Using Stochastic Ray Tracing to Simulate a Dense Time Series of Gross Primary Productivity

Eddy-covariance carbon dioxide flux measurement is an established method to estimate primary productivity at the forest stand level (typically 10 ha). To validate eddy-covariance estimates, researchers rely on extensive time-series analysis and an assessment of flux contributions made by various ecosystem components at spatial scales much finer than the eddy-covariance footprint. Scaling these contributions to the stand level requires a consideration of the heterogeneity in the canopy radiation field. This paper presents a stochastic ray tracing approach to predict the probabilities of light absorption from over a thousand hemispherical directions by thousands of individual scene elements. Once a look-up table of absorption probabilities is computed, dynamic illumination conditions can be simulated in a computationally realistic time, from which stand-level gross primary productivity can be obtained by integrating photosynthetic assimilation over the scene. We demonstrate the method by inverting a leaf-level photosynthesis model with eddy-covariance and meteorological data. Optimized leaf photosynthesis parameters and canopy structure were able to explain 75% of variation in eddy-covariance gross primary productivity estimates, and commonly used parameters, including photosynthetic capacity and quantum yield, fell within reported ranges. Remaining challenges are discussed including the need to address the distribution of radiation within shoots and needles.