutation are investigated. This paper considers the coupling effects between the axial and the equatorial components of the Earth's rotation vector in the dynamical equations, and the effects of the second order lunisolar torque due to the Earth's zonal deformations. Firstly, the coupling effects are shown to contribute for less than 0.1 μ as and are therefore negligible. Secondly, we demonstrate that the 0.7 mas contribution of the rotation rate variations due to zonal tides to the nutation in obliquity deduced by Bretagnon et al. ([CITE], Proc. IAU Coll., 180, 230; [CITE], Celest. Mech. Dyn. Astr., 80, 177) is an artefact which comes from an incomplete way of taking into account the effect of the rotation rate variations. The net contribution is shown to be negligibly small. Thirdly, for an Earth model with an elastic mantle and decoupled liquid core, the contribution of the second-order lunisolar torque due to the Earth's zonal deformations is shown to be 207.9 μ as and –9.7 μ as on the 18.6-year nutation respectively in longitude and in obliquity, and a correction of –4925.9 μ as/century on the precession in longitude.

Entrainment laws and a bulk mixed layer model of rotating convection derived from large‐eddy simulations

Entrainment of rotating convection is investigated using a large‐eddy simulation (LES) model. The model is forced with a uniform destablizing surface buoyancy flux, which varies by about an order of magnitude. The initial mixed layer depth varies from 0 to 3000 m and the background stratification varies over two orders of magnitude. The vertical component of the Earth's rotation rate at 30, 45, and 60°N are used. The corresponding flux Rossby number varies about three orders of magnitude. An empirical formula for the ratio of entrainment buoyancy flux to the surface buoyancy flux as a function of the Rossby number is derived. A bulk mixed‐layer model for rotating convection is formulated based on the entrainment formula. It is suggested this formula can also be used to tune other 1‐D models used in ocean general circulation models to account for the effect of Earth's rotation on convection.

Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits

Orbits repeating their ground track on the surface of the earth are found to be members of periodic-orbit families (in a synodic frame) of the tesseral problem of the Earth artificial satellite. Families of repeat ground track orbits appear as vertical bifurcations of the equatorial family of periodic orbits, and they evolve from retrograde to direct motion throughout the 180 degrees of inclination. These bifurcations are always close to the resonances of the Earth's rotation rate and the mean motion of the orbiter.

Earth rotation and ENSO events: combined excitation of interannual LOD variations by multiscale atmospheric oscillations

Time series of the length of day characterizing the rate of Earth rotation, the atmospheric angular momentum and the Southern Oscillation Index from 1962 to 2000 are used to reexamine the relationships between the ENSO events and the changes in the length of day, as well as the global atmospheric angular momentum. Particular attention is given to the different effects of the 1982–1983 and 1997–1998 ENSO events on the variations of Earth rotation. The combined effects of multiscale atmospheric oscillations (seasonal, quasi-biennial and ENSO time scales) on the anomalous variations of the interannual rates of Earth rotation are revealed in this paper by studying the wavelet spectra of the data series.

Pacific warm pool excitation, earth rotation and El Niño southern oscillations

The interannual changes in the Earth's rotation rate, and hence in the length of day (LOD), are thought to be caused by the variation of the atmospheric angular momentum (AAM). However, there is still a considerable portion of the LOD variations that remain unexplained. Through analyzing the non‐atmospheric LOD excitation contributed by the Western Pacific Warm Pool (WPWP) during the period of 1970–2000, the positive effects of the WPWP on the interannual LOD variation are found, although the scale of the warm pool is much smaller than that of the solid Earth. These effects are specifically intensified by the El Niño events, since more components of the LOD‐AAM were accounted for by the warm pool excitation in the strong El Niño years. Changes in the Earth's rotation rate has attracted significant attention, not only because it is an important geodetic issue but also because it has significant value as a global measure of variations within the hydrosphere, atmosphere, cryosphere and solid Earth, and hence the global changes.

Despinning of the earth rotation in the geological past and geomagnetic paleointensities

Length of day (l.o.d.) values deduced from fossils and tidal deposits suggest that the despinning rate was, on the average, about 5 times smaller during the Proterozoic than during the Phanerozoic and, moreover, that between 250 and 100 million years ago, there was a slight non-linear variation super-imposed on the overall linear trend of the Earth's rotation rate. To explain these observational facts, it has recently been argued that formation of the inner structure of the Earth (mass redistribution within the mantle and/or core formation) had not been fully completed before the Proterozoic, and that the decrease of the inertia moment associated with the evolving terrestrial interior compensated to some extent the rotational effects of tidal friction. There is an another plausible explanation to account for the difference of despinning rates during the Proterozoic and Phanerozoic, namely: the distribution of the continents had been significantly different during these epochs and the world ocean had been much shallower in the Proterozoic than in the Phanerozoic. We used published data for the Phanerozoic, Proterozoic and Archean in order to check whether there had been significant long-term changes of geomagnetic intensity. Our results are based on robust statistical analysis; they indicate that during a time interval coinciding roughly with the Mesozoic, the geomagnetic dipole moment underwent a minimum in a quite similar way as the l.o.d. data. For the Proterozoic (2500–570 million years ago) and the late Archean (3000–2500 million years ago), it is very difficult to draw a conclusion concerning the variation in time of the intensity of the geomagnetic field: the data set we used is incomplete and the statistical scatter is larger than the derived mean value. Nevertheless, we tentatively conclude that the values of the average geomagnetic moment were approximately the same in the Phanerozoic and in the Proterozoic+late Archean, and that there is no significant long-term change in the geomagnetic intensity detectable before the Phanerozoic.

Effect of changes in total atmospheric mass on length‐of‐day modeling

The Earth's rotation rate, and the associated length‐of‐day (LOD), show fluctuations at different timescales. At the decadal timescale, this is due mainly to the interaction between the mantle and the liquid core, while the variations at shorter time scales are attributed to interaction with the external fluid layers, in particular the atmosphere, with the oceans and hydrology contributing at about the 1% level. In this paper, we investigate the effect of changes of atmospheric mass on the length‐of‐day modeling, which are associated with evaporation/precipitation and mass closure problems in the atmospheric analyses. We show that an important part of the residuals between observed LOD and the ocean and atmosphere induced LOD variations can be explained by this mass exchange.

Numerical general circulation experiments of sensitivity to Earth rotation rate

The ECHAM4 general circulation model was tested for its skill in reproducing the sensitivity of the general circulation to the rotation rate of the Earth. The experiments have been designed to investigate the be- havior of the model under conditions that are not typical of the parametric regime under which the model has been developed. The model was set at spectral T30 res- olution, has 19 vertical levels and it includes a rather complete set of physical parametrizations, seasonal and diurnal cycles, and a mixed layer ocean. The other pa- rameters have been prescribed at present climate values to offer a good comparison with the simulation of the present climate (24 h rotation rates). In particular, the present land-sea mass distribution and mountain ranges have been used. The dynamical response to rotation rate changes was investigated by performing sensitivity ex- periments at fixed rotation rates, from 18 to 360 h, each integrated for 20 years. The latitudinal extent and the strength of the Hadley Cell increased as the rotation rate was decreased, as expected from idealized models and theory. The tropospheric jets underwent a similar evo- lution, moving poleward and modifying their intensity, as the rotation rate was decreased. The winter stationary waves have been found to be very sensitive to the rota- tion rate, turning into longer and longer wavelength quickly as the rotation slowed. The model has been also used to investigate the stability of the general circulation to the variations of the rotation rate. The model was run with a rotation period of 240 h and a direct Hadley Circulation equator to pole was observed. The rotation rate was subsequently increased until baroclinic insta- bilities at midlatitudes appeared. The experiment demonstrated how ECHAM4 handles the unstable character of the eddy-free circulation typical of slow rotations and the transition to turbulent, eddy rich, re- gimes. The overall results indicate that rotation rate changes need to be taken into account when designing paleoclimatic simulations. The good agreement between the results of the simulations and the bounds provided by the dynamical theories of the general circulation en- hances our confidence in the capability of the model to represent the general circulation in different situations from the present climate.

Strain accumulation and rotation in western Nevada, 1993–2000

The positions of 44 GPS monuments in an array extending from the Sierra Nevada at the latitude of Reno to near Austin, Nevada, have been measured several times in the 1993–2000 interval. The western half of the array spans the Walker Lane belt, whereas the eastern half spans the central Nevada seismic zone (CNSZ). The principal strain rates in the Walker Lane belt are 29.6 ± 5.3 nstrain yr−1 N88.4°E ± 5.4° and −12.8 ± 6.0 nanostrain yr−1 N01.6°W ± 5.4°, extension reckoned positive, and the clockwise (as seen from above the Earth) rotation rate about a vertical axis is 13.6 ± 4.0 nrad yr−1. The quoted uncertainties are standard deviations. The motion in the Walker Lane belt can then be represented by a zone striking N35°W subject to 16.8 ± 4.9 nstrain yr−1 extension perpendicular to it and 19.5 ± 4.0 nstrain yr−1 right‐lateral, simple shear across it. The N35°W strike of the zone is the same as the direction of the local tangent to the small circle drawn about the Pacific‐North America pole of rotation. The principal strain rates for the CNSZ are 46.2 ± 11.0 nstrain yr−1 N49.9°W ± 6.0° and −13.6 ± 6.1 nstrain yr−1 N40.1°E ± 6.0°, and the clockwise rotation rate about a vertical axis is 20.3 ± 6.3 nrad yr−1. The motion across the CNSZ can then be represented by a zone striking N12°E subject to 32.6 ± 11.0 nstrain yr−1 extension perpendicular to it and 25.1 ± 6.3 nstrain yr−1 right‐lateral, simple shear across it. The N12°E strike of the zone is similar to the strikes of the faults (Rainbow Mountain, Fairview Peak, and Dixie Valley) within it.

Long-term changes in atmospheric circulation, earth rotation rate and north–south solar asymmetry

Earlier studies have demonstrated a relation between long-term changes in the Earth's rotation rate and the prevalence of zonal or meridional types of circulation. The results, however, have been confined to the 20th century and to the Northern hemisphere. In the present paper we compare the long-term changes in the length of the day (LOD) and the temperature contrast between the equator and the pole in the Northern and the Southern hemispheres as an indirect measure for the zonality of the atmospheric circulation. In the 20th century in the Northern hemisphere we find a high negative correlation between the rotation rate and the equator/pole temperature contrast, while in the 19th century the correlation is positive. For the Southern hemisphere, the situation is opposite. The correlation changes when the North–South asymmetry of solar activity also changes sign. The decadal changes in LOD are shown to be related to the changes in the North–South asymmetry of solar equatorial rotation rate supposedly induced by planetary-driven changes in the angular momentum of the solar system, with both quantities showing pronounced periodicities and high squared coherence at 47 years. It is hypothesized that decadal changes in LOD are driven by core-mantle coupling processes regulated by solar wind transferring solar magnetic fields and angular momentum modulated by planetary influences. The atmospheric circulation in the Northern and Southern hemispheres is found to be different not only on decadal time-scales but also in the 11-year solar cycle, and different in even and odd cycles. While long-term changes in geomagnetic activity closely follow sunspot activity changes, the correlation between the two in the 11-year cycle has been decreasing in the last century with the increase of the North–South solar activity asymmetry which modulates also the asymmetry of galactic cosmic rays flux considered a candidate mediator between solar activity and climate.

New technique for reducing the angle random walk at the output of fiber optic gyroscopes during alignment processes of inertial navigation systems

Aboelmagd NoureldinDave Irvine-HallidayUniversity of CalgaryDepartment of Electrical and ComputerEngineeringAlberta, Canada T2N 1N4Herb TablerInternational Downhole Equipment, Ltd.Edmonton, Alberta, CanadaMartin P. MintchevUniversity of CalgaryDepartment of Electrical and ComputerEngineeringAlberta, Canada T2N 1N4E-mail: mintchev@enel.ucalgary.caAbstract. Angle random walk (ARW) is the noise component at the out-put of a fiber optic gyroscope (FOG) and it affects the FOG short-termaccuracy. Practical applications of FOGs inside an inertial navigationsystem necessitate monitoring the Earth’s rotation rate component alongthe FOG sensitive axis to determine the initial attitude of the movingobject. The ARW increases the measurement uncertainty, thus affectingthe overall accuracy. We introduce a new filtering approach that signifi-cantly reduces the ARW at the FOG output to a level that can ensure anaccurate measurement of the Earth rotation rate. The filtering approachemploys the forward linear prediction (FLP) technique to design a tapdelay line filter and a new criterion, based on controlling the step sizeparameter, is introduced to ensure the fastest possible convergence ofthe adaptive algorithm, while keeping the minimal possible mean squareerror. The proposed FLP filter of 300 tap weights is capable of reducingthe ARW from 4.66 to 0.0694deg/h(

Earth Rotation and El Niño—Theory of Air‐Sea Coupling

AbstractApplying the shallow water equations with air‐sea interaction in low latitudes, the influences of the earth's variable rotation on air‐sea coupled system are discussed in this paper by means of normal mode and special functions. It is shown that the variation of the earth's rotation rate on the one hand affects the propagation and stability of Kelvin and Rossby waves and on the other hand can cause the changes of zonal wind, current and sea surface temperature. Particularly, when the earth's rotation rate is decelerated, the anomaly of zonal wind and current is caused and SST in the east part of low‐latitude oceans is increased through the air‐sea interaction, and thus the El Niño events is created which bring about the global climate changes.

On the spatio temporal distribution of global seismicity and rotation of the earth — A review

This article reviews the development of the study of relationship between the earth's rotation and the spatio-temporal distribution of global seismicity by stationary model of seismicity rates and annual seismic energy released. Observed variations of seismic energy release in shallow, intermediate and deep focus earthquakes and their frequency distribution confirms this correlation. The peaks of these parameters are controlled by the earth rotation. There exists a phase relationship among earth's rotation rate minima and maxima with the maxima (peaks) of the above parameters as well as Thrust (T) and the strike slip (S) dominating periods of global seismicity. In order to compare our results with observations, the space-time dependence of the frequency of earthquakes and annual energy release has been established. The results are in very good agreement with previous studies and further enhance our knowledge for global seismicity distribution.

On the energy source for atmospherically induced angular momentum changes of the earth

Orographic torques induce a transfer of angular momentum between the atmosphere and the earth thus changing the earth's rotation and this way also its kinetic energy. Therefore, energy must be transferred as well. However, the standard boundary conditions as used in atmospheric models do not allow for such a transfer of energy. This contradiction is resolved by taking explicitly into account the changes of the earth's rotation rate in the boundary conditions for atmospheric motion. With that, energy conservation is ensured. It is shown, however, that the related energy transfers are so small that this effect need not be included in, say, general circulation models.

Earth Rotation and El Nino—Theory of Waves

AbstractConsidering the variation of the earth's rotation rate with time and applying the equations of shallow‐water model to the geo‐fluids (atmosphere and ocean) in low latitudes, the influences of variation the earth's rotation rate on the atmospheric and oceanic waves are analyzed. It is shown that the variation of the earth's rotation rate affects directly not only the variation of zonal wind and oceanic current, but also the anomaly of sea level and sea surface temperature by the propagation of Kelvin waves and hence can promote the occurrence of the El Nino event. Therefore, the variation of the earth's rotation rate is a significant factor in global climate variability.

Monthly and fortnightly tidal variations of the Earth's rotation rate predicted by a TOPEX/POSEIDON Empirical Ocean Tide Model

Empirical models of the two largest constituents of the long‐period ocean tides, the monthly and the fortnightly constituents, are estimated from repeat cycles 10 to 210 of the TOPEX/POSEIDON (T/P) mission. These models are first validated with tide gauge observations which show residual variances with the T/P‐derived models that are of the order of 2–3 mm² for both the monthly and fortnightly constituents, and which are smaller than residual variances from respective equilibrium models of these long‐period ocean tides. These empirical models are used to predict the contribution that they each have on tidal variations of the Earth's rotation rate. For tidal variations in UT1 these contributions are predicted to be of the order of 0.1 ms with a scatter of the order of 8 and 3 µs for the monthly and fortnightly ocean tides, respectively.

Detection and modeling of NonTidal oceanic effects on Earth's rotation rate

Subdecadal changes in Earth's rotation rate, and hence in the length of day (LOD), are largely controlled by variations in atmospheric angular momentum. Results from two oceanic general circulation models (OGCMs), forced by observed wind stress and heat flux for the years 1992 through 1994, show that ocean current and mass distribution changes also induce detectable LOD variations. The close similarity of axial oceanic angular momentum (OAM) results from two independent OGCMs, and their coherence with LOD, demonstrate that global ocean models can successfully capture the large-scale circulation changes that drive OAM variability on seasonal and shorter time scales.

Oceanic Effects on Earth's Rotation Rate

Changes in the mass distribution of water in Earth9s oceans in turn leads to variations in its angular momentum. In his Perspective, Wilson discusses results presented in the same issue by Marcus et al . in which techniques of radio astronomy were used to measure changes in Earth9s angular momentum. The variations were observed by measuring changes in the length of day, and therefore Earth9s rotation rate. Measurements such as these may serve as an indicator of oceanic behavior, much as other indices are used to keep track of atmospheric climate.