Corrections and Auxiliary Products

A number of corrections and reductions are applied to the Level-2 spherical harmonics to generate Level-3 products that represent variations of the Earth's surface masses as accurately as possible. These post-processed Level-2 coefficients, denoted as Level-2B products, are provided as an additional data set for users who wish to undertake surface mass inversion starting from spherical harmonic coefficients by themselves.

The Level-2B products as well as individual data sets and models used during the post-processing steps mentioned below are available here.

Mean Field

GRACE/GRACE-FO Level-3 products represent mass anomalies, i.e., positive or negative variations about a long-term mean gravity field of the Earth. Essentially, the choice of this mean field is arbitrary, since using a different mean field only introduces a constant bias to the time series of mass anomalies. However, when comparing these Level-3 products to other data or models, all time series should refer to the same reference epoch.

All Level-2B/Level-3 products currently available at GravIS refer to a long-term mean field calculated as unweighted average of the 156 available GFZ RL06 GSM products in the period from 2002/04 up to and including 2016/08.

Anisotropic Filtering

In order to optimally separate signal and noise in the GRACE/GRACE-FO Level-2 data, filtering is necessary. Due to the observation geometry with its pure along-track ranging on polar orbits GRACE and GRACE-FO gravity fields reveal highly anisotropic error characteristics. An adequate filter technique to account for this is the decorrelation method by Kusche et al. (2009), named DDK, which is deduced from a regularization approach using signal and error information in terms of variance and covariance matrices. The filtering is applied in the spectral domain by multiplying the filter matrix to the unfiltered spherical harmonic (SH) coefficients (residual with respect to a mean field). This method has been adapted by Horvath et al. (2018) taking into account the temporal variations of the error variances and covariances, namely VDK filtering.

Hence, our Level-2B products are optionally decorrelated and smoothed with an adaptive filter that explicitly takes into account the error covariance information of the corresponding Level-2 product. We provide the following variants of Level-2B products: filtered with VDK2, VDK3, and VDK5 as well as unfiltered (NFIL) solutions. These variants are distinguishable by respective strings in the product file names.

Kusche, J., Schmidt, R., Petrovic, S., Rietbroek, R., 2009:
Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model
Journal of Geodesy, 83, 10, p. 903—913 , http://doi.org/10.1007/s00190-009-0308-3

Horvath, A., Murböck, M., Pail, R., Horwath, M., 2018:
Decorrelation of GRACE Time Variable Gravity Field Solutions Using Full Covariance Information
Geosciences, 8, 323 , https://doi.org/10.3390/geosciences8090323

C20 Time Series

The spherical harmonic coefficient of degree 2 and order 0 (C20) is related to the flattening of the Earth. Since it is known that monthly GRACE estimates of C20 are affected by spurious systematic effects (e.g. Cheng & Ries, 2017), the C20 coefficients and their formal errors are replaced by estimates derived from satellite laser ranging (SLR) observations that are regarded to be more reliable.

Here, we use a C20 time series processed at GFZ (König et al., 2019) that is based on the six geodetic satellites LAGEOS-1 and -2, AJISAI, Stella, Starlette, and LARES (starting from March 2012) and uses the same background models and standards as applied during GFZ GRACE/GRACE-FO processing, including the Atmosphere and Ocean De-aliasing model AOD1B.

Cheng, M., Ries, J., 2017:
The unexpected signal in GRACE estimates of C20
Journal of Geodesy, 91, 8, p. 897—914 , https://doi.org/10.1007/s00190-016-0995-5

König, R., Schreiner, P., Dahle, C., 2019:
Monthly estimates of C(2,0) generated by GFZ from SLR satellites based on GFZ GRACE/GRACE-FO RL06 background models. V. 1.0.
GFZ Data Services , http://doi.org/10.5880/GFZ.GRAVIS_06_C20_SLR

Cheng, M., Tapley, B., Ries, J., 2013:
Deceleration in the Earth's oblateness
Journal of Geophysical Research: Solid Earth, 118, p. 740—747 , https://doi.org/10.1002/jgrb.50058

GIA Correction

Glacial Isostatic Adjustment (GIA) denotes the surface deformation of the solid Earth (lithosphere and mantle) caused by ice-mass redistribution over the last 100,000 years, dominated by the termination of the last glacial cycle. Due to the Earth's viscoelastic response to mass redistribution between the ice sheets and the ocean, the Earth's gravity field is affected by long term secular trends mainly in previously glaciated regions such as North America, Fennoscandia and Antarctica. Moreover, also coefficients of low degrees and orders are affected.

The Level-2B/Level-3 products provided here are corrected using a GIA model based on ICE-5G ice load history (Peltier, 2004) as applied to the 3D-Viscoelastic Lithosphere and Mantle Model VILMA (Martinec, 2000; Klemann et al., 2008).

Peltier, W.R., 2004:
Global Glacial Isostasy and the Surface of the Ice-Age Earth: The ICE-5G(VM2) Model and GRACE
Annual Review of Earth and Planetary Sciences, 32, p. 111—149 , https://doi.org/10.1146/annurev.earth.32.082503.144359

Martinec, Z., 2000:
Spectral-Finite Element Approach for Three-Dimensional Viscoelastic Relaxation in a Spherical Earth
Geophysical Journal International, 142, p. 117—141 , https://doi.org/10.1046/j.1365-246x.2000.00138.x

Klemann, V., Martinec, Z., Ivins, E.R., 2008:
Glacial Isostasy and Plate Motions
Journal of Geodynamics, 46, p. 95—103 , https://doi.org/10.1016/j.jog.2008.04.005

Degree 1 Time Series

The spherical harmonic coefficients of degree 1 (C10, C11, S11) are related to the distance between the Earth's centre of mass (CM) and centre of figure (CF), which is commonly denoted as geocenter motion. However, a GRACE-like mission as sensor system is insensitive to CF so that the coefficients C10, C11 and S11 are not estimated and thus set to zero by definition.

To add information about geocenter motion to our Level-2B/Level-3 products, which is essential to correctly quantify both oceanic and terrestrial mass distributions, we approximate those coefficients according to the method of Swenson et al. (2008) implemented at GFZ as described by Bergmann-Wolf et al. (2014) and insert them into the Level-2B products.

Swenson, S., Chambers, D., Wahr, J., 2008:
Estimating geocenter variations from a combination of GRACE and ocean model output
Journal of Geophysical Research: Solid Earth, 113, B08410 , https://doi.org/10.1029/2007JB005338

Bergmann-Wolf, I., Zhang, L., Dobslaw, H., 2014:
Global eustatic sea-level variations for the approximation of geocenter motion from GRACE
Journal of Geodetic Science, 4, p. 37—48 , https://doi.org/10.2478/jogs-2014-0006

Aliased Tidal Signals

A global ocean tide model is used as a background model during GRACE/GRACE-FO Level-2 gravity field processing to remove ocean tide signals. However, errors are present in ocean tide models (Stammer et al., 2014), and these errors are known to be amongst the largest error sources in GRACE-like gravity field recovery (Flechtner et al., 2016). Apart from model errors, additional gravity field errors are caused by temporal aliasing of ocean tide signals (e.g. Murböck et al., 2014).

A prominent alias frequency in the GRACE gravity fields has a period of 161 days which is likely caused by model errors of the semi-diurnal solar tide S2 present in both ocean and atmosphere. A harmonic signal at this frequency is estimated together with bias, linear trend, annual, and semi-annual components over the same period as mentioned above for the calculation of the mean field and subtracted from each monthly Level-2B product.

Stammer, D. et al., 2014:
Accuracy assessment of global barotropic ocean tide models
Reviews of Geophysics, 52, 3, p. 243—282 , https://doi.org/10.1002/2014RG000450

Flechtner, F., Neumayer, K.H., Dahle, C., Dobslaw, H., Fagiolini, E., Raimondo, J.-C., Güntner, A., 2016:
What Can be Expected from the GRACE-FO Laser Ranging Interferometer for Earth Science Applications?
Surveys in Geophysics, 37, 2, p. 453—470 , https://doi.org/10.1007/s10712-015-9338-y

Murböck, M., Pail,. R., Daras, I., Gruber, T., 2014:
Optimal orbits for temporal gravity recovery regarding temporal aliasing
Journal of Geodesy, 88, p. 113—126 , https://doi.org/10.1007/s00190-013-0671-y