I first thought of writing this to [name removed] (Bourban), who has experience in this field already with his model of the Earth using TELEMAC.
But this topic could be of general interest because I think it affects everyone doing models at a relatively large scale and using the
TIDE GENERATING FORCE = YES
keyword.
I will try to be brief… but this is a complex topic.
I am running a global model of the Earth on an unstructured grid with TELEMAC2D. The resolution is roughly 1 km at the coastline.
I am talking now about the tide-only simulation: I cold start the model and let the tide generating force do its thing — from flat waters, the tidal cycles start to form around the Earth. TELEMAC computes the direct gravitational acceleration from the Moon and Sun, inferred from their celestial positions. I explain it in more detail in this post: https://gist.github.com/tomsail/c20cd6b6b8bcf0e4f01757ce448bcc05
To assess the quality of the model, I define a score based on two metrics:
score = corr * (1 - rss)
- *corr*
is the Pearson correlation coefficient between model and observed data (ranges from -1 to 1, clipped to 0 if lower than 0).
- *rss*
is the residual sum of squares of tidal constituent amplitudes (clipped to 1 if higher than 1).
The first results are computed using almost all default settings of T2D (Chezy constant of 30). With global models being implemented in the main branch, nothing extra is needed.
I attached the score against 420 cleaned tide gauges around the world.
Now I changed the gravity to 8.83 m/s², based on [name removed]'s suggestion. This value comes from a crude approximation done on the Delft3D-FLOW model more than 10 years ago: https://repository.tudelft.nl/file/File_8f9f49d2-6a5c-4fd9-bc74-d66c221bf640?preview=1, to compensate for SAL (Self Attraction and Loading) — e.g. the retroactive effects of the Earth tides on the oceans.
Applying this coefficient, results are indeed much better.
The worst results seen on the map are mostly because of the mesh and/or the coastal bathymetry not being properly defined (and refined), and thus the hydrodynamics not resolved well.
However, we still see differences in the shape of the signal due to a faulty definition of the actual physics in the model.
And I fear that whichever value I give to the gravity or the local bottom friction, I will never come as close as other models (like FES or probably SCHISM, which we’re about to test on the same grid).
Conclusion:
1. The modification of gravity is a quick but dirty fix.
1. The definition of the tide generating force in TELEMAC is thorough, because it sets the correct gravity forces from the Sun and the [name removed]. However, this definition is incomplete when models become very large, because it disregards Self Attraction and [name removed] effects.
1. Implementing SAL should be a priority before complexifying the model further (going 3D, adding temperature and salinity).
Question to the community:
1. Would people be interested in the definition of SAL in TELEMAC?
1. How many of you had problems with tidal amplitudes and phases in a large regional model? Did bottom friction calibration resolve all your problems?
1. To people that have modeled large enclosed Sea Basins ([group removed], Med, Caribbean etc..): have you noticed important annual/semi-annual fluctuations (corresponding to SA/SSA constituents)? After 3 years of run, they still don't appear and this problem is also seen in FES2022 model
