R. Ray, Space Geodesy Branch, NASA Goddard Space Flight Center

The amplitude and phase of the predicted deformation of the diurnal, *S1*, and semi-diurnal, *S2*, tides derived from the *Ray and Ponte* model [2003], using *Farrell's* [1972] elastic Green's functions in the center of earth frame (CM) are shown here:

(click on image to enlarge as a downloadable pdf file). |
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This web site provides users with two options for computing the 3-dimensional deformations of the earth due to the *S1* and *S2* atmospheric tides:

- Have us compute the results for any number of sites using a global convolution
- Download gridded 3-D deformations and a fortran program for interpolating the gridded 3-D deformations to any point

There is no difference between the results. The user must decide which product suits their applications most appropriately.

To use the online calculator, you must chose the reference frame that you would like the results in and the output format, either amplitudes and phases or the amplitudes of the sines and cosines for the S1 and S2 tides.

The output data for each station is :

- row 1: radial displacement (mm): dr(1), dr(2), dr(3), dr(4)
- row 2: tangential NS displacement (mm): dn(1), dn(2), dn(3), dn(4)
- row 3: tangential EW displacement (mm): de(1), de(2), de(3), de(4).

dr(t) = dr(1)*cos(t*ω1) + dr(2)*sin(t*ω1) + dr(3)*cos(t*ω2) + dr(4)*sin(t*ω2)

where *t* is in fractions of a UT1 day, and
ω1=2πradians/day and
ω2=4πradians/day.

- 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:
- Download at least one of the following files
- 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- The deformations are in mm
- Each displacement component has 4 parameters: cosS1,sinS1,cosS2,sinS2 written in that order in the file
- 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 - total dr(t) = dr(1)*cos(t*ω1) + dr(2)*sin(t*ω1) + dr(3)*cos(t*ω2) + dr(4)*sin(t*ω2)
- 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*: - You will need to specify the input file to read from in
*grdintrp.f*(variable=*iref*) - You will need to specify the output format in
*grdintrp.f*(variable=*iout*) - The program reads 3 variables: STA, longitude, latitude from a file that you create called
*in.grdintrp* - 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 - Customize the program to address your own particular needs
- Compile the program using your favorite fortran compiler; on UNIX or LINUX: f77 grdinterp.f -o grdinterp
- 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
- total dr(t) = dr(1)*cos(t*ω1) + dr(2)*sin(t*ω1) + dr(3)*cos(t*ω2) + dr(4)*sin(t*ω2)
- If
*t*is in fractions of a UT1 day, then*ω1=2π radians/day*and*ω2=4π radians/day*.

e.g.

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

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

If- 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.
#### References

- 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.

- Blewitt, G. (2003), Self-consistency in reference frames, geocenter definition, and srface loading of the solid Earth,