## 4 Discussion
### The Potential of MNDVI in Estimating Winter Wheat Yield  
The _f_PAR estimation results at the satellite scale reveal the MNDVI-based model for estimating large _f_PAR proposed in this study has a certain underestimation at the beginning or end of major phenological periods when compared with physical models. This underestimation phenomenon may still be caused by MNDVI saturation, although MNDVI is relatively less susceptible to saturation as compared with NDVI. Therefore, in future research, it is the key to find a vegetation index that can be less prone to saturation for improving the estimation accuracy of _f_PAR.  
From Table A1, it can be seen that different vegetation _f_PAR have different linear relationships with vegetation indices. Even for the same vegetation type, there are variations in the linear relationship between different vegetation indices and _f_PAR. Different research areas, even with the same crop and different vegetation indices, have obtained different linear relationships. This may be due to differences in observation conditions, satellite data, and even different phenological stages, which can lead to differences in linear relationships [27]. In the North China region, which is mainly characterized by smallholder agriculture, there is a complex cropping structure, different winter wheat varieties, significant climatic variations, and a wide range of phenological stages. If a model is established to relate vegetation indices to _f_PAR based on a specific region or variety of winter wheat,  
Figure 10: Comparison of MNDVI and NDVI response to changes in winter wheat growth.  
it may result in significant differences in \(f\)PAR estimation for the entire region. Therefore, in order to improve the accuracy of winter wheat \(f\)PAR calculation in the North China Plain and to improve the accuracy of winter wheat yield estimation, it is necessary to find vegetation indices that are stable throughout the phenological period and more suitable for \(f\)PAR estimation in the North China Plain. This will enable the construction of a more universally applicable fitting model to improve the accuracy of wheat yield estimation.  
The present study uses simulated Sentinel-2 reflectance data to find that the MNDVI-based index model has high stability and good applicability in estimating winter wheat \(f\)PAR. Moreover, the computation of MNDVI requires only the use of near-infrared and red-band reflectance data, which allows the acquisition of \(f\)PAR data with a spatial resolution of 10 m. This has significant application value in agricultural monitoring of regions with complex crop structures, such as the North China Plain. In particular, it can be combined with existing vegetation index downscaling algorithms, such as STARFM [37] and CRC [38], to reconstruct high spatiotemporal resolution vegetation index data and thereby calculate high spatiotemporal resolution \(f\)PAR data. This is of great reference value for agricultural monitoring in cloudy and rainy areas.  
Due to the difficulty in obtaining high spatiotemporal resolution \(f\)PAR data, existing light use efficiency models mostly rely on 8-day, 15-day, or monthly averages to estimate crop yield. For example, EC-LUE uses Landsat 7/8 to estimate \(f\)PAR based on NDVI every 8 days [39], which can introduce significant errors in the calculation results. If high spatio-temporal resolution \(f\)PAR data can be obtained and combined with light use efficiency models for winter wheat yield estimation, it can improve the accuracy of yield estimation.