Consider, as an illustration, an ensemble of “one dimensional” fronts that contain position and amplitude errors, as shown in Figure. If we were to ask what the mean front is, clearly the simplest solution is to take the mean of these fields, that is, calculate the mean vector. That would be terribly wrong, of course, because the mean simply does not look like any front in the ensemble. It would be terrible, for example, if the mean of an ensemble of hurricane fields produced a mean field with multiple vortices! The solution to this problem is not trivial, but is a fundamental step when quantifying uncertainty and doing analysis. Read more about the coalescence formulation here