Geoscience Reference
In-Depth Information
gain by the atmospheric column and an equivalent loss by the underlying column.
Conversely, if there is a net transfer of energy from the atmospheric column into the
underlying column (a negative net surface flux), this counts as an energy loss from
the atmospheric column and an equivalent gain by the underlying column. The net
surface flux can be written as:
F
sfc
= - (R
sfc
+ Q
H
+ Q
E
)
(3.5)
where R
sfc
is the net radiation at the surface (the sum of the net shortwave and net
longwave radiation fluxes at the surface) and Q
H
and Q
E
are the turbulent sensible
and latent heat fluxes. The terms on the right side of the equation (examined more
closely in
Chapter 5
) are taken as positive downward; the minus sign is consistent
with the convention that the net surface flux is positive upward (into the atmo-
spheric column). Equation
3.5
is saying that, if the net radiation at the surface is not
balanced with the turbulent fluxes, there must be an exchange of energy between
the columns.
We now turn our attention to the energy budget of the underlying column, which
could variously represent ocean with or without a floating sea ice cover (and an
overlying snow cover), soil, soil with vegetation on the top (which may in turn be
covered by snow), an ice sheet, or a glacier. If the column represents ocean, the fol-
lowing applies:
∂O
E
/∂t = ∂/∂t (L
i
+ S
o
) = - F
sfc
−∇•
F
o
+ ∇•
F
i
(3.6)
Which states that the tendency in energy storage in the ocean (∂O
E
/∂t) is (approxi-
mately) represented by the sum of the tendency in latent heat storage in any floating
sea ice and any overlying snow cover (Li)
i
) and the tendency in sensible heat storage
of the ocean water (S
o
). The tendency in ocean energy storage is in turn equal to the
sum of the negative of the net surface heat flux F
sfc
, the horizontal convergence of
the oceanic sensible heat flux (
F
o
), and the horizontal divergence of the latent heat
flux as sea ice (
F
i
). The combination of the last two is the oceanic equivalent of the
atmospheric flux convergence in Equation
3.2
. A convergence (divergence) of oce-
anic heat into the polar cap domain acts to increase (or decrease) the heat content
of the column. A given mass of ice has a lower energy content than a given mass
of water at the same temperature. Assuming that a net export (or divergence) of sea
ice from the column is replaced by the same mass of water at the same temperature,
there is an effective increase in the heat content of the column. The sea ice terms
in Equation
3.6
could include contributions by icebergs. Several small terms are
ignored, including the sensible heat of the ice, sensible heat of the ice transport,
kinetic energy changes in the ocean, and sensible heat transports associated with
river discharge into the ocean.
A key point is that Equations
3.2
and
3.6
are linked through the net surface
heat flux term. Reinforcing the previous discussion, it should be evident that if F
sfc
is positive (a flux from the underlying column into the atmospheric column), this
contributes to a loss of energy from the underlying column, which counts as a gain
