## 3 Results  
### The Impact of Seasonality on the Relationship of SIF to P, VPD, ES and RSM Dynamics  
Firstly, we calculated the spatial \(r\) maps of SIF with P, VPD, ES, and RSM, without any time series adjustment (Figure 2). According to the mechanism relationship between SIF and the four climatic factors, P, ES, and RSM have positive correlations with SIF, and VPD has a negative correlation with SIF. However, in Figure 2, the spatial \(r\) of original SIF with the original P (\(r\) (SIF, P)), VPD (\(r\) (SIF, VPD)), ES (\(r\) (SIF, ES)), and RSM (\(r\) (SIF, RSM)) did not follow the mechanism. More specifically, in the spatial maps of \(r\) (SIF, P) (Figure 2a), \(r\) (SIF, ES) (Figure 2c), and \(r\) (SIF, RSM) (Figure 2d), there were large areas of negative \(r\) values, while in the spatial maps of \(r\) (SIF, VPD) (Figure 2b), the \(r\) values were almost positive.  
We conducted further research and found that the seasonality/periodicity of the time series led to the anomalous phenomenon. We compared the original and deseasonalized time series between SIF and RSM at 50\({}^{\circ}\)N and 70\({}^{\circ}\)E (Figure 3) and found the original time series of SIF and RSM (Figure 3a) had clear seasonality and the dynamic response between SIF and RSM were inconspicuous, while Figure 3b showed a legible response between the deseasonalized time series of SIF (SIF\({}_{\text{ds}}\)) and RSM (RSM\({}_{\text{ds}}\)) dynamics. These indicated that seasonality affected the qualification of the relationship between SIF and the four factors, and even led to incorrect results. Therefore, for qualifying the relationship between SIF and the four climatic factors, the impacts of seasonality need to be removed. Simultaneously, the deseasonalization based on the STL method was a useful means of removing the disturbance generated by periodicity.  
Figure 2: The spatial Pearson’s correlation coefficient (\(r\)) of solar-induced chlorophyll fluorescence (SIF) with precipitation (P), vapor pressure deficit (VPD), evaporative stress (ES), and root zone soil moisture (RSM). (**a–d**) respectively represented the spatial \(r\) of SIF with P (\(r\) (SIF, P)), VPD (\(r\) (SIF, VPD)), ES (\(r\) (SIF, ES)), and RSM (\(r\) (SIF, RSM)).  
After deseasonalizing the time series of SIF, P, VPD, ES, and RSM (SIF\({}_{\text{ds}}\), P\({}_{\text{ds}}\), VPD\({}_{\text{ds}}\), ES\({}_{\text{ds}}\), and RSM\({}_{\text{ds}}\)) based on the STL method, we recalculated the spatial correlation between SIF\({}_{\text{ds}}\) and the four factors (Figure 4). Overall, the spatial \(r\) maps followed the mechanism mentioned above, and ES correlated with SIF best. However, there were still unreasonable \(r\) values between SIF and the four factors. For example, between the 90\({}^{\circ}\)E and 100\({}^{\circ}\)E, in the northern and southern regions of the grasslands, the \(r\) (SIF\({}_{\text{ds}}\), VPD\({}_{\text{ds}}\)) were greater than zero, which they should had been negative correlations between SIF and VPD according to the response mechanism between them. In addition, the corresponding spatial maps of \(p\) showed a large area which did not pass the significance test (\(p\) > 0.05). The area with an insignificant \(r\) between P and SIF (Figure 4e) was the greatest, while that between ES and SIF (Figure 4g) was the lowest. The \(p\) value maps of SIF with VPD (Figure 4f) and RSM (Figure 4h) had analogous spatial distribution.