337
(5)
where a linear equation of state has been assumed, and a and f3 are, respectively, the thermal and haline expansion coefficients. Some support
for the simple relationship (5) derives from the recent results of Hughes
and Weaver (1994). Hs, the virtual surface salinity flux, is related to the
surface freshwater flux E through
E
Hs=SoD'
(6)
where So is a constant reference salinity and E is water loss (gain) of the
low (high) latitude ocean, measured in meters per second. Notice that in
order to convert HI and H2 (which have units eGs-I) into physical heat
fluxes, denoted fIt and H2, they are multiplied by the heat capacity of a
unit water column, which is
cpoD ~ 4 x 10 6 Jm- 3 K- I x 5 x 10 3 m ~ 2 x 1010 Jm- 2 K- I
(7)
We will use the term surface heat flux interchangeably for the heat fluxes
proper and for the induced temperature tendencies.
We assume that heat and moisture capacities of the atmosphere are negligible. This is justified if one only considers timescales longer than the
atmosphere's equilibration time, which is given by radiative cooling for
temperature (order 1 month) and the typical lifetime of a water particle
in the atmosphere (order 1 week, Gill, 1982, p. 31). We assume that we
can parameterize the energy fluxes at the top of the atmosphere and the
meridional energy and water transports in the atmosphere; as a result, the
air-sea exchanges can be determined as the residuals of the steady-state
atmospheric heat and moisture budgets. For the moment, we assume perfect longitudinal mixing in the atmosphere and zero temperature difference
between sea and atmospheric surface temperatures, so that the zonally averaged atmospheric surface temperatures are equal to the oceanic temperatures. Furthermore, we assume a constant atmospheric lapse rate. The
planetary-scale meridional temperature gradients in the atmosphere are
then completely determined by the temperatures in the ocean boxes. In
section 4, the condition of perfect zonal homogenization will be relaxed,
and air temperatures over land computed separately.
The radiation at the top of the atmosphere is parameterized as a linear
function of surface temperature (Wang and Stone, 1980)
(5)
where a linear equation of state has been assumed, and a and f3 are, respectively, the thermal and haline expansion coefficients. Some support
for the simple relationship (5) derives from the recent results of Hughes
and Weaver (1994). Hs, the virtual surface salinity flux, is related to the
surface freshwater flux E through
E
Hs=SoD'
(6)
where So is a constant reference salinity and E is water loss (gain) of the
low (high) latitude ocean, measured in meters per second. Notice that in
order to convert HI and H2 (which have units eGs-I) into physical heat
fluxes, denoted fIt and H2, they are multiplied by the heat capacity of a
unit water column, which is
cpoD ~ 4 x 10 6 Jm- 3 K- I x 5 x 10 3 m ~ 2 x 1010 Jm- 2 K- I
(7)
We will use the term surface heat flux interchangeably for the heat fluxes
proper and for the induced temperature tendencies.
We assume that heat and moisture capacities of the atmosphere are negligible. This is justified if one only considers timescales longer than the
atmosphere's equilibration time, which is given by radiative cooling for
temperature (order 1 month) and the typical lifetime of a water particle
in the atmosphere (order 1 week, Gill, 1982, p. 31). We assume that we
can parameterize the energy fluxes at the top of the atmosphere and the
meridional energy and water transports in the atmosphere; as a result, the
air-sea exchanges can be determined as the residuals of the steady-state
atmospheric heat and moisture budgets. For the moment, we assume perfect longitudinal mixing in the atmosphere and zero temperature difference
between sea and atmospheric surface temperatures, so that the zonally averaged atmospheric surface temperatures are equal to the oceanic temperatures. Furthermore, we assume a constant atmospheric lapse rate. The
planetary-scale meridional temperature gradients in the atmosphere are
then completely determined by the temperatures in the ocean boxes. In
section 4, the condition of perfect zonal homogenization will be relaxed,
and air temperatures over land computed separately.
The radiation at the top of the atmosphere is parameterized as a linear
function of surface temperature (Wang and Stone, 1980)