Brief description of the algorithm for computation of 3D 
displacement caused by the land water storage loading.
The computation procedure follows these steps:

1) Land water storage loading is computed using the surface 
pressure field at an equi-angular latitude/longitude grid with 
resolution 5401x10800 derived from the output of a continental 
water storage model. Soil moisture, water equivalent of snow cover 
and water contents in canopy are converted into pressure exerted 
to the Earth's surface.

2) The land/water mask was derived from the MOD44W model using the 
following procedure: a) original MOD4WW mask was re-sampled to 
resolution 86400x43000 over longitude and latitude. Lakes bigger than 
two cells of the land water pressure, i.e. 7 km are considered as water. 
Changes in bottom pressure of these lakes due to changes in their level 
are not accounted for and their contribution to loading displacements 
is set to zero. Glaciers with surface bigger than two cells are counted 
as water. Therefore, changes in the bedrock pressure exerted by 
glaciers are not accounted for and their contribution to loading 
displacements is set to zero. b) spherical harmonics transform of 
degree/order 21,599 was performed; c) the spherical harmonics transform 
of the mask was multiplied by Blackman window of degree/order 2,699; 
d) the inverse spherical harmonics transform of degree/order 2,699 was 
performed over the results to for, the final bandlimited land-sea mask 
with resolution 10800x5401 over longitude and latitude (2'x2'or ~3.7 km). 
The land-sea mask at a given cell is a number in a range -0.0004 to 
1.0006 that is equal to the ratio of the area covered by land (i.e. 
non-ocean in this context) to the total area of the cell.
 
  3) The Love numbers have been computed using REAR software,
Melini D., Gegout P., Spada G, King M. (2014), "REAR --  a regional 
Elastic Rebound  calculator. User manual for version 1.0", available 
on-line at  http://hpc.rm.ingv.it/rear. Earth reference model STW105 
(Kustowski et al., 2007), which is an update of PREM (Dziewonski and 
Anderson, 1981) was used. The elastic rheology of the Earth derives 
from the waves speed and the density, with the top  three kilometers 
of oceanic water replaced by underneath rock materials. The model 
defines the Earth (hydrostatic) equilibrium, the pressure and the 
gravity inside the Earth; numerical computations allow to take 
compressibility into account. The Love numbers are computed in the 
coordinate system with the centrum at the center of mass of the total 
Earth: solid Earth and land water. Therefore, loading displacements 
computed with using such Love numbers are the displacements with 
respect to the center of mass of the total Earth that includes 
the land water.

  4) The land water surface pressure is multiplied by the land-sea mass
function. Then the spherical harmonic transform of degree/order 2699
is performed. The spherical harmonics expansion coefficients S(k,n) 
are scaled by factors 

   Sv(k,n) = 3*H_n/(2*n+1)/(mean_dens*mean_grav) * S(k,n) (vertical)
   Sh(k,n) = 3*L_n/(2*n+1)/(mean_dens*mean_grav) * S(k,n) (horizontal)

where H_n and L_n are loading Love numbers, k is order, n is degree, 
mean_dens is the mean density of the Earth and mean_grav is the mean 
gravity acceleration at the sea level. Two sets of scaled spherical 
harmonics are generated: vertical Sv(k,n) and horizontal Sh(k,n).

  5) Then the mass loading in the vertical direction is computed by the
inverse spherical harmonics transform of Sv. The horizontal displacements 
in the northern and eastern directions are computed as a partial 
derivative of the inverse spherical harmonics transform of Sh. The result
of these spherical harmonics transform is a global 3D displacement
field at 2'x2' (5401x10800) equi-angular grid.

  6) Sampling correction to the displacement field was applied. The 
sampling correction was computed as a product of surface pressure by the 
differences of the band-limited windowed land-sea mask with resolution 
15"x15" (464x464m) and the band-limited windowed land-sea mask with 
resolution 2'x2. The sampling correction mitigates artifacts of using 
a band-limited windowed mask truncated at degree/order 2,699 instead of 
using the true mask, which is not bandlimited to degree/order at least 
100,000. The sampling correction affects loading within 30 km of the coastal 
line.

  The displacement is computed with respect to the center of the total 
Earth's mass, including the mass of land water.

  The maximum error of displacements due to approximation used in the 
computational procedure is below 0.2 mm. The main error source in loading
displacement is the uncertainty of the model.

References:

   Petrov, L., The International Mass Loading Service, 
      Proceedings of the Reference Frames for Applications in 
      Geosciences Symposium, held in Luxembourg in October 2014, 2015. 
      DOI: 10.1007/1345_2015_218, http://arxiv.org/abs/1503.00191

   Petrov L., J.-P. Boy, "Study of the atmospheric
      pressure loading signal in VLBI observations", Journal of
      Geophysical Research, 10.1029/2003JB002500, vol. 109,
      No. B03405, 2004.
