# Diverse Roles of Previous Years' Water Conditions in Gross Primary Productivity in China
## 3 Results
### Time-Lag Effect of Water Deficit  
Based on the knowledge revealed by the machine learning algorithms in Section 3.3, we further developed the linear regression models between GPP and water deficit conditions in the previous years and current year for the different water deficit scenarios. The results indicate that the water conditions of the current year were positively correlated with GPP (Figure 5), i.e., the better the water conditions, the higher the GPP. When the water conditions in the current year were in a drought condition (\(\text{CWD}_{\text{anomaly}}<-1.5\text{SD}\)), the water deficit conditions in the previous years had no significant effect on the GPP (Figure 5a,d). However, when the water conditions in the current year were normal (\(-1.5\text{SD}<\text{CWD}_{\text{anomaly}}<1.5\text{SD}\)) or wet (\(\text{CWD}_{\text{anomaly}}>1.5\text{SD}\)), the role of water conditions in the previous year positively impacted the GPP (\(p<0.05\); Figure 5b,c,e,f). The water conditions in the second previous year and third previous year, however, were not significant (\(p>0.05\)). The improvement in water conditions in the current year highlights the influence of water conditions in the first previous year on GPP. The effect of water deficit on GPP lagged by approximately one year. This study also found that the GPP was relatively low when the water conditions were in a drought. In contrast, the GPP was relatively high when the water conditions were wet, which suggests that the influence of water conditions in the current year on the GPP was much greater than the effect of water conditions in the previous years, which is consistent with the simulation results of the models in Section 3.3. The advantage of combining the random forest method and linear regression method is obvious. The random forest could quantify the relative importance of different years' water stress, while the linear regression models that are based on a series of water deficit scenarios could identify the causes of higher or lower importance. Specifically, the random forest revealed that the current year's water condition has the highest importance (52.8% (%IncMSE) and 3.8 (IncNodePurity)), which is consistent with results revealed by linear regression models as they found that impact of the current year's water condition on GPP is stable and unconditional which does not depend on the previous years' water condition. For the role of previous year's water condition, however, the random forest found that it is also important but with relatively lower importance (20.4% (%IncMSE) and 0.6 (IncNodePurity)). The reason revealed by linear regression models is that the water influence of the previous year depends on the water deficit condition of the current year. These results are valuable as they imply that we need to consider two years' water conditions to better predict the interannual variation of GPP. Figure 4: Importance analysis of water conditions in the previous years and the current year using a random forest model: (**a**) %IncMSE (the percentage of Increased Mean Square Error) and (**b**) IncNodePurity (the mean decrease in node impurity). 3 rd, 2 nd, 1 st and Current represent the water conditions in the third previous year, the second previous year, the first previous year and the current year, respectively. Figure 5: Statistical relationships between GPP in the current year and water conditions in the previous years and their dependence on the current year’s water conditions. The water conditions in the current year are (**a**) drought (\(\text{CWD}_{\text{anomaly}}\)\(<-1.5\)SD) (Current_drought in the figure), (**b**) normal (\(-1.5\)SD \(\text{CWD}_{\text{anomaly}}\)\(<1.5\)SD) (Current_normal in the figure) and (**c**) wet (\(\text{CWD}_{\text{anomaly}}\)\(>1.5\)SD) (Current_moist in the figure). Purple (cross), red (round), dark green (triangle) and light green (square) colours represent different water conditions in the current year, the first previous year, the second previous year and the third previous year, respectively.