412
w. Beyschlag et al.
radiation, air temperature above the canopy, soil surface temperature, relative humidity, and foliage density and orientation. The distribution of foliage
was then used to weight individual layer calculations to arrive at whole
canopy rates. A list of input parameters for this model is given in Table
20.1 and the basic model computation flow is shown in Fig. 20.1. The structure of these models is modular, allowing for the replacement of specific
routines by formulations. The time steps for the model are arbitrary but 1-h
steps were used throughout the course of daylight hours in this work.
Routines to calculate incident light on leaves, leaf temperature, and the
gaseous exchange of CO2 and H20, follow.
20.3.1.1 Incident Shortwave Radiation on Leaves
Incident shortwave radiation on leaves is calculated for direct beam, sky
diffuse, and reflected and transmitted diffuse within the canopy. The canopy
is assumed to be continuous without borders or edges that receive radiation.
The penetration of direct beam solar radiation into the canopy is calculated
following the classical gap probability functions (Monsi and Saeki 1953;
Warren Wilson 1960; Duncan et al. 1967) and is a function of solar position
in the sky and the surface area, inclinations, and dispersion patterns of
foliage in each layer. While the intensity of direct beam shortwave radiation
does not decrease through the canopy, the area of the beam is reduced by
foliage interception. Thus, the fraction of sunlit leaves within each layer is
calculated with the incident beam being calculated for both sides of the leaf
for the sunlit portions with corrections made for the angle between the leaf
surface and the direct beam (Burt and Luther 1979). Diffuse shortwave
radiation from the sky reaching leaves in the different canopy layers is
calculated in a manner analogous to that for direct beam; however, the intensity of sky diffuse decreases with foliage interception, not area. Different
segments of the sky are taken as the source of radiation, with the hemisphere
divided into nine annular rings of uniform brightness (Duncan et al. 1967).
Diffuse radiation intensity through the canopy from the different sky segments is calculated separately and then integrated for all sky bands for
foliage in each layer. All leaves within a layer are assumed to obtain the
same incident sky diffuse with calculations made for both sides of a leaf
(Duncan et al. 1967). Shortwave radiation is reflected from and transmitted
through foliage as well as reflected from the soil surface. Contributions to
the incident flux on foliage in each layer is calculated from these sources of
diffuse shortwave radiation according to Duncan et al. (1967). The total
incident shortwave radiation flux on leaves is then calculated as the sum of
direct beam, sky diffuse, and reflected and transmitted diffuse of sunlit
leaves and the same without direct beam fluxes for shaded leaves. Similar
calculations can be made for stems if they have photosynthetic potential.
w. Beyschlag et al.
radiation, air temperature above the canopy, soil surface temperature, relative humidity, and foliage density and orientation. The distribution of foliage
was then used to weight individual layer calculations to arrive at whole
canopy rates. A list of input parameters for this model is given in Table
20.1 and the basic model computation flow is shown in Fig. 20.1. The structure of these models is modular, allowing for the replacement of specific
routines by formulations. The time steps for the model are arbitrary but 1-h
steps were used throughout the course of daylight hours in this work.
Routines to calculate incident light on leaves, leaf temperature, and the
gaseous exchange of CO2 and H20, follow.
20.3.1.1 Incident Shortwave Radiation on Leaves
Incident shortwave radiation on leaves is calculated for direct beam, sky
diffuse, and reflected and transmitted diffuse within the canopy. The canopy
is assumed to be continuous without borders or edges that receive radiation.
The penetration of direct beam solar radiation into the canopy is calculated
following the classical gap probability functions (Monsi and Saeki 1953;
Warren Wilson 1960; Duncan et al. 1967) and is a function of solar position
in the sky and the surface area, inclinations, and dispersion patterns of
foliage in each layer. While the intensity of direct beam shortwave radiation
does not decrease through the canopy, the area of the beam is reduced by
foliage interception. Thus, the fraction of sunlit leaves within each layer is
calculated with the incident beam being calculated for both sides of the leaf
for the sunlit portions with corrections made for the angle between the leaf
surface and the direct beam (Burt and Luther 1979). Diffuse shortwave
radiation from the sky reaching leaves in the different canopy layers is
calculated in a manner analogous to that for direct beam; however, the intensity of sky diffuse decreases with foliage interception, not area. Different
segments of the sky are taken as the source of radiation, with the hemisphere
divided into nine annular rings of uniform brightness (Duncan et al. 1967).
Diffuse radiation intensity through the canopy from the different sky segments is calculated separately and then integrated for all sky bands for
foliage in each layer. All leaves within a layer are assumed to obtain the
same incident sky diffuse with calculations made for both sides of a leaf
(Duncan et al. 1967). Shortwave radiation is reflected from and transmitted
through foliage as well as reflected from the soil surface. Contributions to
the incident flux on foliage in each layer is calculated from these sources of
diffuse shortwave radiation according to Duncan et al. (1967). The total
incident shortwave radiation flux on leaves is then calculated as the sum of
direct beam, sky diffuse, and reflected and transmitted diffuse of sunlit
leaves and the same without direct beam fluxes for shaded leaves. Similar
calculations can be made for stems if they have photosynthetic potential.