*4.3. Analysis of the Row Model*

As a GO model, our model mainly uses the geometric relationship between light and medium to calculate the sum of the reflectance. The RGM model is a computer model based on radiosity. It uses the geometric probability between leaves to calculate the sum of the reflectance. Specifically, a view factor describing the overlapping relationship between polygons (leaves) was previously introduced into the RGM model [43]. If we exclude the numerical calculation of reflectance (Gauss–Seidel algorithm [44]) in the RGM model, the geometric principles involved in our model are very similar to those of the RGM model. Therefore, based on similar physical principles, the consistency between the simulation results of our model and the RGM model is high (Figures 6–8, MAD is less than 10% in Table 4). However, our model still shows calculation deviation in the in situ validation, especially in the distribution of the sum of the reflectance on the multiangle observation (Figure 11, MAD is less than 24% in Figure 12). These results imply that the calculation deviation may come from other sources. At present, it is di fficult for multiangle instruments to accurately measure directional reflectance (specifically, bidirectional reflectance distribution function (BRDF) [58]) and obtain an approximate reflectance distribution. In theory, directional reflectance (BRDF) refers to the measurement value at the same time (the same second), and there is no shadow of the instrument (note: the instrument is nontransparent) during the measurement [58], which is hard to achieve with the current instruments. In the multiangle observation, instruments take at least 10 minutes or more to complete the four modes (PP, OP, AR, and OR). Even if the measurement is performed in strict accordance with the measurement specification, changes in environmental variables over time will have a strong influence on measurement [59]. Therefore, the results in the measurements are only an approximation (abnormal points in the black box in Figure 11a,c,e). The instrument had a field of view (FOV) of 25◦ (common FOV of ASD spectrometer), and the observation distance was 5 m (this height is di fferent from the current canopy reflectance model assuming that the sensor is located at infinity) in our study. Therefore, we observed the sum of the reflectance of a limited row cycle (a canopy closure plus a between-row area) in FOV (according to Table 1, we used the triangular relationship to calculate that the observed row cycle changes from 2.2 to 10.4 and from 0◦ to ±60◦ in the zenith angle), which is di fferent from our model assumptions (periodic box-shaped plant materials). However, the validations of computer simulation have not been influenced by time in the multiangle observation. The infinite canopy is set in the RGM model in this study [43], which is the same as our model assumptions. This implies that the validation of computer simulation has more advantages than the current lack of accurate instruments. Our study reconfirmed the conclusion (or objective) from RAMI [4–6,60] and a wide range of mathematical modeling in earth sciences [59], and computer simulation is one of the most effective ways to validate the model of a nonnumerical calculation.

Since the leaves of crops are not randomly distributed in the real world, if the uncertainty in the measurement process is excluded, the most likely cause of this phenomenon is that the state of leaf aggregation on the horizontal plane has not been described, i.e., the clumping index [61]. The calculations of the clumping index and gap probabilities are inseparable. For the calculation of gap probabilities, we used a penetration function (*P* = *e*<sup>−</sup>*ks* in Supplementary Materials B-2). This function is based on the assumption that leaves are randomly distributed in the canopy. Therefore, there may be deviations between this assumption and the actual canopy, which implies that the equation describing the gap probabilities may need to be further refined considering the clumping index (*P* = *<sup>e</sup>*<sup>−</sup>*ks*Ω, where Ω is the clumping index). The clumping index is a hot topic in the field of radiation regimes and agricultural measuring equipment [62–65]. Compared with coniferous forests, the degree of leaf aggregation of crops is not very obvious. Therefore, considering the computational complexity, and whether the clumping index should be the main focus in improving the model, requires further study.
