**4. Discussion**

#### *4.1. Determination of Water and Temperature Factors via Spatial Pattern of CS*

Both observation and simulation studies showed that the strong land–atmosphere coupling zone is mainly located in the semi-arid and sub-humid climate transition zone [5–7,29]. Because coupling is influenced by the evapotranspiration variability, the sensitivity of evapotranspiration to soil moisture, and sufficient water vapor conditions, which are optimal in the transition zone following a compromise, it is strongest in the transition zone. In these land–atmosphere coupling "hot spots", the CS is further influenced by hydrothermal factors.

In semi-arid regions of southeastern South America and Africa, land–atmosphere coupling (soil moisture–precipitation coupling) is negatively correlated with soil moisture, with stronger coupling occurring in areas with lower soil moisture [26,33]. Wei et al. [30] found that the spatial distribution of soil moisture -precipitation CS is linked to the mean soil moisture, and the strong coupling area is mainly distributed in the areas with a soil moisture of 0.4–0.5.

Land–atmosphere coupling can be separated into two components: the terrestrial leg and the atmospheric leg [7]. For instance, soil moisture–precipitation coupling can be separated into soil moisture–evapotranspiration coupling (terrestrial leg) and evapotranspiration coupling (atmospheric leg). The current study focused on ET-P coupling, which is the atmospheric leg of land-precipitation coupling. The CS is found to be positively related to climatological soil moisture, and the data reveal the strong coupling in the climate transition zone with soil moisture in the range of 0.15–0.25, with relatively weak coupling in the arid and humid areas. The soil moisture range of the strongest coupling differs from the strong coupling zone of 0.4–0.55 in Wei's study, which may be related to the different soil moisture data, where they used MERRA-LAND reanalysis soil moisture data (top 1 m), while we used CCI remotely sensed soil moisture (surface 5–10 cm).

Studies have shown that the areas where land–atmosphere coupling is controlled by thermal energy factors are mostly located in moist areas with sufficient moisture [35,39]. In the climate transitional zone of northern China, where the climate is non-humid, the influence of temperature is weak, and the relationship between the spatial distribution of CS and temperature is considerably weaker than that with soil moisture. Therefore, the moisture factor is the main factor dominating the spatial distribution of ET-P coupling.

#### *4.2. Determination of Water and Temperature Factors on Temporal Variation of CS*

The studies on the temporal variation of CS are fewer than those on the spatial pattern of CS. The findings based on GLACE and MERRA-LAND both indicate that interannual variation in land–atmosphere coupling is mainly caused by soil moisture variation, and sugges<sup>t</sup> a phenomenon of "see-saw" that the CS is stronger in the wet period in the dry area and in the dry period in the wet area [30,31]. This is explained by the fact that where the CS is strongest in the transition zone, either the dry zone becomes wet or the wet zone becomes dry, and the coupling is thus enhanced. Recently, Lo et al. showed that hydrological events have a significant effect on temporal evolution of CS by changing the surface state [45]. After large-scale intensive precipitation events, the soil moisture increases significantly, causing evapotranspiration to change from moisture to transitional limitation. Thus, the dependence of evapotranspiration on soil moisture decreases, resulting in a decrease in CS.

In the current study, responding to the intra- and inter-annual fluctuations of environmental conditions, land–atmosphere coupling exhibits distinct intra-annual cycles and inter-annual fluctuations. Soil moisture variability (standard deviation) is the most important influencing factor in determining the CS in the northern China climate transition zone. This is in relation to evapotranspiration being moisture-limited across most of the climate transition zone, and a larger soil moisture variability causes a larger evapotranspiration variability, and subsequently a precipitation variability. This effect is more significant in arid and semi-arid regions.

### *4.3. Positive and Negative Coupling Mechanisms*

Land–atmosphere couplings could be positive or negative. Drylands tend to show positive coupling, i.e., the lager the soil moisture, the higher the evapotranspiration, and the more likely to trigger convective precipitation [5,16]. The mechanism responsible for positive coupling involves dominant moisture recycling in land–atmosphere coupling. Negative coupling was also found in some studies, i.e., negative coupling exists in north Africa [26]. Negative coupling implies that a lower soil moisture is more likely to trigger precipitation. The mechanism responsible for negative CS is that in areas where the boundary layer is wet with a dry surface with strong heating, the convective available potential energy (CAPE) is large and convective inhibition (CIN) is small, causing the boundary layer to be more likely to develop deeper. Although a dry and hot boundary layer causes LCL lift, the well-developed BLH would exceed LCL and trigger convective precipitation. This mechanism is similar to the land–atmosphere coupling mechanism in the southern region of the study area in the current study.

LCL is a key variable in the linkage between surface and precipitation, and the development of LCL is closely related to the type of evapotranspiration [46]. The ET in the southern region of the study area is energy-limited, and the increase in available energy causes both sensible and latent heat to increase, and the increased sensible heat heats the boundary layer and increases the LCL, leading to a positive correlation between ET and LCL. In most northern regions, ET is moisture-limited, and increasing soil moisture results in an increase in ET and a decrease in sensible heat, causing LCL to decrease and the boundary layer to become wet and cold, leading negative correlation of ET with LCL. In contrast, over the whole study area, a lower LCL is more likely to trigger precipitation, and hence, LCL has a negative correlation with P. Thus, it leads to negative ET-P coupling in the part of south region and positive coupling in the north region. Therefore, the main reason for the positive and negative differences in ET-P coupling in the study area is the different driving regimes of evapotranspiration.
