Structure and Properties of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 87

Fig. 3.19 Bulk attenuation coefficients of lake ice in winter 2009 in Estonia and Finland: Lakes
1 Lovoj ä rvi, 2 P ää j ä rvi, 3 Iso Valkj ä rvi, 4 Peipsi, 5 Vanajavesi, and 6 Vesij ä rvi. a Natural
conditions; b snow removed manually from the surface (Lei et al. 2011)

cient depends on the wavelength, showing minimum at
500 - 600 nm and increasing strongly with increasing wavelength (Fig. 3.19 ). In humic
lakes the attenuation coef

The attenuation coef

cient of ice also increases toward shorter wavelengths due to
absorption by CDOM. Consequently, it has become a custom to take the light band as the
part of solar radiation that penetrates through the ice/snow/water surface, and the ultra-
violet and near infrared parts are included in the surface absorption. This optically
transparent

finite thickness, several centimeters, and including it in the
surface boundary condition is feasible for most physics research. However,

' surface ' has

in lake

biology investigations the penetration of UV band into ice may be of concern.
Transmittance of an ice sheet is de

ned as the ratio of the radiation passed through the
ice to the incoming radiation just above the ice:

sðkÞ ¼ E d ð h þ ; k Þ
E d ð 0 ; kÞ

ð 3 : 23 Þ

where h is ice thickness. Thus the transmittance includes the in fl uence of albedo. In

general, the equation = 1 holds, where A is the total absorption of radiation by

the ice sheet. In the case of a layered ice sheet, the attenuation coef

ʱ + A + ˄

cients for the

individual layers determine the transmittance by

" #

X

sðÞ ¼1 r ðÞ ½ exp h i ' K d ;' ðkÞ ð 3 : 24 Þ

'