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Ocean loading: Difference between revisions
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::: <math>\Delta {\mathbf r}</math> is the site displacement vector in (radial, west south) coordinates. | ::: <math>\Delta {\mathbf r}</math> is the site displacement vector in (radial, west south) coordinates. | ||
:::<math>j</math> represents 11 tidal waves: <math>M_2</math>, <math>S_2</math>, <math>N_2</math>, <math>K_2</math>, <math>K_1</math>, <math>O_1</math>, <math>P_1</math>, <math>Q_1</math>, <math>M_f</math>, <math>M_m</math>, <math>S_{sa}</math>. | :::<math>\displaystyle j</math> represents 11 tidal waves: <math>\displaystyle M_2</math>, <math>\displaystyle S_2</math>, <math>\displaystyle N_2</math>, <math>\displaystyle K_2</math>, <math>\displaystyle K_1</math>, <math>\displaystyle O_1</math>, <math>\displaystyle P_1</math>, <math>\displaystyle Q_1</math>, <math>\displaystyle M_f</math>, <math>\displaystyle M_m</math>, <math>\displaystyle S_{sa}</math>. | ||
:::<math>f_j</math>, <math>u_j</math> depend on the longitude of lunar node. | :::<math>\displaystyle f_j</math>, <math>\displaystyle u_j</math> depend on the longitude of lunar node. | ||
:::<math>\omega_j</math> is the tidal angular velocity at time <math>t= 0^h</math>. | :::<math>\displaystyle \omega_j</math> is the tidal angular velocity at time <math>\displaystyle t= 0^h</math>. | ||
:::<math>\chi_j</math> is an astronomical argument at time <math>t= 0^h</math>. | :::<math>\displaystyle \chi_j</math> is an astronomical argument at time <math>\displaystyle t= 0^h</math>. | ||
:::<math>A_{cj}</math> is a station specific amplitude. | :::<math>\displaystyle A_{cj}</math> is a station specific amplitude. | ||
:::<math>\varphi_{cj}</math> is a station specific phase. | :::<math>\displaystyle \varphi_{cj}</math> is a station specific phase. | ||
Revision as of 12:48, 6 February 2012
| Fundamentals | |
|---|---|
| Title | Ocean loading |
| Author(s) | J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain. |
| Level | Intermediate |
| Year of Publication | 2011 |
This is a secondary tidal effect, due to the elastic response of the earth's crust to ocean tides, producing deformation of the sea floor and a surface displacement of an adjacent land.
The ocean loading is more localised than the solid earth tides and for convention it does not have permanent part. For kinematic PPP (see Code and Carrier Based Positioning (PPP)) at the few centimetres accuracy level or few millimetres static PPP over [math]\displaystyle{ 24 }[/math] hours and/or far from the oceans, it can be neglected [Kouba and Heroux, 2000] [1].
A model for the ocean loading is described in the IERS Conventions document [Denis et al., 2004] [2], page 73, whose simplified version can be summarised as [footnotes 1][3]:
- [math]\displaystyle{ \Delta {\mathbf r}= \sum_{j} f_jA_{cj}\cos \left (\omega_jt+\chi_j+u_j-\Phi_{cj} \right ) \qquad\mbox{(1)} }[/math]
where:
- [math]\displaystyle{ \Delta {\mathbf r} }[/math] is the site displacement vector in (radial, west south) coordinates.
- [math]\displaystyle{ \displaystyle j }[/math] represents 11 tidal waves: [math]\displaystyle{ \displaystyle M_2 }[/math], [math]\displaystyle{ \displaystyle S_2 }[/math], [math]\displaystyle{ \displaystyle N_2 }[/math], [math]\displaystyle{ \displaystyle K_2 }[/math], [math]\displaystyle{ \displaystyle K_1 }[/math], [math]\displaystyle{ \displaystyle O_1 }[/math], [math]\displaystyle{ \displaystyle P_1 }[/math], [math]\displaystyle{ \displaystyle Q_1 }[/math], [math]\displaystyle{ \displaystyle M_f }[/math], [math]\displaystyle{ \displaystyle M_m }[/math], [math]\displaystyle{ \displaystyle S_{sa} }[/math].
- [math]\displaystyle{ \displaystyle f_j }[/math], [math]\displaystyle{ \displaystyle u_j }[/math] depend on the longitude of lunar node.
- [math]\displaystyle{ \displaystyle \omega_j }[/math] is the tidal angular velocity at time [math]\displaystyle{ \displaystyle t= 0^h }[/math].
- [math]\displaystyle{ \displaystyle \chi_j }[/math] is an astronomical argument at time [math]\displaystyle{ \displaystyle t= 0^h }[/math].
- [math]\displaystyle{ \displaystyle A_{cj} }[/math] is a station specific amplitude.
- [math]\displaystyle{ \displaystyle \varphi_{cj} }[/math] is a station specific phase.
The FORTRAN code hardisp.f implementing the full IERS conventions Solid-Tides model is available at ftp://tai.bipm.org/iers/convupdt/chapter7/hardisp/HARDISP.F
This routine computes time series of tidal displacements from a input file containing the ocean loading coefficients for a given station. These coefficients can be obtained from the ocean loading service under request trough the web site http://www.oso.chalmers.se/~loading
Notes
- ^ Additional information describing the model of GIPSY-OASIS II can be found in [Webb and Zumberge, 1993]
References
- ^ [Kouba and Heroux, 2000] Kouba, J. and Heroux, 2000. GPS Precise Point Positioning using IGS Orbit Products. Geodetic Survey Division, Natural Resources Canada.
- ^ [Denis et al., 2004] Denis, D., McCarthy and Petit, G., 2004. IERS Conventions (2003). IERS Technical Note 32.. IERS Convention Center., Frankfurt am Main.
- ^ [Webb and Zumberge, 1993] Webb, F. and Zumberge, J., 1993. An Introduction to GIPSY/OASIS-II. Jet Propulsion Laboratory, JPL, 4800 Oak Grove Drive, Pasadena, CA 91109