## 4 Results
### Regional LAI Estimation  
To test the applicability of the NARX model, it was further used for HR LAI estimation in the Huailai study region (blue box in Figure 3). In this way, the 2013-2014 LAI retrieval results for this region were acquired, as shown in Figure 9. The size of each white cell is 500 m \(\times\) 500 m, which is the MODIS pixel resolution. These figures show that more detail can be achieved at HR satellite pixel resolution; for MODIS pixel resolution, the area of one MODIS pixel is approximately equal to the area of 272 HR pixels. In the case where land-cover types of the sample region are consistent, with flat terrain and weak heterogeneity, for instance, the retrieval results at MODIS pixel resolution can be representative. In real-world situations, the probability of such a large-scale uniform surface is low. However, at a spatial resolution of 30 m, most regions can be considered pure pixels, unlike the coarse 500 m resolution MODIS images. On the MODIS pixel scale, the mixed-pixel phenomenon is much more serious than in the HR dataset. Although the background field is MODIS-scale, the surface reflectance of HR data served as the input parameter during estimation, the spatial resolution of the HR data is higher than MODIS data so that the differences in the results obtained through relevant predictions for the same background pixel would present the characteristics of HR data. Based on spatial resolution retrieval results for the regions shown in Figure 9, the entire LAI set of retrieval results for the Huailai area conforms to the tendencies of the measured data. The LAI reached its maximum on the 201 st day of 2013 and on the 217 th day of 2014.  
In the HR regional results and the MODIS data for the same region, the edges of the Guanting Reservoir are shown in the upper left corner, but other areas without vegetation coverage are denoted by invalid values in the MODIS data, which occupy approximately one-half of the entire region. For these invalid values, we use the model constructed by the nearest pixel to retrieval the LAI value. In the comparisons of regional retrieval results, more in accordance with the phenological patterns of maize LAI. In Figure 10, MODIS LAI exhibited a very large jump on day 209 of 2014, it may be due to estimation errors caused by clouds or shadows. For the HR dataset retrieval results, even though fluctuations occurred in the input surface reflectance, leading to variations in the LAI, the feedback action of NARX enabled the LAI retrieval results to remain within a reasonable range, without error accumulations caused by chain reactions. Compared with fluctuations in MODIS, HR results have improved this situation. This capability indicates that the NARX neural network has extremely strong  
Figure 8: Comparison between the HR LAI retrievals and ground measurements, which in 2013 were derived from (**a**) LAINet and in 2014 were derived from (**b**) LAI-2000. The error bars represent the standard deviation of the ground measurements from LAI instrument. The black solid line is the 1:1 reference line, while the red dotted lines show the 95% confidence interval around the NARX model’s estimate.  
fault tolerance. Moreover, for the HR retrieval results, with changes in the day of the year (DOY), no significant fluctuation occurs, and these data effectively conform to surface measurement results.