We use temporal gravity variations from GRACE to investigate changes in a 34-year time series of Earth's oblateness (J2) observed by satellite laser ranging (SLR). We use 2002–2010 GRACE data to compute the effects of Greenland and Antarctic ice mass variations on J2 (2.0 and 1.7 × 10−11/year respectively). Their combined effect on the J2 trend during the GRACE mission is 3.7 × 10−11/year, which agrees well with the GIA-corrected SLR J2 trend over the same time period. The results suggest that at least since 2002, ice loss from Greenland and Antarctica has been the dominant contributor to the current GIA-corrected J2 trend, which apparently began sometime in the 1990s.
 The oblateness of the Earth, represented by the J2 gravitational parameter, refers to the Earth's ellipsoidal shape – its equatorial radius is ∼21 km larger than its polar radius. Most of this oblateness is due to the Earth's rotation, which pushes mass out toward the equator. However, it is also known that J2 changes with time, and these changes can be a sensitive indicator of processes occurring on and within the Earth. In particular, J2 is slowly getting smaller (less oblate) due to glacial isostatic adjustment (GIA) [Mitrovica and Peltier, 1993], but it is also responding to movement of water in the atmosphere, oceans, and cryosphere.
 Here, we interpret a 34-year time series of J2 values determined from satellite laser ranging (SLR) to a number of geodetic satellites (Figure 1) [Cheng and Tapley, 2004]. From 1975–1997, the variability in this time series largely consists of an annual variation [Nerem et al., 1993] superimposed on a secular trend thought to be due to GIA [Mitrovica and Peltier, 1993]. However, starting in the mid-1990s departures from this behavior began to appear [Cox and Chao, 2002], indicating something had fundamentally changed since the satellite observations were initiated in 1975. A variety of explanations have been proposed for some of these changes, including the melting of mountain glaciers [Dickey et al., 2002; Marcus et al., 2009], departures of the 18.6 year tide from its elastic Earth + equilibrium ocean value [Benjamin et al., 2006], and variations related to ENSO [Cheng and Tapley, 2004; Marcus et al., 2009]. However, a definitive explanation of all long-period J2 variability has remained elusive.
 With the launch of the Gravity Recovery and Climate Experiment (GRACE) satellite gravity mission in 2002, a new tool became available that has radically altered our understanding of temporal gravity variations [Tapley et al., 2004]. While SLR and other conventional tracking data (e.g., DORIS, GPS) have at best observed temporal variations of a half dozen gravity coefficients with wavelengths >10,000 km [Cheng and Tapley, 2004; Cheng et al., 1997; Lemoine et al., 2006], GRACE can measure thousands of coefficients on a monthly basis, allowing users to map month-to-month changes in the Earth's gravity field at a few hundred km spatial resolution all over the globe [Wahr et al., 2004]. GRACE has been used successfully to monitor changes in Greenland and Antarctic ice mass [Luthcke et al., 2006; Velicogna, 2009], the melting of glaciers in Alaska [Tamisiea et al., 2005; Luthcke et al., 2008] and Patagonia [Chen et al., 2007], changes in global ocean mass [Chambers et al., 2004], changes in ocean bottom pressure [Morison et al., 2007], changes in continental water storage [Rodell et al., 2009; Tiwari et al., 2009], and a host of other signals. Over the last decade, GRACE has become an invaluable tool for studying the effects of climate change on the Earth's water reservoirs. Here, we use GRACE observations since 2002 to decipher the cause of the recent J2 variations observed by SLR.
 In addition to the GIA signal, the largest long-period changes in the GRACE gravity solutions are from Greenland and Antarctic ice mass loss [Velicogna, 2009]. Here, we use GRACE-based estimates of monthly changes in Greenland and Antarctica to estimate the predicted change in J2 caused by those ice sheets. We employ a two-step process. First, we use GRACE to recover monthly values of the change in total Greenland and Antarctic ice sheet mass (see the paragraph below). Second, we compute the contribution a unit Greenland (or Antarctic) mass change would make to J2, and we multiply that contribution by the GRACE Greenland mass estimates to find the actual monthly effects of Greenland on J2. To compute the J2 contribution from a unit Greenland mass change, we must decide how to distribute that mass over the ice sheet. We use the pattern of GRACE Greenland mass loss trends determined by fitting trends to the entire 8+ years of GRACE data. We find that because J2 is a global-scale coefficient, the details of the spatial distribution are not critical; for example, assuming, instead, a uniform mass change over all Greenland or Antarctica alters the results for each ice sheet at the level of 4% or less. When computing the effects of a unit mass loss, we conserve mass by assuming there is an opposing change in ocean mass spread uniformly over the ocean surface. The details of how we compute the J2 contribution caused by a unit Greenland or Antarctic mass change, are described in the auxiliary material.
 Our method of using GRACE to estimate the average thickness change, H (given in water equivalent height), for each ice sheet is described by Velicogna and Wahr [2006a, 2006b]. Briefly, we remove the temporal mean from each GRACE harmonic gravity (i.e., Stokes) coefficient, and correct the results for GIA using the model of Paulson et al. . We convolve those residual coefficients with the coefficients, WlmC, WlmS, of an ice sheet averaging function, to obtain an unscaled estimate of the average ice sheet thickness change:
where A is the area of the ice sheet [Swenson and Wahr, 2002, equation 27], and the Clm, Slm′s are the residual Stokes coefficients, and J2 = −C2,0. Our final estimate, H, is obtained by applying a scaling factor to H′ to correct for the fact that the averaging function undersamples the ice sheet [Velicogna and Wahr, 2006a, 2006b]. We compute a monthly time series for H using the GRACE monthly solution between August, 2002 and December, 2010, for both the CSR and the GFZ Release 04 fields (replacing the noisy GRACE J2 values with the SLR values from Cheng and Ries ), and we use those values of H to compute monthly J2 variations via (A6) derived in the auxiliary material.
 The justification for using the SLR J2 coefficients in place of the GRACE J2 values needs some explanation, since it might seem like circular reasoning to then use the resulting GRACE mass estimates to compare with the SLR J2 values. Here is one way to think about what we are doing. The SLR J2 values demonstrate that there have been long-period changes in the Earth's mass distribution over the past several decades. But that single J2 harmonic component, by itself, does not have anywhere near the spatial resolution necessary to determine where those changes occurred. By incorporating GRACE, we are supplementing that single coefficient with thousands of others. It's those additional coefficients that give us the resolving power to determine mass variability down to the scales of Antarctica and Greenland (and smaller). In fact, the J2 coefficient plays only a minor role in the GRACE estimates of Greenland and Antarctic mass variability. When we leave out J2 entirely, for example, our estimates of the secular trend in mass change by less than 15% for Antarctica, and by less than 1% for Greenland. Once we have computed the GRACE Greenland and Antarctic mass estimates, we use them to determine the ice sheet contributions to J2, so that we can assess what portion of the SLR time series is caused by the ice sheets.
Figure 2 shows the J2 contributions of Greenland and Antarctica computed from equations (1) and (A6). The contribution to the J2 secular trend over 2002–2010 is 2.0 ± 0.05 × 10−11/year and 1.7 ± 0.1 × 10−11/year for Greenland and Antarctica respectively (the computed trends were virtually the same using either the CSR or GFZ fields). The total mass loss in Antarctica (−143 Gt/year) is much less than in Greenland (−239 Gt/year) [Velicogna, 2009], but because the Antarctic mass loss is closer to the pole, its effect on J2 is amplified. By themselves, neither Greenland nor Antarctica can account for the changes observed in J2 since 2002. However, when Greenland and Antarctica are added together the agreement with the SLR observations is good, as shown in Figure 3. Here, the secular effect of GIA has been removed from the SLR J2 time series using the Paulson et al.  model (2 = −3.6 × 10−11/year). Coincidentally, the sum of the Greenland and Antarctic secular contributions (3.7 × 10−11/year) almost exactly offsets the negative trend predicted from the GIA model.
 There are significant uncertainties in the GIA corrections both for 2 [Tamisiea et al., 2002] and for Greenland and Antarctica. The default GIA model we adopted [Paulson et al., 2007] uses an ice sheet deglaciation model and a viscosity profile (Ice-5G and VM2, respectively, from Peltier ) that were tuned in part to match the SLR 2 value from the early portion of the SLR record. The consequence of this can be seen by noting that the J2 results in Figure 3 show little long-term trend before the mid-1990s. To assess the possible impact of errors in the GIA corrections, we experimented with three different GIA models that had viscosity profiles adjusted to fit the geologically determined relative sea level data from around Hudson Bay and the GRACE secular trends from the same region, but that did not attempt to fit the SLR J2 values [Paulson, 2006]. Each of the three models, denoted as Cases 1, 2, and 3 by Paulson , uses the ICE-5G deglaciation history, and each has a two-layer viscosity profile with an upper/lower mantle boundary at a depth of 1170 km (to be consistent with VM2) and a 120-km thick elastic lithosphere. Case 1 is Paulson's  best fitting model, with an upper mantle/lower mantle viscosity contrast of a factor of 10. Cases 2 and 3 fit the data nearly as well as Case 1, but have extreme upper mantle/lower mantle viscosity contrasts of factors of 3 and 100, respectively.
 Changing the GIA model affects both the 2 used to correct the SLR series, as well as the Greenland and Antarctica J2 predictions (Figure 4). We find that changing the GIA model doesn't alter our conclusion about Greenland and Antarctica dominating the recent GIA-corrected J2 variations, but does introduce uncertainty into the timing of when the J2 variations changed character. The results for Case 1 are nearly identical to those for our nominal GIA model. And both of those results, along with those for Case 2, support the suggestion that the present J2 tend began in the mid-1990s. The Case 3 results, though, are consistent with a trend that began about a decade earlier.
 It seems clear, even from looking only at the post-2002 GRACE-SLR comparison in Figures 3 and 4, that Greenland and Antarctica cannot explain all the time variability in the SLR J2 history. There are interannual variations in J2 not accounted for by the ice sheet results, which are believed (see references above) to be some combination of hydrologic variations related, for example, to ENSO, and unmodelled anelastic contributions to the 18.6-year solid Earth tide. There is also a large interannual J2 variation just prior to the GRACE period (1997–2002), which Marcus et al.  suggest is due to a combination of melting of Alaskan glaciers, ENSO-related land hydrology variations, and ocean mass redistribution. Lavallee et al.  recently showed that this anomaly can be mainly ascribed to hydrologic mass variations. The other interannual variations since 1975 are also likely due to hydrologic variability, as the GRACE results for Antarctica and Greenland are remarkably devoid of interannual variations. We also examined the effect on J2 of melting glaciers in Alaska [Tamisiea et al., 2005], but found their contributions to the secular trend were only 10% of the Greenland + Antarctica contribution and thus they are not included here.
 Although values of the SLR J2 coefficient show that the Earth's large-scale mass distribution has been changing over the last 34 years, this coefficient by itself has nowhere near the spatial resolution required to determine where on the globe those changes are occurring. By using GRACE to supplement that single coefficient with thousands of additional coefficients, we are able to map the spatial pattern of global mass variability. From this pattern we can deduce the contributions of individual regions to J2. The results show that after removing the predicted GIA contributions from the SLR J2 values, the long-period J2 variability since 2002, which is when the GRACE data became available, has been dominated by Greenland and Antarctic ice mass loss (Figure 3). In fact, the cumulative positive trend in J2 from the ice sheets during this time period is nearly the same as the predicted negative GIA trend.
Figure 3 shows that the ongoing positive trend in J2 began sometime in the 1990s; the exact date is uncertain due to interannual variability likely unrelated to the ice sheets [Lavallee et al., 2010] and to uncertainty in the GIA model. The mid-1990s coincides with the time that glaciologists started to observe changes in Greenland [Alley et al., 2005; van den Broeke et al., 2009] such as the speedup of outlet glaciers [Rignot et al., 2008a]. While mass loss from Antarctica has increased since the mid-1990s [Rignot et al., 2008b], it has been proposed that the mass loss started significantly earlier than this date and has been more gradual [Zwally et al., 2005]. Hydrologic variations due to ENSO contribute most of the remaining interannual variability, with mountain glaciers and other phenomena (including the effects of mantle anelasticity on the 18.6-year tide) contributing the rest.
 While GRACE helps explain the origin of the J2 variations observed by SLR, the SLR observations help place the GRACE observations in a longer-term climate context, in effect extending the observations back in time and providing more information on cryospheric changes. This result helps underscore the value of continuing observational programs that use conventional tracking systems (SLR, DORIS, GPS) to monitor the gravity field, especially as a potential gap looms between GRACE and a follow-on mission.
 We thank M. K. Cheng and J. R. Ries for making their J2 time series publicly available. This study was supported by two separate NASA GRACE Science Team investigations and a JPL GRACE MEASURES contract. In addition to Erik Ivins, we thank Frank Lemoine, Ernst Schrama, and two anonymous reviewers for their careful review of the paper.
 The Editor thanks reviewer Erik Ivins for his assistance in evaluating this paper.