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2.2 Surface heat fluxes
The heat budget for the high-latitude atmospheric box reads
(11)
The first integral is the (negative) energy gain at the top of the atmosphere,
integrated over the entire area, FOI , north of the latitude circle dividing the
boxes. The second integral is the (likewise negative) heat gain of the ocean,
integrated over the ocean portion, Fl, of the high-latitude box. The third
term is the integrated meridional energy flux and given by eq. (9). It is
now assumed that HOI and HI are spatially constant (or, rather, that only
the area averaged values matter), and we obtain from (11)
(12)
and hence
(13a)
where to == Fd FOI , the relative ocean coverage of the high-latitude area.
Analogous considerations hold for the low-latitude boxes, and we assume,
for simplicity, that F2 = FI and F02 = FOI . Hence,
(13b)
Using the parameterizations (9) for Hd and (8) for HOI and Ho2 , one
finally arrives at expressions for the surface heat fluxes that are functions
of the oceanic temperatures only,
(14a)
(14b)
The focus will be on the meridional temperature difference,
(15)