ag.algebraic geometry - Gauss manin connection under base change?

Consider for a proper smooth projective morphism f: X--> S-->spec(k), A is a regular k algebra of finite type , S=spec(A), k is a field .

we know that for$ R^n f_*(Omega ^._{X/S})$ we have a Gauss manin connection$nabla$.

And then for a k morphism g:T-->S ,we have a base change .

So what is the relation between the Gauss manin connection of the original and the one after base change. what about in the special situation when T =spec (L), L is the fraction field of A?