# Using Stochastic Ray Tracing to Simulate a Dense Time Series of Gross Primary Productivity
## 4 Discussion  
This study addressed some challenges around time series analysis of 3D radiative transfer in heterogeneous forest canopies with relevance for the integration of photosynthetic assimilation at stand and canopy element levels. The model utilizes three-dimensional canopy structural data to simulate light transport and photosynthesis at the level of individual scene elements from which \(P_{gs}\) is derived through integration. Despite the high level of geometric abstraction applied to the virtual scene, raising questions as to the exact meaning of individual canopy elements, the proposed method demonstrates significant potential for fusing data from diverse scales. The spatial distribution of \(E_{al}\) within the canopy was computed by integrating down-welling diffuse and direct PAR corrected  
Figure 8: Three model inversion cases (2094 observations, no cross validation) using different modifier functions to downregulate the theoretical optimal photosynthetic capacity and quantum yield. Shown are the correlation with eddy-covariance derived gross primary productivity estimates (**a–c**); the distribution of measured and simulated estimates of gross primary productivity against incident photosynthetically active radiation (**d–f**); average diurnal responses (**g–i**); and seasonal variation in the residuals (**j–l**). See Table 1 and text for an overview of parameters used for the different cases and Table 2 for an overview of parameter estimates obtained through model inversion. for the absorption probability that estimates the fraction of photon flux passing through the reference plane from a specific direction that is absorbed by a specific scene element. The model was parameterized using 3D structural data that was acquired with laser scanning technology and field observations of crown architecture, time series measurements of incident diffuse and direct PAR, and leaf-level photosynthesis parameters. While the virtual scene is constructed in forward modeling mode, the photosynthetic parameters were determined through model inversion against EC-derived \(P_{gs}\). Despite differences in scale between the modeled forest plot and the footprint of the EC flux tower, the model optimization resulted in simulated \(P_{gs}\) values matching the range of error typical for the EC technique (e.g., [12; 17; 60]). Moreover, photosynthesis model parameters \(P_{opt}\) and \(\alpha_{opt}\) were found within typical ranges for the leaf level, despite the coarse fidelity that was used to represent the canopy structure. When sun acclimation was introduced into the model using the nitrogen allocation parameter, \(k_{rub}\), estimates of \(P_{opt}\) exceeded those reported in literature, suggesting that other acclimation models need to be considered (e.g., [61]). Our finding that diffuse \(E_{ic}\) is a major control on \(P_{gs}\) confirms the findings by [62; 63]. For example, [PERSON] _et al._[63] found that \(P_{gs}\) of this stand can be effectively modelled with a single big leaf model using the sum of down-welling diffuse \(E_{ic}\) and a fraction (of approximately 20%) of down-welling direct \(E_{ic}\). A number of limitations of the proposed model remain, including neglecting the understory vegetation, the fidelity of the three-dimensional forest scene, assumptions of homogeneity of relative humidity and temperature within the canopy volume. The modelled scene does not represent individual needles or the clumping of needles into shoots, but rather comprises a limited number of canopy elements to represent foliage. Shading within shoots establishes significant effects on quantum yield and photosynthetic capacity [17; 64] that are excluded using our coarse-resolution scene. Inclusion of finer levels of detail is no restriction to the ray tracing method, however, and is increasingly supported through advances in (mobile) laser scanning technology and other 3D acquisition techniques.