Lake Water Body in the Ice Season - Freezing of Lakes and the Evolution of their Ice Cover - page 233

7.4.2 Light Below the Ice Cover

The level of downwelling irradiance beneath ice cover is (see Eq. 3.21 )

Z z

E d z ; ðÞ ¼ 1 r ðÞ

½ E d 0 ; ðÞ ½ K d ðÞ dw

exp

0

" #

ð 7 : 32 Þ

X

¼ 1 r ðÞ ½ E d 0 ; ðÞ

h i ' K d ;' ðkÞ

exp

'

where the lower index refers to optically different layers. The scalar irradiance E 0 is

obtained in analogous manner.
Beneath the ice cover, light has penetrated the snow and ice layers, and its angular and
spectral distributions are different from those above the surface. Due to the strong scat-
tering, radiation is diffuse beneath the ice (Lepp

'

ä ranta et al. 2003a; Arst et al. 2006), and

the spectral modi cation by ice and snow depends on their quality, thickness and OAS

content (Arst et al. 2006). In the presence of congelation ice, the light spectrum is not
white beneath the ice as it is at the surface. In open water and clear sky conditions,
radiation becomes diffuse only at a distance from the surface.
A classical measure of the transparency of lake water is the Secchi depth. 6 It is de

ned
as the depth where a white disc, diameter 30 cm, disappears from sight, and its value is
about twice the optical thickness (e.g., Arst 2003). In principle, Secchi depth can also be
de ned for ice-covered lakes but due to light scattering by the ice sheet its observation

may be dif

cult.
A suitable parameter to describe the angular structure of the light field is the ratio of
planar to scalar irradiance

C ¼ E d = E o . This ratio not only represents the diffusiveness of
light in the water but also the contribution of upwelling light to the formation of scalar
irradiance. It can be easily evaluated for ideal cases: (1) For radiance turning horizontal
C ! 0 C ¼ 1 = 4 ; (3) For

diffuse irradiance from upper hemisphere and zero from lower hemisphere,

; (2) For diffuse irradiance ( (fixed radiance from all directions),

C ¼ 1 = 2 ; and

(4) For zenith radiance . A true diffuse irradiance is never observed in natural

waters, and normally the downwelling irradiance is much stronger than the upwelling
irradiance. In ice-free waters the ratio usually decreases with depth (Reinart 2000). Deeper
in the water column in homogeneous water, the apparent optical properties reach their
asymptotic values, usually 0.4 <

C ¼ 1

< 0.9. The situation can be different in under-ice
waters, because light having just penetrated the ice layer is considerably more diffuse than

ʓ

6

Introduced in 1865 by Italian astronomer Pietro Angelo Secchi (1818 - 1878).