Geog 595 Ecological modeling
Lecture Notes
Spring 2010
Net Radiation for Vegetation Canopies
1. Shortwave Radiation
Given the shortwave radiation intercepted by sunlit leaves and shaded leaves for PAR and NIR, the total absorbed radiation for PAR can be estimated as
where
Similarly, we have the total absorbed radiation for NIR as
where
The total shortwave radiation absorbed by the canopy is
The shortwave radiation entering the forest floor from canopy includes direct PAR, diffuse PAR, direct NIR and diffuse NIR. Given the reflectance of forest floor, ρs, the absorbed shortwave radiation on the forest floor is
Where
2. Longwave Radiation
Any object with temperature greater than 0oK emits radiation. The total amount of energy emitted by a blackbody is given by Stefean-Boltzman’s law:
For real world objects, they are not as efficient emitting radiation as a blackbody. We call the real world object a grey body. The ratio of the total amount of energy emitted by a real world object to that of a blackbody is called emissivity.
Therefore, as long as we know the emissivity of a real world object, we can estimate its total amount of energy emitted at a given temperature as
Scientists found that the emissivity for the real world objects is pretty close to 1. For vegetation canopy, εcanopy=0.98; for forest floor, εfloor=0.95. Therefore, the longwave radiation emitted by vegetation canopy and forest floor can be modeled as
However, the emissivity for atmosphere is more complicated as it varies with cloud cover. For clear skies, the emissivity of the atmosphere can be estimated as (Brustaert, 1975):
Where ea is the vapor pressure of the air in mb (1 mb =100 Pa), and Tair is in degrees Kelvin. For cloudy skies, the emissivity of the air is a function of cloud cover as (Unsworth and Monteith, 1975):
Where c is the fraction of cloud cover of the sky [0,1]. Cloud cover is often not recorded. Song et al. (2009) developed an approach estimating the cloud cover during the day time based on the total transmittance, τ.
Based on our work separating radiation into direct and diffuse component, we know that for a clear day, τ=0.7, i.e. c=0. When τ =0.3, the total radiation is 100% diffuse, i.e. c =1.0, thus
Because the longwave radiation from the atmosphere arrives in all direction, it can be treated as diffuse radiation. Leaves are highly absorptive to the longwave radiation, thus they can be treated as black leaves. The average longwave radiation plant canopy absorb is
At the same time, canopy also absorb longwave radiation from the forest floor, which can be modeled similarly,
The total absorbed longwave radiation by the canopy per unit LAI is
In the meantime, canopy itself is emitting longwave radiation both upward and downward.
Therefore, the net longwave radiation in the plant canopy is
The net canopy radiation is
The total canopy net radiation by both sunlit and shaded leaves is
For the forest floor, it receives longwave radiation from the air through the gaps and from the canopy that is not gap. In the meantime, it emit longwave radiation. Thus, the net long wave radiation for the forest floor is
The net radiation for the forest floor considering both shortwave and longwave radiation is
The total net radiation for the who stand is