Jökull - 01.12.1968, Side 32

where L is the latent heat of vaporization; and
bv ccnvection:
s3 = yKc
d0
dz
q = 0.622 —
0.622
(24)
p - 0.378 e p
The equation of state for moist air gives:
With K = Km these equations can be inte-
grated from zi >> o to Z2 > zj. Some evapora-
tion formulas (e.g. Thornthwaite-Holzman) are
derived in this way. But the use of such for-
mulas requires exact observations in two heights.
The integration of (23) and (24) frorn z = o
is impossible because we do not know the con-
ditions at the surface and the transition from
molecular to turbulent diffusion. Different as-
sumptions leacl to “widely diverging results”
(.Sverdrup 1951).
In accordance with Budyko (1956) we intro-
duce the coefficient B, defined by:
and the integration of (23) and (24) frorn o
to z thus gives
s2 = yBL (qw - qa) (25)
s8 = yBCp (0W — 0a) (26)
where qw is the specific humidity at the water
surface where the air is assumed to be saturat-
ed at the water temperature and 0W is the
water temperature. Indices a refers to the air
at observation height. B must be derived from
experiments and with reference to Sutton’s
equation, (22), we can assume that B = Dvzn
where D and n are constants and vz is the wind
velocity at the height z above the ground.
For practical purposes we will replace y, 0
and q with variables obtained from routine
meteorological observations. Near the ground
the potential temperature is almost equal to
the absolute temperature, T [°K]:
®w - 0a ~ Tw - Ta = Lv - 'a
where t is temperature in °C. The specific
humidity is a function of the vapour pressure,
e, and the atmospheric pressure, p:
3ÓÓ JÖKULL 18. ÁR
Y = -------P--------«-P-
RTa (1 + 0.61 m) RTa
where R is the specific gas constant for dry air
and m = 0.622e/(p — e) is the mixing ratio.
The specific heat of moist air is with slight
approximation (Haltiner and Martin 1957)
cp = Cpa (! + 0.8 m)
where cpd is the specific heat of dry air. We
may therefore consider cp constant.
With this the expressions for the rate of heat
loss per unit area by evaporation and convec-
tion become
0.622 L
S2 = — _ D vzn (ew - ea)
S3 =
R ’ Ta
<VP
R • T„
DV (tw-ta)
(27)
(28)
The ratio between s3 and s^, the Bowen ra-
tio, is
_ _f3_ _ yp j (tw - ta)
s^ 0.622 • L (ew — ea)
(29)
For p = 960 mb, cp = 0.24 kcal kp-l °C-l
and L = 597 kcal/kp (tw s 0 °C), (and e in mb)
r = 0.62
(tw - ta)
(ew - ea)
(30)
The constants D and n must be determined
by experiments, for instance by measurement
of the rate of lieat loss from the surface of a
known volume of water. The rate of heat loss
by radiation should preferably be measured
with radiometers, then the sum S2 + s3 is found
and the ratio s3/s2 is known from eq. (29).
The most rational approach to determine D
and n is to measure the rate of lieat loss from
a considerable reach of a river. Devik (1931)