Thermodynamics of Seasonal Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 102

Table 4.1 Linear heat flux coefficients in southern Finland. The contributions of solar radiation
(Srad), terrestrial radiation (Trad), sensible heat flux (SH) and latent heat flux (LH) are shown
separately, total refers the value of the coefficient
Month

k 0 (W m − 2 ) k 1 (W m − 2 ° C − 1 )

Srad Trad LH Total Trad SH LH Total

September 90

- 45 - 16

29 5.0 5.2 10.5 20.7

October 38

- 45 - 9 - 16

4.7 5.5 8.2 18.4

November 12

- 43 - 5 - 36

4.5 5.8 6.2 16.5

December 3 45 4 46 4.3 5.8 4.7 14.8

- - -

January 2 - 46 - 5 - 49 4.2 5.6 4.0 13.8

February 8

- 48 - 5 - 45

4.2 5.5 3.7 13.4

March 30

- 56 - 7 - 33

4.4 5.5 5.0 14.9

April 76 - 62 - 10 4 4.7 5.5 7.7 17.9

May 193

- 57 - 36

100 5.0 5.5 11.0 21.5

June 209

- 55 - 40

114 5.2 5.2 13.3 23.7

July 203

- 48 - 41

114 5.4 4.9 14.6 24.9

August 151

- 45 - 29

77 5.3 4.9 13.3 23.5

radiation and latent heat fl flux contribute to both parameters k o and k 1 . The former is split

into two parts 3 by T o T a 4T a

ð T a T o Þ . Then the net terrestrial radiation is

Q La þ Q Lo e 0 rðe a T a T 0 Þ ¼ e 0 r ½ ð 1 e a Þ T a þ 4T a ð T a T o Þ ð 4 : 21a Þ

where the truncated binomial formula gives accuracy of about 1 % when |T a − T o |<10 ° C

and T a * C. The latent heat exchange is split using the Clausius-Clapeyron equation

(e.g., Gill 1982) for the saturation water vapour pressure e s . Assuming that humidity is at
the saturation level at the surface, e o = e s (T 0 ), and writing e a = Re s , where R is the relative
humidity, the latent heat

0 °

fl ux can be expressed as

Q e ¼ q a L E C E 0 : 622e s ð T a Þ ð 1 R Þ L E

R v T a ð T a T o Þ

U a ð 4 : 21b Þ

p a

where R v is the gas constant of dry air. Finally, combining all together, the coef cients k o

and k 1 become

Þr T a q a L ES C E 0 : 622e s T ðÞ

k 0 ¼ 1 a ð Þ Q s e 0 1 e a ð ð 1 R Þ U a

p a

ð 4 : 22 Þ

k 1 ¼ 4 e 0 r T a þ q a c p C H U a þ q a L ES C E 0 : 622e s T ðÞ L ES

R v T a U a p a

3 Write T o = T a +(T o − T a )] 4 , use the binomial formula and take the two leading terms.