How to define tidal constituent SA?

[stef]

I have a general oceanography question about the tidal constituent SA. Does it have the period of a tropical or anomalistic year?

I know it's not directly related to ROMS. Sorry, but currently I don't know where else to ask.

In the harmonic analysis packages [1] and [2], SA is defined as inverse of an anomalistic year. For example, in T_Tide ([2], see file tide3.dat), it has Cartwright numbers (0 0 1 0 0 -1), where the "1" is the frequency for a tropical year, and the "-1" for the rotation of the perihelion. In the same file the frequency for SA is 0.0001140741 cph, i.e. a period of about 365.2596 days, consistent with the Cartwright numbers.

In [3], it's apparently defined as inverse of a tropical year. Table A.1 of [3] lists Cartwright numbers of (0 0 1 0 0 0) and an angular speed of 0.0410686 deg/h, which corresponds to a tropical year (consistent with Table 2.1 of [3], where the fundamental astronomical periods are listed). However, on their p. 38, [3] state that:

Sa and Ssa are very small tidal constituents directly generated by the nonuniform changes in the Sun's declination and distance (the perihelion-aphelion effect).

Isn't this a contradiction? Wouldn't one need (0 0 1 0 0 0) for the declination (tropical year), and than a modulation thereof for the perihelion rotation, using (0 0 1 0 0 -1) and (0 0 1 0 0 1). But NOAA seems to generally use the tropical year (see e.g. [4], same angular speed for SA as in [3]). Why??

Also, I just noticed that in the original Cartwright and Taylor/Edden papers [5], the Cartwright number (0 0 1 0 0 0) does not even exist in the tables. Only (0 0 1 0 0 -1) is listed there.


Do people not differentiate because in practical timeseries analysis (harmonic analysis, Fourier analysis etc.) we have no records long enough to separate them?

[1] Foreman M.G.G, 1977: Manual for Tidal Heights Analysis and Prediction. Pacific Marine Science Report 77-10, Institute of Ocean Sciences, Patricia Bay, Sidney, B.C., 58 pp. (2004 revision)
https://www.dfo-mpo.gc.ca/science/data- ... x-eng.html

[2] Pawlowicz, R., Beardsley, B., Lentz, S., 2002: Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE.
https://doi.org/10.1016/S0098-3004(02)00013-4

[3] Parker, B.B., 2007: Tidal analysis and prediction. NOAA Special Publication NOS CO-OPS 3, U.S. Department of Commerce, 378 pp.
https://tidesandcurrents.noaa.gov/publi ... ctions.pdf

[4] https://tidesandcurrents.noaa.gov/harco ... id=8518750

[5] Cartwright, D.E., Edden, A.C., 1973: Corrected tables of tidal harmonics.
https://doi.org/10.1111/j.1365-246X.1973.tb03420.x

[johnluick]

Interesting question, Stef. I would suggest that the people concerned with earth tides might be a better group to ask than those concerned with ocean tides, because for ocean tides, Sa has a large radiational component, making it unsteady (phase and amplitude varying from year to year), whereas the influence on the crust, being purely gravitational, would be quite steady (and hence the two periods you mention would be more separable in a period of a decade or two).

[stef]

Very good, thanks for the advice. The question came up indirectly because [1] don't seem to distinguish between "H1" (aka "alpha_2")in the Foreman software, with Cartwright number (2 0 -1 0 0 1), and the "MA_2" constituent proposed by [2], which IMHO should have Cartwright number (2 0 -1 0 0 0). So I think they are just using different definitions of SA, that's the root cause of the confusion.

Also, I found a constituent list by the IHO [3], which distinguishes them all. It lists two versions of Sa, unfortunately without explaination. I'll send them an email, maybe they can explain is in future versions of the document. It's confusing for beginners...

[1] Müller, M., Cherniawsky, J.Y., Foreman, M.G., von Storch J.S., 2014: Seasonal variation of the M2 tide.
https://link.springer.com/content/pdf/1 ... 0679-0.pdf

[2] Corkan, R.H., 1934: An annual perturbation in the range of tide.
https://royalsocietypublishing.org/doi/ ... .1934.0067

[3] https://iho.int/mtg_docs/com_wg/IHOTC/I ... t_list.pdf

[stef]

Wow, I just saw that appendix A of [1] explains it very well, and it's open access!

[1] Ray, R.D., Loomis, B.D. & Zlotnicki, V. The mean seasonal cycle in relative sea level from satellite altimetry and gravimetry.
https://link.springer.com/article/10.10 ... 21-01529-1

[johnluick]

Hi Stef, thanks for bringing that Ray et al article to my attention, and I am sure others would be interested too. The same point is made in Pugh (Tides, Surges, and Mean Sea Level) on page 314 of the 1987 edition that I have, but Ray et al go into greater detail and make the point more explicitly that as long as one is consistent (ie, use the same convention in predictions as was used in the analysis) it makes little difference. (If one is not consistent, the phase will be out of whack.) Actually the same is true of many harmonics, not just SA. Again, as I said before, for ocean tides the seasonal effects (tropical year) dominate over the gravitational effects (anomalistic year) so it makes sense to use the tropical year, whereas for earth tides, presumably the opposite is true. By the way, I do not remember seeing what I call the "Doodson Numbers" called "Cartwright Numbers". Did I miss something?

[stef]

Again, as I said before, for ocean tides the seasonal effects (tropical year) dominate over the gravitational effects (anomalistic year) so it makes sense to use the tropical year, whereas for earth tides, presumably the opposite is true.

Thanks for pointing this out again, I had not fully understood it reading your previous post. I guess the term "radiational tide" made me think of S1, and not generally of "meteorological tide", but if I understand correctly, the terms are used synonymously to some extent. But now I get it: earth tides are much less affected by meteorology than the ocean tides, so the gravitational SA is more important!


The term "Cartwright number" is used e.g. by [1]. From their sec. 2.2.3. p. 39:

Cartwright numbers are the same as the Doodson numbers but without the added 5's

I see that you use the term "Doodson number" without the added 5's in your publication [2].

[1] Parker, B.B., 2007: Tidal analysis and prediction. NOAA Special Publication NOS CO-OPS 3, U.S. Department of Commerce, 378 pp.
https://tidesandcurrents.noaa.gov/publi ... ctions.pdf

[2] Kowalik, Z., Luick, J.L., 2019: MODERN THEORY AND PRACTICE OF TIDE ANALYSIS AND TIDAL POWER
https://uaf.edu/cfos/files/research-pro ... _tides.pdf