**3. Results**

### *3.1. Environmental Factor Variations*

Figure 3 shows the seasonal variation in the characteristics of the environmental factors at Dingxi and Qingyang. The temperatures at the two stations had unimodal distributions (Figure 3(a1,b1)), reaching a maximum in midsummer and a minimum in January. The average temperature (*Ta*) at Dingxi was 0.2 ◦C higher than the 30 y (from 1988–2017) historical average (6.9 ◦C) during the experimental period. The monthly average minimum and maximum temperatures were −8.63 and 22.61 ◦C, respectively. *Ta* at Qingyang (10.2 ◦C) was 0.5 ◦C higher than the historical average; the average monthly minimum and maximum temperatures were −2.93 and 22.32 ◦C, respectively. During the experiment, maximum monthly precipitation in Dingxi and Qingyang was 148.1 (August 2017) and 246.2 mm (July 2018), respectively. Considering the monthly average precipitation over the past 30 years, the dry months at Dingxi station (April–October) accounted for 57.9% of the total; the dry months at Qingyang accounted for 35.0%. Due to the summer monsoon, more than 65% of the precipitation at the two stations was concentrated from July to September. Soil moisture greater than 40 cm in the tillage layer is very sensitive to precipitation. The monthly average *VPD* at Dingxi Station was 0.78 kPa and was largest in July 2017 (1.14 kPa) and smallest in January 2018 (0.21 kPa). The monthly average *VPD* at Qingyang Station was 0.69 kPa, with minimum and maximum values in November 2015 (0.13 kPa) and July 2019 (1.22 kPa), respectively. During the growing season, the average *VPD* values in Dingxi and Qingyang were 1.10 and 0.89 kPa, respectively. The seasonal variation patterns of the *NDVI* in Dingxi and Qingyang were basically the same. Vegetation growth and the *NDVI* increased in spring as precipitation and temperature gradually increased. The annual average values of the *NDVI* in Dingxi and Qingyang were 0.31 and 0.50, respectively; the respective growing season values were 0.40 and 0.56. The *Gs* trend was very similar to that of the *NDVI*, with an annual maximum from June to August. Precipitation was sufficient during the summer monsoon from June to August, and vegetation photosynthesis and transpiration were the strongest, which made the *Gs* reach the maximum. Vegetation physiological factors had the greatest impact on ecosystem evapotranspiration at this time, resulting in the peak value of *α* (Figure 3(a2,b2)).

**Figure 3.** Seasonal and interannual variations of eco-environmental factors at Dingxi (**a1**,**a2**) and Qingyang (**b1**,**b2**) stations. *Ta* is the monthly mean temperature, *SWC* is the soil water content, *VPD* is the vapor pressure deficit, Rainfall represents monthly precipitation, *Gs* is the canopy stomatal conductance, α is the Priestley–Taylor coefficient, and *NDVI* is the normalized vegetation index.

### *3.2. Energy Balance Characteristics*

The degree of energy closure is one of the most important criteria used to measure the quality and reliability of turbulent flux observation data [49]. The linear regression relationship between turbulent fluxes (*LE + H*) and available energy (*Rn* − *G*) is usually adopted to evaluate the reliability of eddy correlation system observations [50,51]. A large number of studies have shown that the energy imbalance observed by the eddy correlation method is between 10% and 30% [49,52]. Table 2 presents the energy closure of the Dingxi and Qingyang flux stations in the daytime, at night, and throughout the day. From the *OLS* results, the energy closure at both Dingxi and Qingyang was greater in daytime than that at night. This is due to the strong solar radiation during the day. The turbulent air is heated by the surface warming in the near-ground atmosphere, and the exchange is therefore greater [49,53], resulting in a high degree of energy closure. At night, due to the effect of stable atmosphere and low wind speed, the turbulent mixing is insufficient, resulting in low closing energy [12,54]. The increased uncertainty of net radiation measurement at night is also one of the reasons for the low energy closure [55]. When analyzing the degree of energy closure of flux observation systems, it has been reported that the energy balance

components of the land surface are not in the same physical measurement plane, which is also the objective reason for the phenomenon of energy non-closure [56].



The *OLS* method commonly used in energy balance analyses is a simplified processing method based on the assumption of "no random error". The residual frequency distribution can be used to determine whether the model satisfies the hypothesis. Figure 4 shows the residual frequency distribution of the research site during the daytime. It can be seen that both residual density curves followed a normal distribution, indicating that the linear model obtained by the *OLS* method satisfies the assumption of "no random error". For observation data with a longer time scale, the *EBR* can balance the influence of error on energy closure. A large number of studies have shown that the energy closure calculated by this method is generally higher than that calculated by the *OLS* method [12]. It can be seen from Table 2 that the magnitude of the whole-day energy closure of Dingxi and Qingyang stations was between that of day and night, i.e., the closure of surface energy in daytime is greater than that during the whole day and at night. Compared with Li et al. [44], who used the *OLS* (0.49–0.81) and *EBR* (0.58–1.00) methods to evaluate the energy closure of ChinaFlux sites, the energy closure of the research site used in this study was slightly higher. This indicates that the accuracy of the observation data was high, and was suitable for a study of water and heat exchange in farmland ecosystems.

**Figure 4.** Frequency distribution and probability density curve of the energy balance residual.

### *3.3. Diurnal Cycle and Seasonal Variation in Energy Flux*

When the annual average daily change in energy flux (Figure 5) was considered, the difference in the daily peak of net radiation between Dingxi and Qingyang was only 14.3 W/m<sup>2</sup> (Table 3). The daily peak values of the sensible heat flux were almost the same (120.3 and 122.3 W/m<sup>2</sup> in Dingxi and Qingyang, respectively). However, the difference in the latent heat flux between the two locations was large. The daily peak value of the latent heat flux in Qingyang in the semi-humid climate region was almost twice than that in Dingxi in the semi-arid climate region. The daily peak soil heat flux in Qingyang was approximately 2/3 of the Dingxi value. In addition, the latent heat flux (20.95 W/m2) in the arid region of the Loess Plateau was less than the sensible heat flux (28.98 W/m2), whereas the latent heat flux in the semi-humid region was larger than the sensible heat flux, with values of 41.41 and 28.50 W/m2, respectively. According to the ratio of turbulent flux to net radiation (Figure 5e,f), the sensible heat flux in Dingxi was higher than the latent heat flux, with an average difference of 10.3%. In Qingyang, on the contrary, the average difference between the proportion of latent heat flux and the proportion of sensible heat flux was 7.6%. As a consequence, the sensible heat flux played a dominant role in the energy distribution in the semi-arid region of the Loess Plateau, whereas the latent heat flux was dominant in the semi-humid region.

**Figure 5.** Annual average diurnal variation in energy flux (**<sup>a</sup>**–**d**), and the ratio of *H*, *LE*, and *G* to *Rn* at midday at Dingxi (**e**) and Qingyang (**f**). *Rn* is net radiation, *H* is the sensible heat flux, *LE* is the latent heat flux, and *G* is the soil heat flux.


**Table 3.** Annual average daily peak values and average daily values of the energy components.

Figure 6 shows the daily distribution characteristics of the energy flux on a seasonal scale. The net radiation in the semi-arid and semi-humid regions of the Loess Plateau (represented by Dingxi and Qingyang) reached a maximum in summer, with daily average radiation intensities of 109.9 and 119.8 W/m2, respectively, and a minimum in winter, with average values of 25.3 and 26.2 W/m2, respectively (Table 4). The daily peak values of net radiation in Dingxi and Qingyang occurred at 13:00, with summer values of 440.2 and 460.22 W/m<sup>2</sup> and winter values of 226.52 and 240.9 W/m2, respectively. In summer and autumn, the latent heat flux at Qingyang in the semi-humid area accounted for 61.8% and 77.7% of the net radiation, respectively; whereas the sensible heat flux accounted for 25.5% and 33.8% of the net radiation, respectively. The latent heat flux at Dingxi in the semi-arid area in summer and autumn accounted for 32.9% and 41.3% of the net radiation, respectively; whereas the sensible heat flux accounted for 37.8% and 36.3%, respectively. The maximum value of soil heat flux at Dingxi and Qingyang appeared in summer, 125.82 W/m<sup>2</sup> and 214.49 W/m2, respectively. Compared with other energy components, soil heat flux has a larger nighttime variability. This is related to two factors: the change in the direction of soil heat transfer caused by the process of soil freezing and thawing [57]; and the different energy intensity of soil radiation to the atmosphere caused by the diurnal variation in ground temperature difference in different seasons. Zhang et al. [58] reported a similar conclusion in the Loess Plateau.

Figure 7 shows the seasonal variation in energy flux in Dingxi and Qingyang. The net radiation in the semi-arid and semi-humid areas of the Loess Plateau had single-peak distributions, with maximum values in July (111.2 W/m2) and June (125.0 W/m2), respectively, and minimum values in December (21.6 and 19.5 W/m2, respectively). Sensible heat flux and latent heat flux are not only restricted by net radiation, but are also affected by surface vegetation and soil moisture. Dingxi and Qingyang are bare land in the non-growing season, where precipitation is less than 20% of the annual total. Therefore, whether it is a semi-arid or semi-humid area of the Loess Plateau, the ratio of sensible heat flux to net radiation is relatively large (Figure 7(a1,a2)). For the semi-arid area of the Loess Plateau, with the increase in net radiation from March to May, and under the constraint of water conditions, net radiation is mainly transformed into sensible heat flux. Nevertheless, as the summer monsoon advances, the region that is located at the northern edge of the typical summer monsoon transition zone is affected by monsoon precipitation; as a result, the latent heat flux from June to September is generally equivalent to the sensible heat flux (Figure 7(a2)). However, due to the large fluctuation in monsoon precipitation, this area often experiences the phenomenon in which sensible heat and latent heat flux alternately dominate the energy distribution. In contrast, the unimodal distribution of the latent heat flux in Qingyang in the semi-humid region of the Loess Plateau was more prominent than that in Dingxi in the semi-arid region, with a peak value of 77.9 W/m<sup>2</sup> in July. The experimental results showed that the latent heat flux in the growing season in the semi-humid region of the Loess Plateau was 2.4 times than that of the sensible heat flux. The average latent and sensible heat fluxes were 69.4 and 29.1 W/m2, respectively. In the same period, the latent and sensible heat fluxes in Dingxi were similar (33.1 and 39.4 W/m2, respectively).

**Figure 6.** Seasonal average diurnal variation in the energy flux (**<sup>a</sup>**–**d**). Columns 1, 2, 3, and 4 represent spring, summer, autumn, and winter, respectively.


**Table 4.** Peak and daily average values of the seasonal average daily energy fluxes.

**Figure 7.** Seasonal variation in the energy components (**a1**,**a2**) and the ratio of *H*, *LE*, and *G* to *Rn* in Dingxi (**b1**) and Qingyang (**b2**).

In addition, the cumulative fraction curves of the sensible heat flux in Qingyang during the whole year and the growing season basically overlapped, when the cumulative fraction reached 0.6 (Figure 8a). When the cumulative fraction was about 0.4, the annual sensible heat flux was basically consistent with the latent heat flux in Dingxi. The cumulative fraction curves of the sensible and latent heat fluxes in the growing season in the two regions show that the sensible and latent heat fluxes in Dingxi in the semi-arid region were basically the same for cumulative fractions > 0.6, whereas the sensible heat flux in Qingyang in the semi-humid region was almost half of the latent heat flux. These results were consistent with the fluctuation in the sensible and latent heat fluxes in Figure 8b. The average latent heat flux (31.2 W/m2) was less than the average sensible heat flux (34.1 W/m2) in the semi-arid area during the growing season; contrary results were found for the semi-humid area. The interquartile ranges of sensible and latent heat fluxes in semi-arid regions are 23.27–43.42 W/m<sup>2</sup> and 21.00–42.74 W/m2, respectively, and in sub-humid areas the ranges are 22.46–36.72 W/m<sup>2</sup> and 42.45–70.07 W/m2, respectively. Zhang et al. [58] also showed that the summer latent heat and sensible heat flux in the semi-arid area of Northwest China are equivalent, and the summer latent heat flux in the semi-humid area is about twice the sensible heat flux.

**Figure 8.** Cumulative fraction curve (**a**) and box plot (**b**) of the sensible and latent heat fluxes in Dingxi and Qingyang.

The soil heat flux changed from negative to positive from January to February, and from positive to negative from August to September (Figure 7(a2,b2)). This shows that the conversion of the heat source and heat sink occurred in the soil during these two periods. The soil is the conversion period of the heat sink and heat source in spring and summer. In winter, the soil heat flux is transferred from the deep layer to the shallow layer, which serves as a heat source to heat the atmosphere. Yue et al. [45] obtained consistent results in the study of semi-arid grassland in the Loess Plateau.

### *3.4. Bowen Ratio Variation*

Figure 9 shows the seasonal variation in *β*. Overall, *β* of the two stations first decreased, then fluctuated slightly, and finally increased. The seasonal average *β* at Dingxi (6.58) and Qingyang (5.85) was highest in the winter and lowest in the summer (2.51 and 0.71, respectively). The growing season *β* at Dingxi fluctuated around 1, whereas that at Qingyang was < 1. Furthermore, *β* of both stations was low, with multi-year mean values of 2.11 and 0.77, respectively. Precipitation at Dingxi (320 mm) was 1.4 times that of Qingyang

(446 mm) during the same period, and *β* in the semi-arid area was 2.7 times that of the semi-humid area.

**Figure 9.** Seasonal variation in *β* in Dingxi (**a**) and Qingyang (**b**).

### *3.5. Environmental and Ecological Controls on Bowen Ratio*

To fully understand the influence of environmental impacts on *β* of farmland ecosystems under dry and wet conditions on the Loess Plateau, the rainfall data from Dingxi and Qingyang Meteorological Stations in the past 30 years were used to divide the growth period into dry and wet months. Months with monthly precipitation greater than the average of the same period over many years were defined as wet months, whereas the opposite pattern indicated dry months. It was found that *β* was mainly affected by *Ts* − *Ta*, *VPD*, shallow *SWC*, and precipitation. Figure 10 and Table 5 show the relationship between *β* and environmental factors on a monthly scale. The regularity between *β* and *Ts* − *Ta* in the semi-humid region (*R*<sup>2</sup> = 0.51) was better than that in the semi-arid region (*R*<sup>2</sup> = 0.36) whether under dry or wet conditions (Table 5). Under drought conditions, the correlation between *VPD* and *β* in the semi-humid region was more significant (*R*<sup>2</sup> = 0.44), and the coefficient of determination in the semi-arid area was only 0.29. Under humid conditions, the opposite result was observed (Figure 10b). The relationship between effective precipitation (defined as the daily precipitation amount that exceeded 0.5 mm in winter and 4.0 mm in other seasons [28]) and *β* was more significant, and *β* decreased significantly as effective precipitation increased (Figure 10c). As can be seen from the scatter points in Figure 10c, under dry conditions, *β* decreased more rapidly with increased precipitation in the semiarid area than in the semi-humid area. Figure 10d shows the relationship between *β* and *SWC*; the decrease with *SWC* was more prominent in semi-arid areas. Under the humid condition, the goodness of fit in the semi-humid region was the highest, reaching 0.63.

**Figure 10.** Relationship between environmental factors and *β* under different moisture conditions. The solid and hollow dots represent wet and dry conditions, respectively. The red and blue dashed line are the relationships of (**a**) *Ts* − *Ta*, (**b**) *VPD*, (**c**) effective precipitation, (**d**) *SWC*, and *β* in Dingxi and Qingyang, respectively.



The relationship between *NDVI*–*Gs*, *Gs*–α, and *<sup>α</sup>*–*β* was determined to explore the influence of ecological factors on the hydrothermal process. *Gs* increased exponentially as the *NDVI* increased. When the *NDVI* was the same in both areas, *Gs* in the semi-arid area was smaller than in the semi-humid area, and the correlation between *NDVI* and *Gs* in the semi-humid area was more significant (*R*<sup>2</sup> = 0.57). The regulation of transpiration by *Gs* is reflected by the Priestley–Taylor coefficient. Figure 11b shows that α increased logarithmically with *Gs*. The increasing trend of α in semi-humid areas as *Gs* increased is more significant than that in the semi-arid area, with tangent slopes of 0.19 and 0.26, respectively. In addition, *β* decreased exponentially as α increased; this trend was more pronounced in the semi-arid area (Figure 11c).

**Figure 11.** Relationship between (**a**) the *NDVI* and *Gs*, (**b**) *Gs* and α, (**c**) α and *β* on a monthly scale.

We produced path diagrams of the Dingxi and Qingyang stations to further analyze the direct and indirect effects of various influencing factors on *β* (Table 6). On a daily scale, eco-environmental factors at Dingxi and Qingyang explained 60% and 58% of the change in *β*, respectively. From an impact factor perspective, *β* in the semi-arid area was primarily influenced by the direct effect of *NDVI* and the indirect effect of *SWC* (path coefficients of −0.68 and −0.41, respectively). *Ta* and *NDVI* in the semi-humid area were

the most important direct and indirect influencing factors, with contributions of 48% and 17%, respectively. In addition, *SWC* had a more significant overall regulatory effect on *β* in the semi-arid area, with a total path coefficient of −0.63. In the semi-humid area, *β* was primarily affected by *Ta*, with a total path coefficient of −0.53. It is worth noting that the effect of *Ta* on Bowen ratio in the semi-arid and semi-humid regions was completely opposite. This phenomenon can be explained by the influence of the mechanism found by Zhang et al. [59] in the transition zone affected by the summer monsoon, which is related to *Ta* and land surface evapotranspiration. Under the humid condition, the increase in temperature significantly increases the evapotranspiration, whereas under the drought condition, the increase in temperature decreases the land surface *SWC*, thus inhibiting the surface evapotranspiration. Yue et al. [33] found that the effects of *Ta* in dry and wet years on evapotranspiration were similar by studying the long series of observation data of the semi-arid grassland ecosystem on the Loess Plateau.


**Table 6.** Path coefficient between Bowen ratio and impact factor.

To comprehensively assess the effects of farmland ecosystem *Gs*, near-ground aerodynamic characteristics, and the local climate background on *β*, Cho et al. [24] defined the normalized surface impedance (*Rs*∗). Figure 12a shows the relationship between *β* and the monthly mean *Rs*<sup>∗</sup>. There was a significant linear relationship between the *β* and *Rs*∗ in the farmland ecosystem of the Loess Plateau, with a slope of 0.49. As expected, *α* decreased more slowly as *Rs*∗ increased in the semi-arid region than in the semi-humid region due to the growing season. The goodness of fit in the two regions was basically the same ( *R*<sup>2</sup> = 0.81).

**Figure 12.** Relationships between the normalized surface impedance (*Rs*∗) and (**a**) *β* and (**b**) *α* on a monthly time scale. The gray dotted line in the figure represents the overall trend of the above relationship.
