The actual global minimum isn't the ocean but rather the Dead Sea. I imagine this is rather hard to find, since you have to be fairly close to it before the gradient leads toward it rather than the ocean.
In fact we can be very precise. The Dead Sea has a catchment area of 41650 km^2, which is 0.0000816 of the Earth's surface. So we need on average 12200 random initializations in order to find the Dead Sea by gradient descent.
Well, the Dead Sea is certainly below mean ocean level. But the deepest oceanic trenches are far deeper (~11 km below mean ocean level) than the bottom of the Dead Sea (~0.74 km below mean ocean level).
In fact we can be very precise. The Dead Sea has a catchment area of 41650 km^2, which is 0.0000816 of the Earth's surface. So we need on average 12200 random initializations in order to find the Dead Sea by gradient descent.