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S1 and S2 Atmospheric Tide Loading Calculator - Based on the Proposed IERS Conventions...PRELIMINARY UNTIL CONVENTIONS ARE APPROVED

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. Data set/Moddel accessed YYYY-MM-DD at

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:

Radial surface displacement
from S1 and S2 atmospheric tides

(click on image to enlarge as a downloadable pdf file).

The International Earth Rotation Service (IERS) Directing Board is currently considering the recommendatation that the periodic displacements of the Earth driven by the S1 and S2 atmospheric tidal model of Ray and Ponte [2003] be included in the station motion model.

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:

Finally, we provide corrections for both the center of mass of the solid Earth system (Earth+load=CM) and the center of the solid Earth (CE).

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

Method 1: How to Use the Online Calculator:

The On-line Generator takes as input the latitude and longitude of sites where the effects of atmospheric tidal loading are to be computed. The program convolves the 4 annual mean tidal pressure fields (Cosine S1, Sine S1, Cosine S2, Sine S2) [Ray and Ponte, 2003] which are global in extent and have a spacing of 1.125 deg x 1.125 deg in latitude and longitude, with Farrell's Green's Functions in the appropriate reference frame. No ocean response to pressure is assumed.

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 :

Then, for example, the total radial displacement at the sites for any epoch is determined using:

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.

Select reference frame in which displacements are requested:


Select output format:

Amplitudes of Sines and Cosines for S1 and S2
Amplitudes and phases for S1 and S2

Where are your stations located?

Paste your space, tab, comma or semicolon separated data here.

Station [4 chars a-z]Longitude [deg]Latitude [deg]

Method 2: Using the Displacement grids:

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.