Campbell Scientific VisualWeather Software - Manual (Page 58)

Appendix A. Evapotranspiration, Vapor Pressure Deficit, and Crop Water Needs
2b. Calculation of the Radiation Ratio (Rs/Rso)
Rs = measured value of solar radiation (MJ/m 2 /hour)
Rso = clear sky solar radiation; i.e., solar radiation with no cloud cover
(MJ/m 2 /hour)
The general equation used to calculate the solar radiation is:
Rs = (a
s
+ b
s
(n/N))R
a
(4)
where
a
s
= constant = 0.25
b
s
= constant= 0.50
n = actual sunshine hours on a given day
N = expected sunshine hours on a given day
R
a
= extraterrestrial radiation
If the day is entirely clear then n = N and
Rs = (a
s
+ b
s
)R
a
= (0.25 + 0.50)Ra ˜ 0.75Ra = Rso.
If the day is entirely cloudy, then n = 0 and Rs = (a
s
)R
a
˜ 0.25 Ra.
Therefore the ratio, Rs/Rso on a completely cloudy day would be:
Rs/Rso ˜ 0.25 Ra/0.75 Ra ˜ 0.33 about 0.3.
Therefore, 0.3 < Rs/Rso < 1.0 define limits of the ratio.
In the nighttime
Rs = 0 at nighttime. However, Rs/Rso should not be taken to be 0 or 0.3,
since the sky may be cloud free. For the nighttime the radiation ratio 2 to
3 hours before sunset is used. To identify this radiation ratio 2 to 3 hours
before sunset, the following algorithm is used:
When the solar time angle ( ω), satisfies the following condition, the
radiation ratio is saved and used throughout the night:
( ω
s
- 0.79) <= ω <= (ω
s
- 0.52)
where ω
s
is the sunset hour angle (in radians). ω
s
is calculated as follows:
ω
s
= π/2 - arctan[ tan(φ)tan(δ) / X 0.5 ] (5)
where X = 1 -[ tan( φ)] 2 [tan( δ)] 2 and X = 0.00001 if X <= 0
2c. Calculations for R
SO
(clear sky radiation).
Measured values of solar radiation, R
S
, are actually extraterrestrial
radiation (Ra) reaching the earth corrected by daily conditions; i.e.,
whether a particular day is clear or overcast. The following equation
shows this relation:
R
S
= (a
S
+ b
S
(n/N)) R
a
(6)
A-4