Freezing of Lakes - Freezing of Lakes and the Evolution of their Ice Cover - page 19

When salinity variations are ignored, the following simple form can be used for the
density of lake water:

qð T ; 0 ; 0 Þ ¼ q 0 að T T m Þ 2

ð 2 : 6 Þ

(T m , 0, 0) = 999.98 kg m − 3

where fixed reference density, T m is the tem-

perature of maximum density of fresh water, T m (S =0,p = 0) = 3.98

ˁ 0 = ˁ is the

° C, and

10 − 3 kg m − 3 C − 2 is an empirical parameter (Fig. 2.4 ). The parameter ʱ ≈ 8.0 × ° ʱ can be

further tuned fitting the density to the UNESCO (1981) formula after selecting the

applicable temperature range. The

first-order approximation for low salinities is obtained

0.81 kg m − 3 to the right-hand side of Eq. ( 2.6 ). In cold

ʲ· ʲ ≈

just by adding the term S,

waters the in uence of temperature on density is at smallest. Under a stable ice cover,

even small salinity variations can be important, and then it is better to stick to the full
UNESCO (1981) formula.

fl

The average density of a human body is 1,062 kg m − 3 (Krywicki and Chinn
1966). If the water salinity is more than 75

Example 2.2.

oat
free. There are many hypersaline lakes, which satisfy this requirement, perhaps the most
famous ones are the Dead Sea (S

‰ , the water is denser and human bodies fl

1,240 kg m − 3 ) and the Great Salt Lake in ≈ 315 ‰ , ˁ ≈

1,100 kg m − 3 ). Utah (S * 100 ‰ , ˁ *

Fig. 2.4 Density of water as a
function of temperature for
different salinities at zero gauge
pressure: a Pure water density
as a function of temperature,
b Density difference from the
density at 0 ° C in fresh and
brackish water (salinities 0, 1, 5
and 10 ‰ ). The plots are based
on the UNESCO (1981)
standard equation of state