This is another synopsis of what the sloshing modeling results are showing.

The tide gauge numbers are revealing a forced sloshing oscillation with a primary forcing period of two years. This is panel A.

The SOI is showing the same forced oscillation in addition to an unforced sloshing oscillation with no preferred period. This is panel B.

So the tide gauge and SOI share a common forcing (Panel C overlaid curves) but the SOI has another component (Panel C green) based on perhaps a deeper oscillation not emergent as a sea-level change. This could be an oscillation in the thermocline?

All this data is simulated based on applying a Mathieu DiffEq