Method 2: Using the Displacement grids


T. M. van Dam, University of Luxembourg
R. Ray, Space Geodesy Branch, NASA Goddard Space Flight Center

Anyone using this data set directly or products derived from this page is requested to use the following citation:
van Dam, T. and R. Ray, 2010, Updated October 2010. S1 and S2 Atmospheric Tide Loading Effects for Geodetic Applications.

  • The displacement grids are determined at every 1.0 degree of latitude and longitude
  • They have been calculated by convolving 1.125 deg x 1.125 deg S1 and S2 annual mean atmospheric tides
    [Ray and Ponte, 2003] with Farrell's Green's Functions
  • We assume no ocean response to pressure
  • To use the grids and interpolate yourself you must:
    1. Download at least one of the following files
    2. If you do not already have a program for interpolating evenly spaced grid points, you may download, grdintrp.f
  • CE, and CM designate the reference frame in which the displacements are determined. See Blewitt [2003] for further information
  • The ascii grids contain the up (dr), north (vt) and east (vl) components of the sine and cosine amplitudes for the S1 and S2 tides
    1. The deformations are in mm
    2. Each displacement component has 4 parameters: cosS1,sinS1,cosS2,sinS2 written in that order in the file
    3. To read the grids:
      do i=1,nlon (nlon=361)
      do j=1,nlat (nlat=181)
      read(iun,*) rlon,rlat,(dr(k),k=1,4),(vt(k),k=1,4),(vl(k),k=1,4)
      end do
      end do
    4. total dr(t) = dr(1)*cos(t*ω1) + dr(2)*sin(t*ω1) + dr(3)*cos(t*ω2) + dr(4)*sin(t*ω2)
    5. If t is in fractions of a UT1 day, then ω1=2π radians/day and ω2=4π radians/day
  • If you will use your own routine to interpolate the grids, you do not need to muddle through the remainder of this document;
    If you need information on running the supplied interpolation routine, grdintrp.f, please continue
  • To run grdintrp.f:
      1. You will need to specify the input file to read from in grdintrp.f (variable=iref)
      2. You will need to specify the output format in grdintrp.f (variable=iout)
      3. The program reads 3 variables: STA, longitude, latitude from a file that you create called in.grdintrp

    bjfs 115.892487 39.6086006
    blyt 245.285156 33.6104164
    bogt 285.919067 4.64007235
    bor1 17.0734558 52.2769585
    bran 241.722961 34.1848946
    bras 11.1130829 44.1221657
    braz 312.122131 -15.9474754

    1. Note: currently grdintrp.f expects STA to be 4 characters in length, you (of course) must change this specification if you use longer character names
    2. Customize the program to address your own particular needs
    3. Compile the program using your favorite fortran compiler; on UNIX or LINUX: f77 grdinterp.f -o grdinterp
    4. Run program (Type grdintrp at the system prompt)
  • The output file is named grdintrp.dat
  • Data in these files can be used to generate a time series of the surface displacement at the site
    1. total dr(t) = dr(1)*cos(t*ω1) + dr(2)*sin(t*ω1) + dr(3)*cos(t*ω2) + dr(4)*sin(t*ω2)
    2. If t is in fractions of a UT1 day, then ω1=2π radians/day and ω2=4π radians/day.

Center of Mass Corrections:

As with ocean loading, it may be necessary to compute the crust-frame translation (geocenter motion) due to the atmospheric tidal mass, dX(t),dY(t), and dZ(t). These values may be computed according to the method given by Scherneck at∼loading/cmc.html. For example,

dX(t)=A1*cos(t*ω1)+ B1*sin(t*ω1) A2*cos(t*ω2) +B2*sin(t*ω2)

If t is in fractions of a UT1 day, then ω1=πradians/day and ω2=2πradians/day

  1. Download the COM corrections here As with ocean tidal loading, this correction should be applied in transforming GPS orbits from the CM frame to the CF frame expected in the sp3 orbit.


  • Blewitt, G. (2003), Self-consistency in reference frames, geocenter definition, and srface loading of the solid Earth, J. Geophys. Res., ,108, 2103, doi:10.1029/2002JB002082.
  • Farrell, W. E. (1972), Deformation of the Earth by surface loads, Rev. Geophys., 10, 761-797.
  • Ray, R.D. and R.M. Ponte (2003), Barometeric tides from ECMWF operational analyses, Annales Geophysicae, 21, 1897-1910.
  • Ray, R.D. and G. Egbert (2004), The global S_1 tide, J. Phys. Oceanogr., 34, 1922-1935.