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We used field measurements and Monte Carlo simulations of canopy gap-size distribution and gap fraction to examine how beam radiation interacts with clumped boreal forest canopies of aspen ( Populus tremuloides  Michx.), black spruce ( Picea mariana  (Mill.) B.S.P.) and jack pine ( Pinus banksiana  Lamb.). We demonstrate that the Beer-Lambert law can be modified to accommodate transmission of radiation through a clumped forest canopy as a function of path length or sun zenith angle. Multiband Vegetation Imager (MVI) measurements and Monte Carlo simulations showed that values of the zenith element clumping index (Ω e (0)) are typically between 0.4 and 0.5 in jack pine and black spruce and 0.65 in aspen. Estimates of LAI obtained from MVI measurements of the canopy gap fraction and adjusted for canopy clumping and branch architecture yielded LAI values of 3.0 in jack pine, 3.3 in aspen, and about 6.0 in black spruce. These LAI estimates were within 10–25% of direct measurements made at the same sites. Data obtained with the MVI, along with numerical simulations, demonstrated that assumptions of random foliage distributions in boreal forests are invalid and could yield erroneous values of LAI measured by indirect techniques and false characterizations of atmosphere–biosphere interactions. Monte Carlo simulations were used to develop a general equation for beam radiation penetration as a function of zenith angle in clumped canopies. The essential measurements included stem spacing, crown diameter, crown depth, and within-crown gap fraction.

Characterization of radiation regimes in nonrandom forest canopies: theory, measurements, and a simplified modeling approach