Geog595 Ecological ModelingSpring, 2010Due: Feb 3, 2010Lab 2 Radiation Transfer Through Plant Canopies1. Objectives(1) Implement the theory of radiation transfer through plant canopies in Chapter 15 of Campbell and Norman (1998) in a C program.(2) Understand the effect of canopy structure of radiation interception.1. TheoryAssuming we have incoming radiation at the top of the canopy separated in direct anddiffuse radiation as Qob, Qod, respectively, the amount of direct radiation passing the canopy with black leaves is))(exp()( LKQQbobb, (1)and the amount of radiation passing the canopy with scattering leaves is))(exp()( LKQQbobbt,(2)where L is leaf area index and α is the leaf absorptivity. The beam radiation extinctioncoefficient Kb(θ) is 733.022)182.1(774.1)(tan)(xxxKb, (3)where x is the ration of average projected areas of canopy elements on horizontal and vertical surfaces. For spherical leaf angle distribution, x=1; for vertical distribution, x=0, and for a horizontal leaf canopy, x approaches infinity. The diffuse radiation passing through a scattering canopy is)exp( LKQQdodd, (4)where Kd is the diffuse radiation extinction coefficient. In order to estimate Kd, we need to estimate the diffuse radiation transmissivity first asdLKbd)2sin())(exp(2/0 . (5)From Eq (4), we can solve for the diffuse radiation extinction coefficient as LKdd)ln(. (6)The diffuse radiation at the top of the canopy is Qod, and it is Qd at the bottom of the canopy. Based on Eq (4), it is decreasing exponentially, the mean diffuse radiation intensity for the entire canopy should beLKQQQdddd0(7)According to Eqs (1) and (2), we know that the scattering direct radiation intensity isbbtscQQQ (8)Assuming scattering increases linearly through the canopy, the mean scattering intensity of direct radiation is half of the scattering at the bottom of the canopy as there is no scattering of direct radiation at the top of the canopy 2/scscQQ . (9)Therefore, the mean radiation intensity on the sunlit leaves in the canopy isscdobbslQQQKQ  )()(, (10)and the mean radiation intensity on the shaded leaves in the canopy isscdsdQQQ )( (11)2. Computer Experiments and Lab ReportBased on Lab 1, I have created a new program that will calculate the PAR intensity for sunlit and shaded leaves. Read through the program, and make sure how what theprograms are doing and how they relate to theory described above.(1) Assuming spherical leaf angle distribution, x=1 in Eq (3), run the model for LAI=1, 3, 5 and describe how the radiation intensity for sunlit and shade leaves changes with LAI. Graph the output with x-axis being time and y-axis being intercepted radiation, explain how the four components of radiation intercepted by leaves in the canopy change with LAI in the canopy?(2) Set LAI=5, and change x=0.5, 1.0 and 3.0 and run the model. Graph the output with x-axis being time and y-axis being intercepted radiation, explain how the four components of radiation intercepted by leaves in the canopy change with LAI in the canopy?(3) Cut and paste and add programs as necessary, create a separate C program so thatyou can run it independently, it will print zenith angle from 0 to 89 and the corresponding Kb(θ) with the x parameter provided on the command line, e.g. extinctco –x 0.5