Greenland mass variation from time-variable gravity in the absence of GRACE



[1] In a recent paper, the authors succeeded in the inference of time-variable gravity from orbit analysis of the CHAMP satellite. The authors demonstrated the potential of the adopted methods by validation against GRACE data and surface height changes from GPS ground stations. This paper presents the capability of orbit analysis for the spatiotemporal quantification of Greenland mass change trends. Based on CHAMP time-variable gravity fields from January 2003 to December 2009, we estimated the ice mass loss over the entire of Greenland to 246±10 Gt/yr. This result is in line with the findings from GRACE data analysis (223±10 Gt/yr) over the same period; the trend estimates differ by only 10%. Moreover, for some areas, the spatial mass variation patterns are in good agreement, pinpointing dominant deglaciation along the Greenland coastline. We conclude that orbit analysis of low-Earth orbiting spacecraft is suitable to assess Greenland mass balance in the absence of the GRACE satellites.

1 Introduction

[2] Since the turn of the millennium, considerable effort has been put in the computation of mass change in the system Earth from time-variable gravity. In particular, gravity field time series derived from the Gravity Recovery and Climate Experiment (GRACE) project [Tapley et al., 2004a] substantially improved knowledge about mass redistribution on both regional and global scale. During the last decade, the satellite data have frequently been exploited to detect and quantify land surface hydrology variability, ice mass balance in the cryosphere, episodic (earthquake) processes, surface displacements caused by glacial isostatic adjustment, and ocean mass trends [cf. Cazenave and Chen, 2010, and the references therein]. The continuing mass loss of the Greenland ice sheets has gained particular interest, particularly against the background of the ongoing debate on global climate change [e.g., Mote, 2007; Hanna et al., 2008; Velicogna, 2009; Rignot et al., 2011].

[3] Owing to the unpredictable lifetime of the GRACE project, geoscientific communities are seriously concerned about the continuation of gravity field time series, and hence the opportunity to directly quantify surface mass variation. As the GRACE follow-on mission will not become operational before 2017 [Watkins et al., 2013], a gap between GRACE and GRACE follow-on has to be expected. This gap has been proposed to be bridged with gravity field information obtained from GNSS (Global Navigation Satellite Systems) tracking of low-Earth orbiting satellites [cf. Gunter et al., 2011; Lin et al., 2012; Wang et al., 2012; Weigelt et al., 2013], albeit with lower accuracy and resolution as compared to GRACE.

[4] The nondedicated mission Swarm—supposed to be launched towards the end of 2013—can be considered as the most promising bridging candidate; the three spacecraft will orbit Earth at an altitude of about 300–500 km on near-polar near-circular trajectories [ESA, 2004]. The Swarm spacecraft and orbit design is comparable to that of the single-satellite CHAMP (Challenging Minisatellite Payload) mission [Reigber et al., 2001]; as a consequence, time variability as seen by CHAMP provides evidence of space gravimetry based mass variation detection in the absence of GRACE.

[5] Applying a tailored processing strategy based on Kalman filtering, Weigelt et al. [2013] recently demonstrated that surface mass variation can be inferred from GNSS tracking data of the CHAMP satellite. In this paper, we investigate Greenland deglaciation as seen by CHAMP in more detail. We present a comparative analysis of CHAMP and GRACE time-variable gravity fields spanning the period January 2003 to December 2009 (seven integer years). We examine the mass change trend of the Greenland ice sheets as a whole but also have a closer look on the spatial mass variation patterns.

2 Data and Methods

[6] We used monthly CHAMP and GRACE (release 05) gravity field solutions provided by the University of Luxembourg [Weigelt et al., 2013] and the Center for Space Research at the University of Texas [Tapley et al., 2004b], respectively. Each gravity solution is given in terms of spherical harmonic coefficients up to degree and order (d/o) 60. We replaced the flattening coefficients c20 by in-house values obtained from Satellite Laser Ranging (SLR), cf. Figure 1. SLR-derived geocenter coordinates [Cheng et al., 2010] have been converted to degree-1 spherical harmonic coefficients in order to account for geocenter motion, cf. Wu et al., [2012]. Due to the large uncertainties in Glacial Isostatic Adjustment (GIA) modeling, our mass change rates are not corrected for the rebound signal caused by post-glacial land uplift. We want to emphasize that the GIA signal over Greenland is assumed to be in the order of a few Gt/yr [e.g., Velicogna, 2009], and hence has a minor effect on the results presented here.

Figure 1.

Time series of the flattening coefficient c20, reduced by the mean values. Green: GRACE CSR-RL05; blue: SLR (from Center for Space Research (CSR), cf. Cheng and Tapley [2004]); red: SLR (in-house, cf. Maier et al. [2012]). The SLR values have been derived from measurements to five geodetic satellites.

[7] Point-mass modeling according to Baur and Sneeuw [2011] has been applied to infer mass variation from time-variable gravity. The method attributes gravitational disturbances at satellite altitude to individual surface locations. In order to compute gravitational disturbances, δg, we first reduced the temporal means from the monthly sets of spherical harmonic coefficients cmn and smn; m and n denote the degree and order, respectively, of the spherical harmonic expansion. Next, we fit a regression line to each of the residual coefficient time series. From the regression curves, we extracted the secular change within the 7 year period; these are hereafter referred to as Δcmn and Δsmn.

[8] Based on Δcmnand Δsmn, the gravitational disturbances were evaluated on an equidistant grid at the space locations Qi(i=1,…,q) with geocenter distance ri=r=a+500km (Figure 2); a indicates the major semi-axis of a reference ellipsoid of revolution. The number of pseudo-observations is q=1223. Making use of the equivalence principle, the relation between the gravitational disturbances at satellite altitude and mass variations δmj(j=1,…,p) at the points Pjon the Earth's surface reads

display math(1)

Therein, G denotes the gravitational constant; li,jis the distance between the space location Qiand the surface location Pj. We covered the Greenland area by an equidistant grid of p=306 potential mass variation locations (Figure 2). As q>pholds true, equation (1) yields an overdetermined system of equations. We applied least squares adjustment to fit the signal in space to surface change rate magnitudes.

Figure 2.

Gravitational disturbances evaluated from GRACE gravity field solutions at an altitude of 500km. Red dots indicate the (equidistantly distributed) point-mass variation candidates on the Earth's surface (Albers projection).

[9] The point-mass modeling technique requires neither filtering (“destriping”) of spherical harmonic coefficients nor spatial averaging of the mass variation signal. However, the downward continuation procedure constitutes an ill-posed problem, and hence regularization of the normal equations system is necessary. We stabilized the inverse problem by Tikhonov regularization in combination with heuristic regularization parameter estimation adopting the L-curve criterion [e.g., Hansen et al., 2007]. In this context, it should be noted that regularization can be interpreted as filter operation, as has been pointed to by Kusche [2007] and Swenson and Wahr [2011].

[10] Besides the quantification of basin-wide change rates, point-mass modeling allows for the spatial localization of mass trends. As such, the method shows remote affinity to the mascons approach as has been applied, for instance, by Jacob et al. [2012] exploiting time-variable global gravity fields. Whereas mascons are small, arbitrarily defined regions, each point mass can be interpreted as a point-shaped drainage system.

3 Results

[11] Figure 3 shows the mass variation trend signals as sensed by CHAMP and GRACE. In order to suppress high-frequency CHAMP errors, Gaussian smoothing with a radius of 1000km was applied. We applied the same filter to the GRACE pattern. This is for the sake of consistency; we are aware of the fact that owing to superior measurement performance, smoothing radii down to ≈300km are typically considered for GRACE studies. Over vast parts of the globe, noise clearly dominates the CHAMP pattern; for instance, the signals in North Africa, Central America, North India as well as most of the oceanic signals turn out to be artifacts when validated against GRACE. On the other hand, most of the GRACE features either do not show up in the CHAMP pattern (e.g., North Canada and South Africa) or deviate considerably in geographical location and/or magnitude (e.g., Amazon basin, Alaska and Fennoscandia). Hence, the correlation between the CHAMP and GRACE pattern is rather limited. An exception is the signal in Greenland, what we attribute to its large magnitude compared to the other mass variation signals (cf. Figure 3, bottom).

Figure 3.

Mass trends from (top) CHAMP and (bottom) GRACE time-variable gravity over the period January 2003 to December 2009. A regression line was fitted to time series of residual equivalent water height values at each point of a global 1°×1° grid. Gaussian smoothing with a radius of 1000km applied (Robinson projection).

[12] Based on point-mass modeling, we quantified the basin-wide Greenland change rate to −246±10 Gt/yr and −218±10 Gt/yr for CHAMP analysis and GRACE analysis, respectively. These numbers hold for the truncation of the spherical harmonic series at d/o 20. We found this truncation to be the optimum trade-off between signal loss (cf. third column in Table 1) and the impact of CHAMP errors (cf. fifth column in Table 1). For truncation above d/o 20, the signal loss decreases but the high-frequency errors increasingly distort the CHAMP solutions. For truncation below d/o 20, the situation is vice versa. Truncation at d/o 20 roughly corresponds to a Gaussian filter with a radius of 1000 km, which is in line with the smoothing used by Weigelt et al. [2013].

Table 1. Basin-wide Greenland Change Rates
  Error (%) Error (%)
 GRACEwith respect toCHAMPwith respect to GRACE
d/oa(Gt/yr)d/o 60(Gt/yr)same d/od/o 60
  1. a

    Maximum degree and order of spherical harmonics. Uncertainties are given at the 95% (2σ) confidence level.


[13] The spatial variation in secular mass change is presented in Figures 4a and 4b. Both CHAMP and GRACE suggest mass loss along the entire Greenland coastline and slight mass accumulation in the interior. Figure 4c and Table 2 provide a more differentiated view on the consistency of the findings. In the East of Greenland (drainage systems 2 and 5), the results are in very good agreement; the change rates differ by less than 10%. A degree of disagreement of 20–30% holds for the central West and the interior of Greenland (drainage systems 3 and 4). The discrepancies in the Southwest (drainage system 1) and in the North (drainage system 6) are 70% and 150%, respectively.

Figure 4.

Spatial mass variation patterns from time-variable gravity; (a) CHAMP, (b) GRACE, (c) difference between CHAMP and GRACE. The spherical harmonic expansion is truncated at degree and order 20. Delineations and numbers indicate drainage systems as listed in Table 2(Albers projection).

Table 2. Change Rates in Drainage Systems (cf. Figure 4)
System (Gt/yr) (Gt/yr)

4 Discussion

[14] As has been shown by previous studies [e.g., Jacob et al., 2012] and is underlined by Figure 3, compared to any other region around the globe, the Greenland mass trend is by far the strongest in magnitude; this trend signal can be attributed to persistent deglaciation. Accordingly, mass loss of the Greenland ice sheets is the main driver for nonsteric sea level rise, provided that melt water drains into the world's oceans. Therefore, the continuous monitoring and quantification of Greenland ice mass variation is of fundamental relevance from a scientific, socioeconomic, but also political perspective.

[15] Amongst other measures, Weigelt et al. [2013] assessed the performance of the CHAMP gravity field solutions by the estimation of mass trends in a geographically rectangular area with extension 15°W to 75°W in longitude and 60°N to 85°N in latitude. They found that the signal RMS within this area deviates by 23% when compared to GRACE. A Gaussian filter with a smoothing radius of 1000 km has been applied. On the one hand, these numbers demonstrate the potential of CHAMP time-variable gravity to detect mass trends of the Greenland ice sheets. On the other hand, the coarse delineation of the region of interest and the neglect of corrections for signal leakage hamper more realistic mass change trend estimation.

[16] Our CHAMP result (−246±10 Gt/yr, truncation at d/o 20) and GRACE results (−218±10 Gt/yr, truncation at d/o 20; −223±10 Gt/yr, truncation at d/o 60) deviate by 13% and 10%, respectively. As such, Weigelt et al. [2013] underestimated the performance of Greenland mass variation from CHAMP gravity fields by a factor of about two. The agreement of the basin-wide trend values is remarkable. For some areas also the spatial mass variation patterns show good correlation. However, especially for the Southwest and North of Greenland, significant differences exist. We attribute these discrepancies to the considerably higher noise level of the CHAMP gravity fields as opposed to GRACE (cf. Figure 3); they clearly reveal the present limits of mass variation detection from orbit analysis.

[17] We validated point-mass modeling against an independent inference method, namely the leakage correction procedure as proposed by Baur et al. [2009]. The independent approach estimates the basin-wide GRACE change rate to −226±11 Gt/yr, which is consistent with the findings from point-mass modeling.

5 Conclusions

[18] Against the background of CHAMP-derived time-variable gravity field information, we demonstrated that tailored orbit analysis of low-Earth orbiting spacecraft has the potential to substantially contribute to monitor, localize, and quantify secular mass variation on the Earth's surface. However, it has to be stressed that—at least for the time being—the detection of meaningful mass change rates from CHAMP time-variable gravity is limited to the Greenland region; investigations in other areas turned out to be unsuccessful due to the higher noise level of the data as opposed to GRACE. Future methodological refinements and the combination with GNSS orbit information from other satellites may improve the situation.

[19] It is very unlikely that the exploitation of data collected by nondedicated satellite missions (such as Swarm) will ever reach the GRACE performance—even if information of a variety of spacecraft is dealt with in a joint inversion. As a consequence, the detection of temporal variability from orbit analysis constitutes a bridging technique but should not be considered as substitute for much more accurate intersatellite tracking.


[20] The author is grateful to the Center for Space Research (CSR) and the University of Luxembourg for providing the data for this study. The GRACE data have been retrieved from the Integrated System Data Center at the Geoforschungszentrum Potsdam (ISDC,; the CHAMP data have been downloaded from the website of the International Centre for Global Earth Models (ICGEM, Figure 3 was drawn using the free software package GMT [Wessel and Smith, 1991]. The SLR c20 series used in this study has been provided by my colleagues Andrea Maier and Sandro Krauss. Last but not least, the author acknowledges helpful comments by Jennifer Bonin and Matthias Weigelt during the review process.

[21] The Editor thanks Matthias Weigelt and Jennifer Bonin for their assistance in evaluating this paper.