the effect of atmospheric pressure on sea level's been looked at by the science
one paper here
https://journals.ametsoc.org/doi/pdf/10.1175/2007JCLI1803.1
"
Since the early studies of Patullo et al. (1955) and Rossiter (1962), the effects of surface pressure changes on estimates of seasonal variations in sea level and longer-term trends have been addressed repeatedly, although studies were mostly hampered by the lack of sufficient data. As an example, Woodworth (1987) investigated the effect of atmospheric loading on estimates of mean sea level trends around the British Isles. In addition, Holgate and Woodworth (2004) investigated the evidence for enhanced coastal sea level rise during the 1990s. Church et al. (2001), in their discussion of future sea level change projections, estimated the effects of changes in ib to be only of the order of 0.2 mm yr1 and dismissed this effect as unimportant. Not considered was the potential that through increased changes in atmospheric sea level pressure those effects might increase in amplitude in the future and that changes in the atmospheric loading effect show strong regional variations."
as the paper elsewhere describes, the science looks at water uptake with a warming atmosphere, but observes that the pressure effects of that water loading vary with lattitude
also, please don't suggest I endorse or "recognise" any particular dataset
a) we haven't discussed pressure datasets before that I can recall and I have no view on relevant datasets and don't recognise any, one way or another
b) scientists understand the limitations of datasets pretty well and use them with care accordingly, I can't say at this stage that I am aware of any flaws or idiosyncracies or differences between pressure datasets, but I would not necessarily endorse them in ways that you chose to use them
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