*2.1. Description of the Row Model*

### 2.1.1. General Form of Row Crops Based on a Geometric Optics Approach

In previous studies [17,30,31], the row canopy has been assumed to comprise periodic box-shaped plant materials with bare soil between the box-shaped scene (Figure 1a). Our study uses this assumption of the row canopy. The box-shaped plant materials are isotropic along the row (on the *y*-axis in Figure 1b). The reflectance at the top of the canopy of row crops (*r*) is of two proportions (i.e., *A*1/(*A*1 + *A*2) for the canopy closure and *A*2/(*A*1 + *A*2) between-row area) as well as the corresponding representative reflectance for each component, i.e., the reflectance at the top of the canopy closure (*rcanopy\_closure*) and

the reflectance at the top of the between-row area (*rbetween\_row*). The equation of reflectance at the top of the canopy of row crops is

$$\begin{split} r &= \frac{A\_1}{A\_1 + A\_2} r\_{\text{canopy\\_closure}} + \frac{A\_2}{A\_1 + A\_2} r\_{\text{between\\_row}} \\ &= \frac{A\_1 r\_{\text{canopy\\_closure}} + A\_2 r\_{\text{between\\_row}}}{A\_1 + A\_2} \end{split} \tag{1}$$

**Figure 1.** Sketch of the scene of row crops. (**a**) Overlapping relationship between leaves and canopy closures involved in the calculation of gap probabilities; (**b**) three-dimensional map of row crops. Here, *A*1 is the row width, *A*2 is the between-row distance, and *h* is the canopy height.

Here, *A*1 is the row width and *A*2 is the between-row distance. To facilitate a full understanding, *r*, *rcanopy\_closure*, and *rbetween\_row* are, respectively, called the sum of the reflectance of row crops, the reflectance of the canopy closure, and reflectance of the between-row area for short. In Equation (1), there are differences in the radiation mechanism of the canopy closure and between-row area. Therefore, the sum of the reflectance of row crops (*r*) is separated into the reflectance of the canopy closure (*rcanopy\_closure*) and between-row area (*rbetween\_row*) for consideration. According to Equation (1), the width of the row (*A*1) and between-row distance (*A*2) can be measured as input parameters. Therefore, *rcanopy\_closure* and *rbetween\_row* are key in row modeling. When *rcanopy\_closure* and *rbetween\_row* are calculated, it is implied that *r* can be calculated. As a result, we can establish a row model. Moreover, the sum of the reflectance of row crops (*r*) is composed of single- and multiple-scattering contributions [30,31]. Therefore, more detailed modeling examples for the singleand multiple-scattering contributions in the two areas are presented in the next two sections.
