Jökull - 01.12.1968, Page 29

In some cases, e.g. deep and slow-flowing
rivers, it is unlikely that the variation of T
with z can be neglected and eq. (9), (or (11)),
must be used. It is even possible that the dif-
fusion in the x-direction must be taken into
account but experiments are necessary to see
whether eq. (9) is adequate to describe the heat
transfer in these cases. The logarithmic velocity
distribution, (5), is well supported by experi-
ments. The diffusion model should be satis-
factory for parallel flow but in rivers it is pos-
sible that secondary flows or cross currents will
have a great effect upon the heat transfer.
The assumption of uniform temperature in
the y-direction will generally not liold for rivers.
At least in swift rivers we can still use eq. (14)
with cross-sectional means of the temperature.
THE HEAT BALANCE OF RIVERS
The factors that govern the heat balance of
rivers are:
a) Heat exchange with the atmosphere.
b) Heat exchange with the river bed.
c) Groundwater movement.
d) Frictional heating.
The first term is the most important and it
will be discussed in some detail. It can be
shown (Devik 1931) that the heat exchange
with the bed is generally very small compared
to the heat exchange at the surface. Inflow of
groundwater has a very marked effect upon the
heat balance and ice conditions of many Ice-
landic rivers but presumably this is rather rare
elsewhere. Frorn the fact that 1 kcal equals 427
kpm it follows that frictional heating is very
sniall compared to the heat exchange with the
atmosphere. If the river is ice covered the heat
exchange with the atmosphere is reduced ancl
the other terms may then be prevailing.
HEAT EXCHANGE
VVITH THE ATMOSPHERE
The factors that affect the lteat exchange
between a water surface ancl the atmosphere
are the following:
Radiation (solar and terrestrial).
Evaporation.
Convection.
Precipitation.
In some cases floating ice or other changes
in the state of the surface must also be taken
into account.
The first three factors are the most import-
ant and will be discussed in sorne detail. As
we are concerned with ice problems we will
denote the heat exchange as heat loss from
the water surface.
Radiation
VVith reference to wavelength and origin
radiation is divided into solar radiation ancl
terrestrial radiation (Haltiner and Martin 1957).
Solar radiation is in the wavelength range
0.15 to 4.0 p. Approximately 99% of the
sun’s radiation is contained in this wave-
length range. Insolation is the flux of solar
radiation received on a horizontal surface.
The solar radiation is divided into direct
and scattered or diffuse radiation.
Terrestrial radiation is the radiation emitt-
ed by the earth and the atmosphere. The
major portion of this radiation lies within
the infrared wavelength range 4.0 to 80 p.
The absorption and reflection of water is
quite different for solar radiation and terrestrial
radiation (Devik 1931).
Of the solar radiation a certain portion, de-
pending upon the altitude of the sun and the
condition of the surface, is reflected from the
water and the rest penetrates the water and
is mostly absorbed there or at the bottom.
Water is practically opaque to terrestrial
radiation. Only a very thin film at the suríace
emits radiation and the back radiation from
the atmosphere is absorbed in this same water
film.
Solar radiation
Where observations of solar radiation are not
available from a nearby location one is thrown
upon empiricial formulas for estimation. There
are numerous such formulas, see for instance
Budyko (1956) and Berliand (1960). The most
common expressions are of the form
G = G0 (a + bNm)
JÖKULL 18. ÁR 363