Structure and Properties of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 80

Fig. 3.16 Absorption
spectrum of clearest natural
waters (Smith and Baker 1981)
and bubble-free polycrystalline
ice (Grenfell and Perovich
1981)

coef ed in different applications. Curry and Webster

(1999) noted that this equation tends to overestimate the solar radiation by as much as 6 %
and should not be used for N < 6 %. Both forms ( 3.13a , b ) are linear in cloudiness and the
zenith angle makes a small modi

cient c N has been slightly modi

cation (less than 0.05 in polar regions).
A narrow band of solar radiation travels through liquid or solid phase of water in lakes,
about 300

1,200 nm (UV-A, light, and most of IR-A). Shorter wavelengths do not
penetrate the atmosphere, and pure water (liquid or solid) itself absorbs longer wave-
lengths effectively (Fig. 3.16 ). In wavelengths longer than 1,200 nm the absorption
coef

-

cient is more than 1 cm − 1 in pure water. Ultraviolet and near-infrared fractions
attenuate fast, and only light is left from the solar radiation beneath 1 m layer of pure ice
or water. In the light band the absorption coef

cient is less than 0.03 cm − 1 . Within the

band 300 1,200 nm, ozone absorbs in UV-A, and oxygen (O 2 ) and water vapour

absorption peaks occur at 760 and 1,100 nm, respectively (Fig. 3.15 ).
Transfer of sunlight is a key issue in lake ice research. Absorption of radiation in pure
ice is much as in pure liquid water. In the absorption spectrum, due to hydrogen bonding
the peaks are shifted toward lower energy in the ice.

-

3.4.2 Radiance and Irradiance

The basic quantity in the radiation transfer is radiance,de ned as the light intensity

(I) emitted in direction ʾ by an in nitesimal small element of the source area dA through

an in nitesimally small element of the solid angle ʩ ( ʾ ),

L ðnÞ ¼ dI ð n Þ
dA

ð 3 : 14 Þ

cos h

where (see, e.g., Dera 1990; Arst

2003 for a more complete treatment). Radiance can be spectral (W m − 2 nm − 1

ʸ is the angle between the normal to the surface and ʾ

sr − 1 )or

integrated over the wavelengths (W m − 2 sr − 1 ).