Global grids of ocean tide loading displacements and more


Download the tar file of 3-D displacements   (or xz-compressed)
(renewed 2017-DEC-25 14:40 UTC)
renewed again 2018-JAN-07 20:00 UTC

Download the tar file of Tide generating potential due to ocean load (260 Mb) (or xz-compressed, 175 Mb)
Please send a note to  hgs kanelbulle chalmers dot se  if you download the tar. I will notify you of subsequent updates.

Displacements have been computed with an FFT-accelerated algorithm. This implies reduced precision with respect to site-specific calculations using the Free Ocean Loading Provider. Coastlines could not be resolved beyond the tide models' grid constant.

Use of the grids might be helpful in those cases when loading parameters are needed off-line, when maps are to illustrate a regional setting, etc.

The grid files have been derived from the ocean tide model TPXO.7.2 (Oregon State University, 2010). They are available in netCDF format. For each partial tide (of which there are 11) and component they come in pairs of amplitude (m) and phase (degrees, oceanographer convention). For example in the case of the M2 the tar contains
RADI_amp.m2  RADI_pha.m2
EAST_amp.m2  EAST_pha.m2
NRTH_amp.m2  NRTH_pha.m2
Choice fell on the TPXO.7.2 model since it has a reasonably high resolution (grid constant 0.25 deg) and thus a manageable size for distribution. The grids were computed within a few hours. At the resolution 1/16 degrees as in the case of FES2014b, each pair of fields needs 1:20 hours to compute. The tangential components are actually the result of a finite-difference operation on a scalar, potential-like field.     

The Greens function for the loading effects has been computed with Astyanax (Machiel S. Bos) for an anelastic, spherically symmetric earth with PREM structure.
More information on this aspect will be included soon.

Phasor plots comparing the new sets with respect to alternate ocean models and with the solutions of the Free Ocean Loading Provider have been produced for a set of 30+ critical sites, most of them located near coasts.

The grd-files can be processed with GMT grd-utilities (Wessel et al., 2013). Use option -Rg to access the entire region and preserve the implication of global.
Interpolation to retrieve parameters at random locations, however, urges that grdmath is used to first convert from polar (amp, pha) to plane (real, imag) representation, e.g.
grdmath RADI_pha.m2 COSD RADI_amp.m2 MUL = RADI_re.m2
grdmath RADI_pha.m2 SIND RADI_amp.m2 MUL = RADI_im.m2
Then you can use grdtrack on each of the grids _re, _im
Example:
echo 11.936 57.396 | grdtrack -GRADI_re.m2 | awk '{print $3}' > ONSA-M2.re
echo 11.936 57.396 | grdtrack -GRADI_im.m2 | awk '{print $3}' > ONSA-M2.im
paste -d' ' ONSA-M2.re ONSA-M2.im | awk '{print sqrt($1**2 + $2**2), atan2($2,$1)}'
The last line prints the ocean loading coefficient for tide M2, radial displacement at site ONSA (longitude E 11.936, latitude N 57.396), namely amplitude Ua in metres and phase Up in radians.
To compute a time series,
u(t) = Ua cos(a(t) - Up)
where a(t) is the astronomical argument of the corresponding luni-solar tide at the zero-meridian. 

grdinfo of an amplitude file shows
RADI_amp.m2: Title: dist/RADI_amp.m2
RADI_amp.m2: Command: xyz2grd -R-180/180/-90/90 -I0.25000/0.25000 -bi -fg -Gdist/RADI_amp.m2
RADI_amp.m2: Remark:
RADI_amp.m2: Gridline node registration used
RADI_amp.m2: Grid file format: nf (# 18) GMT netCDF format (float)  (COARDS-compliant) [DEFAULT]
RADI_amp.m2: x_min:   -180.00000 x_max:    180.00000 x_inc:      0.25000 name: longitude [degrees_east] nx: 1441
RADI_amp.m2: y_min:    -90.00000 y_max:     90.00000 y_inc:      0.25000 name: latitude [degrees_north] ny: 721
RADI_amp.m2: z_min:      0.00000 z_max:      0.06277 name: z
RADI_amp.m2: scale_factor:      1.00000 add_offset:      0.00000
Note that the grid is global; thus, interpolation can succeed across the boundary at 180 degrees east/west.

Maps of the grids for tide M2 can be seen here

Radial
East
North
Tide generating potential


Reference:
    Wessel, P., W. H. F. Smith, R. Scharroo, J. F. Luis, and F. Wobbe, Generic Mapping Tools: Improved version released, EOS Trans. AGU, 94, 409-410, 2013.