Compute the daily net radiation of the system using incident radiation, air temperature, wind speed, relative humidity and the albedo. A clear description of this methodology can be found in Allen et al. (1998) or in An et al. (2017).
Rad_net( DOY, RAD, Tmax, Tmin, VPD, Rh = NULL, Latitude, Elevation, albedo, sigma = Constants()$sigma, Gsc = Constants()$Gsc )
| DOY | Ordinal day, which is the day of year from 1st January (\(day\)) |
|---|---|
| RAD | Incident daily total radiation (\(MJ\ m^{-2} d^{-1}\)) |
| Tmax | Maximum daily air temperature (celsius degree) |
| Tmin | Minimum daily air temperature (celsius degree) |
| VPD | Mean daily Vapor Pressure Deficit (\(hPa\)), only needed if |
| Rh | Average daily relative humidity ( |
| Latitude | Latitude (\(deg\)) |
| Elevation | Elevation (\(m\)) |
| albedo | Shortwave surface albedo (-) |
| sigma | Stefan-Boltzmann constant (\(W\ m^{-2} K^{-4}\)), default to |
| Gsc | Solar constant (\(W\ m^{-2}\)), default to |
\(Rn\), the daily net radiation (\(MJ\ m^{-2} d^{-1}\))
The daily net radiation is computed using the surface albedo. This method is only a
simple estimation. Several parameters (ac, bc, a1 and b1) are taken from
Evett et al. (2011). The net radiation is computed as:
$$Rn=(1-\alpha)\cdot RAD-(ac\cdot\frac{RAD}{Rso}+bc)\cdot(a1+b1\cdot ea^{0.5})\cdot\sigma\cdot\frac{T_{\max}^4+T_{\min}^4}{2}$$
And is derived from the equation :
$$Rn= (1-\alpha)\cdot RAD-Rln$$
where \(Rln\) is the net upward longwave radiation flux, \(\alpha\) is the albedo, \(R_{so}\) the
daily total clear sky solar irradiance, computed as follow:
$$R_{so}= (0.75+0.00002\cdot Elevation)\cdot R{sa}$$
where \(R_{sa}\) is the daily extra-terrestrial radiation, computed using Rad_ext().
The actual vapor pressure \(ea\) can be computed using either VPD or the relative
humidity and the maximum and minimum daily temperature. If both are provided, Rh will
be used.
An, N., S. Hemmati, and Y.-J. Cui, Assessment of the methods for determining net radiation at different time-scales of meteorological variables. Journal of Rock Mechanics and Geotechnical Engineering, 2017. 9(2): p. 239-246.
# Daily net radiation on january 1st at latitude 9 N : Rad_net(DOY= 1,RAD= 5,Tmax= 16,Tmin= 10,VPD=1.05, Latitude=9,Elevation=1000,albedo=0.146)#> [1] 4.270029