**4. Discussion**

Potential CCC-sensitive but MTA-insensitive satellite broadband vegetation indices were developed. To our knowledge, this is among the few studies that have focused on specifically designing this type of vegetation index. The vegetation indices were calibrated with field measurements and validated with widely used PROSAIL model simulations. The canopy reflectance model can be used to accurately simulate the actual reflectance spectra without the inherent bias caused by the specific growth conditions at any study sites.

Actual field-measured datasets have limited ranges of variables of interest and specific data distributions (with possibly site-specific) internal correlations. This limits their generality for calibrating vegetation indices. While model-based fits are universal, they inevitably include simplifications, such as the absence of material other than leaves. Before application, all theoretical models need to be validated in the field. A compromise is to link an existing field-measured dataset with model simulations as suggested in a previous study [82]. An efficient vegetation index should be supported both by field measurements and model simulations. In this study, the identified best indices for each satellite presented a good match between measurements and simulations.

The newly developed indices performed better than the tested existing vegetation indices and are recommended to remotely estimate crop CCC from satellites across species and seasonality. Theoretically, three-band vegetation indices have a larger information content and flexibility than two-band combinations. However, in our study, the three-band vegetation indices did not show a great advantage over the simpler two-band formulations. For the simulated Sentinel-2 and GaoFen-6 bands, the best indices were two-band, while for the WorldView-2 and RapidEye, the identified best indices were three-band.

Regardless of the number of bands, all the best indices for each satellite were constructed from NIR and red edge bands. This agreed with previous studies performed by [33], who demonstrated that these two band combinations are minimally affected by crop phenology and can potentially be used as generic algorithms to crop CCC estimation. Red edge reflectance is strongly negatively correlated with MTA [44,46], and the addition of this channel can attenuate the sensitivity of vegetation indices to leaf angles [83]. Sentinel-2 MSI performed better than the other evaluated satellite sensors in both field-measured data and model simulations, indicating a more optimal spectral band combination. Similarly, in all tested vegetation indices, the CIred edge computed with Sentinel-2 data was the best vegetation index strongly correlated with CCC (*R*<sup>2</sup> CCC = 0.68 in field measured data and *R*2 CCC = 0.90 in model simulated data) and no correlation with MTA (*R*<sup>2</sup> MTA = 0.05 in field measured data and *R*<sup>2</sup> MTA = 0.00 in model simulated data). In previous studies, the performance of CIred edge has been evaluated for single crop species either from real Sentinel-2 imagery or resampled from field canopy reflectance. The following relationships have been reported in the literature for CIred edge and CCC: *R*<sup>2</sup> CCC = 0.58 for potato [34], *R*<sup>2</sup> CCC = 0.86 and 0.94 for maize and soybean, respectively [33], and *R*<sup>2</sup> CCC = 0.74 for wheat [35]. These relationships agree with the results in this study, which can be explained by the fact that the CIred edge was suitable for crop CCC estimation under a mixed pixel scenario [3].

For the other vegetation indices derived from Sentinel-2 bands, such as NDVI, NDRE1, NDRE2, MTCI, TCARI/OSAVI and TCARI/OSAVIred edge, *R*<sup>2</sup> CCC varied between 0.12 and 0.64 for field measured data and between 0.50 and 0.82 for model simulations. In a previous study, these correlations were between 0.66 and 0.78 for single wheat species [35], which are larger than that found in the field-measured data but within the range of our model simulations. Especially for the MTCI, which is specifically designed for the MERIS spectrometer, the correlation between CCC and real MERIS data-derived MTCI is *R*<sup>2</sup> CCC = 0.24 for soybean [26]. The value is better than that from Sentinel-2 data (*R*<sup>2</sup> CCC = 0.12) but lower than that from GaoFen-6 data (*R*<sup>2</sup> CCC = 0.48). The model-simulated MERIS-based MTCI presented a stronger correlation with CCC (*R*<sup>2</sup> CCC = 0.69) than real MERIS data [26], but this value is lower than the model simulation based on Sentinel-2 (*R*<sup>2</sup> CCC = 0.76) and GanFen-6 (*R*<sup>2</sup> CCC = 0.82) data in this study and even lower than that of proximal spectrasimulated Sentinel-2 data (*R*<sup>2</sup> CCC = 0.89) for maize and soybean [33].

Except for Sentinel-2, the three other satellites (WorldView2, RapidEye and GaoFen-6) have been widely used for remote sensing of vegetation. Surprisingly, there are few reports on their use for the estimation of CCC for field crops. In all tested vegetation indices, PSND had the strongest correlations with CCC in the field-measured data (*R*<sup>2</sup> CCC = 0.49–0.52), and similar results were found in PROSAIL model simulations (*R*<sup>2</sup> CCC = 0.56–0.68). TCARI/ OSAVI presented the best correlation with CCC in PROSAIL model simulations (*R*<sup>2</sup> CCC = 0.82–0.88) and no correlation with MTA (*R*<sup>2</sup> MTA = 0.01), but this good performance was not consistent in field measurements. The matrices of difference between *R*<sup>2</sup> CCC and *R*2 MTA for the three two-band RI and NDI are similar (Figure 4), and identical bands were identified for the best vegetation indices of both types. This can be explained by their mathematical similarity [84]. However, comparing the four satellite sensors, large differences in performance were found among the best vegetation indices of each type in both field measurements (Tables 4 and 5) and model simulations (Table 6). Thus, finding the right type is also very important for optimizing vegetation indices.

For CCC estimation, it is essential to use band combinations. CCC effects on the responses of MTA to individual broadband reflectance varied with the combination of LAI and Cab. Even at similar CCC levels (CCC = 90–100 in Figure 3 in the second and third columns), this relationship can vary greatly. This is mainly because LAI and Cab determine the reflectance of different broadband separately. Generally, the MTA responses to NIR reflectance were determined by LAI and those to visible reflectance were determined by Cab.

Although the identified vegetation indices for the four satellite spectral configurations in this study produced good results in both field-measured and model-simulated data and are recommended for crop CCC estimation, there are some limitations in this study. First, the derived vegetation indices were not validated with real satellite imagery. Satellite sensor imaging needs to consider the atmospheric radiation and transmittance, geometric characteristics, spatial resolutions and signal-to-noise ratio, which limit the transferability of the vegetation indices developed in this study. Unfortunately, real satellite imagery could not be acquired simultaneously for the particular study area over a given time. In the future, more effort needs to be put into vegetation index evaluations using real satellite imagery.

The potential CCC-sensitive but MTA-insensitive satellite broadband vegetation indices developed in this study may provide a convenient method for accurately estimating crop CCC with diverse canopy architectures using satellite remote sensing data.
