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The goal of this study is in improvement of the short-term prediction of the polar motion in the context of state-space modeling suitable for the Kalman filter operations, such as the Kalman Earth Orientation Filter (KEOF) at Jet Propulsion Laboratory.
Analysis of nonseasonal polar motion excitation and atmospheric mass equatorial angular momentum (EAM) over land for the period 1980-1989 reveals a clear pattern of high power and correlation during the northern hemisphere (NH) winter followed by low power and correlation during the NH summer. A special case of this pattern occurs for longer than 14 months (from January 1987 to March 1988) when the correlation throughout the NH summer remains statistically significant. During this epoch an average of 72% of the nonseasonal polar motion excitation power at frequencies between -30 and +12 cycles/yr linearly related to atmospheric EAM over land. During the southern hemisphere winter there is significant correlation between the atmospheric EAM over midlatitude southern oceans and polar motion excitation indicating the existence of a dynamic atmosphere-ocean excitation. The atmospheric excitation power is too small to explain the large correlation during the NH winter. The effects of winds probably account for the deficit in power. The implication of these results is that there are two main excitation sources each dominant at different seasons. Atmospheric mass redistribution over land forces polar motion during the NH winter, and a dynamic atmpshere-ocean response is important during the SH winter.
This study compares observed polar motion for the period 1900-1985 with meteorologic and hydrologic data for the world over the same period, in an effort to determine whether water storage, in combination with air mass redistribution, can account for the observed variance of polar motion. Monthly time series of estimated continental water storage and air mass excitation functions have been compared at the annual frequency and at the Chandler frequency using power, coherence, multiple coherence, and phase spectra. There is a discrepancy in accounting for more than half the variance of polar motion across a broad range of frequencies. Similar results have been obtained in recent studies of polar motion at frequencies above 1 cycle per year using modem space geodetic determinations of polar motion. The persistence of the discrepancey at the annual frequency and its broadband nature suggest a source of polar motion excitation due to air and water motion which has either not been correctly estimated or not yet identified.
Based on the analysis of the polar motion behavior, the possibility of predicting polar motion up to one year in advance was found. Comparing these predicted polar coordinates with the observed ones (smoothed), the root mean square (rms) of the differences is about 0.02 seconds. The differences of the relative polar motion are much smaller. For any time interval of 20 to 30 days throughout the whole year, the rms of the relative polar motion differences is about 0.01 second. Compared with the best available VLBI results (from 1977 to 1980), the rms of pred. to obs. is 0.013 seconds, and the relative rms (for time intervals less than two months) is 0.008 seconds (here the observed data is unsmoothed). It appears that 80 to 90% of the polar motion is composed of the stable, predictable Chandler and annual terms. The UT1-UTC has more complicated changes than polar motion making it difficult to find a satisfactory method of long term prediction. So far the rms prediction error is 0.0023 s for up to 30 days.
The time and polar motion calibration support provided to the MM'71 mission is discussed. Specifically, a description is given of the data gathering system and the data processing system by which calibrations were obtained. An introductory discussion of the effects of timing and polar motion error on spacecraft navigation, along with a description of the system used to support Mariners 6 and 7, is given. A complete discussion of the way in which timing is used in orbit determination is also given.
Polar motion estimates obtained by satellite laser ranging (SLR) and VLBI are analyzed and compared. The JPL Kalman filter was utilized to smooth the polar motion estimates. Variations in the smoothing residuals for the X and Y components of polar motion for SLR and VLBI are examined. It is observed that the rms differences between the SLR and VLBI estimates for X and Y are about 2-3 marcsec. Power spectra of the differences are studied in order to measure possible periodic systematic errors. The data reveal that the SLR and VLBI polar motion data have a rms difference of about 15-20 marcsec and no significant systematic errors.
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 × 10(exp 19) Nm, to excite, and hence explain, the decadal polar motion to magnitude of approximately 10 mas.
A comparison of polar motion results from three sources (Bureau International de l'Heure (BIH), Defense Mapping Agency Hydrographic/Topographic Center (DMAHTC-Doppler), the International Polar Motion Service (IPMS)) was performed using lunar laser ranging (LLR) data. The rms errors, both of the LLR data and of the determinations of polar motion by the three services, decreased in recent times. The BIH and Doppler polar motion are comparable in quality (12 + or - 6 cm for BIH values taken from August 1976 through May 1980, 14 + or - 7 cm for Doppler results taken from June 1977 through May 1980). The IPMS errors were substantially larger (33 + or - 7 cm for data taken from August 1976 through May 1980). All three analyses give 13 + or - 3 cm as an estimate for the combined LLR modeling, fitting, and instrumental error (noise) for the last four years.
The rotational motion of the earth is decomposed into spin, polar motion and local motions. The rotation vector components are associated to phenomena such as precession, nutation, diurnal spin, polar motion and local motions. The above decomposition is accomplished without refering to an earth-fixed CIO pole or BIH zero meridian. The time-like variations of the coordinates of a surface point in a geocentric equatorial reference frame are presented as a function of the rotation vector components. In the rigid earth approximation three scalar parameters are necessary for evaluating point coordinate variations, namely spin rate of the earth, polar motion magnitude and spin rate of the polar motion vector. Two numerical examples are given as an illustration.
A recent reanalysis of the International Latitude Serivce (ILS) polar motion data-day has been processed using Kalman filtering techniques to generate the polar motion excitation function over the time-span from 1960 to 1965. The resulting excitation function has been examined for the effects of 1960 Chile in an attempt to determine experimentally how large earthquake affect polar motion. The resulting upper bound of about 75 x 10 to the 22nd N-m for a 10-deg dip (about 36 x 10 to the 22nd N-m for 20-deg dip) is consistent with results obtained from previous seismic studies, including a recent normal mode excitation result. Following future great earthquakes, monitoring of polar motion by space-based techniques such as VLBI should continue at high temporal resolution for several weeks in order to directly measure the rheological parameters of the upper mantle.
An analytical theory is developed to describe diurnal polar motion in the earth which arises as a forced response due to lunisolar torques and tidal deformation. Doodson's expansion of the tide generating potential is used to represent the lunisolar torques. Both the magnitudes and the rates of change of perturbations in the earth's inertia tensor are included in the dynamical equations for the polar motion so as to account for rotational and tidal deformation. It is found that in a deformable earth with Love's number k = 0.29, the angular momentum vector departs by as much as 20 cm from the rotation axis rather than remaining within 1 or 2 cm as it would in a rigid earth. This 20 cm separation is significant in the interpretation of submeter polar motion observations because it necessitates an additional coordinate transformation in order to remove what would otherwise be a 20 cm error source in the conversion between inertial and terrestrial reference systems.
The annual wobble in Earth's polar motion is a forced motion, as opposed to an excited natural oscillation which is the Chandler wobble in the case of polar motion. It is forced by the combination of many angular momentum variations in the geophysical fluids that exchange these variations with the solid Earth, hence changing its rotation. Among all forcing sources of the annual wobble the geophysical fluid that has the dominant contribution is the atmosphere, while the oceans and the land hydrology make up the remaining budget together with tidal influences. The latter include that from the solid Earth deformation and that from the ocean tides at the annual period. The combined forcing produces both prograde and retrograde wobbles; the prograde wobble gets magnified substantially by the near-by presence of the natural Chandler wobble resonance. On the other hand, the closeness of the prograde annual forcing power to the Chandler period is an indication that some of the power leakage into the Chandler period band becomes the main excitation source for the Chandler wobble. In this paper we will review our knowledge about annual wobble and show the status in the effort of closing the budget with the annual angular momentum variations from the various geophysical fluids.
A Kalman filter was designed to yield optimal estimates of geophysical parameters from Very Long Baseline Interferometry (VLBI) group delay data. The geophysical parameters are the polar motion components, adjustments to nutation in obliquity and longitude, and a change in the length of day parameter. The VLBI clock (and clock rate) parameters and atmospheric zenith delay parameters are estimated simultaneously. Filter background is explained. The IRIS (International Radio Interferometric Surveying) VLBI data are Kalman filtered. The resulting polar motion estimates are examined. There are polar motion signatures at the times of three large earthquakes occurring in 1984 to 1986: Mexico, 19 September, 1985 (Magnitude M sub s = 8.1); Chile, 3 March, 1985 (M sub s = 7.8); and Taiwan, 14 November, 1986 (M sub s = 7.8). Breaks in polar motion occurring about 20 days after the earthquakes appear to correlate well with the onset of increased regional seismic activity and a return to more normal seismicity (respectively). While the contribution of these three earthquakes to polar motion excitations is small, the cumulative excitation due to earthquakes, or seismic phenomena over a Chandler wobble damping period may be significant. Mechanisms for polar motion excitation due to solid earth phenomena are examined. Excitation functions are computed, but the data spans are too short to draw conclusions based on these data.
A comprehensive, experimental study of the predictability of the polar motion using a homogeneous BIH (Bureau International de l'Heure) data set is presented. Based on knowledge of the physics of the annual and the Chandler wobbles, the numerical model for the polar motion is constructed by allowing the wobble periods to vary. Using an optimum base length of 6 years for prediction, this floating-period model, equipped with a non-linear least-squares estimator, is found to yield polar motion predictions accurate from 0.012 to 0.024 inches depending on the prediction length up to one year, corresponding to a predictability of 91-83%. This represents a considerable improvement over the conventional fixed-period predictor, which does not respond to variations in the apparent wobble periods. The superiority of the floating-period predictor to other predictors based on critically different numerical models is also demonstrated.
The second-degree zonal tide raising potential, which is responsible for tidal changes in the Earth's rotation rate and length-of-day, is symmetric about the polar axis and hence can excite the Earth's polar motion only through its action upon nonaxisymmetric features of the Earth such as the oceans. Ocean tidal excitation of polar motion in the diurnal and semidiurnal tidal bands has been previously detected and examined. Here, the detection of ocean tidal excitation of polar motion in the long-period tidal band, specifically at the Mf' (13.63-day) and Mf (13.66-day) tidal frequencies, is reported. Spectra of the SPACE94 polar motion excitation series exhibit peaks at the prograde and retrograde fortnightly tidal periods. After removing effects of atmospheric wind and pressure changes, an empirical model for the effect of the fortnightly ocean tides upon polar motion excitation is obtained by least-squares fitting periodic terms at the Mf and Mf' tidal frequencies to the residual polar motion excitation series. The resulting empirical model is then compared with the predictions of two hydrodynamic ocean tide models.
The causes and effects of diurnal polar motion are described. An algorithm is developed for modeling the effects on very long baseline interferometry observables. Five years of radio-frequency very long baseline interferometry data from stations in Massachusetts, California, and Sweden are analyzed for diurnal polar motion. It is found that the effect is larger than predicted by McClure. Corrections to the standard nutation series caused by the deformability of the earth have a significant effect on the estimated diurnal polar motion scaling factor and the post-fit residual scatter. Simulations of high precision very long baseline interferometry experiments taking into account both measurement uncertainty and modeled errors are described.
Estimates of the near-fortnightly Mf ocean tide from Topex/Poseidon satellite altimetry and from numerical solutions to the shallow water equations agree reasonably well, at least in their basin-scale features. For example, both show that the Pacific Ocean tide lags the Atlantic tide by roughly 30 degrees. There are hints of finer scale agreements in the elevation fields, but noise levels are high. In contrast, estimates of Mf currents are only weakly constrained by the TP data, because high-wavenumber Rossby waves (with intense currents) are associated with relatively small perturbations in surface elevation. As a result, a wide range of Mf current fields are consistent with both the TP data and the hydrodynamic equations within a priori plausible misfit bounds. We find that a useful constraint on the Mf currents is provided by independent estimates of the Earth's polar motion. At the Mf period polar motion shows a weak signal (both prograde and retrograde) which must be almost entirely caused by the ocean tide. We have estimated this signal from the SPACE2000 time series, after applying a broad-band correction for atmospheric angular momentum. Although the polar motion estimates have relatively large uncertainties, they are sufficiently precise to fix optimum data weights in a global ocean inverse model of Mf. These weights control the tradeoff between fitting a prior hydrodynamic model of Mf and fitting the relatively noisy T/P measurements of Mf. The predicted polar motion from the final inverse model agrees remarkably well with the Mf polar motion observations. The preferred model is also consistent with noise levels suggested by island gauges, and it is marginally consistent with differences observed by subsetting the altimetry (to the small extent that this is possible). In turn, this new model of the Mf ocean tide allows the ocean component to be removed from Mf estimates of length of day, thus yielding estimates of complex Love numbers less contaminated by oceanic effects than has hitherto been possible.
Long time geodetic observation records show that the orientation of the Earth's rotation axis with respect to the terrestrial reference frame, or polar motion, changes on a broad range of timescales. Apart from external torques from the luni-solar tides, these changes are excited by interactions among different components of the Earth system. The convective fluid outer core has long been conjectured a likely contributor to the observed polar motion on timescales upward of decades, such as the 30 year Markowitz wobble. We investigated the electromagnetic coupling scenario across the core-mantle boundary via numerical geodynamo simulation for different geodynamo parameters (Rayleigh numbers and magnetic Rossby numbers). Our simulated polar motion varies strongly with the dynamo parameters, while its excitation on decadal timescales appear to converge asymptotically within the adopted range of numerical Rossby numbers. Three strongest asymptotic modes emerge from numerical results, with periods around 30, 40, and 60 years for the prograde excitation and around 24, 30, and 60 years for the retrograde excitation. Their amplitudes are all larger than 5 times 10 (sup minus 8), or approximately 10 milliseconds of arc.The results suggest that the electromagnetic core-mantle coupling could explain a substantial portion, if not all, of the observed decadal polar motion. In particular, the predicted 60 year polar motion deserves special attention for future observations and studies.