Optimization of Apple Tree Canopy's Dynamic Light Energy Response Based on Ray Tracing Method and Whale Optimization Algorithm

Abstract

In the gullied regions of the Loess Plateau, effective utilization of solar energy within apple tree canopies is crucial for optimizing fruit yield and quality. This paper proposes a three-dimensional canopy morphology optimization method that combines ray tracing and whale optimization algorithms. Taking Luochuan County in Shaanxi Province, a key area within the global "Golden Apple Belt," as the research object, a dual-coordinate system light transmission model considering topographic effects is constructed. This model reconstructs 300-point cloud data into a triangular mesh canopy using an alpha shape function and simulates the interaction between sunlight and the canopy using the Möller–Trumbore algorithm. A dynamic lighting simulation is employed to establish an objective function that maximizes the annual average cumulative intercepted radiation (COR), as shown in Equation (20). After 1000 iterations of the whale optimization algorithm (WOA), the optimal canopy takes on a northwest-southeast ellipsoidal shape with an annual average COR of 49%. Increasing the curvature radius at the top by 22% enhances midday light capture, while the northwest extension mitigates topographic shading, concentrating 49% of the points receiving more than eight hours of light in this area. Furthermore, 78% of the points receiving more than eight hours of light are distributed in the middle and upper layers of the canopy, ranging from 1.2 to 1.8 meters, which aligns with the light requirements during fruit expansion. These findings provide insights into tree pruning in complex terrains to improve light efficiency.