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Data are values of elastic surface loading deformations (radial, horizontal, gravity) calculated by a patched Greens function approach. Loading values are given on a 0.5°x0.5°regular global grid for 24h (HYDL) or 03h (NTAL, NTOL) time steps.

For more information on the individual mass loading data please look for the appropriate README file in each subdirectory.

When using loading data, the data and the approach should be cited as

Dill, R. and H. Dobslaw (2013), Numerical simulations of global-scale high-resolution hydrological crustal deformations,
J. Geophys. Res. Solid earth 118, doi:10.1002/jgrb.50353.

Extract data subsets:
Data sets are organized in folders as aggregated girds. Thus the parent folder can serve like one combined data set of all its individual subfolders and files. Data files are joined along the time axis.
URL commands
URL commands allow to query for data subsets and extract time series at specific grid points. Please be aware that via URL commands or the button 'Extract Time Series' only nearest neighbour interpolation will be performed.
extractlatlon_bilinintp_remote (please use only the UPDATED VERSION from 2022-09-05)
Run the bash remote script locally on your machine to download station time series. The script downloads the time series around the station location and performs bilinear interpolation. It is also possible to download station time series for sums of loading products, e.g. NTAL+NTOL or NTAL+HYDL.
For the local bash script you have to download the relevant datasets, concatenate them and run the script on your local machine. This might be faster for a larger number of stations. The local script performs fast bicubic interpolation from the 0.5° gridded values to the station location using NCO and CDO libraries. If CDO operators are not available on your machine, only slow bilinear interpolation is possible. For a large number of stations using CDO operators works much faster! Do not use CDO version 1.6.4 as it cannot handle unstructured grids (tested with CDO version 1.7.2).

You can use the -m option to avoid interpolation over the coastline as the deformation response might be completely different between ocean and land due to a high contrast in the mass load along the coastline (e.g. IB correction over the ocean). The appropriate land/ocean mask file is With option -m the script uses nearest-neighbour interpolation, if the station is located along the coastline to avoid bicubic interpolation over the coastline between ocean and land gridcells. For time series of total loading (NTAL+NTOL+HYDL) it is recommended to add the gridded NTAL, NTOL, and HYDL contributions in advance and extract the station time series afterwards, the -m option might become redundant. With the script extractlatlon_bilinintp_remote it is also possible to download NTAL+NTOL+HYDL .

Requests of loading time series with the remote script can take a bit of time to fulfill, especially for larger aggregations like NTAL time series over 40 years, so please be patient. You can approximately calculate with:

  • 40-60 sec for 3-hourly data, e.g. NTAL, NTOL, NTAL24h, NTAL+NTOL, NTAL+HYDL
  • 3 sec for 24-hourly, e.g. HYDL, SLEL
per station, per year.

Loading Approach (Patched Green's Function Approach):
Elastic surface deformations are calculated in the spatial domain by convolving loading Green's function with with modelled mass destributions from the models ECMWF, MPIOM, LSDM. Spatial calculation are performed on a 0.125° x 0.125° global grid in the near-field (0° - 3.5°) and on a 2.0° x 2.0° grid in the far-field (3.5° - 180°). Gridded loading displacements are stored on a regular 0.5° x 0.5° global grid with 24h (HYD, SLEL) / 03h (NTAL, NTOL) according to the time steps of the modelled mass datasets. The loading Green's functions are computed in the center of Earth's figure frame (CF) and the center of Earth's mass (CM) on the basis of load Love numbers given for the elastic Earth model "ak135" (Kennett et al., 1995).

According to Farrell (1972) the displacements at a gridcell center with coordinates (lon,lat) at time t due to all global gridded mass loads dm at gridcells (i,j) are given by

duV(lon,lat,t) = sum( dm(i,j,t)*Gr(D) )
duNS(lon,lat,t) = sum( -dm(i,j,t)*Gh(D) * cos(A) )
duEW(lon,lat,t) = sum( -dm(i,j,t)*Gh(D) * sin(A) )
dg(lon,lat,t) = sum( dm(i,j,t)*Gg(D) )

where D is the angular distance from (lon,lat) to (i,j) and A is the azimuth.

The Green's functions are defined by

Gr(D) = R/M * sum( hn * Pn(cos(D)) )
Gh(D) = R/M * sum( ln 1/dD * dPn(cos(D)) )
Gg(D) = g/M * sum( n+2hn-(n+1)kn) * Pn(cos(D)) )

with R=6371000, M=5.973e24, g are radius, mass, mean surface gravity of the Earth; hn, ln, kn are the load Love numbers of degree n for radial, horizontal, and gravitational changes due to loading, Pn is the Legendre polynomial of degree n.
Green's functions are calculated using Kummer's transformation with load Love numbers from Wang (2012) for the elastic Earth model "ak135" from degree n=1 up to 46340 and the following values for degree n=1 and infinity

CE (ak135) CM CF CE (IERS conventions)
h(1) = -0.28954527 CE -1.0 2/3(h-l) = -0.26310049 -0.28587758
l(1) = 0.10510547 CE -1.0 -1/3(h-l) = 0.13155025 0.103918207
k(1) = 0.0 CE -1.0 -1/3h-2/3l = 0.02644478 (1+k) = 1

h(inf) = -5.4630734
l(inf) = 0.000041954371
k(inf) = -0.000056284140

This Green's functions for "ak135" deviate slightly from Green's function for the "PREM" model, mostly in the near-field, angular distances below 1° (100km).

W.E Farrell. Deformation of the earth by surface loads.
Rev. Geophys. and Spac. Phys., 10(3):751-797, 1972

H. Wang et al. Load Love numbers and Green's functions for elastic Earth models PREM, iasp91, ak135, and modified models with refined crustal structure from Crust 2.0.
Computers and Geosciences, 49, 190-199, 2012

B.L.N. Kennett et al. Constraints on seismic velocities in the Earth from travel times.
Geophys. J. Int. 122, 108-124.

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