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Figure 2.7
Annual cycles of the heat fluxes
into the water column for a large area of the
English Channel and southern North Sea
based on 50 years' worth of data, after
(Maddock and Pingree,
1982
) courtesy of the
Marine Biological Association, UK. (a) Net
rate of heat input through the sea surface
Q
i
¼
Q
s
(1
A)
Q
u
; (b) Rate of input of
heat by advection Q
v
; (c) The rate of
change of heat content
(a)
Q
i
100
0
-100
(b)
50
@
H
T
@
Q
v
t
¼
Q
s
ð
1
A
Þ
Q
u
þ
Q
v
0
(c)
∂
H
T
∂
t
100
0
-100
J
F
MMJ
A
J
A
S
O
N
D
Month
In many areas of the shelf seas, Q
v
has been found to be small in relation to the
vertical flux terms, so that H
T
is controlled by Q
s
(1
A) and the loss terms Q
u
(e.g. Bowden,
1948
;Dietrich,
1951
; Maddock and Pingree,
1982
).
Figure 2.7
illus-
trates the average annual cycle of the terms in the heat budget based on an analysis of
50 years of observational data for a large, well mixed area of the English Channel
and the southern North Sea (Maddock and Pingree,
1982
). The net heat input
through the surface Q
i
¼
Q
u
(
Fig. 2.7a
) is seen to be an order of
magnitude greater than Q
v
(
Fig. 2.7b
) and so dominates the seasonal cycle of
Q
s
(1
A)
@
H
T
/
@
t
(
Fig. 2.7c
).
The net change in heat storage, averaged over one or more seasonal cycles, should
be close to zero. Hence, where Q
v
is negligible, the total heat input by Q
s
(1
A) must
be balanced by the combined heat loss. This condition of no net change over the
seasonal cycle can serve as a useful check on the consistency of flux estimates,
providing, of course, that we can neglect the net changes due to longer term cycles
or trends.
It is apparent from
Fig. 2.5
and
Fig. 2.7
that the time course of the net heat input
Q
i
¼
Q
s
(1
A)
Q
u
over the seasonal cycle may reasonably be approximated by the
sinusoidal form:
Wm
2
Q
i
¼
A
0
sin
ð
o
a
t
þ
d
Þ
ð
2
:
8
Þ
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