
ZENO
®
-3200 USER MANUAL
Coastal Environmental Systems (206) 682-6048 Page D-21
a
long-wave emissivity of the atmosphere
s
long-wave surface emissivity, taken equal to 0.98
c cloud cover fraction
Stefan-Boltzmann constant (5.6710
-8
W m
-2
K
-4
)
The fits to the short-wave surface albedo and the cloud cover fraction both depend on the solar altitude
;
this quantity is used both directly, and to evaluate the estimated radiation flux in the absence of cloud
cover. The calculation of
is given in the following equations, where t is the time in hours (not using
daylight saving), and D is the day of the year, found from the internal ZENO clock:
360
365
23 27 801
01654 2 18 4 0 0058 3 15 3
12
15
15
12
12
o
oo
ooo
o
D
d
E
t
L
E
dd tt
t
s
t
;
.sin .;
. sin . . sin . ;
;
sin sin sin cos cos cos .
0.1227sin - 4.3
l
(3)
In these equations, all angles are in degrees and all times are in hours. The locally calculated quantities
are as follows:
the angle corresponding to the day of the year
d solar declination
E
t
equation of time (the difference between mean solar time, or clock time, and true solar time, or sundial
time)
t
12
the clock time corresponding to mean solar time
and the inputs, additional to the day and hour of the measurement, are:
L
s
the longitude of the standard meridian for the time zone of the site
l the actual site longitude
site latitude
Stefan-Boltzmann constant (5.6710
-8
W m
-2
K
-1
)
Given the value of the solar altitude
, measured in degrees, the quantities in equation (2), and hence the
net short-wave radiation, are calculated as follows. The cloud cover is estimated from the downward solar
radiation when
10º:
SS
c
S
S
p
t
p
079
375
1133 133
0
0294
.
.
sin ;
min , . .
.
o
;
(4)
Cloud cover when
<10º (overnight) is taken equal to the last measured value of c before sunset. If the
ZENO has started up since sunset when the net radiation calculation is carried out, the ZENO returns an
error code.
The albedo
is estimated to be 0.26.
The long-wave emissivity
a
of the atmosphere is calculated as:
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