## 4 Results  
### 2013 and 2014 LAI Estimations from Satellite Data  
After twice updating the background information of the HR data in the 2011 and 2012 estimation processes, the HR LAI results of 2013 were estimated. The time series comparison between the LAI retrievals from satellite and ground observations at Huailai sites is shown in Figure 6 for 2013 and in Figure 7 for 2014. We note that there is no significant fluctuation in the LAI time series dynamically predicted by the NARX model. The time series from 2008 to 2010 is MODIS LAI data products, and that from 2011 to 2014 is the HR LAI time series.  
Figure 6: LAI dynamics derived from HR data using NARX prediction over the study sites and comparison with ground-measured LAI values by LAINet. 1–4 are the four ground sites in 2013. Mean values derive from multiple measurements by the LAINet instrument. Error bars indicate standard deviations of the LAINet measurements.  
Figure 6 depicts the LAI time series estimated using our method at the Huailai sites in 2013. The time series from 2008 to 2010 is MODIS LAI products, and that from 2011 to 2014 is the LAI time series retrieved from HR data. The results show the classical temporal pattern for maize, with increasing LAI during the vegetative stage, a peak LAI during the reproductive stage, and a subsequent relatively rapid decline. With the increases in HR data during the estimation process, the LAI appears to be significantly different in the time series. Figure 6 (1-4) shows the temporal trajectories of LAI differences for the 2013 site with the maize crop biome type. The retrieval values, except for those contaminated by residual clouds, are 1 and 2 LAI units higher than the MODIS values during the reproductive stage. In Figure 6, the accuracy of the LAI estimation in the reproductive stages is slightly lower than in the other vegetation stages. The possible reason is that the retrieval results are inaccurate due to the image being covered by clouds during the maturity of the corn.  
Direct comparisons of the ground measurements from LAINet and the retrieval LAI values demonstrate that the NARX method provides good performance for the HR data in 2013 (R\({}^{2}\) = 0.87 and RMSE = 0.288) and in 2014 (R\({}^{2}\) = 0.864 and RMSE = 0.296). Most LAINet measurements have a small standard deviation, but there are a few data with very large deviations, and the standard deviation of the LAI-2000 measurements is relatively consistent. The LAINet is an automatic measuring device that may cause large deviations in certain results during the measurement process due to weather. The average of multiple measurements will weaken the error, preventing it from having a significant impact on the final verification result. It can be seen in Figure 8 that the mean of the measurements is substantially within the 95% confidence interval.  
Figure 7: LAI dynamics derived from HR data using NARX prediction over the study sites and comparison with ground-measured LAI values by LAI-2000. 5–8 are the four ground sites in 2014. Mean values derive from multiple measurements by the LAI-2000 instrument. Error bars indicate standard deviations of the LAI-2000 measurements.