**5. Conclusions**

Employing an evapotranspiration–precipitation coupling index (CS) proposed by Zeng (2010), this study found that CS decreases gradually from the northwest to southeast in the north China climate transition zone, with strong positive coupling in the northwest and negative coupling in the southeast and northeast corners. The CS decreases sequentially in the spring, summer, autumn and winter, and is considerably stronger in spring than in other seasons. On the interdecadal scale, coupling is highest in the 1980s, lowest in

the 1990s, and moderate in the 2000s and 2010s. The trend of CS gradually shifts from a significant declining trend in the west to an increasing trend (not significant) in the east.

The spatial distribution of CS is closely related to the distribution of climatology of moisture and temperature. The CS remained at a strong level and increased slightly by increasing soil moisture when it was below 0.2, and decreased with increasing soil moisture when the soil moisture was above 0.2. In the zone of study, areas with soil moisture below 0.25 have positive CS, areas with soil moisture between 0.25 and 0.35 experience a transitional coupling from positive to negative, and areas with soil moisture greater than 0.35 exhibit negative CS. The relationship between soil moisture and the CS trend is roughly opposite to that between the soil moisture and CS. The CS shows an exponential decreasing trend with the increase in temperature, while the CS trend gradually increases with increasing temperature. Climatological soil moisture plays a more dominant role in determining the distribution of CS.

The CS exhibits evident intra- and inter-annual variability in the climate transitional zone of northern China. Soil moisture variability has the highest correlation coefficient with the intra-annual CS, dominating the intra-annual variation in ET-P coupling in the northern region. At the interannual scale, soil moisture variability is significantly and positively correlated with CS in arid and semi-arid regions, determining the interannual variability in CS in these regions. In humid and semi-humid areas, the CS is more complex in relation to the hydrothermal factors, and subject to the combined effect of hydrothermal factors.

The boundary layer thermodynamic analysis revealed that the main reason for positive and negative differences in CS across the study area is the different driving regimes of evapotranspiration. ET is energy-limited in the southern part of the study area, leading to a positive correlation between ET and LCL, while in most of the northern part, ET is moisture-limited, and ET is negatively correlated with LCL. The effect of moisture recycling from evapotranspiration on precipitation represents the main pathway of ET-P coupling, and LCL has a negative correlation with P across the study area, therefore leading to a negative ET-P coupling in part of the south and a positive coupling in the north.

**Author Contributions:** Conceptualization, Z.Y. and Q.Z.; Methodology, Z.Y. and Q.Z.; Investigation and Data Acquisition, Z.Y.; Formal Analysis, Z.Y., Q.Z. and P.Y.; Writing—Original Draft Preparation, Z.Y.; Writing—Review & Editing, Z.Y., Q.Z., Y.Z., P.Y., L.Z. and J.Z.; Visualization, Z.Y. and Y.Q.; Funding Acquisition, Z.Y., Q.Z. and Y.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the National Natural Science Foundation of China (Grant No. 42005071 and 41630426) supporting Z.Y. and Q.Z. The Second Tibetan Plateau Scientific Expedition and Research (STEP) program (grant no. 2019QZKK0102) supporting Y.Z. and Z.Y.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available online: Evapotranspiration product can be download from https://dapds00.nci.org.au/thredds/catalog/ks32/CLEX\_ Data/DOLCE/v3-0/catalog.html (accessed on 30 July 2021); Precipitation and near-surface air temperature data from China Meteorological Forcing Dataset can be obtained from http://data. tpdc.ac.cn/zh-hans/ (accessed on 10 May 2021); CCI soil moisture data are available at http: //www.esa-soilmoisture-cci.org/node/202 (accessed on 19 November 2020); Boundary layer heights of ERA5 are available at https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-singlelevels-monthly-means-preliminary-back-extension?tab=form (accessed on 18 November 2021).

**Conflicts of Interest:** The authors declare no conflict of interest.
