*2.3. Methods*

### 2.3.1. Evapotranspiration-Precipitation Coupling Strength

An evapotranspiration–precipitation coupling index proposed by Zeng et al. [6] was employed to diagnose the strength of land–atmosphere coupling. Considering that surface state variables always affect the atmospheric state via near-surface fluxes, evapotranspiration was selected as the surface impact factor. In the index, the covariance of evapotranspiration and precipitation reflects the synchronous change in evapotranspiration and precipitation, and the ratio of the covariance to the precipitation variance reflects the contribution of evapotranspiration changes to total precipitation changes. This method has a solid physical mechanism and is widely used in diagnostic studies of land–atmosphere CS. The equation for its calculation is as follows:

$$
\Gamma = \frac{\sum\_{i=1}^{N} P\_i^{\prime} E\_i^{\prime}}{\sum\_{i}^{N} P\_i^{\prime 2}} \tag{2}
$$

This can also be rewritten as:

$$
\Gamma = r\_{P,E} \frac{\sigma\_E}{\sigma\_P} \tag{3}
$$

where Γ is the land–atmosphere CS, *Pi* and *Ei* are anomalies of precipitation and evapotranspiration, respectively, N is total number of months or years, *rP*,*<sup>E</sup>* is correlation coefficient of precipitation and evapotranspiration, *σE* and *σP* are the standard deviation of evapotranspiration and precipitation, respectively. This index reflects the proportion of precipitation changes caused by evapotranspiration in total precipitation using the relative magnitude of the covariance between precipitation and evapotranspiration and the variance of precipitation. The more consistent the pace of change between the two variables, and the larger the magnitude of change, and the stronger the land–atmosphere coupling. The positive and negative values can also reflect the respective coupling between evapotranspiration and precipitation.

This method examines the ET–P relationship statistically and does not reflect the specific physical processes and influence mechanisms. To identify the significant strong CS areas, a correlation-coefficient significance test can be used to test the significance of the CS [7]. i.e., the ET–P coupling is deemed to be significant if the p value of the correlation coefficient is less than 0.05.

The evapotranspiration–precipitation CS was calculated using monthly or yearly ET and P data. The bulk CS in Figure 4 was calculated using data of all months during the study period. The seasonal CS in Figure 5 was calculated using monthly data in each of the four seasons. The decadal CS in Figure 6 was calculated by using yearly data in each decade. The yearly CS was calculated using monthly data of each year, and subsequently the yearly CS was used to calculate the linear trend of CS in Figure 7. The warm season CS was calculated using monthly data of April-September.

### 2.3.2. Lifting Condensation Level

The lifting Condensation Level (*LCL*) can be calculated by:

$$LCL \approx 125(T\_{2m} - D\_{2m})\tag{4}$$

where *T*2*m* and *D*2*m* are 2-m air temperature and dew point temperature, respectively.

### *2.4. Validation of CCI Soil Moisture*

ESA CCI soil moisture data were validated using observations at four sites in the study area in 2007. Figure 2 shows that the correlation coefficients between CCI and observations are 0.71, 0.69, 0.66, and 0.65 for NM, QY, SACOL, and YC, respectively. The RMSE values for the four sites are 0.033, 0.041, 0.043, and 0.072 m3/m3, respectively. YC station, in a semi-humid region with higher soil moisture, has a larger root mean squared error (RMSE) compared to other sites. This is consistent with the results of other studies [43,44], and CCI has a relatively high accuracy in the climate transitional zone of northern China with a correlation coefficient of about 0.7. Therefore, CCI soil moisture is applicable in the climate transitional zone of northern China.

**Figure 2.** Taylor diagram of ESA CCI soil moisture data.
