3. Environmental Factors Affecting PC2 Changes
Figure 2 shows the evolution of SST patterns regressed to PC2 from the preceding winter to the subsequent winter. In both winters, we can see an El Niño-like pattern, which indicates that warm SST in the eastern Pacific Ocean corresponded to positive precipitation in California. Other than the decreased level of relevance, this characteristic was similar to PC1; thus, the environmental factors in the Pacific Ocean are not discussed here.
Figure 2. Same as in Figure 1, except for PC2.
The situation was different in the Indian ocean. The relationship between PC2 and SST in the Indian Ocean in the preceding summer was significantly positive. In order to determine how the SST in the Indian Ocean influences California precipitation, index 3 was defined as the average SST in the mostly positive related region (40° S–10° N; 50–100° E; left red box in Figure 2c) in the preceding summer. Figure 3 shows the relative vorticity and horizontal velocity at 850 hPa and 200 hPa in winter regressed to index 3. From the figure, we can see that, at the upper level, the key region is controlled by positive vorticity and a cyclone, whereas at the lower level, the situation is complex. In the south of California, there is positive vorticity. Combined with circulation at the lower level, such positive vorticity is beneficial for positive precipitation. On the other hand, in the north of California, there is negative vorticity, which is unfavorable for precipitation. As a result, the combination of upper and lower circulation is favorable for precipitation in the south but unfavorable in the north, leading to a dipole mode of precipitation, which is consistent with EOF2.
Figure 3. Relative vorticity (shading; 10−7 s−1) and horizontal velocity (vector; m/s) at 850 hPa (a) and 200 hPa (b) in winter regressed to the box-averaged SST (the left red box in Figure 2c). The green box represents the selected California area. Areas with dots exceed the 90% confidence level.
4. Summary and Discussion
In this study, the environmental factors affecting precipitation in California during 1948–2020 were investigated. Considering the seasonal mean and standard deviation of precipitation, this paper focused on winter as the main rainy season with the greatest variation. According to the EOF analysis of winter precipitation, the first EOF mode described a consistent change, with a variance contribution of 70.1%. The second EOF mode exhibited a south–east dipole change with an 11.7% variance contribution.
For EOF1, the relationship was positive between SST in the central Pacific in the preceding summer with PC1 in winter and negative between SST in the southeast Indian Ocean in the preceding summer with PC1 in winter. Due to the slow change and continuity of SST, the warm SST in the central Pacific Ocean would be maintained from summer to winter. Thus, the positive precipitation induced would exist in the subsequent winter in the central Pacific Ocean, thereby inducing a PNA-type wave train response to influence the California precipitation. Regardless of whether the lower level or the upper level was considered, the key region was located to the southeast of the anomalous cyclone induced. The southwesterly wind would transport warm and wet flow from the ocean, beneficial for precipitation. There is another possible process underlying how warm SST in the central Pacific Ocean would affect California precipitation. California is located around the boundary of the tropical belt, at the edge of the Hadley cell sinking phenomenon. The edge of Hadley cells features a hot and dry climate. Yang et al. (2020) 
proposed that poleward shift of the meridional temperature gradients would cause expanding tropics. Therefore, the El Nino-like pattern in EOF1 favors an equator contraction of the meridional temperature gradient, contributing to a narrower Hadley cell, which is then favorable for California precipitation. For the Indian ocean, the positive SST would induce an anomalous cyclone at the lower level and an anticyclone at the upper level in the northern Indian Ocean according to the Gill response. This was confirmed by both the observation and the AGCM model experiments. Following an anomalous heating in the eastern Indian Ocean in the model, there was a cyclone anomaly response at the lower level and an anticyclone anomaly response at the upper level in the northwest. The induced Rossby wave train extends from the Indian Ocean to the Atlantic Ocean. The key region is controlled by the biotrophically high pressure, which is unfavorable for precipitation.
As for PC2, the situation in Pacific Ocean was similar to that for PC1. There was a positive relationship between SST in the central Pacific Ocean in the preceding summer and California precipitation in winter. However, the circumstances were different in the Indian Ocean, whereby the relationship between SST in the Indian Ocean in the preceding summer and California precipitation in winter was also positive. Due to the slow change and continuity of SST, the warm SST would be maintained from summer to winter, which would induce a Rossby wave train from the Indian Ocean to California. Since the key region of the Indian Ocean is shifted westward, the wave train is shifted correspondingly. As a result, at the upper level, California is controlled by positive vorticity, whereas at the lower level, there is positive vorticity in the south and negative vorticity in the north. This combination of circulation at the upper and lower levels would lead to a dipole mode of precipitation, positive in the south and negative in the north.
It is worth mentioning that, in this study, how the summer conditions affect winter precipitation was mainly attributed to the slow change and continuity of SST. However, other possibilities, such as human activities, should be considered. Furthermore, only the effect of SST in the preceding summer was analyzed. Other environmental factors, such as geopotential height, in other seasons, such as in the preceding autumn, should also be considered. In this study, we only used AGCM to confirm the physical processes. Other models, such as ECHAM, should be applied. Further studies are needed to solve these questions. Having now found the precursor signals, further studies are needed to determine whether they can be adopted in precipitation forecasts.