Estimation of net radiation

Net radiation, Rn,tot, would ideally be supplied as a measured time-series but in most cases it has to be estimated from other meteorological variables. It can be deduced from global radiation, Ris, air temperature, Ta, vapour pressure, ea, and relative duration of sunshine, nsun, as the sum of net short-wave radiation, Rsnet, and net long-wave radiation, Rlnet given here by Brunt's formula:

                                                       (4.77)

where

                                                        (4.78)

and

                       (4.79)

where ar is the surface albedo (relative short-wave reflectance), r1 to r4 are empirical parameters and σ is the Stefan-Boltzmann’s constant. See viewing function Net Long Wave Radiation, One formula approach.

As an alternative formula for the net long-wave radiation (see switch LongWaveBalance) the user may also chose:

                     (4.80)

where the temperature of the soil surface (and/or the canopy and snow surface temperatures) Ts is explicitly used. This corresponds to the use of two separate equations for the incoming and outgoing long-wave radiation. The emissivity of the surface, εs, is assumed to be equal to 1 and the emissivity of the atmosphere can be calculated from one of (4.81)- (4.83)  as determined by the switch InLongRad:

                    (4.81)

                                             (4.82)

                           (4.83)

 

where ea is the vapour pressure in the air, nc is the fraction of cloud covered sky and rk1-3, rb1-3 and rs1-2 are parameters. The formula from Konzelmann et al (1994) is recommended for most cases (eq (4.81)). The original formulations of Brunt and Satterlund are complemented with a cloud correction term based on a general formula from Monteith "Principles of environmental Physics" (eq (4.82)  & (4.83)). See also viewing functions Incoming and outgoing long-wave radiation, Brunt's formula, Incoming and outgoing long-wave radiation, Konzelmann and Incoming and outgoing long-wave radiation, Satterlund.