Ice-Covered Lakes Environment - Freezing of Lakes and the Evolution of their Ice Cover - page 247

suspended matter take place in the snow melting period, with meltwater fl flushing the soil

surface, and after heavy rain events.

8.1.3 Quantum Irradiance

Attenuation of light in ice and water is wavelength-dependent as discussed in Sect. 3.4 .At
the depth z, the spectral distribution of scalar irradiance is (e.g., Arst 2003):

" #

Z z

j 0 z 0 ; k Þ dz 0 E 0 z ; ðÞ ¼E 0 0 ; ðÞ exp ð ð 8 : 2 Þ

0

where cient of scalar irradiance. The energy of a photon is

E = hc 0 / ʻ , where h = 6.6255 × 10 − 34 J s is Planck ' s constant, and c 0 = 2.9979 × 10 8 ms − 1
is the velocity of light in vacuum, and consequently the quantum scalar irradiance is

ʺ 0 is the attenuation coef

k
hc 0 E 0 z ; ðÞ

q 0 z ; ðÞ ¼ ð 8 : 3 Þ

The scalar irradiance is taken since for the photosynthesis just the number of photons
accounts for. The number of light quanta is obtained by integration of the photon

fl ux:

k
hc 0 E 0 z ; ð d k

k 2

Z

q ðÞ ¼ ð 8 : 4 Þ

k 1

where ʻ 2 = 700 nm are the wavelength limits of the PAR band. The

transformation between irradiance power and quanta units can be made by

ʻ 1 = 400 nm and

qhc 0 ¼ k E 0 ; k ¼ 1
E 0

k 2

Z

k E 0 z ; ð d k ð : Þ

8 5

k 1

where E 0 is the mean PAR irradiance and k = is the irradiance-weighted mean PAR-
wavelength. For white light k ¼ 550 nm

q = E 0 ¼ 4 : 60 lmol J 1 as nor-
mally used for the irradiance above a lake surface. This is a good approximation since the
light spectrum is fairly even in the air. But within any lake, the light spectrum changes
signi

, and therefore

cantly with depth. Deeper in clean water k \ 500 nm

, and deeper in humic or turbid

water k \ 600 nm q = E 0 ¼ 4 : 60 lmol J 1 is

less than 20 %, often less than 10 %. In Finnish and Estonian lakes this ratio increases
from 4.6

, and thus the bias of using the constant ratio of

mol/J deeper in the water (Reinart et al.
1998). Dry and clean snow or snow-ice keeps the even shape of the light spectrum, but
congelation ice acts much as clear lake water.

μ mol/J at the surface to about 4.8 5.5 μ

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