**4. Discussion**

### *4.1. Bowen Ratio Variation*

*β* comprehensively reflects the wet and dry conditions of an ecosystem. A *β* of 1 is usually used as the critical value for assessing dry and wet conditions in an ecosystem [58]. Figure 9 indicates that *β* in the Loess Plateau was extremely sensitive to climate fluctuations; semi-arid areas represented by Dingxi were mostly dry. *β* still fluctuated around 1 in summer when precipitation was relatively concentrated. Thus, the land surface ecosystem in the region was largely on the border of the dry and slightly wet areas and was primarily in a state of drought in winter and spring. The fluctuation in *β* at Dingxi in the semiarid area during the growing season was more significant than that of Qingyang in the semi-humid area. This was due to the low annual total precipitation in this area and the large precipitation variability during the summer monsoon, which led to prominent nonuniformity in the spatio-temporal distribution of soil moisture in the underlying surface and quickly transformed the surface energy distribution. In addition, the precipitation in the semi-humid area was 1.4 times higher than that in the semi-arid area; however, *β* of 2.7 was higher in the semi-arid area than in the semi-humid area. Thus, the *β*—which reflects the comprehensive effect of land surface water and heat—is more sensitive than relative precipitation in the transition zone from the semi-humid to semi-arid regions of the Loess Plateau.

Huang et al. [60] found that climate change aggravates drought in semi-arid regions of East Asia and humidifies semi-arid regions of North America. Our findings are comparable with *β* (0.26–0.36) in a farmland ecosystem observed by AmeriFlux [26–28]. The ratio in the farmland ecosystem in the Loess Plateau was approximately 2–3 times higher than that in similar climate regions of North America, indicating that the degree of water stress of the farmland ecosystem in the Loess Plateau is higher than that in North America. This also means that the impact of climate change, especially drought, on the ecosystem of the Loess Plateau in China is greater than that in North America.

#### *4.2. Influence of Environmental and Ecological Factors on the Bowen Ratio*

Solar radiation [61], rainfall dynamics, and irrigation [60] affect the water potential gradient and surface resistance, and change the soil moisture and evaporation composition of *LE*, thus impacting *β* [3,62]. For the same climatic region, *β* is more sensitive to the changes in *Ts* − *Ta* under arid conditions. Further analysis showed that *β* decreased with an increase in *SWC*. This trend was more prominent in semi-arid areas, because the land surface parameters in semi-arid areas were more sensitive to changes in *SWC* [34]. Effective precipitation indirectly affects energy distribution by affecting the content of shallow soil moisture (Figure 10c) [28]. Comparing the relationship between *β* and effective precipitation in semi-arid and semi-humid regions of the Loess Plateau, it was found that the response speed of *β* to effective precipitation is faster than that of the latter. Thus, the change in the effective precipitation in this region had an important impact on the key physical parameters of the land surface ecosystem, and regulated the water and heat exchange of the ecosystem through ecological factors. In this study, the change in *β* with environmental factors was clearer in semi-arid areas than in semi-humid areas; further, the response of *β* to environmental factors was more severe under dry conditions than under humid conditions.

Ecological factors are the principal regulators of *ET* and affect the process of energy distribution through canopy conductance. Evapotranspiration is also closely related to vegetation growth [20,61]. Yue et al. [28] indicated that the *NDVI* regulated transpiration in the ecosystem by affecting *Gs*, which in turn had an important regulatory effect on *β*. Differences between climatic regions with various vegetation growth statuses lead to differences in the correlation between the *NDVI* and *Gs*. The ecosystem was less affected by water stress in the semi-humid area than in the semi-arid area, and the growth state of vegetation was better. Because vegetation transpiration is very sensitive to stomatal impedance, the intensity of transpiration increases as *Gs* increases. In theory, when *Gs*

reaches a critical value, α tends to reach equilibrium as *Gs* increases; thus, the magnitude of evapotranspiration is not limited by *Gs*, and vegetation transpiration reaches a maximum [63]. McHaughton and Spriggs [64] reported the theoretical critical value of ecosystem *Gs* (12–16 mm/s). Yue et al. [28] found that the critical value of *Gs* in semi-arid grasslands on the Loess Plateau was 8.2 mm/s. However, this study did not find an obvious *Gs* threshold in the farmland ecosystem in the Loess Plateau, indicating an ecosystem under water stress. As *Gs* increased, the α value in the semi-arid area increased less than in the semi-humid area, indicating that ecological factors in the semi-arid area had a more prominent inhibitory effect on evapotranspiration.

### *4.3. Biometeorological Controls on the Bowen Ratio*

The water and heat distributions of farmland ecosystems in different climatic regions are restricted by different influencing factors. For semi-humid areas, the energy distribution is affected by the air temperature, which indicates the type of energy constraint. However, the hydrological conditions of *β* are more significant in semi-arid areas and show the characteristics of water restriction. Because the surface of the semi-humid area was relatively humid and the vegetation grew well, the increase in *Ta* promoted surface evaporation and vegetation transpiration, resulting in the latent heat flux being the dominant energy distribution process. The surface was dry in the semi-arid area, and therefore the lower *SWC* inhibited soil evaporation and vegetation transpiration, and energy distribution through the sensible heat flux played the leading role in the increase in *β*. The effect of *Ta* on *β* was the opposite in the semi-arid and semi-humid regions. This phenomenon is related to *Ta* and land surface evapotranspiration [32,59]. Under humid conditions, a temperature increase significantly increases evapotranspiration; under drought conditions, a temperature increase decreases the land surface *SWC*, thus inhibiting surface evapotranspiration.

In this study, *Rs*∗ was used to show the consistencies and differences among different climatic zones of farmland ecosystems on the Loess Plateau. The consistency is reflected in the relationship between *Rs*∗ and *β*, which was significantly linear (Figure 12a). Fraedrich et al. [65] found that *Rs*∗ was larger when the surface was dry, that the physiological activity of vegetation was weak, and that the Bowen ratio was accordingly larger. Cho et al. [24] analyzed AmeriFlux observation data and found a positive correlation between *β* and *Rs*<sup>∗</sup>, which is very sensitive to the physiological vegetation processes. The slope of the regression equation between *β* and *Rs*∗ was 0.21 ( *R*<sup>2</sup> = 0.65). Yue et al. [28] found that the slope of *β* and *Rs*∗ in the semi-arid grassland of the Loess Plateau was 0.34 ( *R*<sup>2</sup> = 0.95). The slope of the regression equation for the relationship between *β* and *Rs*∗ of the farmland ecosystem in the Loess Plateau was 0.49 ( *R*<sup>2</sup> = 0.91), which indicates that the comprehensive influence of the eco-environmental factors of the farmland ecosystem on the Loess Plateau led to a larger *β* than that of the grassland ecosystem in this region. Therefore, the effect of water stress on the farmland ecosystem is more serious than that on the grassland ecosystem. Figure 12b shows the difference between the semi-arid and sub-humid regions and the relationship between α and *Rs*<sup>∗</sup>. A significant negative correlation between the two was found in the semi-arid farmland ecosystem of the Loess Plateau. For the same α value, the *Rs*∗ of the semi-arid area was greater than that of the semi-humid area, indicating that *Rs*∗ increased as the aridity of the regional climate increased. Additionally, *Rs*∗ had a stronger limiting effect on evapotranspiration in semi-arid areas.

## **5. Conclusions**

Under the background of global change, differences in precipitation caused by the duration of the dry and wet seasons in different climate regions are likely to be enhanced. The Loess Plateau in China has both semi-arid and semi-humid climate zones, and it is located in the transitional zone of the East Asian summer monsoon, in which the seasonal variation in precipitation is particularly obvious. Due to the intensity of the monsoon and its advancing northern edge, the land surface processes in the farmland ecosystem of this region display large interannual and seasonal changes. In particular, *β*, which characterizes

the intensity of land surface water and heat exchanges, is very sensitive to environmental factors. The precipitation in Qingyang during the growing season was 1.4 times that in Dingxi, but the Bowen ratio in Dingxi was 2.7 times that in Qingyang, indicating that the land surface water and heat exchanges on the Loess Plateau were more sensitive than the precipitation variations. In addition, the farmland ecosystem of the Loess Plateau was more affected by water stress than farmland ecosystems in North America, and the impact of drought on the ecosystem in this region was also greater than in North America. According to the experimental observations, *β* in the Loess Plateau was extremely sensitive to climate fluctuations, and most of the time in the semi-arid region it indicated a dry state. Even during the summer monsoon, the regional land surface ecosystem was subject to water stress. The fluctuation in *β* around 1 indicated that the semi-arid region of the Loess Plateau was on the borderline of dry and slightly wet conditions for long periods. Compared with the semi-humid region of the Loess Plateau, there was less annual total precipitation in the semi-arid region and the precipitation variability was larger during the summer monsoon, which led to obvious fluctuations in the contributions of the latent and sensible heat fluxes to the energy distribution; this was a factor affecting the stability of *β* in the semi-arid region of the Loess Plateau during the summer monsoon.

The main environmental factors affecting *β* of the farmland ecosystem under different dry and wet conditions on the Loess Plateau are *Ts* − *Ta*, *VPD*, shallow *SWC*, and precipitation. The positive correlation between *β* and *Ts* − *Ta* in the Loess Plateau was stronger in the semi-humid region than in the semi-arid region. Under drought conditions, the correlation between *VPD* and *β* in the semi-humid area was more significant. *β* of the farmland ecosystem in this region decreased with the increase in *SWC*, especially in semi-arid areas, because the land surface water and heat exchanges in semi-arid areas were more sensitive to changes in *SWC*. Ecological factors regulated evapotranspiration through canopy conductance, which then affected *β*. The *NDVI* controlled the transpiration process within the ecosystem by affecting *Gs*, and then played an important role in regulating *β* of the ecosystem. Theoretically, when *Gs* reaches a critical value, α tends to remain stable with a further increase in *Gs*, and the transpiration of vegetation reaches a maximum at this point. According to our observations, there was no obvious threshold for the farmland ecosystem on the Loess Plateau, but previous studies have found that there is a sensitivity threshold for *Gs* in the semi-arid grassland on the Loess Plateau, demonstrating that the farmland ecosystem in this region is in a state of water stress. Therefore, from the response of the land surface water and heat exchange processes to the summer monsoon, restoring farmland to grassland in the Loess Plateau may reduce the demand for water evapotranspiration and help to maintain the stability of the regional ecosystem. A path analysis showed that *NDVI* and *SWC* had obvious direct and indirect effects on *β* in the semi-arid area, whereas *β* in the semi-humid area was directly and indirectly affected by *Ta* and *NDVI*. The influence of *Ta* on *β* in the semi-humid and semi-arid regions had the opposite effect. An increase in temperature in the semi-humid region significantly increased evapotranspiration, whereas an increase in temperature in the semi-arid region decreased the land surface *SWC* and inhibited surface evapotranspiration.

**Author Contributions:** Conceptualization, Q.Z. and P.Y.; Data curation, X.R.; Formal analysis, X.R.; Funding acquisition, P.Y.; Resources, S.W.; Supervision, Q.Z., P.Y. and J.Y.; Validation, P.Y. and J.Y.; Visualization, X.R.; Writing–original draft, X.R.; Writing–review and editing, X.R. and P.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China under gran<sup>t</sup> Nos. U2142208, 41975016, 41705075, and the Basic Science Fund for Creative Research Groups of Gansu Province, gran<sup>t</sup> number 20JR5RA121.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data not available due to legal restrictions and observation team requirements.

**Acknowledgments:** We are grateful to the NASA Goddard Space Center for providing remote sensing data for this study.

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