Explicit convection happens in one of two ways. The default is the scheme of Rahmstorf (the fullconvect scheme from MOM 2, now the default). Option oldconvect employs the older style explicit convection. In either case, when option save_convection is enabled, the results of explicit convection can be subsequently analyzed. Both explicit convection schemes are explained below. The following discussion is taken from Stefan Rahmstorf (rahmstorf@pik-potsdam.de), which is largely taken from ``A fast and complete convection scheme for ocean models'' Ocean Modeling, volume 101.
Imagine having three half-filled glasses of wine lined up in front of you. On the left a German Riesling, in the middle a French Burgundy and on the right a Chardonnay from New Zealand. Imagine further that you're not much of a connoisseur, so you want to mix the three together to a refreshing drink, with exactly the same mixture in each glass. The trouble is, you can only mix the contents of two adjacent glasses at a time. So you start off by mixing the Riesling with the Burgundy, then you mix this mixture with the Chardonnay, then... How often do you need to repeat this process until you get an identical mix in all glasses?
Incidentally, putting this question to a friend is a good test to see whether she (or he) is a mathematician or a physicist. A mathematician would answer ``an infinite number of times'', while a physicist would be well aware that there is only a finite number of molecules involved, so you can get your perfect drink with a finite mixing effort (only you would have no way to tell whether you've got it or not).
In any case, the number of times you need to mix is very large, and this is the problem of the standard convection scheme of the GFDL ocean model (Cox 1984), which mixes two adjacent levels of the water column if they are statically unstable. The model includes the option to repeat this mixing process a number of times at each time step, as an iteration process towards complete removal of static instabilities. The minimum number of iterations needed to mix some of the information from layer 1 down to layer n is n-1.
To avoid this problem, one needs to relax the condition that only two levels may be mixed at a time. To achieve complete mixing, a convection scheme is required that can mix the whole unstable part of the water column in one go. I have been using such a scheme back in 1983 in a one-dimensional mixing model for the Irish Sea, and I'm sure many other people have been using similar ones. Marotzke (1991) introduced such a scheme into the GFDL ocean model. It appears that it hasn't been taken up as enthusiastically as it might have been, and an implicit convection scheme (which increases the vertical diffusivity at unstable parts of the water column) has been preferred because of lower computational cost (e.g. Weaver et al, 1993). However, it is not difficult to set up a complete convection scheme which uses less computer time than the implicit scheme.