2.2.1. Preparations for Validation-Based Computer-Simulated Data

We used a 3D computer simulation to validate (or compare) the row models. In this study, the 3D computer simulation used an extended 3D Radiosity–Graphics Combined Model (RGM) [43,44]. The RGM model is a radiosity model based on a bilinear equation (a simple nonlinear di fferential

equation) [2]. It uses a numerical calculation method (Gauss–Seidel) to calculate the scattering of polygons in a scene constructed by a computer graphics method with high calculation accuracy [43,44]. To calculate the sum of the reflectance of row crops (*r*) for the RGM model, we divided it into two steps. In the first step, we used computer graphics to establish a computer scene similar to the assumption of our row model (the turbid medium bound in the periodic box-shaped vegetation material) (abstract scenes in Figure 4). For the abstract scene, we generated four representative scenes of row crops, namely the proportion of between-row dominance (Stage\_rc1), proportions of between-row and canopy closure equality (Stage\_rc2), the proportion of the canopy closure dominance (Stage\_rc3), and continuous crops (Stage\_cc). The parameters constructed in the abstract scene are shown in Table 1. In the second step, based on the established abstract scene, we used the RGM model to calculate polygonal scattering in the abstract scene, and finally calculated the sum of the reflectance of row crops (*r*). Moreover, the sum of the reflectance of row crops (*r*) calculated by the RGM model can be used as a "true value" to validate the sum of the reflectance of row crops calculated by our model with the same parameters in Table 1. In setting the angle, the solar zenith angle was 25◦ and the solar azimuth angle was 130◦ for both models. Moreover, to keep the computer scene consistent with the periodic box-shaped plant materials assumed by our model, we used the infinite canopy of the RGM model in this study (Appendix B in [43]). This set implies that the reflectance calculated by RGM is not the reflectance of the one- or two-row cycle shown in Figure 4, but the reflectance of the scene where the row cycle is infinitely extended. The output results of reflectance are shown in Section 3.1.

**Figure 4.** The abstract scenes of row crops. (**a**) The proportion of between-row dominance (Stage\_rc1), (**b**) proportions of between-row and canopy closure equality (Stage\_rc2), (**c**) proportion of the canopy closure dominance (Stage\_rc3), and (**d**) continuous crops (Stage\_cc).


**Table 1.** Values required when constructing abstract scenes with computer graphics.

1 Here, the inclined leaf angle and azimuth leaf angle are set to a random distribution. By counting the leaf inclination angle and width of the leaves for each polygon, we obtained the average leaf inclination angle (θl) and the characteristic width of leaves ( *Wp*).

### 2.2.2. Preparations for Validation-Based In Situ Data

The measurements include two sites in arid Northwestern China: Zhangye, Gansu Province, and Zhongwei, Ningxia Hui Autonomous Region. Field and satellite measurements were performed in Zhangye and Zhongwei, respectively.

## 1. Field measurement data in Zhangye

The in situ data of Zhangye came from Watershed Allied Telemetry Experiment Research (WATER) [45,46] and were measured from 20 May to 11 July 2008. A plot with an area of 180 × 180 m was selected, and the center coordinates of the plot were 38.857056◦N, 100.410444◦E (Figure 5). The type of crop in the plot was corn, and four quadrats were randomly selected to measure the

required parameters for validation. In the measurement of optical parameters, the reflectances of the illuminated leaf (*rc*), shaded leaf (*ri*), illuminated soil (*rz*), and shaded soil (*rg*) were measured by the ASD FieldSpec Pro Spectrometer [47,48]. The sum of the reflectance of row crops (*r*) (blue line in Figure 9) was measured by the ASD FieldSpec Pro Spectrometer, and the distance from the sensor to the top of the canopy was about 1 m, ensuring that at least one row cycle was observed. The measured spectral curve was from 400 to 2500 nm. The measurement time was 22 May, 25 May, 1 June, 16 June, 22 June, and 1 July (Table 2) [47,48]. Since the row structure was obvious on 22 June (Table 2), we performed a multiangle observation. The sum of the reflectance of row crops (*r*) (blue triangle scatter and blue line in Figure in Section 3.2.2) was measured by the ASD FieldSpec Pro Spectrometer combined with the multiangle frame. The distance between the instrument and ground was 5 m, the field of view was 25◦, and a complete row cycle was observed. The zenith angle was from −60◦ to 60◦ with 10◦ for an interval [49]. The study considered the anisotropy of reflectance. Measurements were separated by four modes in the azimuth: the principal plane (PP), orthogonal plane (OP, viewing azimuth angle perpendicular to the sun azimuth angle), along-row plane (AR, the plane along the row direction), and orthogonal row plane (OR, the plane perpendicular to the row direction). The other structure parameters used the direct measurement method [50–52]. These parameters were the leaf area index (*L*), average leaf inclination angle (θ*l*), row width ( *A*1), between-row distance ( *A*2), canopy height (*h*), characteristic width of leaves ( *Wp*), and row azimuth angle ( ϕ*r*). The measurement results are shown in Table 2. The output results of the spectral curve for the growing season are displayed in Figure 9. Corresponding output results of the distribution of reflectances in the multiangle observation (22 June, in Table 1) are displayed in Section 3.2.2.

**Figure 5.** Geographic location of the study area (**a**) Plots in Zhangye and Zhongwe; (**b**) World-View 3 image in the Zhongwei area and its corresponding quadrats. Here, the field measurement was performed in Zhangye, hence there is no satellite image. The green points in (**b**) represent the quadrats in the field measurement with the same size as the resolution of the World-View 3 image.
