Campbell Scientific VisualWeather Software - Manual (Page 57)

Appendix A. Evapotranspiration, Vapor Pressure Deficit, and Crop Water Needs
2. Calculations for R
n
(net radiation at the crop surface).
The net radiation, R
n
, is the algebraic sum of radiation at the crop's
surface, with the sign convention that the incoming radiation is positive
and the outgoing radiation is negative. The incoming radiation is higher in
energy (i.e., shorter in wavelength) than the outgoing radiation (which is
longer in wavelength). The net radiation at the crop's reference surface is:
nl ns n
R R R − =
where: R
ns
= Shortwave Radiation = 0.77Rs
R
nl
= Longwave Radiation
In the daytime incoming net radiation > outgoing net radiation, R
ns
> R
nl
,
therefore R
n
is positive.
In the nighttime incoming net radiation < outgoing net radiation, R
ns
<
R
nl
, therefore R
n
is negative.
The overall value of R
n
is positive over a 24-hour period.
2a. Calculations for R
nl
(long wave radiation at the crop surface).
The amount of energy radiated back into the atmosphere is proportional to
the fourth power of the absolute temperature of a radiating surface (R
nl
αT 4 ). This is known as Stefan-Boltzmann's law, in context with black
body radiation. The proportionality constant for this relation is known as
Stefan-Boltzmann constant,
σ.
The value of the Stefan-Boltzmann constant is:
σ =
4.903x 10 MJ m K day = 4.903x 10 x 10
(1 day x 24 hours / day x 3600 sec / hour)
-9 -2 -4 -1 -9 6
= 5.675 x 10 -8 W m -2 K -4
However, the radiation emitted into the atmosphere gets absorbed by
clouds, vapors, dust and gases like CO
2
. Thus the magnitude of R
nl
would
be less than that predicted by the Stefan-Boltzmann law. Therefore, in
calculating R
nl
, the Stefan-Boltzmann law has to be corrected by
considering factors such as humidity and clouds and assuming that
concentrations of other absorbers remain constant. The following
equation is used to calculate the long wave R
nl
.
R
nl
= σ T
hr
4 (0.34 - 0.14 (e
a
) 1/2 ) (1.35 (R
S
/ R
SO
) - 0.35) (3)
where, R
nl
= net outgoing longwave radiation (MJ m -2 hour -1 )
σ = 2.043 x 10 -10 (MJ m -2 K -4 hour -1 )
e
a
= actual vapor pressure (kPa)
R
S
= measured solar radiation (MJ m -2 hour -1 )
R
SO
= calculated value of clear-sky solar radiation (MJ m -2 hour -1 )
R
S
/R
SO
= relative value of short wave radiation, 0.2 <R
S
/R
SO
<=
0.8 (no units)
T
hr
= hourly average temperature in Kelvin
A-3