In this paper the authors calculate the barotropic stream function from an output of a numerical model as:
over a global domain and this is the result:
In the caption, they specify that the value at the African continent was subtracted from the result of the integral.
If I interpret correctly, this is necessary because the domain is periodic and we need to ensure that the integral over the globe (excluded the Southern Ocean) is zero. Is this correct?
If yes, what is the rationale for choosing the values at the African coast? wouldn't the value at Cape Horn be more natural?
Another aspect of this calculation that I do not understand is the fact that the values of $\psi$ near the coasts are not zero. I would expect the values of the stream function to be zero near the coast in order to ensure a zero transport across the coast. Why is this not an issue?