Estimation of net radiation

Net radiation, R_n,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, R_is, air temperature, T_a, vapour pressure, e_a, and relative duration of sunshine, n_sun, as the sum of net short-wave radiation, R_snet, and net long-wave radiation, R_lnet given here by Brunt's formula:

                                                       (4.77)

where

                                                        (4.78)

and

                       (4.79)

where a_r 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) T_s 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, ε_s, 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 e_a is the vapour pressure in the air, n_c is the fraction of cloud covered sky and r_k1-3, r_b1-3 and r_s1-2 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.