Article Using Stochastic Ray Tracing to Simulate a Dense Time Series of Gross Primary Productivity Martin van Leeuwen 1,2, *, Nicholas C. Coops 1 and T. Andrew Black 3 Received: 22 September 2015; Accepted: 10 December 2015; Published: 18 December 2015 Academic Editors: Qi Chen, Huaiqing Zhang, Dengsheng Lu, Ronald E. McRorberts, Erkki Tomppo, Guangxing Wang, Randolph H. Wynne and Prasad S. Thenkabail 1 Forest Resources Management, University of British Columbia, 2424 Main Mall, Vancouver, BC V6T 1Z4, Canada; nicholas.coops@ubc.ca 2 Department of Geography, University College London, 26 Bedford Way, London WC1H 0AP, UK 3 Faculty of Land and Food Systems, University of British Columbia, 2357 Main Mall, Vancouver, BC V6T 1Z4, Canada; andrew.black@ubc.ca * Correspondence: vanleeuwen.martin@gmail.com; Tel.: +44-7-565-847-611; Fax: +44-20-7679-0565 Abstract: 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. Keywords: laser scanning; canopy structure; gross primary productivity; eddy covariance; data fusion 1. Introduction Monitoring forest productivity not only widens our ecological understanding, but is increasingly used as a diagnostic tool for evaluating silvicultural practices and testing compliance with political regulations regarding sustainable resource use. From an ecological point of view, information about forest productivity is often indicative of biodiversity richness [1] and can be used to explain how anthropogenic influences and climatic changes affect forest health and functioning [2]. A key variable is the gross primary productivity (P g ) that defines the uptake of carbon from the atmosphere before any losses due to respiration are subtracted. Estimates of P g are based on the amount of photosynthetically active radiation that is absorbed by the canopy (E ac ) and its pathways in photosynthesis [3–5]. The modelling of P g is challenging, however, due to the size and variability of the global forest resources, the multitude of environmental drivers, and the lack of control over these drivers in the field. As a result, a wide range of models exists that operate at a wide range of Remote Sens. 2015, 7, 17272–17290; doi:10.3390/rs71215875 www.mdpi.com/journal/remotesensing