Canopy Semi-analytic Pgₐₚ And Radiative Transfer (CanSPART) model: Formulation and application

We present CanSPART: a model of gap probability (Pgₐₚ) based on a simple but flexible geometric vegetation canopy structure, coupled to a one-dimensional radiative transfer scheme, to account for the effects of crown structure and trunks on vertically resolved canopy radiation fluxes. The Pgₐₚ component of the model is intended for use in inverting ground-based and airborne gap-frequency data for biometric variables, while the full CanSPART model is intended for application within a one-dimensional multilayer soil-vegetation-atmosphere-transfer model. Our approach to modelling Pgₐₚ is novel because it uses an analytic approximation to the crown porosity, which makes it computationally efficient. Further, it can accommodate any distribution of crown and trunk heights and dimensions, allowing the model to be applied to complex canopy structures with multiple layers. The Pgₐₚ model is readily rewritten in terms of a clumping factor as a function of height and angle. Simulations of Pgₐₚ(θ,z) for idealised canopies compared favourably with those of two other models: the Analytical Clumped Two-Stream (ACTS) model (Ni-Meister et al., 2010) and an adaptation of the Nilson (1999) model. We test the analytic approximation to the crown porosity, also inherent in the Nilson (1999) model, and the applicability of a single clumping factor without angle nor height dependence. Both simplifications are demonstrated to be valid. Lovell et al. (2012, this issue) provide quantitative assessment of the Pgₐₚ component of CanSPART against ground-based lidar measurements from sites spanning a range of canopy structures. The radiative-transfer part of the model is an extension of the two-stream scheme, using Pgₐₚ as input and requiring the solution of a single matrix equation. In contrast to existing modified two-stream models which use a clumping factor, we account for both the primary effect of clumping (enhanced uncollided flux intensities) and the secondary effect (enhanced interception of scattered radiation). Application of CanSPART to three contrasting Australian field sites show that Pgₐₚ, the absorption of radiation by leaves, Qₗₑₐf, and albedo are sensitive to the clumping of leaves into crowns. Except for the most sparsely vegetated site, albedo predictions were significantly too high, unless both primary and secondary effects of clumping were included. This highlights the importance of accounting for the enhanced interception of radiation scattered by leaves in a clump