Inter-Annual Variability

Because the CS is the highest in the warm season (April–September) in the climate transitional zone of northern China, warm season CS was chosen as a representative to analyze the inter-annual variation of the CS with moisture and thermal factors. First, the inter-annual evolution of soil moisture and air temperature and their variability were analyzed. Soil moisture changed little during the study period, with a weak increase in all areas (Figure 13a). Instead, soil moisture variability fluctuated dramatically and declined during the study period (Figure 13b). Soil moisture variability was larger in the arid zone than other regions. In addition, temperature showed a significant increasing trend (Figure 13c), while the temperature variability displayed a fluctuating decreasing trend during the study period (Figure 13d).

Responding to changes in climatic conditions, the CS fluctuated strongly during the study period, and showed a slight decreasing trend in all subregions (Figure 14a). To find the dominant factors of inter-annual variation in CS, first, the time evolution of CS was compared with that of moisture and thermal factors. Soil moisture and temperature fluctuations were small, while soil moisture variability and temperature variability fluctuations were large and more similar to the inter-annual variation of CS. Figure 14b further presents the correlation of CS with soil moisture and temperature related variables for different soil moisture backgrounds in the warm season. The CS was significantly positive and correlated with soil moisture variability in arid and semi-arid regions, suggesting that inter-annual variation in soil moisture variability has a significant impact on the variation in ET and subsequently the variation in P. CS was negatively correlated with the soil moisture, demonstrating that soil moisture experiencing a relative dry state could cause a stronger CS. In the humid and sub-humid region, soil moisture and temperature related variables were weakly correlated with CS. This may be due to the joint influence of soil moisture and air temperature on CS giving rise to a more complex influence mechanism.

**Figure 13.** Inter-annual variation in warm season (**a**) soil moisture, (**b**) standard deviation (standard deviation of monthly data within warm season of a year) of soil moisture, (**c**) temperature, and (**d**) standard deviation of temperature under different dry-wet climatic backgrounds.

**Figure 14.** (**a**) Inter-annual variation of warm season ET-P CS and (**b**) its correlation coefficients with soil moisture (SM), standard deviation of soil moisture (SMCD), air temperature (TA) and standard deviation of temperature (TASD) under different dry-wet climatic conditions.

### *3.3. Reasons of Spatial Differences in Coupling Strength*

To investigate the mechanism for the opposite signs of CS over different regions of the climate transitional zone of northern China, we analyzed boundary layer characteristics as an intermediate process of ET-P coupling. The distribution of correlation coefficients between the LCL and precipitation is shown in Figure 15a. The precipitation and LCL are negatively correlated in the majority of study areas, demonstrating that a lower LCL is more likely to trigger precipitation. This implies that the role of water vapor in precipitation is very prominent in the study area. The more saturated the atmosphere is, the lower the LCL, and the easier it is to trigger precipitation. This also shows that the effect of moisture recycling from evapotranspiration on precipitation is the main pathway of ET-P coupling.

**Figure 15.** Distribution of correlation coefficients between (**a**) P and LCL, (**b**) ET and LCL, (**c**) ET and BLH (dot denotes correlation coefficient passing 0.05 significance test).

The spatial distribution of correlation coefficients between ET and LCL is shown in Figure 15b. ET and LCL are negatively correlated in the majority of the study area, where CS are mainly positive; ET and LCL are positively correlated in the southern humid zone and eastern northeast, where CS is mainly negative. In fact, in the negative ET-LCL correlation zones in the climate transitional zone of northern China, the ET type is water-limited, and the increase in soil moisture causes an increase in ET, which increases air humidity and thus decreases LCL. Meanwhile, the increase in ET reduces the energy partitioning available to sensible heat, and the decrease in sensible heat inhibits the boundary layer development and decreases the boundary layer height (BLH), resulting in a negative correlation between ET and BLH in these regions (Figure 15c). In contrast, in the positive ET-LCL correlation zone in the south and northeast, the ET type is energy-limited, and an increase in the available energy leads to an increase in both sensible and latent heat. Hence, the boundary layer is developed, resulting in an increase in LCL and BLH.

The main reason behind positive and negative ET-P coupling is the different driving regimes of evapotranspiration in the study area: ET is energy-limited in the southern and northeast corner of the study area, leading to a positive correlation between ET and LCL, while ET is water-limited, and ET is negatively correlated with LCL in most of the northern part. Meanwhile, LCL has a negative correlation with P in the whole study area, it therefore leads to a negative ET-P coupling in the south and northeast corner and a positive coupling in the most northern region. Combined with the scatter plot of CS and soil moisture in Figure 8a, CS is positive in areas with soil moisture below 0.25, corresponding to moisturelimited evapotranspiration; both positive and negative CSs exist in areas with soil moisture in the range of 0.25–0.35, corresponding to the transition zone of evapotranspiration from moisture-limited to energy-limited; CS is negative in areas with soil moisture greater than 0.35, corresponding to an energy-limited evapotranspiration.
