Variation Of J2 Research Articles

Using GRACE to Explain Variations in the Earth's Oblateness

AbstractWe present a new approach to estimate time variations in J2. Those variations are represented as the sum of contributions from individual sources. This approach uses solely Gravity Recovery And Climate Experiment (GRACE) data and the geoid fingerprints of mass redistributions that take place both at the surface and in the interior of the solid Earth. The results agree remarkably well with those based on satellite laser ranging, while estimates of the sources explain the observed variations in J2. Seasonal variations are dominated by terrestrial water storage and by mass redistribution in the atmosphere and ocean. Trends, however, are primarily controlled by the Greenland and Antarctic ice sheets and by glacial isostatic adjustment. The positive trend from surface mass variations is larger than the negative trend due to glacial isostatic adjustment and leads to an overall rising trend during the GRACE period (2002–2017).

Detection of Antarctic oscillation signals in Earth’s oblateness variations

Variations of Earth’s oblateness (J 2) reflect a large scale mass redistribution within the Earth system. The climate effect causing J 2 interannual variations is still not clear, though previous studies indicated it may be related to EI Nino–Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO). However, we have a new discovery of the significant Antarctic oscillation (AAO) signals in J 2 interannual variations, especially on 4–6 year scales based on cross wavelet and wavelet coherence analysis with 95% confidence test during 1979–2012. The results additionally indicate that the close phase relationship between J 2 and AAO (AAO leading J 2 variations by 3 ± 2 months in phase) is far superior to that between J 2 and ENSO/PDO on 4–6 year scales. In this work, we discuss, for the first time, a possible geophysical mechanism of AAO effecting J 2 variations. The investigations are based on the definition of AAO and its spatial–temporal behavior influencing the large-scale mass movement. Finally, an approximate quantitative estimate of the AAO imprint on J 2 with an emphasis on the atmospheric contribution is made.

Optimizing estimates of annual variations and trends in geocenter motion and J2 from a combination of GRACE data and geophysical models

AbstractThe focus of the study is optimizing the technique for estimating geocenter motion and variations in J2 by combining data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission with output from an Ocean Bottom Pressure model and a Glacial Isostatic Adjustment (GIA) model. First, we conduct an end‐to‐end numerical simulation study. We generate input time‐variable gravity field observations by perturbing a synthetic Earth model with realistically simulated errors. We show that it is important to avoid large errors at short wavelengths and signal leakage from land to ocean, as well as to account for self‐attraction and loading effects. Second, the optimal implementation strategy is applied to real GRACE data. We show that the estimates of annual amplitude in geocenter motion are in line with estimates from other techniques, such as satellite laser ranging (SLR) and global GPS inversion. At the same time, annual amplitudes of C10 and C11 are increased by about 50% and 20%, respectively, compared to estimates based on Swenson et al. (2008). Estimates of J2 variations are by about 15% larger than SLR results in terms of annual amplitude. Linear trend estimates are dependent on the adopted GIA model but still comparable to some SLR results.

A Tikhonov regularization method to estimate Earth's oblateness variations from global GPS observations

Earth's oblateness is varying due to the redistribution of Earth's fluid mass and the interaction of various components in the Earth system. Nowadays, continuous Global Positioning System (GPS) observations can estimate Earth's oblateness (J2) variations with the least squares method, but are subject to ill-conditioned equations with limited GPS observations and aliasing errors from truncated degrees. In this paper, a Tikhonov regularization method is used to estimate J2 variations from global continuous GPS observations. Results show that the J2 has been better estimated from GPS observations based on a Tikhonov regularization method than the usual least squares method when compared to SLR solutions. Furthermore, the amplitudes and phases of the annual and semi-annual J2 variations are closer to the SLR results with truncated degrees from 2 to 5. Higher truncated degrees will degrade the J2 estimate. Annual J2 variations are best estimated from GPS observations with truncated degree 4 and semi-annual J2 variations are best estimated with truncated degree 2.

Deceleration in the Earth's oblateness

For over three decades, satellite laser ranging (SLR) has recorded the global nature of the long‐wavelength mass change within the Earth system. Analysis of the most recent time series of 30 day SLR‐based estimates of Earth's dynamical oblateness, characterized by the gravitational degree‐2 zonal spherical harmonic J2, indicates that the long‐term variation of J2 appears to be more quadratic than linear in nature. The superposition of a quadratic and an 18.6 year variation leads to the “unknown decadal variation” reported by Cheng and Tapley (2004). Although the primary trend is expected to be linear due to global isostatic adjustment, there is an evident deceleration () in the rate of the decrease in J2 during the last few decades, likely due to changes in the rate of the global mass redistribution from melting of the glaciers and ice sheets as well as mass changes in the atmosphere and ocean.

Analysis of the characteristics of the harmonics coefficient J 2 of the Earth’s gravity field in different periods

The characteristics of the geopotential coefficient J2 in different periods are analyzed using satellite laser ranging data spanning the last 27 years. The satellites used in the analysis are Lageos1 and Lageos2. The variations in J2 are obtained by determining the dynamic orbit. The results show that there are strong seasonal and long-term variations. For different data spans, the seasonal variations agree well in terms of both amplitude and phase. Using all the data, the amplitude and phase of the annual term are 2.5 × 10−10 and 127°, respectively, while the amplitude and phase of the semiannual term are 0.94 × 10−10 and 213°, respectively. In the case of long-term variation, the secular variation in J2\(\left( {\dot J_2 } \right)\) is −2.2 × 10−11 a−1 from 1984 to 2010. \(\dot J_2\) differs for the different periods because of interannual variations, such as the “1998 anomaly”. Another anomaly may have taken place during 2007–2010. Although the cause of the anomaly is unknown, it is an important observational constraint on the shape of the Earth.

Variation in lipid reserves of second-stage juveniles of Meloidogyne exigua in a coffee field and its relationship with infectivity

AbstractIn this study we assessed the variations in lipid content of second-stage juveniles (J2) of Meloidogyne exigua, recovered from a coffee field, by staining and quantifying the neutral lipids using image analysis. Our results showed that annual variations in J2 stained lipid area correlate with temperature, rainfall and total number of J2 per 100 cm3 of soil. Laboratory and glasshouse experiments showed that decreases in the lipid stained area of J2 of M. exigua led to decreased infectivity and reproduction on tomato. The susceptibility of tomato cvs Kada and Nemadoro to M. exigua varied according to the stained lipid area of the J2 inoculated on roots. Only J2 containing an average of 80% stained lipid area were able to infect cv. Nemadoro, which contains the Mi resistance gene, whereas J2 containing 20% stained lipid area were still able to infect cv. Kada, considered to be highly susceptible. In this study we show for the first time the dynamics of lipid variation in J2 of M. exigua in a coffee field and the dependence of infectivity and parasitism on the resistance level of tomato cultivars and the lipid stained area in J2.

Ocean cooling: Constraints from changes in Earth's dynamic oblateness (J2) and altimetry

[1] Dynamic oblateness (J2) observations reflect changes in the latitudinal distribution of mass within the Earth system, and hence can give insights into processes involving water transport and sea level rise. We seek to use records of J2 variations deduced from satellite laser ranging, together with altimetry results, to provide an independent geodetic constraint on changes in ocean heat content (OHC). We show that the size and signature of the J2 signal presented here do not support a recently published report of rapid oceanic heat loss beginning in 2003, which was subsequently attributed to Argo and other instrumental bias effects. Our results are consistent with recent findings of a flattening of the OHC trend at this time inferred from the bias-corrected Argo data, and demonstrate that J2 observations, in combination with other observational and model data types, can provide useful constraints for monitoring and validating ongoing changes in the Earth system.

Determination of frame-dragging using Earth gravity models from CHAMP and GRACE

Using the new generation Earth’s gravity field models EIGEN-2S, GGM01S and EIGEN-GRACE02S generated by the space missions CHAMP and GRACE, we have obtained an accurate measurement of the Lense–Thirring effect with the LAGEOS and LAGEOS II satellites analyzing about 10 years of data with the EIGEN-2S and GGM01S models and about 11 years of data with EIGEN-GRACE02S. This new analysis is in agreement with our previous measurements of the Lense–Thirring effect using the LAGEOS satellites and obtained with the JGM-3 and EGM96 Earth’s models. However, the new determinations are more accurate and, especially, more robust than our previous measurements. In the present analysis we are only using the nodal rates of the two satellites, making no use of the perigee rate, as in our previous analyses. The perigee is affected by a number of non-gravitational perturbations difficult to be modelled and whose impact in the total error budget is not easy to assess. Using the EIGEN-2S model, we obtain a total error budget between 18% and 36% of the Lense–Thirring effect due to all the error sources. Specifically, by using EIGEN-2S, we obtain: μ=0.85, with a total error between ±0.18 and ±0.36, with GGM01S we get μ=1.06 with a total error between ±0.19 and ±0.24 and with EIGEN-GRACE02S we obtain μ=0.99, with a total error between ±0.05 and ±0.1, i.e., between 5% and 10% of the general relativistic predicted value of the Lense–Thirring effect. In addition to the analyses using EIGEN-2S, GGM01S and EIGEN-GRACE02S without the use of the perigee, we have also performed an analysis using the older model EGM96 with our previous method of combining the nodes of the LAGEOS satellites with the perigee of LAGEOS II. However, this analysis was performed over a period of about 10 years, i.e. about 2.5 times longer than any our previous analysis. The result using EGM96 over this longer period of observation agrees with our previous results over much shorter periods and with the EIGEN-2S, GGM01S and EIGEN-GRACE02S measurements of μ. In addition to the accurate determination of frame-dragging and in agreement with our previous analyses of the orbits of the LAGEOS satellites, we have observed, since 1998, an anomalous change in the Earth quadrupole coefficient, J2 which agrees with recent findings of other authors. This anomalous variation of J2 is accurately observed both on the node of LAGEOS and LAGEOS II and it is independent of the model used, i.e., it is observed by using the model EGM96 or by using EIGEN-2S, GGM01S or EIGEN-GRACE02S. However, this anomalous variation of the Earth quadrupole coefficient does not affect at all our determination of the Lense–Thirring effect thanks to the total elimination of the J2-induced errors with our especially devised estimation technique.

Estimation of the frictional dissipation of lunisolar tide

Lunisolar tidal friction and variation in the earth's moment of inertia are the major factors for the long-term change in the length of day (lod). This article uses the latest geophysical and paleontological clock data to study and compare numerically the lunisolar tidal friction, variation in the terrestrial moment of inertia and long-term change in the lod for the past 1500 Ma. Two important conclusions are obtained: 1) the variation in J2 can not be explained solely by the rotational deformation of the earth, which shows that gravitational differentiation still exists in the earth; 2) tidal friction was much greater a few hundred million years ago than it is now. If it is assumed that tidal dissipation is inversely proportional to the cube of the distance between the earth and the moon, then the theoretical results of the numbers of days in a tropical year and in a synodic month accord rather well with the paleontological clock data.

Precession, nutation, and space geodetic determination of the Earth's variable gravity field

Precession and nutation of the Earth depend on the Earth's dynamical flattening, H, which is closely related to the second degree zonal coefficient, J2 of the geopotential. A small secular decrease as well as seasonal variations of this coefficient have been detected by precise measurements of artificial satellites (Nerem et al. [CITE]; Cazenave et al. [CITE]) which have to be taken into account for modelling precession and nutation at a microarcsecond accuracy in order to be in agreement with the accuracy of current VLBI determinations of the Earth orientation parameters. However, the large uncertainties in the theoretical models for these J2 variations (for example a recent change in the observed secular trend) is one of the most important causes of why the accuracy of the precession-nutation models is limited (Williams [CITE]; Capitaine et al. [CITE]). We have investigated in this paper how the use of the variations of J2 observed by space geodetic techniques can influence the theoretical expressions for precession and nutation. We have used time series of J2 obtained by the “Groupe de Recherches en Géodésie spatiale” (GRGS) from the precise orbit determination of several artificial satellites from 1985 to 2002 to evaluate the effect of the corresponding constant, secular and periodic parts of H and we have discussed the best way of taking the observed variations into account. We have concluded that, although a realistic estimation of the J2 rate must rely not only on space geodetic observations over a limited period but also on other kinds of observations, the monitoring of periodic variations in J2 could be used for predicting the effects on the periodic part of the precession-nutation motion.

Surface gravitational field and topography changes induced by the Earth?s fluid core motions

Using a Love number formalism, the elastic deformations of the mantle and the mass redistribution gravitational potential within the Earth induced by the fluid pressure acting at the core–mantle boundary (CMB) are computed. This pressure field changes at a decadal time scale and may be estimated from observations of the surface magnetic field and its secular variation. First, using a spherical harmonic expansion, the poloidal and toroidal part of the fluid velocity field at the CMB for the last 40 years is computed, under the hypothesis of tangential geostrophy. Then the associated geostrophic pressure, whose order of magnitude is about 1000 Pa, is computed. The surface topography induced by this pressure field is computed using Love numbers, and is a few millimetres. The mass redistribution gravitational potential induced by these deformations and, in particular, the zonal components of the related surface gravitational potential perturbation (ΔJ2, ΔJ3 and ΔJ4 coefficients), are calculated. Overall perturbations for the J2 coefficient of about 10−10, for J3 of about 10−11 and for J4 are found of about 0.3×10−11. Finally, these theoretical results are compared with recent observations of the decadal variation of J2 from satellite laser ranging. Results concerning ΔJ2 can be described as follows: first, they are one order of magnitude too small to explain the observed decadal variation of J2 and, second, they show a significant linear trend over the last 40 years, whose rate of decrease amounts to 7% of the observed value.

Variations in the Earth's oblateness during the past 28 years

Analysis of satellite laser ranging (SLR) data indicates that the Earth's dynamic oblateness (J2) has undergone significant variations during the past 28 years. The dominant signatures in the observed variations in J2 are (1) a secular decrease with a rate of approximately −2.75 × 10−11 yr−1, (2) seasonal annual variations with a mean amplitude of 2.9 × 10−10, (3) significant interannual variations with timescales of 4–6 years, and (4) a variation with period of ∼21 years and an amplitude of ∼1.4 × 10−10 with minimum in December 1988. Two large interannual variations are related to the strong El Niño‐Southern Oscillation events during the periods of 1986–1991 and 1996–2002, and it appears that another interannual cycle may have started in late 2002. The superposition of the decadal variation on the interannual signal makes the J2 fluctuation appear to be anomalously large during the 1996–2002 period. Contemporary models of the mass redistributions in the atmosphere, ocean, and surface water can explain a major part of the 4‐ to 6‐year fluctuations. However, the cause of the decadal variation remains unknown.

Why the 18.6 year tide cannot explain the change of sign observed in <i>j<sub>2</sub></i>

Abstract. Recent studies show a change, starting in 1998, in the behavior of the variation of the dynamical flattening of the Earth (J2), supposed to be constant (secular), and mainly due to the post glacial rebound effect. In this paper, we study to what extent this behavior can be correlated or not with the 18.6 year tide: with more than twenty years of tracking data on LAGEOS-1, that is to say more than a period of 18.6 years, this effect can now be separated from the secular variation. We use our theory of mean orbital motion, dedicated to studies of the long period effects on the orbital motion. We build one single arc of LAGEOS-1 from 1980 to 2002, which provides a continuous description of the orbital parameters. This is the great originality of our approach. We focus our attention on the ascending node of LAGEOS-1, and we show that the change observed in j2 cannot be attributed to a statistical error due to a correlation, in short arcs results, between the secular variation of J2 and the 18.6 year tide. The proof is based on the adjustment of amplitudes and phases of the long period tides, and on the shape of the residuals.Key words. secular variation of J2, 18.6 year tide, mean orbital motione

Seasonal variations in low degree zonal harmonics of the Earth's gravity field from satellite laser ranging observations

Seasonal variations in the Earth's gravity field were determined using satellite laser ranging (SLR) observations from multisatellite. The time series for the variations of the even zonal harmonics, Jl(l = 2, 4, 6, and 8), were determined using the SLR data from the geodetic satellites, including Starlette, Ajisai, Stella, LAGEOS I and LAGEOS II, during the period from October 1993 to December 1996. Owing to uncertainties in the eccentricity excitation for LAGEOS I and II, the variations of J3 and J5 were determined using only the SLR data from Starlette, Ajisai, and Stella. The seasonal variations of J2, J4, J6 and J8 become separable using the existing multisatellite SLR data sets collected in 15‐day time intervals. The amplitude (normalized and in units of 10−10) and phase (in a cosine conversion and in units of degrees) for the annual variation in Jl (l= 2, 3, 4, 5, 6, and 8) are estimated to be (1.25 ± 0.1, 140 ± 10), (2.16 ± 0.21, 341 ± 19), (1.07 ± 0.1, 338 ± 15), (1.12 ± 0.16, 152 ± 16), (0.26 ± 0.17, 337 ± 9), and (1.03 ± .016, 209 ± 10), respectively. The observed annual variations of J3 and J5 are essentially opposite in phase. This phenomenon results in a different lumped sum effect for various satellites. For example, the lumped sum of J3 and J5 annual variation from LAGEOS I is twice as large as that from Starlette. The excitation due to the mass redistribution in the atmosphere and ocean and the changes in continental water storage were considered in this study using the available global geophysical data, which included the European Centre for Medium‐Rang Weather Forecasts atmospheric surface pressure, the TOPEX/Poseidon altimetry derived sea surface anomalies, and the World Monthly Surface Station Climatic Data. Overall, the variation in the even zonal coefficients due to the atmospheric mass redistribution is responsible for 30% to 60% of the observed annual variations in the node residual for Starlette and LAGEOS I. Comparison indicates that the oceanic mass movement, in particular, the continental water change produce comparable contributions to the seasonal zonal variations. The amplitude of the observed annual variation of J2 is found to fall between the values predicted from the models of the surface water, ocean, and atmosphere with and without the inverted barometer (IB) oceanic response, but the phase is in good agreement with the IB models. The nontidal mass redistributions in atmosphere, ocean, and continental water change can only account for ∼13% of the semiannual variation in J2 but are the primary excitation sources for semiannual variations in the higher‐degree zonal terms.

Temporal variations of the Earth's gravitational field from satellite laser ranging to Lageos

We have estimated monthly values of the J2 and J3 Earth gravitational coefficients using LAGEOS satellite laser ranging (SLR) data collected between 1980 and 1989. For the same time period, we have also computed corresponding estimates of the variations in these coefficients caused by atmospheric mass redistribution using surface atmospheric pressure estimates from the European Center for Medium Range Weather Forecasts (ECMWF). These data were processed both with and without a correction for the “inverted barometer effect,” the ocean's isostatic response to atmospheric loading. While the estimated zonal harmonics in the orbit analysis accommodate gravitational changes at a reduced level arising from all other higher degree zonal effects, the LAGEOS and atmospheric time series for J2 compare quite well and it appears that the non‐secular variation in J2 can be largely attributed to the redistribution of the atmospheric mass. While the observed changes in the “effective” J3 parameters are not well predicted by the third degree zonal harmonic changes in the atmosphere, both odd zonal time series display strong seasonality. The LAGEOS J3 estimates are very sensitive to as yet unmodeled forces acting on the satellite and these effects must be better understood before determining the dominant geophysical signals contributing to the estimate of this time series.

Geodynamic parameters derived from 7 years of laser data on Lageos

Seven years (1984 through 1990) of Laser data on Lageos have been.analysed to recover absolute stations velocities and j2. Relative motions between stations located in stable tectonic regions agree well with the NUVEL‐1 model predictions within 5 mm/yr rms. Relative motion across the San Andreas Fault is found to be − 33.±1. mm/yr. Solution for the secular variation of J2 is (−2.8±0.04) × 10−11/yr.

Snow load effect on the Earth's rotation and gravitational field, 1979–1985

A global, monthly snow depth data set has been generated from the Nimbus 7 satellite observations using passive microwave remote‐sensing techniques. In this paper we analyze 7 years of data, 1979–1985, to compute the snow load effects on the earth's rotation and low–degree zonal gravitational field. A uniform sea level decrease has been assumed in order to conserve water mass. The resultant time series show dominant seasonal cycles. The annual peak‐to‐peak variation in J2 is found to be 2.3 × 10 −10, that in J3 to be 1.1 × 10−10, and believed to decrease rapidly for higher degrees. The corresponding change in the length of day is 41 μs. The annual wobble excitation is (4.9 marc sec, −109°) for the prograde motion component and (4.8 marc sec, −28°) for the retrograde motion component. The excitation power of the Chandler wobble due to the snow load is estimated to be about 25 dB less than the power needed to maintain the observed Chandler wobble. The superior quality of the satellite data over conventional data acquired by ground observations and modeling is demonstrated. We also discuss the role of atmospheric water and the problems arising from the lack of snow load observations over the Antarctic and Greenland ice sheets.