Global inter-annual gravity changes from GRACE: Early results

1. Introduction

[2] The twin GRACE satellites have completed more than two successful years in orbit since their launch on March 17th, 2002 through the joint partnership between the US National Aeronautics and Space Administration (NASA) and the German Deutschen Zentrum für Luft- und Raumfahrt (DLR) [Tapley and Reigber, 2000].

[3] GRACE is capable of measuring large-scale mass re-distributions within the entire Earth system with unprecedented accuracy [Tapley et al., 2004], but it is not capable of discriminating between the different contributors such as atmosphere, ocean, water-storage on land or solid earth contributions.

[4] In the following we will investigate the inter-annual gravity field changes due to continental water storage change between 2002 and 2003 and to which accuracy they can be inferred from GRACE gravity field observations. The result will be evaluated with four of the most widely used global hydrological models in terms of visual inspection and spatial correlation coefficients.

2. GRACE Data and Processing

[5] During 2004 the GRACE science team released the following 15 monthly gravity field solutions irregularly spaced in time: April/May and August through November of 2002; February through May and July through December of 2003. No solutions have been released for the months of January and June. Data are released as spherical harmonic geopotential coefficients to harmonic degree and order 120, and each monthly solution is accompanied with a “best guess” calibrated error file.

[6] In order to investigate the change in continental water storage, data were corrected for other known contributors to gravity changes by the GRACE science team at the Center of Space Research (CSR) at the University of Texas (Level-2 data). Each monthly solution was corrected for temporal gravitational accelerations due to solid Earth tides; ocean tides; ocean circulation (barotropic model); atmosphere; pole tide and N-body perturbations using various models [Bettadpur, 2003a, 2003b]. All monthly solutions were subsequently expanded to spherical harmonic degree and order 15 and smoothed using a Gaussian filter with a half-width of 1000 km [Wahr et al., 1998]. Degree zero and one terms were not included in the GRACE solutions, and the C₂₀ term was omitted as it shows large un-physical variability during 2002.

[7] The choice of degree and order 15 for the spherical harmonic expansion is based on early GRACE investigations suggesting that the monthly data are presently dominated by errors at spherical harmonic degree larger than roughly 15 corresponding to spatial signals of 1300 km and shorter [Wahr et al., 2004].

[8] Annual and inter-annual gravity field changes were derived by submitting the GRACE monthly gravity fields with their associated error fields to a stochastic least squares inversion [Jackson, 1979]. In this inversion the signal is modeled as a mean plus a linear trend plus annual varying cosine and sine terms centered on Jan 1st 2003. With only two years of data the linear trend will represent the inter-annual gravity change between 2002 and 2003. Modeling the inter-annual signal as a linear trend is considerably more stable than computing annual means or monthly differences (i.e., August 2003–August 2002). A joint modeling of trend and annual signal is important to avoid possible leakage between the two signals because the data are irregularly distributed in time. Gravity changes observed from GRACE are shown in Figure 1. One of the largest signals is the nearly 3 μGal gravity decrease in central Europe. Central Europe suffered from flooding in 2002 and a record-breaking heat-wave in 2003 with associated ground water discharge. Western Canada shows a decrease in gravity of 2 μGal between 2002 and 2003. In 2003 Western Canada also suffered from drought. Gravity increased by more than 2.5 μGal over eastern India, which is most likely linked to extensive flooding in 2003. Gravity also increased over central Australia by almost 1.5 μGal. Annual rainfall estimates by the Commonwealth Bureau of Meteorology showed that 2002 was Australia's 4th driest on record, whereas 2003 was a normal year.

[9] Post Glacial Rebound (PGR) signal could also show up in the above trend analysis, as no attempt has been made to remove the signal from the GRACE data. The PGR signal has maximum amplitude of 1 cm/year over regions like the Hudson Bay and Scandinavia, but is generally smaller than a few millimeters per year in most other regions [Velicogna and Wahr, 2002]. In the present analysis we have excluded the Hudson Bay and we do not see a clear signal over Scandinavia related to PGR.

3. Inter-Annual Gravity Changes From Hydrology

[10] Four of the most widely used global hydrological models were analysed for their skill in predicting inter-annual gravity field signal. These are the Au&Chao model [Au et al., 2003], the Climate Prediction Center (CPC) model [Fan and van den Dool, 2004], the Global Land Data Assimilation System (GLDAS) [Rodell et al., 2004] developed jointly at NASA/NOAA, and the Land Dynamics Model (LadWorld) [Milly and Shmakin, 2002]. The LadWorld model stops in June 2003 resulting in only 18 months for the comparison.

[11] We submitted the monthly averaged output of all hydrological models to the same analysis as the GRACE data in terms of spherical harmonic expansion and smoothing. If the water stored on land is approximated using a thin layer of water the resulting change in gravity is derived using

where k′_n are the loading Love numbers, ρ_w is the density of water, g is the normal gravity acceleration, P_nm are the normalized Legendre functions, and C_nm and S_nm are dimensionless coefficients. The nm index indicate that the water layer of thickness h_nm(t) has been expanded into spherical harmonic coefficients. For n → ∝ the expression becomes the Bouguer plate correction [Knudsen and Andersen, 2002]. The Bouguer plate correction provides the “rule-of-thumb” that 1 μGal gravity change equivalents 2.4 cm water thickness change.

[12] The estimated gravity changes between 2002 and 2003 for the four hydrological global models are shown in Figure 2. GLDAS is visually the model that best resembles the GRACE observations. In order to investigate this, spatial correlation coefficients between the GRACE observations and continental water storage induced gravity field change was computed globally over land. (See Table 1.) The northern and southern hemispheres were treated separately as most observations entering the hydrological models are found on the northern hemisphere. The Au&Chao, CPC and LadWorld models are largely uncorrelated with the GRACE observations on these scales, whereas there is high agreement between GLDAS and GRACE with a spatial correlation coefficient of 0.65 on the northern hemisphere. The reason why GLDAS is superior to the other models in modeling inter-annual water storage is most likely because this model is forced with observed data especially precipitation.

4. GRACE Accuracy Assessment

[13] The initial GRACE evaluation by Wahr et al. [2004] has shown that the accuracy on the monthly GRACE solutions is presently 40 times worse than the GRACE baseline target accuracy. However, at low degree the GRACE errors are still small enough to measure inter-annual changes in continental water storage. The accuracy of the estimated inter-annual gravity field changes can be estimated in several ways.

[14] An upper bound to the error can be obtained by using GRACE observations over the ocean where the inter-annual signal should be significantly smaller than on land. The GRACE observations confirm this, which indicate that the signal is likely a real physical signal. Over the deep ocean (depth > 1000 meters) away from the coast the maximum amplitude of the inter-annual signal reaches 1.1 μGal (2.5 cm water thickness) in two north-south going patches across the Pacific Ocean. There is presently no plausible physical origin of these signals and they are believed to be GRACE errors. As such, 1.1 μGal can be taken as the upper limit to the uncertainty to which the inter-annual signal can be determined from GRACE using the applied method.

[15] A somewhat more realistic error estimate can be derived by computing the RMS of the inter-annual signal from GRACE over the deep ocean within the 50° parallels in the Pacific Ocean. This region was chosen, as the Hadley Center HADCM3 model [Collins et al., 2001] shows virtually no inter-annual signal in this region in terms of bottom pressure signal. The averaged inter-annual signal over this region from GRACE is then a realistic error estimate. It has a RMS signal of 0.3 μGal (7 mm water thickness).

[16] A rigorous error estimate is given by the stochastic inversion, which was applied to estimate the annual and inter-annual signal from the GRACE data and associated error fields. The inversion yields an error estimate on the predicted parameters based on the “best guess” errors provided on each of the 15 monthly input fields. The error estimate has a mean of 0.4 μGal corresponding to 9 mm of water thickness ranging from 5 mm near the Poles to 13 mm around the Equator. The error has a clear zonal structure reflecting the increase in GRACE data-coverage with latitude. This stochastic estimate is slightly more pessimistic than the 7 mm obtained from the RMS over the Central Pacific Ocean. This confirms the conservatism of the “best guess” estimates provided with the GRACE data, which are possibly too pessimistic (S. Bettadpur, personal communication, 2004).

[17] Even with a conservative accuracy estimate of 0.4 μGal (9 mm in water thickness), GRACE provides very valuable information on global inter-annual water storage change of importance to future hydrological modeling. The standard deviations on the inter-annual gravity changes computed from the four hydrological models, are larger than the 0.4 μGal GRACE accuracy level in most regions of the world, and in many locations larger than 1 μGal (i.e., Europe and the Amazon Basin).

5. Summary

[18] Fifteen monthly gravity field solutions from the GRACE satellite in 2002 and 2003 have been studied to estimate gravity field changes between 2002 and 2003. The results demonstrate that GRACE is capable of capturing the changes in continental ground water on inter-annual scales with accuracy of 0.4 μGal corresponding to 9 mm water-thickness on spatial scales of 1300 km and longer.

[19] Comparisons with global hydrological models demonstrate the quality of the GLDAS model in predicting these inter-annual changes in water storage between 2002 and 2003. Whereas the other investigated hydrological models were virtually un-correlated with the GRACE observations, the spatial correlation coefficient between GRACE observations and the GLDAS modeled gravity field changes from water storage is 0.65 over the Northern Hemisphere.

[20] Even with a conservative accuracy estimate of 0.4 μGal it was shown that GRACE provides very valuable information about global inter-annual water storage changes of importance to future hydrological modeling.