The Improved Canopy Shading Model Based on the Apple Intercropping System (Case Study: Loess Plateau, China)

The canopy shading model is widely used in agroforestry systems. However, the canopy shading model cannot be verified by the measured shading distribution of an apple tree due to the uneven ground and adjacent apple trees. This paper measures the spatial‒temporal distribution of the shading of apple trees based on the similarity principle of parallel solar light combined with 3D printing technology to improve the canopy shading model. The following results are drawn: (1) The current widely used canopy shading model does not consider the effect of the canopy penumbra, resulting in poor simulation accuracy in the shading distribution compared to the actual measurement; (2) The effect of canopy penumbra causes the deflection of sunlight. Hence, the paper presents the deflection equation of sunlight with statistically defined parameters derived using measured data of the shading distribution. The deflection equation of sunlight is added to the improved canopy shading model. The improved model can accurately simulate the shading distribution of an apple tree, and the simulation accuracy exceeds 94.12% when compared with the shading distribution of an apple tree; (3) The improved canopy shading model is applied to simulate the spatial‒temporal distribution of the shading of apple trees in a conventional arrangement (4 m × 5 m), and the simulation accuracy exceeds 89%. Thus, the improved canopy shading model can be applied to simulate the spatial‒temporal distribution of shading of apple trees.