AIUB-RL02: a time series of monthly gravity models from L1B-RL02 GRACE data that were computed using the Celestial Mechanics Approach

U. Meyer, A. Jaeggi, Y. Jean und G. Beutler


Monthly gravity models AIUB_RL02_YYMM_60 (AIUB:AFTP) and AIUB_RL02_YYMM_90 (AIUB:AFTP)

The availability of the reprocessed GRACE L1B-RL02 data motivated a reprocessing of the monthly GRACE gravity models at AIUB. To this purpose the background models used to separate the Earth's gravity field from tides or short term atmospheric and oceanographic variations were also updated. The stochastic parametrization was revisited to optimally fit the new data and models. The spectral resolution of the monthly solutions was increased up to degree and order 90. As a priori gravity model the static part of AIUB-GRACE03S was used up to full degree and order 160. Strictly speaking the static coefficients of the a priori model beyond the maximum degree and order of the monthly solutions are part of the monthly solutions. But because they do not include any variations with time they are ommitted in the monthly fields. The quality of the reprocessed AIUB-RL02 gravity fields is very much comparable to that of the official CSR-RL05 models. In terms of the short term variability over the oceans which mostly represents the noise of the monthly models AIUB-RL02 seems to be advantageous during the first years of the GRACE mission, while the noise in CSR-RL05 is significantly lower since 2011 and especially during the period of 3-day orbit resonance in 2012 (Fig. 1). AIUB-RL02 is available in two different versions, one set up to a maximum degree and order of 60, the other to degree and order 90. The two versions fo AIUB-RL02 are denoted AIUB-RL02(60) or AIUB-RL02(90) throughout this text.


Fig. 1: Noise of the monthly gravity fields, as derived from their variability over the oceans, where no short term variations are expected. Seasonal variations were modeled and removed not to bias the results.

The quality gain of AIUB-RL02 with respect to AIUB-RL01 might be split into improvements due to reprocessed input data (Fig. 2) or updated background models (Fig. 3). The largest improvement due to the new input data is expected from the reprocessed geometrical correction of the K-Band observations (light blue in Fig. 2). The kinematic GRACCE orbits were also reprocessed due to the availability of reprocessed orbits of the GPS satellites that refer to the reference system IGb08 and are based on the new conventions IERS2010 (AIUB-RL01 was based on IERS2003). The kinematic satellite positions are used by the Celestial Mechanics Approach as pseudo observations instead of the GPS code and phase obervations. The effect of the new kinematic orbits on the monthly gravity models is rather small and confined to low degrees (as might be expected considering the sensitivity of GPS versus that of K-Band).


Fig. 2: Changes from AIUB-RL01 to AIUB-RL02 in terms of difference degree amplitudes. Considered are changes due to the reprocessed L1B-RL02 input data and to the reprocessed kinematic satellite orbits.

The changes of the background models include an update of the dealiasing product for short term mass variations in the atmosphere and the oceans from AOD1B-RL04 to AOD1B-RL05 and of the ocean-tide model from EOT08A to EOT11A. Additionally shallow tides (admittances) were linearily interpolated from the main tides of EOT11A. The effects of the model updates are detailed in Fig. 3.


Fig. 3: Effect of model updates and the implementation of shallow tides (admittances) on a monthly gravity field solution.

The spherical harmonic coefficient C20 was not well determined in AIUB-RL01 and included large artificial variations with the S2-aliasing period of 161 days (Fig. 4, blue line). These could be reduced by the use of the reprocessed L1B-RL02 input data and the update of the background model, but the results were still not acceptable (Fig. 4, green line). It turned out that the artefacts with 161 day period can be further reduced by the estimation of daily accelerometer scale factors. Now the C20-coefficient (Fig. 4, red line) agrees well with that of CSR (Fig. 4, black line). Note that there still exists a bias to C20-values determined from satellite laser ranging (SLR) using the LAGEOS satellite (Fig. 4, magenta line) and some variations with 161 day period. We therefore recommend to replace the C20 coefficient in the AIUB-RL02 monthly solutions by SLR-derived values. SLR-derived C20-values can be extracted, e.g., from monthly gravity fields derived at AIUB from SLR data to 8 satellites that are available here (AIUB:AFTP).


Fig. 4: C20-coefficients of several series of monthly models derived from GRACE data and for comparison from SLR to the LAGEOS satellite.

The quality of the monthly gravity fields is characterized by the formal errors of the spherical harmonic coefficients. But these formal errors only represent the noise of the original observations and the strength of the solution due to the orbit geometry during the month under consideration. They do not consider the errors of the background models that play an important role in the overall accuracy.

More realistic error estimates may be derived from the short term temporal variability of the spherical harmonic coefficients. Seasonal or secular variations are modeled and subtracted from the monthly gravity fields. The calibrated errors are computed as the standard deviations of the remaining temporal variations. These calibrated errors are pessimistic error estimates because not all of the short term variations are due to noise.

Figures 5 and 6 show the calibrated errors of AIUB-RL01 and -RL02(60). The noise level was reduced by nearly one order of magnitude in RL02 with respect to RL02. This is nicely visible at resonant orders (15, 31 and 46) but also for coefficients of high orders. In the final version of AIUB-RL01 only coefficients up to order 45 were estimated on a monthly basis because beyond order 45 the noise dominated anyway. AIUB-RL02 is determined and delivered in two versions to full degree and order 60 or 90.


Fig. 5: Calibrated errors of the spherical harmonic coefficients of AIUB-RL01 (left the S-coefficients, right the C-coefficients).

Fig. 6: Calibrated errors of the spherical harmonic coefficients of AIUB-RL02(60) (left the S-coefficients, right the C-coefficients).

In Figs. 7 and 8 the formal errors of AIUB-RL02(90) are compared to the calibrated errors. While the general distribution of errors remains the same (i.e., increasing noise with increasing degree and order of the coefficients), the calibrated errors are deteriorated near orders 0, 15, 31, 46, 61 and 76. These orders are related to orbit resonance (the GRACE satellites circle the Earth approximately 15.3 times per day). The resonant orders are prone to aliasing from long periodic geophysical phenomena, e.g., tides. At low degrees the calibrated errors indicate an increased variability that is not related to any seasonal cycle or long periodic changes. Most probably much of this variability represents real time-variable signal that is misinterpreted as noise in Fig. 8.


Fig. 7: Formal errors of the spherical harmonic coefficients of AIUB-RL02(90) (left the S-coefficients, right the C-coefficients).

Fig. 8: Calibrated errors of the spherical harmonic coefficients of AIUB-RL02(90) (left the S-coefficients, right the C-coefficients).

The dependence of the calibrated errors on order that is visible in Figs. 6 and 8 suggests the derivation of order-specific calibration factors. They were computed by the mean of all factors of the same order (S- and C-coefficients of the same order were treated in the same way). The coefficients of the very low degrees and orders were ignored in the computation of the mean (only coefficients where l + m > 30 were considered; l: degree, m: order). The order-specific calibration factors are shown in Fig. 9 and can be downloaded here (AIUB:AFTP)


Fig. 9: Order-specific calibration factors to derive calibrated errors from the monthly formal errors of AIUB-RL02(90).

The quality of the monthly gravity models cannot be judged by the formal or calibrated errors only. The main factor that has to be considered is the signal content and strength. In the monthly models the focus is on the temporal variations. The largest variations of interest are caused by the hydrological cycle. They follow seasonal patterns and can be modeled in a deterministic way by simple sin- and cos-waves on annual and semi-annual frequencies.

Another reason for regional mass variations is the redistribution or melting of ice in polar and in glaciated high alpine regions. While the latter are of a rather local nature and only detectable by GRACE in a few cases, like Alaska or Fireland, ice mass change in Greenland or Antarctica leads to secular changes in gravity that are very well visible in the time series of monthly gravity fields. Due to the discussion on climate change these mass trends are in the focus of current research. Related to ice mass change and not separable by GRACE observations alone is the isostatic adjustment of the crust that also leads to mass trends visible in the monthly fields.

Periodic and secular variations are determined coefficient-wise from the monthly gravity fields. The significance of the estimated parameters may be evaluated using standard statistical tests, like the F-test (assuming normally distributes errors and consequently chi2-distributed variances). Significantly estimated periodic or secular variations of a specific spherical harmonic coefficient indicate sensitivity of this coefficient to the corresponding mass variations. The cummulative distribution functions (as a measure of the significance) for secular and periodic variations in the S- and C-coefficients is provided in Figs. 10 and 11 for AIUB-RL02(90). Beyond degree 70 and order 45 only very limited sensitivity to the tested temporal variations can be confirmed. On the other side there exist studies that prove that very local phenomena may be detectable by GRACE, as long as their intensity is high. We therefore provide the AIUB monthly gravity models up to degree and order 90 (as is done by other processing centers).


Fig. 10: Sensitivity of gravity field coefficients for secular variations (left the S-coefficients, right the C-coefficients). Dark colors indicate high sensitivity.

Fig. 10: Sensitivity of gravity field coefficients for periodic variations with annual period (left the S-coefficients, right the C-coefficients). Dark colors indicate high sensitivity.

The secular or saisonal variations may be derived from the spherical harmonic coefficients in the spectral domain, or from grids of gravity variations in the spatial domain. Figures 12 and 13 show the amplitudes of the periodic annual variations, derived in the spatial domain and expressed in equivalent water heights. The reduction of noise from AIUB-RL01 to AIUB-RL02(60) is obvious. The artificial striping that is related to the special along-track geometry of the GRACE K-Band observations is the dominating feature in Fig. 12, where AIUB-RL01 was evaluated. The same feature is much reduced in Fig. 13, derived from AIUB-RL02(60). Now the dominating features clearly show processes of hydrological origin in large river basins at low latitudes. Figures 12 and 13 were created without any filtering of gravity field coefficients or smoothing of the grids.


Fig. 12: Amplitudes of annual gravity field variations that were derived from AIUB-RL01, expressed in equivalent water heights. No smoothing was applied.

Fig. 13: Amplitudes of annual gravity field variations that were derived from AIUB-RL02(60), expressed in equivalent water heights. No smoothing was applied.

A comparable reduction of stripes can be observed for secular vatiations that also were derived from grids of monthly gravity variations expressed in equivalent water heights. Figures 14 and 15 show the trends derived from AIUB-RL01 or AIUB-RL02(60). Again no smoothing was applied. A strong ice mass loss is visible at the coast of Greanland and in western Antarctica, bus also in heavily glaciated regions of Alaska or Fireland. The signal visible near the coast of Sumatra is related to the big Earthquake in December 2014 that caused a sudden change in gravity that is misinterpreted as a trend by our evaluation. In Fennoscandia and near Baffin Bay a positive trend due to glacial isostatic adjustment (GIA) is visible.


Fig. 14: Mass trends, derived from monthly grids of AIUB-RL01 gravity variations, expressed in equivalent water height. No smoothing was applied.

Fig. 15: Mass trends, derived from monthly grids of AIUB-RL02(60) gravity variations, expressed in equivalent water height. No smoothing was applied.

An important application of the monthly gravity models is the calibration and validation of global hydrological models. To this end the mass variations observed by GRACE are integrated over river basins. In Fig. 16 mass variations within the basins of seven of the major rivers of the world are compiled, as derived from AIUB-RL02(60). No filtering/smoothing of the gravity field coefficients had to be applied. A slightly increased scatter of the monthly values during the fall of 2004 and in 2012 are related to periods of orbit resonance where the coverage by ground tracks of the GRACE satellites was reduced.


Fig. 16: Mass variations within selected river basins, expressed in equivalent water heights. The mass variations were derived from AIUB-RL02(60). No smoothing was applied.

Another application of the GRACE gravity fields concerns the observation of ice mass variations in polar regions. These are of special interest in the context of the discussion on global climate change and therefore actually in the center of interest. Figures 17 and 18 focus on mass trends in Greenland and Antarctica derived from the monthly fields of 2010 to 2014. The mass trends are evaluated per 1 degree bin (note that the size of these bins varies with latitude). The ice mass loss along the coast of Greenland and at the West coast of Antarctica is clearly visible. The ice mass change is superimposed by the signal of glacial isostatic adjustment (GIA). For any quantification of ice mass loss these two signals have to be separated. The accuracy of such evaluations is actually limited mainly by the accuracy of the models of GIA.


Fig. 17: Mass trends in Greenland, evaluated per 1 degree bin from AIUB-RL02(60) monthly models of 2010-2014.

Fig. 18: Mass trends in Antarctica, evaluated per 1 degree bin from AIUB-RL02(60) monthly models of 2010-2014.

The monthly solutions AIUB_RL02_YYMM_60 and AIUB_RL02_YYMM_90 can be downloaded here (AIUB:AFTP) or from the website of the ICGEM. They are available as sets of spherical harmonic coefficients. Degree 1 terms are excluded, because they cannot be observed by GRACE. SLR-derived degree 1 terms can be downloaded here (AIUB:AFTP). The C20 terms derived from GRACE are impaired by aliased signal with 161 day period. It is recommended to replace C20 by SLR-derived values. A C20 time-series that was derived at AIUB by evaluation of SLR data to 8 satellites may be extracted from the monthly SLR gravity fields provided here (AIUB:AFTP).


Page last modified: 22-Feb-2018 12:48:18 CET