Modelling radiation interception by strongly clumped vegetation — a combined monte‐carlo and analytical model

The study of solar radiation penetration into plant stands is important to studies of energy balance and photosynthesis. A large literature deals with horizontally uniform canopies of random leaf placement, in which a simple model based on Poisson statistics accounts for the probability, P ( z ), of ray penetration without interception to depth x: P ( z ) = exp [‐ k (η) A ( z )/cosη] where η is the ray origin zenith angle, k depends upon the distribution of leaf orientations and A ( z ) is leaf area per unit ground area to depth z . When leaf location is either clumped or regular other statistical models are applied. These, unlike the above model, require the empirical determination of parameters by fitting to interception data. More extreme clumping, into isolated plants or hedgerows, has been handled by calculating ray path lengths through the stand within an envelope defining the plant shape and applying the above model for uniform random leaf arrangement along these parts of the paths. For regular arrangements of uniform sized plants this is a matter of straightforward but lengthy calculation. The problem considered here, of randomly placed plants of non‐uniform size, cannot be treated by the same method. To determine within‐plant pathlengths, the intersection points of randomly chosen rays with the outlines of plants were first computed, then the above model was applied along each within‐plant path and the results of many rays from each direction were averaged. There are no parameters to be empirically fitted. Results are presented for cylindrical, conical and spherical plant outlines.