3.3.3. Physically Based Methods

RTM use optimization algorithms for inversion to infer the N content of crops from observed spectral data. Depending on the scale of the object of study, it is mainly divided into leaf radiative transfer models and canopy models. At the leaf scale, the PROSPECT model is the most widely used and has been continuously optimized and improved [146–148]; at the canopy scale, the SAIL model is one of the first models applied, mainly for uniformly distributed continuous vegetation surfaces [149]. Combining PROSPECT and SAIL models to invert vegetation physiological and biochemical parameters is a common approach nowadays, mostly around canopy and LCC, water content and leaf area [29,75,150,151]. Most studies derive crop N status through empirical relationships based on significant associations between leaf area or Chl and N. Despite the long-standing stability and reliability of RTM in the inversion of physicochemical parameters, different configurations of the model by users may lead to equally plausible results [152,153], so it is necessary to constrain the model using a priori information. Combining the DSSAT cropping system model CSM and PROSAIL model, complementing the interaction between crop growth stages and the environment for the constraints of the input parameters of the PROSAIL model, plays a unique advantage in the inversion of crop physicochemical parameters, not only with high accuracy, but also with the statistics of physicochemical parameters among different varieties of crops [154].

Yang et al. [155] used N uptake coefficients to equivalently replace the Chl uptake coefficients in the original PROSPECT model, and established the N-PROSPECT model based on the PROSPECT model to directly invert leaf N content. The N-PROSAIL model, established by combining the N-PROSPECT model and the SAIL model, achieves the diagnosis of N status at the leaf and canopy scales, and reduces the model error by setting a priori parameters at different growth stages [156]. The RTM expresses the crop growth process from a physical point of view, which is more stable in the inversion, but has the problem of being time-consuming. Combined with the Lookup Table (LUT) it can reduce the computational demand. Li et al. [157] constructed a multi-LUT for wheat LAI, LND and two spectral indices (MSR and MCARI/MTVI2), which not only reduced the LUT size and improved the computation time, but also had better accuracy of N estimation. On the other hand, since protein is also a major N-containing component in crops, coupling protein specific absorption coefficients into the PROSPECT model to form PROSPECT-PRO, which is combined with the 4SAIL model to form PROSAIL-PRO, can also be used for crop N status diagnosis [31,158]. RTM with strong explanations is better expressed in the inversion, but because the model expression depends on the input of more parameters and complex computational process they are less used in current research. Reducing the complexity of models and complementing the advantages of statistical models, hybrid RTM and machine learning models have become a future research need.

#### **4. Influential Factors on Accuracy of Remote Sensing Monitoring of Canopy N**

Spectral reflectance information has been shown to be sensitive to the N content of canopy leaves, but differences in data acquisition, vertical distribution of leaf N, dynamic changes in N during the growth stages, and physiological differences between different plants can all have an impact on the correlation between crop spectral information and canopy N indicators.

#### *4.1. Differences in Data Acquisition Angles*

Both portable spectrometers and UAV sensors usually acquire spectral data for crop N monitoring within a range of VZAs, which can vary by 30◦ and more. The spectral indices in crop N status studies are usually developed from vertical angle data. However, due to the variation in the angle of view of data acquisition caused by different experimental conditions, and the anisotropy of vegetation reflectance, the accuracy and robustness of using these indices directly to estimate the N content are not sufficient. The reflectance in the VIS, red edge and NIR bands decreases gradually from VZAs from −60◦ to 0◦, with relative changes in reflectance ranging from 34.7% (+60◦) to 265.5% (−60◦), and 81.7% (+60◦) to 89.3% (−60◦) in the VIS and NIR bands, respectively [53]. Therefore, developing an index that is sensitive to N content and insensitive to VZAs is of great practical importance to adapt to different experimental conditions, improve prediction accuracy and enhance model stability.

Higher viewing angles allow better extraction of crop biochemical information compared to the nadir orientation [159]. The change in view angle significantly affects canopy reflectance, especially in the red and NIR bands, which in turn makes VIs based on these spectral bands sensitive to angle [160]. The introduction of angle-insensitive bands to construct indices, such as the normalized difference red edge (NDRE), the green and blue bands, and the green band Chlorophyll Index (CIgreen), can improve the accuracy of canopy N inversion of different VZAs remote sensing images, significantly expanding the range of suitable viewing angles for determining crop N status by remote sensing, and thus adapting to the differences between different experimental conditions [53,161,162]. For the angular insensitivity index cannot be simply attributed to the effect of a single band; green, blue and NIR bands may have played a joint role in improving the index adaptation. It is difficult to obtain accurate spectral collection perspectives in the applications. A unified N monitoring model under a range of perspectives can help with the flexible application of crop N diagnosis. Like other VIs, Li et al. [53] developed angular insensitivity vegetation index (AIVI) to have the best LNC estimation accuracy at −20◦ view angle, but at the same time the correlation between AIVI and LNC has high stability at −10◦ to −40◦ with R2 of 0.83. Similarly, floating-position water band index (FWBI) has the highest correlation with LNC at −10◦ view angle (R<sup>2</sup> = 0.852), also has superior N content estimation accuracy at 0◦ to 30◦ (R2 = 0.835) [161]. The statistics on angular differences show that back-scatter direction has better LNC prediction accuracy than the forward-scatter view angle.

However, the spectral information obtained by whatever VZAs inevitably has information such as soil background, light shading, etc. Different growth stages and different light conditions will change the crop spectral reflectance, which is a common noise in inversion. The study reduces their effects by spectral preprocessing such as first-order differentiation and wavelet transform, suitable vegetation index, and threshold segmentation [27,63,82,93]. The water background of rice is a unique feature that differs from other crops; water has an absorption effect on the NIR band, and when the canopy cover is small, the water depth and turbidity have an isotropic effect on the spectral reflectance of the red-edge region [163]. Therefore, when converting reflectance to vegetation index, this effect can be eliminated or attenuated by calculating between multiple bands. The individual N content was significantly improved in accuracy before and after removal, and the group indicators indicated the total amount per unit area, which was less influenced by background noise and had a smaller enhancement effect [82].
