Method of Measurement of Transmissivity of Atmospheric Radiation and of Calculation of Net Long Wave Radiation within Plant Communities

Abstract

In this paper the method of measurement of transmissivity of atmospheric (long wave) radiation through plant layer and of calculation of net long wave radiation within plant communities are described.
(1) There are two methods for determining the transmissivity. The first method is used under isothermal conditions at night. The method is described in the followings. The net radiation at the top surface of plant communities, R_n0, is expressed by
R_n0=L₀^↓-σT⁴ (1)
where L₀^↓ is the atmospheric radiation and T is the plant temperature. If the transmissivity of atmospheric radiation through the plant layer between z=0 and z=z is t_z, the emissivity of the layer (1-t_z). Then the downward long wave radiation from the plant layer above z is (1-t_z)·σT⁴. Net long wave radiation at z, R_nz, is written as
R_nz=t_z·L₀^↓+(1-t_z)·σT⁴-σT⁴ (2)
The first term in the right-hand side of eq. (2) represents the contribution of atmospheric radiation, and the third term the up-ward radiation from the plant layers below z and the soil surface. From eqs. (1) and (2)
t_z=R_n0/R_nz (3)
Thus, t_z is obtained from observed values of net radiation at z=0 and z=z.
The second method can be used under the condition of arbitrary vertical distribution of plant temperature. The transmissivity can be determined more directly than in the first method. Let L₀^↑ be the up-ward radiation at z=0, L_pz^↓ downwrd radiation from the plant layers above z, L_z^↑ up-ward radiation from the plant layers below z and the soil surface, R_n0 and R_nz are expressed by
R_n0=L₀^↓-L₀^↑ (4)
R_nz=t_z·L₀^↓+L_pz^↓-L_z^↑ (5)
Sudden change in incoming long wave radiation at the top is applied-in practice, plants were covered with a large sheet of linen. Under this condition, L₀^↑, L_pz^↓ and L_z^↑ remain practically unchanged. Hence net radiation at z=0 and at z=z, R′_n0 and R′_nz, are expressed by
R′_n0=L′₀^↓-L₀^↑ (6)
R′_nz=t_z·L′₀^↓+L_pz^↓-L_z^↑ (7)
wher L′₀^↓ is downward long wave radiation emitted from the sheet. From eqs. (4)-(7)
t_z=(R_nz-R′_nz)/(R_n0-R′_n0) (8)
Then the transmissivity is calculated from eq. (8) with four observed values of net radiation. This experiment was conducted at night. Fig. 1 shows variation of the transmissivity with height within a paddy field by the second method. The transmissivity may be expressed by
t_z=exp(-∫A(z)dz)
where A(z) is a function of plant densities.
(2) Provided that the transmissivity of atmospheric radiation in the plant layer is given, net long wave radiation within plant layers can be calculated. The transmissivity at a, b, z, c and d are expressed as t_a, t_b, t_z, t_c and t_d respectively (Fig. 3). The transmissivity of long wave radiation thro