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[1] Analysis of satellite laser ranging (SLR) data indicates that the Earth's dynamic oblateness (J_{2}) has undergone significant variations during the past 28 years. The dominant signatures in the observed variations in J_{2} 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 J_{2} 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.

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[2] Mass variations within the Earth's dynamic system have a temporal spectrum ranging from hours to decades and longer, all superimposed on a secular trend, and many of these are related to both long-term and short-term climate forcing. Satellite laser ranging (SLR) data have recorded the global nature of these variations for almost three decades. Recently, a significant variation in J_{2} was reported based on analysis of the SLR tracking data. Interannual behavior of the J_{2} variation had been shown previously by Cheng and Tapley [2000], but the variation that occurred after 1998 has attracted significant attention, and has been interpreted as a possible reversal of the secular decrease of J_{2} [Cox and Chao, 2002 (hereinafter referred to as CC)] (noted as 1998 J_{2} anomaly). Chao et al. [2003] reported the J_{2} variation is returning to normal in 2002. There have been several attempts to interpret the CC result as the influence of a mass shift in the tropical oceans and in global glaciers [Dickey et al., 2002]. However, a principal concern on previous analysis based on the CC result is whether the fluctuation in J_{2} that started in 1998 is a unique event or even an unusual anomaly. In this paper, we present a new time series of the variations in J_{2} from SLR data (hereinafter referred to as CT) and emphasize the nature of the long-term variations. Interest is directed to the recurrent 4- to 6-year fluctuations in J_{2}, which can be related to El Niño-Southern Oscillation (ENSO) events. The following sections will discuss the determination of that J_{2} time series, and the nature of the temporal variations for timescales ranging over seasonal, interannual, 18.6-year, decadal, and secular. The different spectral components in the J_{2} time series are determined using wavelet technique. Finally, the possible causes of the recurrent 4- to 6-year interannual J_{2} variations are given based on the predicted J_{2} variations from atmosphere-ocean-surface water data. A summary will be given for the understanding of the J_{2} variations gained from this study.

2. Determination of the J_{2} Variations

[3] The results presented here are based on the 28 years SLR data set for seven geodetic satellites: Starlette, Ajisai, Stella, LAGEOS 1 and 2, and Etalon-1 and -2, along with a recent tracking data set for Beacon Explore-C (BE-C) beginning from 15 July 1999. Except for BE-C, the satellites used are “cannonballs,” where the spherical shape of these satellites allows the surface forces to be modeled with less error and the zonal gravitational perturbations are more clearly recovered [Tapley et al., 1993; Cheng et al., 1997]. The satellite models used in this analysis were based on the IERS 2003 standards [McCarthy and Petit, 2003], except for the use of the TEG4 gravity field model and the CSR4.0 ocean tide model (where the long-period ocean tides are modeled as equilibrium tides).

[4] Geopotential coefficients, up to degree and order 3 plus J_{4}, and the variations of the geocenter components (x, y, z) were adjusted for each 30-day interval on the basis of an optimal weighting procedure using the SLR data available from whichever of the eight satellites during the period from 1976 to 2003. The gravitational constant parameter (GM) was adjusted over the 28-year data span to ensure that the scale for the solution of the geopotential coefficients was consistent. The estimated value for GM was 3.986004414 × 10^{−14} m^{3} s^{−2}, nearly identical to the value of 3.986004415 × 10^{−14} m^{3} s^{−2} determined by Ries et al. [1992]. The time series of the J_{2} variation from this solution is analyzed in the following discussion.

3. Nature of the Temporal Variation in J_{2}

[5]Figure 1 shows the estimated variations of J_{2} with the formal error bar for each 30-day interval during the 28-year time period. The standard deviations of the solutions are reduced as the data accuracy improves and data from more satellites are included, with a significant improvement noted in 1987. The J_{2} variations were determined by only LAGEOS 1 and Starlette over the period prior to the 1987. Detection of the interannual variations in J_{2} was limited by the distribution and accuracy of the SLR tacking data during that period [Cheng and Tapley, 2000].

[6] The J_{2} time series contains a broad spectrum of signals. The secular trend and annual variations appear to be the strongest, but multiyear fluctuations are also visible. To study the nature of these variations, it is necessary to distinguish the signature of the different frequency components, in particular the long-wavelength variations, contained in the J_{2} time series. Except for the secular trend and the tidal harmonic variations, the variations in J_{2} are meteorologically related with a stochastic behavior. The seasonal signal in the observed J_{2} time series has a varying amplitude and phase, which is influenced by atmospheric variations and the exchange of water mass among the continental and ocean components. Consequently, subtracting the atmospheric J_{2} variation predicted from surface pressure data is not an effective approach to remove the seasonal and high-frequency components in the total J_{2} time series determined from SLR data since this procedure could introduce aliasing effects into the interannual variations. To deal with signals in which amplitude and phase vary with time, wavelet analysis, a “lexicon of time series analysis” [Emery and Thomson, 1997, p. 500], is used. The advantage of wavelet analysis is that it gives a localized, instantaneous estimation of the amplitude and phase for each spectral component and has the ability to decorrelate even highly correlated time series [Percival and Walden, 2000].

3.1. Wavelet Analysis

[7] We applied the dmey wavelet in MATLAB to decompose the signals with different frequency components in the J_{2} time series derived from SLR data analysis and in that predicted by geophysical models. In wavelet analysis, a signal is split into an approximation (A) and a detail (D), which describe the low- and high-frequency components of the signal, respectively. The approximation (A) is then split into a second-level approximation and detail. This process can be expressed as A_{j} = A_{j+1} + D_{j+1} and is repeated until the individual detail consists of a signal pixel [Misiti et al., 1997]. Thus the signal (S) at any time can be represented by the multiple-level approximation and detail coefficients, e.g., S = A_{6} + sum of D_{j} (j = 1, 6) for a six-level wavelet decomposition tree. The lower level of the detail coefficients, for example, D_{1} and D_{2}, represents the noise and high-frequency parts of the signal. The D_{3} coefficients characterize the seasonal variations in J_{2} as shown in Figure 1. The D_{4} coefficients represent the biennial variation. The A_{4} component contains the portion of the signals with a period longer than 2 years as shown by the solid red line in Figures 1 and 2. In addition, the A_{4} component can be reconstructed as A_{4} = A_{6} + D_{56}, where the A_{6} coefficient represents the secular trend and the variations with a timescale greater than 10 years (after removed the linear trend in A_{6}), D_{56} = D_{5} + D_{6} consists of the variations with a timescale of ∼4–6 years (discussed in section 4). A_{6} can be further represented as A_{6} = A_{7} + D_{7}, where D_{7} coefficient represents a decadal variation with amplitude of 0.3 × 10^{−10} and period of ∼10.6 years. As with other transform techniques, the secular and the longer-period behavior at the end of the time series will lead to a certain distortion of the shorter-period variation, such as a small edge effect on D_{56.} This can be reduced by an extension of the data span.

[8] The CT time series were derived with a uniform 30-day time interval between the data points. However, the CC time series were derived using a time interval varying in the range from 90 to 29.5 days [Cox and Chao, 2002]. The variable time interval leads to a difficulty in using time series analysis to identify the signature of the different frequency components. Interpolating the CC time series into an even-time interval could misrepresent the signals contained in the original time series. A 360-day moving average approach was applied to the CC and CT time series. Figure 2 compares the long-wavelength variations from (1) CT (solid circle with black line), (2) CC (open circle with gray line) time series using a moving average filter, (3) the A_{4} (blue line) and (4) the A_{6} (dashed gray line) component using wavelet analysis to CT time series. The difference between A_{4} and A_{6} is the interannual variation, which will be discussed later. The patterns for the long-term variations in J_{2} are apparently similar for the two time series for the period after 1992. The comparison clearly demonstrates that the wavelet analysis effectively captured the long-wavelength signals contained in the time series of J_{2} from SLR data. The A_{4} component excludes the short-period (<2 years) variations of J_{2}, which have no effect on the current study for the J_{2} interannual variations. Thus signals represented by D_{3}, A_{4}, D_{56} and A_{6} components are analyzed as follows.

3.2. Seasonal Variations

[9] The climate related seasonal variations vary from year to year with mean amplitude of 2.9 × 10^{−10} during the 28-year time span as shown in Figure 1. It has been recognized in a number of papers that the annual variation in J_{2} can be explained, in an average sense, by the existing models of mass redistribution in the atmosphere, ocean, and continental water [Cheng and Tapley, 1999]. Detailed analysis of these observed seasonal variations and their variability is still a subject for further study. The longer-wavelength variation with multiple-year timescales is the principal interest in the following discussion.

3.3. Interannual Variations

[10]Figure 2 clearly shows the nature of the long-wavelength variations in J_{2}, including the secular trend and the interannual variations with multiyear to decade timescales. The linear trend shown in Figure 2 is obtained from a least squares fitting to the entire data. A longer-period variation with a timescale greater than 10 years is visible, where the J_{2} variations are above the secular trend for the period from 1976 to middle of 1984 and the period from 1998 to 2002, which is a part of the interval when the 1996–2002 variation occurred. These longer-period signals and secular variations together are characterized by the A_{6} component shown in Figure 2. The wavelength character for the longer-period variations will be different for the CT and CC time series because they are based on a different linear trend and time span.

[11] After removing the secular trend from the 360-day moving average of the CT and CC time series (or from the A_{4} component of the CT time series shown in Figure 2), the residual fluctuation during the period of 1996–2002 (described as the 1998 “anomaly” in all of the previous studies) appears to be the largest interannual variation. However, decadal variations or the variations with a timescale greater than 10 years are also visible in the above residual fluctuation. In fact, after removing A_{6} from the A_{4} component, the fluctuations contained in the D_{56} (=A_{4} − A_{6}) component over the time periods of 1987–1991 and 1996–2002 are approximately the same magnitude, as shown in Figure 4b in section 4. This analysis suggests that the apparent anomalous “1998 event” is actually the result of the 4- to 6-year variation superimposed on a variation with longer timescale. The interannual variation during the period of 1987–1991 was not recognized by previous studies based on the CC results except for the analysis by Benjamin et al. [2003].

[12] It is necessary to rule out the effects of the longer-period variations to understand the nature of the interannual variations in J_{2}. One of the principal components in the longer-period variations is related to the 18.6-year tide.

3.4. The 18.6-Year Tide and Decadal Variation

[13] Theoretically, the principal low-frequency variations in J_{2} are caused by tidal forcing with periods of 9.3 and 18.6 years [Eanes, 1995]. The effects of these tides are modeled as equilibrium ocean tides and the solid Earth tides, including the effects of mantle anelasticity [Wahr and Bergen, 1986]. The effect of the 9.3-year equilibrium ocean tide is ∼30 times smaller than 18.6-year tide, and the contribution of the error in the 9.3-year tide model is negligible for studying the multiyear variations in J_{2}. However, analysis of tide gauge data indicates that the amplitude of the 18.6-year ocean tide could be 1.13 ± 0.22 times the equilibrium amplitude (0.967 cm) [Trupin and Wahr, 1990]. The effects of mantle anelasticity on zonal coefficients are evaluated using a complex δk_{f}, which is the difference between the mantle anelasticity induced variations in the body tide k Love number, k_{nm}^{(0)}, at frequency f and its nominal value k_{nm} based on the IERS 2003 Standard [McCarthy and Petit, 2003, equation (5)]. The real and imaginary parts of δk_{f}, for zonal tide (n = 2 and m = 0) at the 18.6-year period (hereafter anelasticity δk_{18.6}) are 0.01347 and −0.00541 with respect to the nominal value k_{20} = 0.3019 based on the IERS 2003 standard. A significant deviation from IERS model for the anelasticity δk_{18.6} has been reported [Eanes, 1995; Cheng et al., 1997]. The anelasticity effect consists of the in-phase (cos) and out-of-phase (sin) component of the J_{2} variation characterized by the real and imaginary component of the anelasticity δk_{18.6}. The out of phase component has completed one cycle during the past two decades with a maximum in 14 March 1983, a minimum in the 4 July 1992 and the second maximum in 24 October 2002. The in-phase component reached its maximum and minimum with 4.65 years ahead the out-of-phase component. Thus an error in modeling the anelasticity δk_{18.6}, in particular the imaginary part, will affect the pattern of the interannual variation after 1997. The real and imaginary part of δk_{18.6} were estimated to be 0.027 ± 0.009 and −0.002 ± 0.024 by Wahr et al. [2003] based on CC time series assuming a nominal value of k_{20} = 0.296 was used. Separation between the real and imaginary part of δk_{18.6} and the J_{2} rate from time series of J_{2} variations will be affected by the time span used and the formal standard derivations of J_{2} estimate, which become more stable only after 1987, as discussed earlier. Furthermore, amplitude of the decadal variation with a timescale of ∼10.7 years (D_{7} component) is comparable with that of the errors of δk_{18.6} induced variations in J_{2}. We used A_{7} component and added different values ranging from 0.5 to 2.0 to the formal standard derivation of data after 1987 in order to balance the contributions of data (30-day J_{2} solution) in the optimal weighting estimation. The solution of the imaginary part of δk_{18.6} is decreasing almost linearly with the data span increasing (also shown by Wahr et al. [2003]). While the solution of the rate of J_{2} is increasing almost linearly with the data span increasing. It is difficult to choose the correct value. However, the solutions of the real part of δk_{18.6} were spread with different calibration sigma after in middle of 1997. We take the average from the values obtained using different calibration sigma as the estimate of the corrections to the complex δk_{18.6} and rate of J_{2}, which are 0.01889, −0.00746, and −2.73 × 10^{−11} yr^{−1}, respectively using the data from 1976 to middle of 1997. The lower bound for the uncertainty of these estimates could be −0.007 and −0.001 based on the difference with the average of the estimates using entire data from 1976 to 2003. These estimates of δk_{18.6} are in general agreement with that from Wahr et al. [2003] within the range of the defined uncertainty.

[14] To reveal the effects of the 18.6-year tide model error, the J_{2} variation (represented by the A_{6} component) was adjusted by using different anelasticity δk_{18.6} based on (1) the values (0.03236, −0.01287) estimated from CT J_{2} time series (denoted as C1) and (2) (0.0195, 0.0) (denoted as C2), which was obtained by subtracted the 0.96 cm amplitude of the equilibrium tide from the 1.41 cm ocean tide amplitude used by Cox and Chao [2002].

[15]Figure 3 shows a long-term J_{2} variation (denoted as C0) from the A_{6} component, which is based on the IERS model for the anelasticity δk_{18.6}, after removing a secular trend. Comparison of C0 and C1 shows that the effects of the model error of the 18.6-year anelasticity δk_{18.6} cause a multiyear variation over the period from 1985 to 1993, and reduce the maximum of variations. Comparison between the curve C2 and the others in Figure 3 indicates the effect of errors in the out-of-phase component of the 18.6-year anelastic Earth tide. This effect (with a large imaginary δk_{18.6}) tends to flatten the interannual J_{2} variation after 1994. The apparent variation of J_{2} would be more precipitous from 1994 to 2002 with a different model of 18.6-year anelasticity δk_{18.6}.

[16] Using the estimated value of the 18.6-year anelasticity δk_{18.6}, the C1 curve reveals a variation in J_{2} decreasing from a maximum in November 1978 to a minimum in December 1988, and then increasing to a second maximum in January 2001. This variation may be a results from a longer-period variation in conjunction with the mantle anelasticity induced 18.6-year J_{2} variation, which has a minimum in March 1989 and maximum in December 1979 and July 1998. The effects are small due to the ocean tide error assumed to be 5% of the equilibrium value [Wahr et al., 2003]. The spectral analysis indicates that the periods of the dominant variations in the C1 curve are approximate ∼21 and 10.7 years, which will be denoted as the decadal variation hereafter. Amplitude of the 21-year variation is to be 1.42 × 10^{−10}, which is 2.6 times larger than the later variation, and depends on the adopted value of 18.6-year anelasticity δk_{18.6}. For example, 80% smaller amplitude (with minimum at a different epoch) will be obtained using the value of 18.6-year anelasticity δk_{18.6} from Wahr et al. [2003]. To improve the understanding of the nature of the decadal variation in J_{2}, a comprehensive analysis is required to obtain an accurate estimate of the anelasticity δk_{18.6} (R. J. Eanes, personal communication, 2003).

3.5. Secular Variation

[17] The interannual and longer-term variations will also affect the determination of the rate of J_{2}. The secular rate for J_{2} was estimated to be −1.95x × 10^{−11} yr^{−1} and −2.75 × 10^{−11} yr^{−1} from a least squares fit to the CC and CT time series, respectively, as shown in Figure 2. The small rate of J_{2} from CC time series is mainly due to the lack of information about the J_{2} variations before 1980 to balance the significant variations after 1998. This effect of the longer-term variations leads the rate of J_{2} to be as small as −1.0 × 10^{−11} yr^{−1} using the data over the period from 1985 to 2002. Thus the early data is an invaluable resource for studying the secular variations in the Earth gravity field.

[18] The value of the J_{2} rate from the CT time series is in good agreement with the published results, which was determined first in 1983 [Yoder et al., 1983]. The secular decrease of J_{2} has been intensively studied during the past two decades. The postglacial rebound (PGR) of the Earth's mantle is considered to be the primary cause of the decrease of J_{2} over multidecade timescales [Peltier, 1983] with other secondary excitations due to, for example, mountain glaciers and water reservoirs. The negative trend in J_{2} has not been revised during the past two decades, but the value of J_{2} has undergone significant recurrent fluctuations with timescales of 4–6 years and longer-period variations. In particular, a large fluctuation with a duration of ∼5.8 years occurred from the middle of 1996 to the end of 2002. Another fluctuation with approximately the same amplitude occurred during the period from 1987 to 1991 with a duration of ∼4.1 years as shown in Figure 4b in section 4. It appears that another interannual cycle began in late 2002 as shown in Figure 2. In addition, the decadal variation is increasing from a minimum in 1989 to a maximum in January 2001 as shown in Figure 3.

4. Predicted Interannual Variations and Comparison

[19] Many temporal variations in the Earth's gravity field are the consequence of mass redistribution within the Earth's dynamic system due to tidal and climate forcing. Extensive studies have been made to interpret the apparent changes after 1998 reported in the CCJ_{2} time series [Cox and Chao, 2002; Dickey et al., 2002; Cazenave and Nerem, 2002; Chao et al., 2003]. The analysis presented here focuses on possible geophysical mechanism of the interannual fluctuations in J_{2} related to the ENSO phenomenon. First, we examine the contributions of the meteorological mass redistributions in the major components of the Earth system (oceans, atmosphere, and continental water) to the observed multiyear fluctuations in J_{2}.

4.1. J_{2} Variations From Geophysical Models

[20] The time series of J_{2} variations with 30-day average over a period by end of 2002 were calculated based on (1) the surface pressure of the National Centers for Environmental Prediction (NCEP) reanalysis data [Kalnay et al., 1996] with the assumption of the inverted barometer effect (IB); (2) the monthly global climatological soil moisture data [Fan and van den Dool, 2004] and snow depth data from the NCEP/DOE AMIP-II Reanalysis-2 [Kanamitsu et al., 2002; also see http://wesley.wwb.noaa.gov/reanalysis2]. This study used the oceanic J_{2} time series given by Chen et al. [2003] based on the ocean bottom pressure from the Consortium for “Estimating the Circulation and Climate of the Ocean” (ECCO) model.

[21] Wavelet analysis indicates that considerable successive variations occur with a period of 4–5 years for all of those components of J_{2} since 1976 as shown in Figure 4a. The largest J_{2} fluctuations due to the soil moisture changes occur over the period of 1987–1992 and 1998–2001 when the atmosphere induced variations were relatively smaller than the variations over other periods. The atmospheric interannual variations are opposite to the variations induced by soil moisture changes over the period 1980 to 1984 and 1995–1998 as shown in Figure 4a. Oceanic J_{2} fluctuations start to have significant interannual signals only after 1993. This may represent the strength from assimilating TOPEX/Poseidon sea level data into the ocean model beginning in 1993. It is not clear whether the interannual variation signals are recovered accurately by the ECCO model prior to 1992.

[22]Table 1 summarizes the observed and modeled interannual variations during the period of 1987–1992 and 1996–2002. The amplitudes were obtained by the best fit to data over the corresponding durations. The dominant contribution to the observed interannual variations in J_{2} appears to be from soil moisture changes, based on the model output. Figure 4b compares the observed interannual variations in J_{2} with the combination of the atmosphere, ocean, soil moisture, and snow model. A major part (90%) of the observed 4- to 6-year variations from SLR can be accounted for by the interannual mass redistribution in the atmosphere, ocean and surface water, and the phase is in good agreement starting from 1998. Figure 4b and Table 1 show that the duration for the modeled interannual variation is almost 1 year shorter than those observed variations after 1998. This may be an indication of the deficiency of the existing models, or may suggest that there are additional significant sources contributing to the observed J_{2} interannual variations, such as the melting of polar and subpolar glaciers. Thus improved models for those components are required.

Table 1. Comparison of the Observed and Modeled Variations in J_{2}

[23] None of the model outputs can explain the observed decadal variation in J_{2} except for the oceanic J_{2} variation, which appears to increase continuously from 1980 to present as shown by C3 curve in Figure 3. Dickey et al. [2002] have suggested that the melting of subpolar mountain glaciers is responsible for much of the residual long-period signal in J_{2} based on the glacier volume change over the period from 1961 to date by Dyurgerov [2001]. However, information about the temporal and geographic distribution of subpolar mountain glaciers is not available yet for a reliable estimate of the contribution of their melting. Thus a major part of the observed decadal J_{2} variation remains unknown.

4.2. ENSO/PDO Effects

[24] An essential question is the cause of the 4- to 6-year variations. A natural supposition is that it is related to the El Niño-Southern Oscillation (ENSO) phenomenon, the largest interannual climate signal in the Tropical Pacific, occurring every 3 to 7 years. Increased rainfall or drought over different regions is a result of the water mass transport associated with the ENSO cycle. Long-term SLR data have recorded the signals associated with these ENSO related mass transports. In fact, strong fluctuations in J_{2} occurred during the strong El Niño/La Niña events over the period of 1986–1991 and 1996–2002 based on the comparison with the timing of ENSO events represented by the Southern Oscillation Index (SOI) (see http://www.cgd.ucar.edu/cas/catalog/climind/soi.html).

[25]J_{2} variations are calculated as the weighted sum of zonal net mass changes, and represent the imbalance of the zonal mass variations between the “tropical” area (in the range of ±35.3° latitude) and “extratropical” area. Figure 5 compares the soil moisture changes induced J_{2} variations from (1) the tropical area (blue dot), (2) the extratropical area (small black circle) after removing a bias, with the smoothed curve for SOI (dashed red line) after a positive time of 7 months and an empirical scaling for visual comparison. It suggests that the J_{2} variations induced by soil moisture changes are primarily seasonal over the extratropical area, but appear to exhibit a multiyear timescale over the tropical area. The tropical soil moisture change induced J_{2} variation exhibits a good temporal correlation with the ENSO events with a 7-month delay, and dominates the interannual variations in J_{2} induced by the soil moisture changes (sum of two areas). As shown in Figure 5, these variations are below the average in the El Niño episode (<0) and above the average during the La Niña episode (>0). It follows that the observed J_{2} variations tend to increase when the ENSO shifts from the warm phase (El Niño) to the cold phase (La Niña) in 1987 and 1998. It is because the global soil moisture changes induced variations is a dominant component in the J_{2} variation over these two periods as shown in Figure 4a and Table 1.

[26] The atmosphere induced J_{2} variations are primarily seasonal over both areas. Figure 6 compares the atmospheric interannual J_{2} variations from the extratropical area with the sum of both areas. Figure 6 shows that dominant atmospheric interannual signals in J_{2} come from the extratropical area, and the contribution from the tropical area is particularly small during 1986 to 1991. Detailed comparison indicates that dominant interannual signals in J_{2} come from the areas with latitude beyond ∼±75°, which may be a result of the atmospheric teleconnections from forcing of the extratropical Rossby waves by anomalous tropical heating associated with the ENSO phenomena as discussed by Trenberth et al. [1998]. The magnitudes of the atmospheric interannual J_{2} variations during 1988–1992 and 1996–2001 are smaller than those occurred during 1977–1981 and 1992–1996. In addition, the atmospheric J_{2} variations have a minimum during the period of 1995–1997 while the ENSO was in a cold phase (La Niña) during this period. Finally, a general temporal correlation between the atmosphere induced interannual J_{2} variation and SOI can only be found during 1986–1992 because the atmospheric J_{2} variations are connected, but not synchronous with ENSO events [Trenberth and Hoar, 1996].

[27] In summary, the 4- to 6-year variations in J_{2} due to the mass variation in the atmosphere, ocean and surface water, as shown in Figure 4, are related to the ENSO phenomena. A full explanation of the observed 4- to 6-year fluctuation in J_{2} would require a reliable climatic general circulation model (GCM), which should be capable of predicting the ENSO events and associated mass transports in the Earth system.

[28] The Pacific Decadal Oscillation (PDO) is a long-lived El Niño-like pattern of Pacific climate variability. These two oscillations have similar spatial climate fingerprints, but very different temporal behavior. The PDO is most visible in the North Pacific/North American sector with the secondary signature in the tropics; the opposite is true for ENSO (see http://tao.atmos.washington.edu/pdo). The 20th century PDO fluctuations were most energetic in two timescales from 15–25 years and 50–70 years [Minobe, 1999]. Although typical ENSO events persisted for 6 to 18 months, the frequent occurrence and the strong El Niño followed by a strong La Niña episode make the global effects of ENSO persist with a longer duration in the past two decades. Unlike the ENSO phenomena, causes of the PDO are currently unknown. PDO regime shifts have been reported in 1977 and 1989 [Hare and Manutua, 2000]. Comparison of the SOI and PDO index indicates a strong anomaly in both oscillations over the period from 1998 to 2002. The coincidence with the ENSO phase shift could enhance the ENSO related J_{2} variations, although the PDO effects are expected to be decadal or longer. The temporal correlation between the PDO and J_{2} variations, shown by Chao et al. [2003], is more likely due to the ENSO than the PDO. Although for the 1998–2002 interannual variation with a 5.8-year period, both could be involved. Further efforts are required to understand if the mass transport within the Earth system associated with PDO phenomena can cause the J_{2} variations with the timescale greater than 10 years.

5. Summary

[29] We have obtained an accurate determination of the long-term variations in J_{2} by analysis of the SLR data from multiple geodetic satellites over the past 28 years. In addition to the secular change of −2.75 × 10^{−11} yr^{−1} induced primarily by postglacial rebound and the annual variations, successive 4–6 years and a variation with a timescale of ∼21 years are observed in the post-1976 J_{2} variations. In particular, two large fluctuations in J_{2} are correlated with the strong ENSO events of 1986–1991 and 1996–2002. Contemporary models of the Earth's mass redistributions can account for a major part of the observed 4- to 6-year variations during the strong ENSO events. The apparent 1998 anomaly is due to the superposition of the 5.8-year variation with a decadal variation. An improved model of the 18.6-year anelasticity effect is required for understanding the nature of the variations with timescale of ∼21 years. The cause of the decadal variations remains unknown. Additional effort is required to improve understanding of the large-scale global mass redistribution associated with global climate changes due to the ENSO and PDO events.

Acknowledgments

[30] We thank B. Chao, J. C. Ries, R. J. Eanes, and D. P. Chambers for helpful discussions and advice and C. Cox, M. Dyurgerov, J. Dickey, J. Chen, and A. Au for providing useful data for this study. We also thank Steve Dickman and Roberto Sabadini for their review and helpful comments. This research is supported in part by NASA grant NAG11636.