## Dimensional models

The thermodynamic model of the ocean-atmosphere-continent ice system developed by Verbitskii and Chalikov (1986) is a 1.5-dimensional model. In this model the World Ocean is represented in the form of three meridional oceans of different zonal extent A, a southern ring (the analogue of the Southern Ocean), and the North Polar Ocean. The depth of all the oceans is assumed to be constant and equal to H = 3700 m. Meridional oceans limited from the West and East by continents are divided into two areas: the western boundary layer of constant angular width 10 and the open ocean. Both these areas, in turn, are divided into two layers: the upper (with thickness h = 600 m) and a deep layer. Within each of them the temperature is assumed to be equal to its mean (over the vertical and longitude) value. Thus, the thermal regime of the meridional ocean is described by a system of four one-dimensional heat budget equations derived from the initial equations of heat conductivity after averaging over depth and longitude within the limits of the layer in question, and after replacing the average products of the velocity and temperature by the product of averages, with the temperature at the western boundary layer/open ocean interface or at the upper layer/deep layer being equal to half the sum of its average values. When the heat transport across the eastern ocean boundary is equal to zero these equations take the form

-z----7~7-r^---- + -— i [»ii]ru - —— ) cos «¡j dt a(A — X0) cos cp 2 acoscpd(p\ a dtpJ

+ -;--T-+-— [»21 lT2i - kH —— cos cp dt aX0 cos <p 2 a cos (p d(p\ a d(p