A Probability Box Model of a Convective Ocean

Abstract

A new modeling approach is proposed for representing a subpolar ocean, whose upper layer is partly convected with the lower layer. A simple box model, built as a reference, has one active box to be the upper layer of a colder ocean, which interacts with the warmer box and the lower box. The active box receives atmospheric forcing (cooling and precipitation) and a parameterized freshwater (or sea ice) flux as well, while the other boxes have their properties fixed. The active box, interacting with the warmer box, possesses a thermal-driven state, at which the warmer water enters the active box, is cooled by the atmosphere, and becomes denser. The lower box adds another solution: a convected state appears in the vicinity of the nonconvected state. The nonconvected state either separates from or is absorbed into the convected state; that is, the entire upper box is convected with the lower box, once the lower-box density is close to the upper-box density. The new component to the simple model is a probability distribution function (PDF) on the temperature?salinity (T?S) plane for the active box. The PDF in this probability box model represents heterogeneity in the upper layer, whereas one box has to be homogeneous in an ordinary box model. A T?S distribution retains only the probabilities of different water types, while their locations are discarded. The mechanisms to increase and reduce heterogeneity are modeled by the divergence and convergence of the PDF on the T?S plane, respectively. The heterogeneity is generated by the intrusion of exterior water as well as variability in the atmospheric forcing and freshwater flux, while the heterogeneity is reduced by horizontal diffusion within the box. Convection with the lower box tends to concentrate the PDF to the T, S of the lower box. Under the exterior condition that could produce both nonconvected and convected states in the simple box model, there is only one state of the upper box, which is partly convected, in the probability model. This intermediate state is possible when the divergent mechanism is intense, and the convergent mechanism is weak. Thus, the on?off convection in the simple box model is replaced with an intermediate state between the convected and the nonconvected states. It is suggested that, once mesoscale variability maintains heterogeneity, convection in the subpolar ocean is more robust against freshwater input.