Physical forcing of the shelf seas: what drives the motion of ocean? - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 32

Figure 2.6 Heat fluxes affecting a water column. Q u = Q b + Q e + Q c

Q s ( 1-A )

∂ H T

∂ t

Q v

Q sed =0

we shall see in Chapter 6 , has a seasonal cycle that is also controlled by a
combination of depth and vertical mixing.
As with Q b the back radiation term, Q e and Q c involve the transfer of heat from, or
into, a thin surface microlayer of thickness 1 mm. So all heat loss from the sea is

drawn from this thin surface microlayer. This is in contrast to the radiational heat
input Q s which, while mostly absorbed in the first few metres, has components in the
visible band which penetrate tens of metres below the surface.
The processes controlling the heat budget of the water column are shown schemat-
ically in Fig. 2.6 . The total heat stored in the water column H T (J m 2 )isdefinedas:

∼

surface

ð

H T ¼ c p T K ð z Þ dz ð 2 : 6 Þ

bottom

where c p is the specific heat of seawater and T K (z) is the temperature of the water
column at level z. The time rate of change of H T is determined by the net exchange
through the sea surface combined with Q v , which is the gain or loss of heat due to the
horizontal transport by the current. Note that Q v is the difference between the heat
entering and the heat leaving through the side walls of the column. Heat exchange
between the water and sediments Q sed at the seabed is small because of the low
thermal conductivity of the sediments, which means that heat cannot penetrate far into
the sediment bed. Over the seasonal cycle, the effect of heat exchange with the sediment
has been shown to be roughly equivalent to adding an extra metre to the depth of
the water column (Bowden, 1948 ), and may usually, therefore, be assumed negligible.
With this assumption, the heat budget of the water column can be expressed as:

@ H T

@ t ¼

Q s ð 1 A Þ Q u þ Q v

ð 2 : 7 Þ

with Q u ¼ Q b þ Q e þ Q c :