GRACE MONTHLY MASS GRIDS - LAND
THE POSTPROCESSING FOR THE LAND AND OCEAN GRIDS ARE DIFFERENT
AND HAVE BEEN OPTIMIZED FOR LAND OR OCEAN APPLICATIONS.
Please download ALL MONTHS from these new solutions
and discard previous versions in order to work with a consistent time series
LAND DATA PROCESSING
- The land data are based on the RL05 spherical harmonics from CSR, JPL and GFZ
- The degree 2 order 0 coefficients are those derived from Satellite Laser Ranging by Cheng and Tapley (2004), rather than those observed by GRACE
- The degree 1 coefficients are those derived by Swenson, Chambers, and Wahr (2008)
- A postglacial rebound signal in the data has been removed according to the model of Paulson et al, 2007, as revised by Geruo A and J. Wahr (U. Colorado, 2012).
- A destriping filter has been applied to the data, to minimize the effect of an error whose telltale signal are N-S stripes in GRACE monthly maps.
- A 200 km wide gaussian filter has also been applied to the data.
- A spherical harmonic filter cutoff at degree 60 acts as a third filter on the data.
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 GRID SCALING
THE USER SHOULD MULTIPLY THE LAND GRACE DATA PROVIDED HERE BY THE SCALING GRID also provided here. The scaling grid is a set of scaling coefficients, one for each 1 degree bin of the land grids, and are intended to restore much of the energy removed by the destriping, gaussian, and degree 60 filters to the land grids. To use these scaling coefficients, any time series at one grid (1 degree bin) location must be multiplied by the scaling factor at the same 1 degree bin position.
The scaling coefficients were computed by applying the same filters applied to the GRACE data to a numerical land model (NCAR's CLM) and finding the coefficient that, when multiplied by the model smooth time series at any geographic location, best fits the unfiltered model time series at that same location. These coefficients depend on the specific land model used and are independent of the GRACE data proper, hence they are given as a separate file; furthermore, these coefficients are not suitable to retrieve trends from the land data, as they are dominated by the annual cycles of water storage, and the trends in the models are very uncertain.
DATA PROCESSING and CAVEATS DESCRIPTION FOR LAND GRIDS (PDF, 3.68 MB)
The netcdf file with scaling factors is CLM4.SCALE_FACTOR.DS.G300KM.nc in the netcdf directory , and it must be applied to the GRACE grids in the same directory (an identical grid in ascii format can be found in the ascii directory) .
NOT SUITABLE FOR CRYOSPHERIC STUDIES
These grids are not suitable for quantitative studies of Greenland or Antarctica, or glaciers and ice caps. In those regions one must use region-specific mass distributions, one must remove contamination from nearby land hydrology, and not only traditional GIA but in certain regions one must remove the continuing effects of the deglaciation from the Little Ice Age. We recommend the paper by Jacob et al (Nature 2012, full citation below), including the online supplement, for a thorough discussion of these topics.
The units of the 'equivalent water thickness' grids are cm of water thickness. The units of the error grids are cm. The scaling factors are dimensionless. If each grid node is g(x,y,t) where x is longitude index, y is latitude index, t is time (month) index, and the scaling grid is s(x,y), then the time series is simply
g'(x,y,t) = g(x,y,t)*s(x,y)
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 provided in
- NETCDF format, suitable for automatic ingestion into several software packages.
- ASCII, a plain text format (compressed with gzip)
- Error estimates due to the measurement and errors due to leakage are also provided, in separate files (ascii) or together with the scaling coefficient file (netcdf).
To compute error estimates for the scaled values, two additional grids are provided (as separate ASCII files or in the same netCDF file as the scaling coefficients).
1. The errors given in CLM4.*.DS.G300KM.txt are in millimeters (not centimeters, like the data).
2. The measurement errors have already been scaled so no further multiplication is necessary.
3. The leakage errors are residual errors after filtering and rescaling, such that the total error in Total Water Storage for a given grid pixel is:
total_err_pix = sqrt(leakage_err_pix^2+measurement_err_pix^2).
4. The errors in nearby pixels are correlated. Therefore, if the total error in a region of adjacent pixels is desired, this covariance needs to be considered. Here is pseudocode to get the total leakage (lerr) and measurement (merr) errors for a region:
var_merr = 0. ; measurement error
var_lerr = 0. ; leakage error
betam = 300. ; km ~ mearement error de-correlation length
betal = 100. ; km ~ leakage error de-correlation length
for i=0, npix-1 do begin
for j=0, npix-1 do begin
dist = sqrt((lon[i]-lon[j])*cos(lat[i]))^2.+(lat[i]-lat[j])^2.) * (pi/180) * 6371. ; lon, lat in degs, dist in km
expdbm = exp(-(dist^2.)/(2.*betam^2.))
expdbl = exp(-(dist^2.)/(2.*betal^2.))
var_merr = var_merr + merr[i] * merr[j] * expdbm
var_lerr = var_lerr + lerr[i] * lerr[j] * expdbl
sigma_merr = sqrt(var_merr)/npix
sigma_lerr = sqrt(var_lerr)/npix
(Note: This formula corrects an error present in the pseudo code until 2011-09-11; we thank F. Landerer for the correction)
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 2004 to Dec 2009. 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).
BROWSE IMAGES and NUMERIC DATA
The LAND gridded data and browse images are available here
ACKNOWLEDGEMENT and CITATION
When using these data, please acknowledge
GRACE land data were processed by Sean Swenson, supported by the
NASA MEaSUREs Program, and are available at http://grace.jpl.nasa.gov
Landerer F.W. and S. C. Swenson, Accuracy of scaled GRACE terrestrial water storage estimates. Water Resources Research, Vol 48, W04531, 11 PP, doi:10.1029/2011WR011453 2012.
Swenson, S. C. and J. Wahr, Post-processing removal of correlated
errors in GRACE data, Geophys. Res. Lett., 33, L08402,
If you encounter any problems with the data, please contact the person listed at bottom right.
ADDITIONAL REFERENCES used above:
Cheng, M. and Tapley, B.D.: Variations in the Earth's oblateness during the past 28 years, J. Geophys Res v109, B9, 2004
Jacob T., J. Wahr, W.T.Pfeffer, and S. Swenson, Recent contributions of glaciers and ice caps to sea level rise. Nature 2012. doi:/10.1038/nature10847
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.
LAST UPDATE: 2012-10-29 Zheng Qu, V.Zlotnicki, F. Landerer. We thank Holly Maness and Sean Swenson for their contributions.