WHAT IS 'EQUIVALENT WATER THICKNESS'?

The mass of the atmosphere is removed during processing using ECMWF fields, so these grids do not reflect atmospheric variability over land, except for errors in ECMWF.

Similarly, an ocean model is used to remove high frequency, wind and pressure-driven ocean motions. The values of that model are removed during processing. The resulting gravity fields would not reflect ocean variability if the model were perfect. To use these results over the oceans, the GRACE solutions provided here have the monthly averaged ocean model grids added back. This is the reason we provide OCEAN and LAND grids separately. The GRACE data are the same but the ocean grids have the ocean + atmosphere model added back while the land grids assume the atmosphere model removed was perfect.

Available here are changes in equivalent water thickness. The basic method is explained in Wahr et al., 1998. However, the specific processing used here is due to Chambers 2006, and the
specific details are given here. A simplified overview is given below.

SPHERICAL HARMONIC DATA VERSIONS

GRACE is a first-of-a-kind mission, so not surprisingly, revisions to the data processing are more frequent than for more mature satellite measurements.

Three centers are part of the GRACE Ground System and generate level 2 data (spherical harmonic fields): CSR (U. Texas / Center for Space Research); GFZ (GeoForschungsZentrum Potsdam); and JPL (Jet Propulsion Laboratory). Their output include spherical harmonic coefficients of the gravity field and of the dealiasing fields used to compute them.

The data we offer here are based on those produced by these data centers (the official releases of the GRACE Project), and have additional, postprocessing steps, summarized below.

At present (11/2008) Release 04 from CSR and GFZ, and 4.1 from JPL are the most current official releases from the GRACE Project. Those are input to our postprocessing steps. We call our current version 'dpc200711'.

Please download ALL MONTHS from these new solutions, dpc200711, and discard previous versions in order to work with a consistent time series.

DEGREE 2 ORDER 0 coefficients

Spherical harmonic coefficients of (degree,order) (2,0) sometimes disagree with those from satellite laser ranging. The RL02 and later solutions from all centers have more reliable (2,0) coefficients from GRACE than RL01. However, Sean Swenson (U. Colorado) pointed out a large semiannual signal over Antarctica in the (2,0) coefficients of all processing centers. Don Chambers and colleagues at the U. of Texas then pinpointed it as a 161 day fluctuation, the GRACE alias for the S2 tide. Because of this known error in the (2,0) coefficient, all (2,0) coefficients used in the grids provided here have been replaced by those from SLR (satellite laser ranging).

DEGREE 1 coefficients

GRACE cannot retrieve spherical harmonic coefficients of degree 1, proportional to the position of the Earth’s geocenter relative to an Earth-fixed reference frame. An estimate of these coefficients based on Swenson, Chambers, and Wahr, Estimating geocenter variations from a combination of GRACE and ocean model output, J. Geophys. Res., in press, 2008 is available here

POST-GLACIAL REBOUND (GLACIAL ISOSTATIC ADJUSTMENT)

The data provided here as version dpc200711 have YES been corrected with a PGR model . Specifics are described in our separate page. PGR discussion.

DESTRIPING and SMOOTHING

A source of error, whose telltale signature are N-S stripes is present in the data after the previous steps. Swenson and Wahr (2006) observed a peculiar property of the spherical harmonic coefficients associated with the striping, and designed a class of filters to remove the problem.

The GRACE satellites fly at over 400 km altitude. The gravity field weakens with altitude, and short wavelengths attenuate more than longer ones. As a consequence it is necessary to smooth short wavelengths to recover the set of masses on the Earth surface that cause the
gravity field seen by GRACE at its altitude. To reduce this source of noise, a spatial averaging smoother is applied.

The dpc200711 grids provided here are an implementation of the carefully calibrated combination of destriping and smoothing of Chambers (2006b), who calibrated his results against sea surface height corrected for climatological steric expansion and contraction. For this set, the lower 11x11 set of harmonics was left unchanged, all higher coefficients were adjusted.

Users need to be aware that the monthly grids have higher errors when the orbit is near exact repeat. Such months include July_December 2004.

The data contain no wavelength shorter than ~1,000km because the destriping filter cuts off at spherical harmonic degree 40. However, the 'bandpass' at longer wavelengths is not a uniform value of 1. Three smoothing values are given, expressed as the half-width of the equivalent gaussian smoother: For LAND, they are 0, 300 and 500 km half width. For the oceans they are 300,500,and 750 km. All these filters attenuate signal even at wavelengths longer than 1000km. The value '0' does not mean the grids are not smoothed: the cutoff at spherical harmonic degree 40 is the smoother. The 0km grids are fairly noisy relative to the weak ocean signals, but not so relative to the larger land hydrologic signals. They are provided for users who wish to average the pixels over larger areas. The SAMPLING of all grids is 1 degree in both latitude and longitude (approx. 111 km at the Equator), but that does not mean that two consecutive samples are 'independent' precisely because of the smoothing applied.

LAND CONTAMINATION OF OCEAN SIGNALS

Ocean signals are typically weaker than land signals, by factors of 2 or 3. This is true both on seasonal and interannual time scales. High latitude ocean signals are stronger than low latitude ocean signals. The spatial filters (gaussian averages) used to decrease high wavenumber error also imply that a value at an 'ocean pixel' within, say, 200 km of land, will include part of that land signal. If that land signal is very large it may overwhelm the ocean value. A special iterative procedure is applied in version dpc200711 to minimize this leakage from land signals onto ocean signals (but not the converse).

BROWSE IMAGES and NUMERIC DATA

Browse images are provided for the whole time span, for at least one dataset (CSR, or GFZ or JPL).

The time-average over the time period 1/2003 to 12/2007 of all datasets have been removed from the data (note that in previous versions we removed the 2003-2005 or 2003-2006 time-average).

The gridded data and browse images are available here

UNITS and FORMAT

• The units of the 'equivalent water thickness' are cm of water thickness
• Separate grids are provided for LAND and OCEANS, for the reasons explained above
• A document fully explaining the processing is included here.
• Separate BROWSE images are provided for oceans and land, suitable for the different dynamic range of the respective signals.
• These grids have 360 longitudes (0.5,1.5,2.5,...,359.5), and 180 latitudes (-89.5, -88.5, ..., -0.5, +0.5, ...+89.5). However, missing grid points are not included in the ascii files

The data are now provided in three formats:

GEOTIFF, suitable for GIS software
NETCDF, suitable for automatic ingestion into several software packages.
ASCII, a plain text format described below (the 'ascii' directory, not the 'ascii_0' directory).

More details on the format are provided
in this file.

TIME SPANS OF EACH MONTHLY SOLUTION

'Monthly' is used somewhat loosely: please see the TABLE OF ACTUAL DATA DAYS used for each 'monthly' solution.

TIME AVERAGE REMOVED FROM MONTHLY SOLUTIONS

Each monthly grid here represents the difference in the masses for that month, and the average over Jan 2003 to Dec 2007. If you compare against other data or model, it is critical that anomalies from the same time-average be compared. This is simple to do: for example, if using the 2004-2006, average these grids over 1/2004 to 12/2006, and subtract that one average grid from all others (including those at times outside this range).

CITATION

When using these data, please include this phrase in the acknowledgements

GRACE data were processed by D. P. Chambers, supported by the NASA MEASURES Program, and are available at http://grace.jpl.nasa.gov

and cite:

Chambers, D.P.: Evaluation of New GRACE Time-Variable Gravity Data over the Ocean. Geophys. Res. Lett., 33(17), LI7603, 2006. (PDF, 255 KB)

If you encounter any problems with the data, please contact Prof. Chambers, dchambers at marine.usf.edu. For problems with the website, or clarifications, please contact the person listed at bottom right.

REFERENCES used above:

Chambers, D.P.: Evaluation of New GRACE Time-Variable Gravity Data over the Ocean. Geophys. Res. Lett., 33(17), LI7603, 2006

Chambers, D. P: Observing seasonal steric sea level variations with GRACE and satellite altimetry, J. Geophys. Res., 111 (C3), C03010, 10.1029/2005JC002914, 2006.

Cheng, M. and Tapley, B.D.: Variations in the Earth's oblateness during the past 28 years, J. Geophys Res v109, B9, 2004

Swenson, S. C. and J. Wahr, Post-processing removal of correlated errors in GRACE data, Geophys. Res. Lett., 33, L08402, doi:10.1029/2005GL025285, 2006.

Swenson S.C , D. P. Chambers, and J. Wahr: Estimating geocenter variations from a combination of GRACE and ocean model output. J Geophys. Res.-Solid Earth, Vol 113, Issue: B8, Article B08410. 2008.

Wahr, J., M. Molenaar, and F. Bryan, Time-variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE, J. Geophys. Res., 103, 32,20530,229, 1998.