Modeling BRDF over Row Crops Canopy with Effects of Intra-Row Heterogeneity

Row crops are regarded as a transitional type between continuous and discrete vegetation. Previous studies idealized row crops as periodic hedgerows with rectangular cross-sections. However, these models relied on oversimplified assumptions, failing to capture the intrinsic heterogeneity of canopy or its dynamic evolution over the life cycle. In 2020, we proposed a row crop model with a gradual decrease in leaf area volume density (LAVD) from the center of the row to the edge, partially overcoming these limitations. Building on this previous model, this paper introduces the leaf shape factor proposed by Mõttus et al. into the model. Three control parameters, a leaf width control parameter (β), leaf length control parameter (ψ), and leaf azimuth control parameter (e), are proposed to regulate the spatial distribution of LAVD. Additionally, an empirical exponential function from Watanabe et al. is adopted to describe the leaf zenith angle distribution, enabling the realistic calculation of the G-function and Γ-function in conjunction with leaf azimuth distribution. The LAVD is formulated at three hierarchical scales: individual scale, row scale, and scene scale. The model delivers two key advancements: enabling pronounced spatial heterogeneity and high tunability of the LAVD, and accurately simulating row crops throughout the life cycle, which bridges the row structure and continuous stages of row crops. Radiative transfer simulations are conducted to derive the bidirectional reflectance distribution function (BRDF), which is validated against the discrete anisotropic radiative transfer (DART) model. Comparisons across three growth stages demonstrated good consistency. Furthermore, this paper investigates the sensitivity of the BRDF to three control parameters (β, ψ, and e). The results indicate that changes in three parameters significantly affect the reflectance in the darkspot direction, leading to a maximum error of 22.6%. In carrying out remote sensing applications such as parameter inversion and yield estimation for row crops, the new model is recommended for more accurate BRDF simulations.