**1. Introduction**

The farmland ecosystem is the foundation of the existence and development of human society, and represents an orderly structure composed of organisms in an environment that can realize the conversion of energy and matter [1]. In-depth research and scientific understanding of the influencing factors and regulatory mechanisms of farmland ecosystems can provide high-quality information that may potentially guarantee the sustainable development of society. Due to the interactions between biogeochemical cycles, climate, soil available water, and plant physiology, the distributions of sensible and latent heat fluxes in farmland ecosystems differ [2–4]. Studies have shown that climate change affects the energy change between the earth and the atmosphere through the water cycle [5–8]. In addition

**Citation:** Ren, X.; Zhang, Q.; Yue, P.; Yang, J.; Wang, S. Environmental and Biophysical Effects of the Bowen Ratio over Typical Farmland Ecosystems in the Loess Plateau. *Remote Sens.* **2022**, *14*, 1897. https:// doi.org/10.3390/rs14081897

Academic Editors: Massimo Menenti, Yaoming Ma, Li Jia and Lei Zhong

Received: 20 March 2022 Accepted: 11 April 2022 Published: 14 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

to climate change, human activities (such as water conservancy projects and changes in land utilization) can also alter the water balance, thereby affecting the evapotranspiration process [5,9,10]. Meteorological and environmental factors, and the development of vegetation, can affect the distribution of surface energy during the growing season [11,12], in which the latent and sensible heat fluxes can change the environmental variables that affect matter and energy transfer between the atmosphere and the ecosystem. It has also been found that evapotranspiration in farmland ecosystems is mainly controlled by net radiation, but the regulation of latent heat transfers by vegetation indexes and canopy stomatal conductance (*Gs*) cannot be ignored [13–15]. In addition, vegetation phenology also affects the partitioning of net radiation to turbulent fluxes and soil heat flux [16–18].

The Bowen ratio (*β*) is a comprehensive physical index of the land surface climate, which comprehensively reflects the effects of microclimate and hydrological processes on ecosystem energy distribution and water use [19]. In previous studies of land–atmosphere interactions in ecosystems, *β* has been found to be a very important factor [2,20]. However, due to changes in regional climate conditions (such as temperature, precipitation, and soil moisture) [12,21,22], and seasonal differences in the physiological characteristics of vegetation [13–15], there are often large differences in *β* of ecosystems [23,24]. AmeriFlux observations have shown that the monthly average value of *β* in farmland ecosystems is between 0.26 and 1.3 [25–27]. Even during a relatively stable growing season, there are still significant differences in *β* among different farmland ecosystems [2,28]. For different ecosystems in the same climate region, there is an obvious contrast in their ability to regulate water and heat exchange, which is an internal factor leading to an apparent discrepancy in *β*. Precipitation is the most important driving factor in this process [2,24]. In the Loess Plateau, where precipitation fluctuates substantially, the ecological environment is fragile. The process of water and heat exchange in this region is also extremely sensitive to climate change [24], which makes *β* more dependent on the driving effect of environmental factors. Therefore, studying the seasonal variation in *β* of the typical farmland ecosystem of the Loess Plateau is of grea<sup>t</sup> significance for better understanding the land–atmosphere interaction mechanism in semi-arid regions.

The Loess Plateau in China is located within a typical semi-arid and semi-humid climate zone, which is not only a transitional zone for the East Asian summer monsoon, but is also positioned at the intersection of the water and heat gradient zones in China [25]. Therefore, the spatial distribution and temporal variation in land surface physical parameters in the Loess Plateau are very significant and highly sensitive to the advance and retreat of the monsoon and changes in its intensity. Due to the influence of the summer monsoon, the annual precipitation in this region is relatively concentrated, with about 65% of the total annual precipitation received from June to September. However, the interannual variability of precipitation is very large, which leads to visible spatial differences in the vegetation distribution [29,30]. The seasonal fluctuations of precipitation will undoubtedly lead to seasonal changes in *β*, which will cause the water and heat exchange of farmland ecosystems to display significant dry–wet conversion characteristics in turn [31,32]. The *β* and its influence on grassland in the Loess Plateau have been studied in depth [24], and the evapotranspiration in farmland ecosystems and its environmental impact in this region are also well understood [33–35]. However, there have been few studies of water and heat exchange in farmland ecosystems on the Loess Plateau, especially in terms of *β* and its influencing factors, despite it being a surface parameter that can comprehensively reflect the effects of water and heat. This has prevented the interactions between the land surface and the atmosphere in the farmland ecosystem of the Loess Plateau from being fully understood, and has prevented an in-depth understanding of water and heat exchange.

This study aimed to identify the effects of environmental factors on *β* of farmland ecosystems in different climate regions of the Loess Plateau using experimental land– atmosphere interaction data for two typical farmland ecosystems in Dingxi and Qingyang, which are semi-arid and semi-humid regions, respectively. The remainder of this paper is organized as follows: The study area, data and method employed are described in Section 2.

The results of physiological and ecological factors relating to water and heat exchange are investigated briefly in Section 3. The discussion of the results is provided in Section 4. In Section 5, the conclusions of this paper are presented.

### **2. Materials and Methods**

### *2.1. Site Description*

Dingxi Station (35.58◦N, 104.62◦E) is located in the elevated extension area of the Loess Plateau, with an altitude of 1896.7 m. Precipitation from June to September accounts for 66% of total annual precipitation. The mean annual temperature and precipitation are 6.7 ◦C and 386 mm, respectively. The average annual pan evaporation is 1400 mm, and the annual mean sunshine duration of 2344 h is typical for a semi-arid climate. Qingyang Station (35.44◦N, 107.38◦E) is located in Dongzhiyuan on the Longdong Loess Plateau at an altitude of 1421 m and has an average annual temperature and precipitation of 8.8 ◦C and 562 mm, respectively. Precipitation from June to September accounts for 67% of the annual total. The average annual pan evaporation is 1470 mm, and the annual average sunshine duration of 2250 h is typical for a semi-humid climate. During the study, the principal crops in Dingxi were potatoes and spring wheat, whereas the principal crops in Qingyang were winter wheat and spring corn. The canopy height of the crops during the vigorous growth period was approximately 50 cm [34]. Both experimental sites are rain-fed farmland. Figure 1 shows the specific geographic locations.

**Figure 1.** Geographical location of the study area. The stars show the Dingxi and Qingyang stations.

### *2.2. Observation Method and Data Processing*

The data used in this paper include turbulence flux data observed by the eddy covariance system, temperature, humidity, and wind gradient data observed by a near-ground gradient tower, and radiation, soil temperature, and humidity gradient. Conventional observation data from meteorological stations were also used. The data period of turbulent flux in Dingxi is August 2016–May 2019; for Qingyang, multi-segment data were used, such as July 2011–July 2012, May 2013–October 2013, December 2015–May 2016, and May 2018–July 2019. In addition, the observation data of Dingxi and Xifeng meteorological stations from 1980 to 2010 were used. The installation height and details of the specific models of the measuring instruments are shown in Table 1.


**Table 1.** Measurement instruments and installation height.

The turbulent flux data were processed by the EdiRe software (v1.5.0.32, Robert Clement, University of Edinburgh, Edinburgh, UK), which was developed by the University of Edinburgh for quality control and pre-processing. The operations included wild point removal, rotation coordinates, turbulence stationarity calculation, and water and CO2 lag corrections. After quality control, the data were processed into 30 min average results. After excluding the outliers and precipitation period data, missing data for periods of less than 6 h were linearly interpolated, whereas missing data for periods of more than 6 h were interpolated by a look-up table method, which was based on the correlation between sensible heat, latent heat, net radiation, and water vapor pressure deficit (*VPD*) [36]. In addition, turbulent flux is greatly affected at night [37–40], and using midday data (09:00–15:00) can make the calculation results more reliable [2,41]. Beijing time was used in the study.

Due to the lack of station vegetation index observation data, the normalized difference vegetative index (*NDVI*) retrieved from the Aqua Moderate Resolution Imaging Spectroradiometer (MODIS, Phoenix, AZ, USA) data was used, with a temporal resolution of 16 days and a spatial resolution of 250 m (https://ladsweb.modaps.eosdis.nasa.gov/search/order/ 1/MOD13Q1--61). The *NDVI* of the experimental site was obtained from the average values of the four nearest grid points.

### *2.3. Energy Balance*

The surface energy balance can be expressed as:

$$R\mathbf{n} = H + LE + G + S + Q \tag{1}$$

where *Rn* is the net radiation (W/m2), *H* is the sensible heat flux (W/m2), *LE* is the latent heat flux (W/m2), *G* is the soil heat flux (W/m2), *S* is canopy heat storage, and *Q* is the sum of all additional energy sources and sinks. Typically, *Q* is neglected as a small term. McCaughey [42] and Moore [43] suggested that canopy heat storage had a grea<sup>t</sup> effect on the degree of energy balance closure when the vegetation height was more than 8 m. Hence, the canopy heat storage term (*S*) was not taken into account in this study. The two principal methods for evaluating the degree of surface energy closure are the energy balance ratio (*EBR*) and the ordinary least squares (OLS) methods.

The EBR determines the degree of surface energy closure by calculating the ratio of turbulent flux to available energy during the study period:

$$EBR = \frac{\sum (H + LE)}{\sum (Rn - G)} \tag{2}$$

For *EBR* = 1, the surface energy is in an ideal equilibrium state. This method is ideal for evaluating the long-term energy closure state.

The *OLS* method is a simple regression model based on a hypothesis. It is based on the principle of the least squares method and is widely used in parameter estimation. When the sum of squares between the estimated value of the model and the experimental observation is at a minimum, the estimated value model is considered the optimal fitting model, and can describe the relationship between turbulent flux and available energy to the greatest extent. The slope of the regression model reflects the degree of surface energy closure. When the intercept of the regression curve is 0 and the slope is 1, the surface energy reaches the ideal closed state. Figure 2 shows the surface energy closure obtained by the *OLS* method. The black dotted line is the ideal state, and the grey shadow part (the slope ranges from 0.49 to 0.81) is the result reported by Li et al. [44] in evaluating the energy closure of flux observations of the terrestrial ecosystem in China. The slope calculated by the *OLS* method is closer to 1, indicating that the degree of surface energy closure is higher.

**Figure 2.** Surface energy closure obtained by the OLS method.

### *2.4. Soil Heat Flux Correction*

The soil heat flux can be corrected to the surface value by the temperature integral method using the soil heat flux observed at 5 cm and soil temperatures at depths of 0 and 5 cm [45,46]:

$$G = G\_{\sf S} + \frac{\rho\_s c\_s}{\Delta t} \sum\_{z=5 \text{cm}}^{z=0} [T((z\_i, t) + \Delta t) - T(z\_i, t)] \Delta z \tag{3}$$

where *G* is the soil heat flux corrected to the surface (W/m2); *G*5 is the soil heat flux at 5 cm measured by the heat flux observation board (W/m2); *<sup>T</sup>*(*zi*, *t*) is the soil temperature (◦C) at depths of 0 and 5 cm; and *ρscs* is the volumetric heat capacity of the soil, which was 1.24 × 10<sup>6</sup> J/ <sup>m</sup>3·K in the calculation. The soil temperature at 0 cm can be converted from surface long-wave radiation as follows:

$$T\_0 = \left(\frac{R\_L^\uparrow - \left(1 - \varepsilon\_{\mathcal{S}}\right) R\_L^\downarrow}{\varepsilon\_{\mathcal{S}} \sigma}\right)^{1/4} \tag{4}$$

where *R*↑*L* and *R*↓*L* are the upward and downward long-wave radiation from the surface (W/m2), respectively; *εg* is the surface specific emissivity (0.96); and σ is the Stefan– Boltzmann constant (5.67 × 10−<sup>8</sup> W/m2·K<sup>2</sup>).

### *2.5. Bowen Ratio*

The Bowen ratio (*β*) comprehensively reflects the impact of climate and hydrological processes on the energy distribution of land surface ecosystems and is expressed as the ratio of the sensible and latent heat fluxes:

$$
\beta = \frac{H}{LE} \tag{5}
$$

For *β* > 1, the sensible heat flux plays a dominant role in the energy distribution; for *β* < 1, the latent heat flux plays the leading role.

### *2.6. Overall Land Surface Parameters*

Canopy resistance (*Rs*), dynamic resistance (*Ra*), and climate resistance (*Ri*) are important parameters that affect the study of land-atmosphere interaction [14]. *Rs* is obtained by the Penman–Monteith equation [47]:

$$R\_{\delta} = \frac{1}{Gs} = \frac{\rho c\_p VPD + R\_d LE(\Delta \beta - \gamma)}{\gamma LE} \tag{6}$$

where *Gs* is stomatal conductance (*m*/*s*); *ρ* is air density kg/m<sup>3</sup>; *cp* is the specific heat of air (1005 J/(kg·<sup>K</sup>)); *VPD* is the saturated vapor pressure deficit (kPa); *LE* is the latent heat flux (W/m2); *Δ* is the slope of saturated vapor pressure curve (kPa/K); *β* is the Bowen ratio; *γ* is the dry and wet bulb constant (kPa/K); and *Ra* is the aerodynamic impedance at the height of the canopy (s/m). *Ra* can be calculated by the Monteith–Unsworth equation [48]:

$$R\_d = \frac{u}{u\_\*^2} + 6.2u\_\*^{-0.67} \tag{7}$$

where *u* is the wind speed at 2 m (m/s); and *u*∗ is the friction velocity (m/s). *Δ* can be calculated by the following formula:

$$\Delta = \frac{4098 \left[ 0.6108 \epsilon x \, p \left( \frac{17.277}{T + 237.3} \right) \right]}{\left( T + 237.3 \right)^2} \tag{8}$$

where *T* is the air temperature (K).

Climatic resistance *Ri* reflects the degree of atmospheric demand for moisture under different surface available energy conditions [14]:

$$R\_i = \frac{\rho c\_p VPD}{\gamma (Rn - G)} \tag{9}$$

Using Equations (6), (7), and (9), it can be shown that *Rs*, *Ra*, and *Ri* satisfy the following relationship:

$$\frac{R\_s}{R\_a} = k\_0 + k \sqrt{\frac{R\_i}{R\_a}} \tag{10}$$

where *k*0 and *k* are empirical coefficients that depend on vegetation physiology and soil moisture status. For a clearer understanding of the impact of vegetation physiological processes on the water and heat exchange of the ecosystem, the normalized surface resistance

*Rs*∗ is defined to eliminate the difference in aerodynamic resistance and climate resistance caused by local changes in the underlying surface [23]:

$$R\_s^\* = \frac{R\_s}{\sqrt{R\_i R\_a}}\tag{11}$$

In addition, the Priestley–Taylor coefficient (*α*) can reflect the influence of environmental meteorological elements and vegetation physiological factors on ecosysterm evapotranspiration:

$$\alpha = \frac{LE}{LE\_{eq}}\tag{12}$$

where *LEeq* (W/m2) is the latent heat flux on a wide surface that is not restricted by moisture, defined as:

$$LE\_{eq} = \frac{\Delta(Rn - G)}{\Delta + \gamma} \tag{13}$$

The value of *α* can be used to determine whether the evapotranspiration of the ecosystem is restricted by water conditions. When *α* < 1, the evaporation of the ecosystem is limited by water. When *α* > 1.26, there is no water stress in the ecosystem, and the factor affecting evaporation is only surface available energy (*Rn* − *G*) [49].
