**3. Results**

### *3.1. Spatial and Temporal Variation of Evapotranspiration-Precipitation Coupling Strength*

To evaluate the spatial pattern of evapotranspiration-precipitation coupling over the climate transitional zone of northern China, the spatial distribution of evapotranspiration, precipitation, and their variations are shown in Figure 3. Precipitation gradually transitions from more than 800 mm in the southeast to less than 100 mm in the northwest. The standard deviation of precipitation has similar spatial distribution to annual precipitation, decreasing from southeast to northwest. This spatial distribution of precipitation is consistent with the situation of the study area of north China in the transition zone from the East Asian

summer monsoon-influenced zone to the non-monsoon zone, where the monsoon precipitation gradually increases from the non-monsoon zone to the monsoon zone. Similarly, evapotranspiration likewise decreases from the southeast to northwest, with a maximum of about 600 mm in the southeast and a minimum of a few tens of millimeters in the northwest. The spatial distribution of evapotranspiration is similar to that of precipitation, indicating a close relationship between evapotranspiration and precipitation. Furthermore, the distribution of standard deviation of evapotranspiration is more complicated, which is larger in the middle region of transition area and smaller in wet and dry areas.

**Figure 3.** Spatial distribution of (**a**) climatology of annual precipitation, (**b**) standard deviation of annual precipitation, (**c**) climatology of evapotranspiration, and (**d**) standard deviation of evapotranspiration in the climate transitional zone of northern China.

The results from the above analysis highlight a general consistency of the spatial distribution of mean precipitation and evapotranspiration. This suggests a close relationship between precipitation and evapotranspiration in the study region. Furthermore, an index of evapotranspiration–precipitation CS was applied to assessing the spatial and temporal variation in CS in the climate transitional zone of northern China. The spatial pattern of CS shows sharp transition features in the climate transitional zone of northern China (Figure 4), decreasing from the northwest to southeast. The northwest half of the study region is a strong positive coupling area, with CS between 0.2 and 0.6 (passing 0.05 significance test), while the southeast and northeast horn depict negative coupling zone, with CS ranging from –0.2 to –0.5 (passing 0.05 significance test). The middle region of the two regions marks the transition zone from positive to negative coupling, and CS is relatively small.

Due to the temporal changes in climate variables, land–atmosphere couplings also vary with time. Despite having a similar spatial pattern in all seasons, the CS is strongest in spring, when it is significantly larger than the other seasons, followed by summer, and the smallest coupling in autumn and winter (Figure 5). This indicates that the contribution of surface evapotranspiration to precipitation occurs mainly in spring.

On an interdecadal scale (Figure 6), the CS was highest in the 1980s and lowest in the 1990s. The spatial distribution of CS with stronger coupling in the 1980s and 2000s is similar to the distribution of annual coupling; however, it shows a more heterogeneous spatial pattern in the 2010s and 1990s.

**Figure 4.** Spatial distribution of evapotranspiration-precipitation CS in the climate transitional zone of northern China (dot denotes CS passing 0.05 significance test).

**Figure 5.** Seasonal changes in spatial distribution of evapotranspiration–precipitation CS in the climate transitional zone of northern China, (**a**) for winter, (**b**) for spring, (**c**) for summer, and (**d**) for autumn (dot denotes CS passing 0.05 significance test).

The trend of annual CS was examined for the climate transitional zone of northern China for the period 1980–2018 (Figure 7). The CS showed a significant decreasing trend in the central and western parts. Except for a small area showing an increase trend in the northwest corner, the overall trend of CS gradually shifts from significant negative in the west to insignificant positive in the east. The northwest region has the strongest decreasing trend of CS, about –0.003/year, whereas the southeast region has a weak increasing trend of CS, with a rate of about 0.001/year.

**Figure 6.** Decadal changes in spatial distribution of evapotranspiration–precipitation coupling in the climate transitional zone of northern China, (**a**) for 1980–1989, (**b**) for 1990–2000, (**c**) for 2000–2009, and (**d**) for 2010–2019 (dot denotes CS passing 0.05 significance test).

**Figure 7.** Spatial distribution of evapotranspiration–precipitation coupling trends in the climate transitional zone of northern China (dot denotes trend passing the significance test).

### *3.2. Spatial and Temporal Variation of Evapotranspiration-Precipitation Coupling in Relation to Moisture and Thermal Conditions*

#### 3.2.1. Spatial Variation of CS in Relation to Spatial Moisture and Thermal Conditions

The CS has large spatial differences and displays transitional characteristics in the climate transitional zone of northern China, which is closely related to the fact that the region is in a climatic transition zone with large spatial gradients of hydrothermal conditions in the region. Soil moisture and air temperature can aptly reflect hydrothermal conditions in the study region. Therefore, this section analyzes the dependences of CS on soil moisture and air temperature.

First, the spatial patterns of climatological mean soil moisture and air temperature were analyzed for the study region. Soil moisture has large spatial variability in the climate transitional zone of northern China, gradually increasing from 0.1 in the northwest to 0.4 in the southeast (Figure 8a). From the northwest to southeast, the climate is arid, semi-arid, sub-humid, and humid. Most of the study area belongs to a semi-arid or sub-humid climate, with only the northwest and southeast corners being arid and humid zones. Moreover, temperature has a similar spatial pattern as soil moisture (Figure 8b), increasing from the northwest of −8 ◦C to southeast of 16 ◦C in the study area. Notably, the southeast area was generally warmer with a lower gradient. In total, the soil moisture and air temperature have a general reversed spatial pattern compared to CS, and the spatial pattern of soil moisture is closer to that of CS in the study area.

**Figure 8.** Distribution of climatology of (**a**) soil moisture and (**b**) air temperature in northern China.

To examine the influence of soil moisture on spatial CS, Figure 9a displays the relationship between CS and climatological soil moisture. Generally, CS increases slightly and is maintained at a strong level when the soil moisture is below 0.2, and CS decreases gradually with increase in soil moisture when the soil moisture is larger than 0.2 (Figure 8a). In areas where the soil moisture is greater than 0.35, the CS is negative; in areas where the soil moisture is below 0.25, the CS is positive; in areas where the soil moisture is between 0.25 and 0.35, CS gradually transits from negative to positive. The determination coefficient R<sup>2</sup> of 0.4 indicates that variation in soil moisture explains 40% of the variation in CS. Figure 9b illustrates the relationship between the CS trend and soil moisture. The relationship between the CS trend and soil moisture is roughly opposite to that of between soil moisture and CS. In the range of soil moisture below 0.2, the CS trend decreases with increasing soil moisture; while in the range of soil moisture larger than 0.2, the CS trend increases with increasing soil moisture. Further, a negative CS trend occurs at moderate soil moisture, while a positive CS trend occurs at very dry or wet soil moisture.

**Figure 9.** (**a**) Variation in evapotranspiration–precipitation CS and (**b**) its trend with soil moisture (shades of color indicate the density of the points).

Similarly, the relationships between CS, CS trend, and air temperature were analyzed to examine the influence of air temperature on the spatial distribution of CS and the CS trend. Figure 10a illustrates that CS logarithmically decreases with increasing temperature. CS is mainly positive below zero degrees, and both positive and negative coupling exist above zero degree. The percentage of negative coupling increases as the temperature rises. The determination coefficient R<sup>2</sup> of 0.4 indicates that Ta only explains 26% of the variation in CS. In the contrary, the CS trend increases with increasing temperature (Figure 10b). The CS trend is negative below zero degrees, and the proportion of positive trend increases with increasing temperature. Clearly, the relationship between CS and temperature shows a significantly wider spread than that between CS and soil moisture. The spatial variation in soil moisture explains more of the spatial variation in CS compared to the spatial variation in TA. Therefore, the climatological soil moisture plays a more dominant role in determining the spatial pattern of CS compared to the temperature.

**Figure 10.** (**a**) Variation in evapotranspiration-precipitation CS and (**b**) its trend with air temperature (shades of color indicate the density of the points).

3.2.2. Temporal Variation of CS in Relation to Hydrothermal Conditions Inner-Annual Variability

The intra-annual variations of soil moisture and temperature were analyzed first (Figure 11). The soil moisture exhibits an evident intra-annual cycle reaching its minimum in the winter, followed by a rise in spring and autumn, and reaching its maximum in the summer (Figure 11a). Precipitation mainly concentrates in the summer over the waterscared northern areas, which serves as the primary method to replenish the soil moisture. Figure 10b shows the intra-annual variation in soil moisture variability. The soil moisture variability was small in winter and relatively larger in spring, summer, and autumn in

all areas. The soil moisture variability is small in arid areas due to low soil moisture. Moreover, the air temperature in all regions shows a unimodal pattern of a low winter and high summer, peaking in July (Figure 11c). Temperature variability is U-shaped, with large variations in the winter and small in the summer (Figure 11d). Furthermore, the temperature variability is larger in semi-arid regions than in others.

**Figure 11.** Intra-annual variation in (**a**) soil moisture, (**b**) standard deviation of soil moisture, (**c**) temperature, and (**d**) standard deviation of temperature (standard deviation of each month data for the 39 years) under different dry-wet climatic backgrounds.

Figure 12a further illustrates the intra-annual variation in CS, and shows that CS is smallest in winter months, reaching the maximum in spring months, and then decreasing again in summer and autumn months across all areas. The semi-arid region has the largest CS, followed by arid and semi-humid areas, and it has the smallest CS in humid areas. The CS is weak in the humid region, with small negative or positive values fluctuating around zero.

To determine this intra-annual variability of CS in relation to moisture and thermal factors, the intra-annual pattern of CS was compared to that of moisture (i.e., soil moisture and its variability) and thermal factors (i.e., temperature and its variability) for each dry and wet climate background. The intra-annual variation in CS is similar to the intra-annual variation in soil moisture variability, and temperature, and has roughly opposite characteristics to the intra-annual variation in temperature variability. Notably, soil moisture peaks in March–October, temperature peaks in July–August, temperature variability is at its minimum in May–August, whereas CS peaks in March–May. Generally, the coupling is most similar to the intra-annual variation of soil moisture variability.

**Figure 12.** (**a**) Intra-annual variation in 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 backgrounds.

From the correlation analysis of the CS with moisture and thermal factors (Figure 12b), soil moisture variability was found to have the highest correlation coefficient with CS, with the correlation coefficients larger than 0.4 in all regions. This suggests that a large soil moisture variability causes a large ET variability, and subsequently a large P variability, leading to a stronger ET-P coupling. The correlation coefficients of CS with temperature and temperature variability are large in semi-arid regions, but small in other regions, indicating that thermal factors have an important influence in semi-arid regions. Moreover, a higher temperature and temperature variability supplies more energy for the land–atmosphere interaction. The correlation coefficient between CS and soil moisture is low. Therefore, soil moisture variability is the main factor dominating the intra-annual variation of CS in the climate transitional zone of northern China.
