Geoscience Reference
In-Depth Information
where
d
snow
is the depth of the snow layer (in the case that other luxes at the snow
surface, like
K*
and
H
, are not zero, they could be simply included by replacing
L*
by the net total lux). Because heat transport is related to the temperature gradient (see
∂
∂
=−
T
z
1
λ
G
Eq. (
2.29
), rewritten as
) the above expression for
G
snow
(
z
d
) can be
snow
d
snow
used to derive, by integration, an expression for the temperature proile in the snow:
1
1
2
1
2
2
2
G
Tz
()
−
T
()
0
=−
zd
⋅
−
zL
*
+
z
(2.46)
snow
snow
dsnow
d
d
λ
d
snow
snow
where
z
d
is the depth (positive downward) below the snow surface. If we assume a
fresh layer of snow with a thickness
d
snow
of 10 cm, in a typical winter night with
L*
=
‒50 W m
-2
and no supply of heat from the soil, the temperature difference between
the top and the bottom of the snow layer would be 25 K, and the layer would cool by
nearly 6 K per hour (rate of change of mean temperature is
L*/
(
d
snow
C
snow
)). This is a
dramatic difference with the situation without snow: an equivalent layer of sandy soil
would give a temperature difference of 1-2 K between top and bottom, and a cooling
of less than 1 K per hour.
In
Figure 2.29
an example is given of the variation of temperatures above and under
a thin snow pack over the course of one cloud-free day (two half nights). Indeed, the
surface temperature, as well as the air temperature just above the snow, drop very
quickly as soon as the net radiation becomes negative and less than the supply of heat
from the soil. The cooling rate of the snow surface over the period 14-17 UTC is more
than 3 K per hour, with a peak cooling at around 16 UTC of more than 4 K per hour. In
contrast, the soil temperature at 5 cm depth does not change at all, owing to the insula-
tion by the snow (and the grass). The inal temperature difference over the snow pack
plus the upper 5 cm of soil is approximately 16 K. The levelling off of the cooling after
18 UTC is consistent with the near-balance between the supply of heat by the soil heat
lux and the loss of heat by net radiation, although the magnitude of the cooling sug-
gests that the energy loss was smaller in magnitude than the observed
Q*
‒
G
= ‒10
W m
-2
). The increase of the surface temperature between 23 and 24 UTC is related to
an increase of the wind speed to above 2 m s
-2
, which increases mixing and results in a
downward sensible heat lux (the same holds for the period between 0 and 4 UTC).
Apart from the effect of snow on the heat transport by conduction, the occurrence of
phase changes in the snow (sublimation or melt) will affect the surface energy balance
as well. Sublimation may occur under certain conditions (see
Chapter 7
): if the air is dry
enough and the supply of energy is suficient (warm air and/or high levels of radiation).
For sublimation it is not necessary that the temperature of the snow is at or above the
freezing point of water. However, sublimation will be a slow process as the amount of
energy involved in sublimation is about 10 times the energy needed for melting only (the
latent heat of sublimation is the sum of the latent heats of fusion
L
f
(~ 0.33 10
6
J kg
-1
)
and vaporization
L
v
(~2.5 10
6
J kg
-1
)). Hence, a quick decrease in the thickness of a snow
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