Campbell Scientific VisualWeather Software - Manual (Page 59)

Appendix A. Evapotranspiration, Vapor Pressure Deficit, and Crop Water Needs
Where n = number of hours of actual sunshine (hours)
N =maximum possible number of hours of expected sunshine
(hours)
For a completely overcast day n = 0; therefore,
R
S
= a
S
Ra, the constant a
S
= fraction of extraterrestrial radiation reaching
the earth on a overcast day.
For an entirely clear day n = N
R
S
= (a
S
+ b
S
)Ra = clear sky radiation , a
S
+ b
S
= fraction of extraterrestrial
radiation reaching the earth on a clear day. Thus,
R
S
= (a
S
+ b
S
)Ra = R
SO
(7)
When calibrated values of a
S
and b
S
are not available,
R
SO
= (0.75 + 2 x 10 -5 z )Ra (8)
Where: z= station elevation in meters
2d. Calculations for R
a
(extraterrestrial radiation).
The extraterrestrial radiation, Ra, can be calculated as follows:
Ra =
12 (60)
G dr[( 2 - 1)sin( )sin( ) + cos( )cos( )(sin( 2) - sin( 1))]
Sc π
ω ω φ δ φ δ ω ω (9)
G
Sc
= Solar constant = 0.0820 MJ m -2 Min -1 =1.36 x 10 3 W/m 2 = 1.36 k
W/m 2
d
r
= inverse relative distance Earth-Sun =
1 + 0.033 cos ( (2 π /365) J ) , J is day of the year (10)
δ = solar declination (radians) =
0.409 sin ((2 π/365) J - 1.39) (11)
φ = latitude of the location (radians ) = ( π/180) x latitude in degrees
ω
1
= solar time angle at the beginning of period (radians) =
ω - π t
1
/24 = ω - π /24 for hourly step (12)
ω
2
= solar time angle at the end of period (radians) = ω + π t
1
/24 = ω + π
/24 for hourly step, since t
1
= 1
ω = solar time angle at midpoint of the period =
( π/12) [ (time + 0.06667( Lz - Lm ) + S
c
) -12] (13)
time = standard (military) clock time at the midpoint of the period
(hours); e.g., t =14.5 hours between 1400 and 1500 hours.
A-5