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I have recently started working on calculating a Geopotential model based on GGM05C. In order to obtain a model as accurate as possible, some corrections must be applied to the normalized Stokes' coefficients provided in GGM05C (Cnm and Snm).

Chapter 6 of this IERS note describes in detail the process. From my understanding, it comprises 5 types of corrections: secular (long-term) corrections, solid Earth tides corrections, ocean tides corrections, solid Earth pole tides corrections and ocean pole tides corrections.

I have been able to grasp the idea behind each of these (or so I hope!), except for the case of ocean tides. The main difference I see with all the other corrections (including solid Earth tides) is that the corrections due to each frequency of ocean tides comprises a positive and negative component (both on the Cnm and the Snm components), which, if I understand correctly, must be added before applying the total, resulting correction to the corresponding Cnm/Snm. See for example equation 6.15 here. This will then lead to partial cancellation between the 2 (positive and negative) parts. But why is this the case? Both solid Earth tides and ocean tides seem to be an ensemble of periodic effects with different frequencies and amplitudes, but they seem to be treated differently. Why don't we have directly just a single term for each Cnm/Snm, as is the case for solid Earth tides?

I am also puzzled by the fact that ocean pole tides do not comprise the same combination of positive and negative terms, and are instead modeled as a single component as can be seen in equations 6.24 here, in a very similar way as done for the solid Earth pole tides.

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I don’t know for sure that the feature of ocean tides I am about to describe is the reason, or the only reason, for the difference in treatment you ask about. But it seems likely.

Unlike the other corrections, ocean tides have a complicated spatial structure. The forcing is of course exactly the same as it is for earth tides, but the response is very different. Whereas earth tides basically distort the entire sphere slightly, the ocean tides behave like waves, excited by astronomical forcing but constrained by the boundaries and bathymetry of ocean basins. The result is, again, complicated: if you look at a world map of the phase of, say, the M2 (lunar semi diurnal) tide, you’ll see many amphidromic points around which high and low tides propagate. It looks nothing like a map of earth tide phase—lines of constant earth tide phase would look a lot like meridians. It does not seem surprising that accounting for the gravitational effects of the more complicated spatial structure of ocean tides would require a more complicated treatment.

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  • $\begingroup$ I see, thanks a lot! It makes indeed sense that, due to the very different response, the treatment also needs to be different. I'm still going through it but I think I start to intuitively understand from where this treatment is coming! $\endgroup$
    – Rafa
    Jan 23, 2022 at 4:53

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