**Xu Ma and Yong Liu \***

College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China; max15@lzu.edu.cn **\*** Correspondence: liuy@lzu.edu.cn; Tel.: +86-139-1940-7135

Received: 21 September 2020; Accepted: 27 October 2020; Published: 2 November 2020

**Abstract:** The canopy reflectance model is the physical basis of remote sensing inversion. In canopy reflectance modeling, the geometric optical (GO) approach is the most commonly used. However, it ignores the description of a multiple-scattering contribution, which causes an underestimation of the reflectance. Although researchers have tried to add a multiple-scattering contribution to the GO approach for forest modeling, di fferent from forests, row crops have unique geometric characteristics. Therefore, the modeling approach originally applied to forests cannot be directly applied to row crops. In this study, we introduced the adding method and mathematical solution of integral radiative transfer equation into row modeling, and on the basis of improving the overlapping relationship of the gap probabilities involved in the single-scattering contribution, we derived multiple-scattering equations suitable for the GO approach. Based on these modifications, we established a row model that can accurately describe the single-scattering and multiple-scattering contributions in row crops. We validated the row model using computer simulations and in situ measurements and found that it can be used to simulate crop canopy reflectance at di fferent growth stages. Moreover, the row model can be successfully used to simulate the distribution of reflectances (RMSEs<0.0404). During computer validation, the row model also maintained high accuracy (RMSEs < 0.0062). Our results demonstrate that considering multiple scattering in GO-approach-based modeling can successfully address the underestimation of reflectance in the row crops.

**Keywords:** canopy model of row crops; multiple scattering for geometric optical approach; the gap probabilities of row crops; overlapping relationship; hotspot
