## 4 Discussion  
### FPAR Estimation and Its Uncertainties  
In this study, an ANN model-based FPAR\({}_{\rm ANN}\) was generated having both longer-term and finer spatial resolution than previously available. Importantly, it was more consistent in terms of spatiotemporal similarity with the FPAR product (MCD15A2) of MODIS. Meanwhile, the NDVI3g and FPAR\({}_{\rm BNU}\) showed lower similarity though both data have long-term records [28; 56]. The MCD15A2 product was found to have higher performance for present temporal-spatial changes modeling for global vegetation [57; 58]. This study, on the other hand, extended the MODIS product back to a final data span from 1980 to 2018 and could be further extended, along with the output of MODIS data, without extra data processing except the SG filter used to remove some noise.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Slope** & **Intercept** & \(R^{2}\) & \(p\)**-Value** \\ \hline SC & 0.001 & 0.557 & 0.44 & \(<\)0.001 \\ SE & 0.0008 & 0.539 & 0.43 & \(<\)0.001 \\ CC & 0.001 & 0.478 & 0.43 & \(<\)0.001 \\ SW & 0.0009 & 0.481 & 0.47 & \(<\)0.001 \\ NE & \(-\)0.0002 & 0.389 & 0.024 & \(>\)0.05 \\ NC & 0.0011 & 0.328 & 0.58 & \(<\)0.001 \\ IM & \(-\)0.0003 & 0.252 & 0.02 & \(>\)0.05 \\ TP & 0.004 & 0.201 & 0.1 & \(>\)0.05 \\ NW & 0.0025 & 0.193 & 0.41 & \(<\)0.001 \\ Total & 0.001 & 0.351 & 0.46 & \(<\)0.001 \\ \hline \end{tabular}
\end{table}
Table 4: The effect of the nitrogen deposition was analyzed by linear regression for the FPAR over Chinese terrestrial ecosystems from 1980 to 2010.  
Figure 6: The relationship between FPAR and each climate variable over the terrestrial ecosystems in China and its nine regions from 1980 to 2018. The independent variables include annual average air temperature (TAVG), annual total precipitation (ATP), annual total solar shortwave radiation (SWRad) and atmosphere CO\({}_{2}\) concentration. The FPAR and the climate variables were normalized by the z-score method.  
The newly developed FPAR data showed not only more similarity but also comparable performance with the NDVI3g and FPAR\({}_{\text{BNU}}\) when evaluating with on-the-ground GPP observations from eddy covariance towers in terms of seasonal change. However, it is important to note that satellite remote sensing has inherent uncertainties that can lead to errors in the data. The algorithm of the MODIS product (MCD15A2) itself was found to have uncertainties dependent on its inherent model, input parameters, the effect of vegetation clumping and scale [59; 60]. On the other hand, data quality was influenced by some noise induced by clouds, rainy weather and the saturation phenomenon in tropical and subtropical regions [61; 62; 63], which exerts a great challenge to improving data quality for optical-based remote sensing. Similarly, the new FPAR dataset was influenced by the above factors on quality, which would result in lower performance in sub-tropic or tropic forests. The uncertainty associated with the data will have implications for its application, such as modeling gross primary production. As a result, further research is warranted to enhance the algorithm and improve data quality in future studies [64]. However, the FPAR\({}_{\text{ANN}}\) data showed comparable performance with more similarity to FPAR\({}_{\text{MCD15A2}}\), which makes it useful with its longer period, spanning nearly 4 decades from 1980 to 2018. The data could be potentially applied as inputs for ecosystem modeling, or for soil erosion estimations, and other research on the responses, adaptation and sustainability of terrestrial ecosystems to global changes, benefitting particularly from such a long-term dataset. More importantly, it provides a chance to directly use the upcoming FPAR\({}_{\text{MCD15A2}}\) and a method framework to fuse other remote sensing products in future research.