Simple but realistic modeling of radiation transfer within heterogeneous canopy has been a challenging research question for decades and is critical for predicting ecological processes such as photosynthesis. The Markov model proposed by [Nilson, T., 1971. A theoretical analysis of the frequency of gaps in plant stands. Agric. Meteorol. 8, 25–38] is theoretically sound to meet this challenge. However, it has not been widely used because of the difficulty of determining the clumping factor. We propose an analytical approach to calculate clumping factors based on the average characteristics of vegetation distributed across a landscape. In a savanna woodland in California, we simulate the photosynthesis of the landscape in three different ways: (1) the crown envelope and location of each tree is spatially explicitly specified, (2) the canopy is assumed to be horizontally homogeneous within which leaves are randomly dispersed as a Poisson process, and (3) the canopy is horizontally homogeneous but leaves are clumped and distributed with a Markov process. We find that the Markov model can achieve much better performance than the Poisson model by incorporating the crown-level clumping. The results indicate that our approach of calculating clumping factors has applications in terrestrial ecosystem modeling, particularly where accurate representation of “system heterogeneity” (e.g., savannas and woodlands) is required.
