<0, where Rf = — gaT(hJu^) Qtu/Poco 1s the flux Richardson number; ^e — U*i/C3\f\ is the thickness of the Ekman boundary layer in the ocean; S(hJhE) is the function equal to 1 as h1 < hE, and otherwise to 0; m^j is the wind friction velocity; / is the Coriolis parameter, aT is the coefficient of sea-water thermal expansion; Cu C2 and C3 are non-dimensional numerical constants.
The velocity w of vertical motions in the upwelling area appearing here and above can be considered as a model parameter. But it is possible to express it differently in terms of the meridional temperature difference in the system of ocean boxes (say, by means of (T2 — 7i)), that is, to assume, following Stommel (1960), that not only the processes of cooling in the area of cold deep water formation participate in the formation of the deep circulation but also the processes which control the dynamics of currents in temperate and low latitudes. In this case w = C4(T2 - T0)/ad(p°, (5.5.20)
where a is the Earth's radius; 8(p° is a difference in latitudes of the ocean boxes; C4 is a dimensional factor.
As is known, in box ocean models the spatial variability of the UML is usually neglected. Meanwhile, the comparison of mean (over the North Atlantic area) values of temperature in the UML calculated from local and space-averaged data show that this assumption leads to systematic understating of the UML temperature. To eliminate this disadvantage we parametrize the spatial correlation J = /Ji<(£?=i Qtu/Poco ~ Qh-o)) (here angle brackets signify spatial averaging) in the form j = cact; - T2),
where C5 is one more dimensional constant. We also add the same term (but with inverse sign) in the equation for the DOL in order to ensure the condition of heat conservation in the system of ocean boxes.
To parametrize the diffusive heat transport Fj in the ocean determined by the correlation between synoptic disturbances of the meridional components of velocity and temperature, we assume that the meridional and zonal components of the current velocity are proportional to each other (this assumption is justified for blocking of zonal flows), and that the meridional mass transport from the UML into the area of cold deep water formation, and from this area to the DOL, should be associated with w by the condition of mass conservation. Then
where A is the baroclinic radius of deformation, C6 and C'6 are non-dimensional numerical constants.
We parametrize the meridional heat transport Fj in the atmosphere in accordance with Stone (1972). Normalizing this transport to the atmospheric box area we have
FA r T2
where S(pA is the difference in latitude of the atmospheric boxes; (pr is the latitude of the boundary between them; C7 is a dimensional constant.
Heat sources and sinks , (the first superscripts are omitted here) are presented in the form
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