Nonuniqueness in a Single-Column Model for Moist Convection

We investigate a moist atmospheric column convection model by considering the atmosphere as a single vertical column of air parcels, each of which contains water vapor. The moist convective adjustment of both air and water mass in the column is considered from an (unstable) initial state to a statically stable final configuration of parcels. Two variations of an algorithm based upon swapping neighboring parcels are compared: after swapping, no parcels remain supersaturated. The results of these algorithms are compared directly with those of the adjustment algorithm of Cheng et al., which adjusts an atmospheric column to achieve the global maximum of a relevant cost functional. Two examples are considered: in the first, the algorithms adjust to similar arrangements, showing that the global maximum of the functional is the dynamically preferred state, while in the second, the algorithms adjust to significantly different states. Thus, we identify a nonuniqueness to the solution to the adjustment problem in terms of local and global cost functional maximizers. We then discuss the relevance of this nonuniqueness to numerical prediction in weather and climate models.