Geoscience Reference
In-Depth Information
In limnology as well as in oceanography the concept of euphotic depth is used to
describe the maximum depth where photosynthesis can be maintained by the available
light. This is usually taken as the depth where the downwelling planar irradiance has
gone down to 1 % of its level just below the surface (see Smetacek and Passow 1990; Arst
2003). The de
nition has two shortcomings: it is relative rather than absolute, and it
accounts for the radiation level and not for the photon
flux. Therefore this euphotic depth
serves just as a scaling depth of the photosynthetic layer. We can think that the magnitude
of the noon irradiance is 500 W m
−
2
in high latitudes in spring and summer. For wet, bare
ice surface the albedo is
fl
1/3, and therefore the 1 % level corresponds to the power of
3.3 W m
−
2
or to the photon
*
mol m
−
2
s
−
1
. Depending on the water quality
fl
flux of
15
μ
*
xed PAR irradiance power E
0
. Also it has
been suggested that in cold waters, when the rate of metabolism is lower, a smaller photon
fl
the photon
fl
flux can range by about 25 % for a
flux is suf
cient to maintain photosynthesis.
In open water conditions, the euphotic depth is z
e
*
· ʺ
−
1
· ʺ
−
1
, where
log(100)
≈
4.61
ʺ
cient. However, it is best to consider the full
spectral attenuation as a function of depth and integrate for the irradiance spectrally for
any depth. Then the euphotic depth of photosynthesis can be more accurately evaluated.
Thus,
is the mean PAR-band attenuation coef
"
#
E
d
ð
z
Þ
E
d
ð
0
Þ
k
2
E
d
ð
0
;
k
Þ
E
d
ð
0
Þ
Z
z
Z
j
z
0
; k
Þ
dz
0
¼
exp
ð
d
k
k
1
0
"
#
ð
8
:
6
Þ
1
k
2
k
1
k
2
Z
z
Z
j
z
0
; k
Þ
dz
0
exp
ð
d
k
k
1
0
where the last identity comes from the assumption that the spectrum of downwelling
irradiance is even at the surface.
Example 8.1.
Assume that
the attenuation coef
cient
is independent of depth,
ʺ
(z;
ʻ
). Then the spectral integral of the light attenuation can be approximately taken as
the Riemann sum over an even division of PAR-band to n intervals
)=
ʺ
(
ʻ
Z
k
2
m
m
1
k
2
k
1
D
k
k
2
k
1
ðj
i
z
Þ
¼
1
n
exp
ðj
z
Þ
d
k
exp
exp
ðj
i
z
Þ
i¼1
i¼1
k
1
where
ʺ
i
'
κi's are taken at the centre points of the intervals. With n = 3 and assuming
ʺ
2
≪ ʺ
1
,
· ʺ
−
1
; but taking the mean attenuation coef
ʺ
3
, euphotic depth is z
e
≈
3.5
cient for the
ʺ
3
)]
−
1
. For
ʺ
2
=1m
−
1
and
ʺ
3
=10m
−
1
,
whole PAR-band, we have z
e
≈
·
½
ʺ
1
+
ʺ
1
,
4.61
[
(
ʺ
3
=3m
−
1
, they would be 3.5
these depths would be 3.5 and 0.46 m, respectively; for
ʺ
1
,
and 2.0 m, respectively.
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