## 3 Results
### The Influence of Response Period on \(r\) of SIF with P, VPD, ES and RSM  
Certainly, the delayed response of SIF to the four climatic factors means there are time lag effects between them. By using the methods mentioned in Section 2.3, we determined the lag phases of SIF to the four factors (Figure 5, masked by the significant extremum \(r\) of SIF to the four climatic factors). SIF had a time lag effect on the four factors over the grasslands and the lag phases were mainly within one month. Combing Figures 4 and 5, the spatial \(r\) of SIF with P, VPD, ES, and RSM were consistent with the spatial lag phase maps of SIF to the four factors. Specifically, poor (\(p\) > 0.05) or opposite correlations between SIF and these factors were mainly located in areas with lag phases greater than one month. Collectively, the \(r\) values were affected by the response periods and the longer the period, the greater the impact. In addition, in Figure 5, the area with response periods of SIF to ES of more than one month were the lowest among the four factors, which meant the response of SIF to ES was timely. We integrated the maximum \(r\) of SIF with P, ES, and RSM and the minimum \(r\) of SIF with VPD, and the corresponding spatial \(p\) maps were also integrated (Figure 6). Compared with Figure 4, the spatial \(r\) maps were more reasonable, and the qualification of the relationship between SIF and climatic factor was improved (by comparing the colors). The overall spatial \(r\) of SIF with P, VPD, ES, and RSM in Figure 6 showed improvement, especially in the areas with poor or even inverse correlations. Additionally, the areas with \(p\) > 0.05 were noticeably decreased. Since the extremum \(r\) values were obtained by adjusting the time series, this indicated that the delayed response of SIF to the four climatic factors, or the time lag between them, impacted the assessment and qualification of the relationship among variables. Figure 3: Comparison between the original time series of SIF and RSM at 50\({}^{\circ}\)N and 70\({}^{\circ}\)E and the deseasonalized time series of them. **(a)** represented the original time series of SIF and RSM, and **(b)** showed the deseasonalized time series of SIF (SIF\({}_{\text{ds}}\)) and RSM (RSM\({}_{\text{ds}}\)). Figure 4: The spatial Pearson’s correlation coefficient (\(r\)) and corresponding significance test (\(p\)) of deseasonalized solar-induced chlorophyll fluorescence (\(\mathrm{SIF_{ds}}\)) with deseasonalized precipitation, vapor pressure deficit, evaporative stress, and root zone soil moisture (\(\mathrm{P_{ds}}\), \(\mathrm{VPD_{ds}}\), \(\mathrm{ES_{ds}}\), and \(\mathrm{RSM_{ds}}\)). (**a–d**) respectively represented the spatial \(r\) of \(\mathrm{SIF_{ds}}\) with \(\mathrm{P_{ds}}\) (\(r\) (\(\mathrm{SIF_{ds}}\), \(\mathrm{P_{ds}}\))), \(\mathrm{VPD_{ds}}\) (\(r\) (\(\mathrm{SIF_{ds}}\), \(\mathrm{VPD_{ds}}\))), \(\mathrm{ES_{ds}}\) (\(r\) (\(\mathrm{SIF_{ds}}\), \(\mathrm{ES_{ds}}\))), and \(\mathrm{RSM_{ds}}\) (\(r\) (\(\mathrm{SIF_{ds}}\), \(\mathrm{RSM_{ds}}\))). (**e–h**) respectively represented the spatial \(p\) of \(\mathrm{SIF_{ds}}\) with \(\mathrm{P_{ds}}\) (\(p\) (\(\mathrm{SIF_{ds}}\), \(\mathrm{P_{ds}}\))), \(\mathrm{VPD_{ds}}\) (\(p\) (\(\mathrm{SIF_{ds}}\), \(\mathrm{VPD_{ds}}\))), \(\mathrm{ES_{ds}}\) (\(p\) (\(\mathrm{SIF_{ds}}\), \(\mathrm{ES_{ds}}\))), and \(\mathrm{RSM_{ds}}\) (\(p\) (\(\mathrm{SIF_{ds}}\), \(\mathrm{RSM_{ds}}\))). Figure 5: The spatial lag phases of solar-induced chlorophyll fluorescence (SIF) to precipitation (P), vapor pressure deficit (VPD), evaporative stress (ES), and root zone soil moisture (RSM). (**a–d**) were the spatial lag phases of SIF to P, VPD, ES, and RSM respectively. In addition, we conducted comparative statistical analyses (shown in Figures 4 and 6), and the results (Figure 7) showed that all of the \(r\) of SIF with the four factors were improved.