## 1 Introduction  
The frequency of droughts will significantly increase under climate change, especially in arid/semi-arid regions. Although there are several studies on the effects of water deficit on the water-carbon cycle at different levels of the ecosystem, systematic research on the water-carbon coupling process at different spatial and temporal scales is still scarce. Under water stress, the water conductivity ability of leaves decreased and caused stomatal closure in [1, 2]. The stomatal conductance of leaves in crop plants is reduced under drought stress to reduce water loss and improve transpiration efficiency [3]. [PERSON] et al. [4] found that the biomass of plant leaves varies with the degree of water deficit, and the biomass allocation of the farmland system has no obvious response to short-term drought [5]. In addition to the direct effects on plant growth [6], the most affected process is related to photosynthesis [7, 8]. The direct effects of drought on photosynthesis are caused by stomatal closure [9] and occur earlier, while the indirect effects are caused by the downregulation of photosynthetic metabolism that occurs under long-term or more severe stress [10, 11]. [PERSON] et al. [12] suggested that drought, high temperature, and their synergistic stress could reduce the grain yield of spring wheat from seedling emergence to the flowering stage. Drought reduces plants' morphological and physiological traits, photosynthesis, leaf water potential, and sap movement, mainly due to stomatal closure [13]. The coupling between the leaf An and Tr of plants forms the basis of the coupling between carbon and water in terrestrial ecosystems. Previous studies have attributed the coupling of An and Tr to joint stomata control, but they lack comprehensive analyses of the coupling mechanism. Plants' stomatal behavior is a complex process regulated by multiple factors. It is influenced by environmental factors such as the temperature, radiation, wind speed, and hydraulic conductivity of plant organs. It has been found that in a short period, stomatal behavior is mainly driven by environmental factors, PAR, Ta, CO\({}_{2}\) concentration, and VPD deficit [14; 15; 16]. It is generally expected that the joint control of stomata to regulate the entry and exit of CO\({}_{2}\) and water vapor into and out of leaves is the reason for the formation of An-Tr coupling and the physiological and ecological basis for the coupling of the carbon-water cycle in terrestrial ecosystems [17; 18; 19]. However, stomata are only one of the biological factors regulating An and Tr. Environmental factors such as light, temperature, and saturated water vapor pressure also have significant effects on An and Tr [20]. [PERSON] et al. [21] concluded that Tr and An have a positive linear correlation, ensuring an excellent linear coupling relationship between photosynthesis and transpiration in the process of diurnal variation. Temperature is another important environmental factor affecting Tr. An increase in temperature increases the diffusion rate of water molecules and promotes Tr. The regression relationship between An and Tr reflects the coupling characteristics of carbon and water in plants to a large extent [22]. [PERSON] et al. [23] stated that the main environmental factors (PAR, Ta, and VPD) have a strong driving effect on the An-Tr coupling relationship; when PAR, Ta, and VPD are at high levels, the relationship is destroyed, a certain decoupling phenomenon occurs, and the An-Tr slope becomes smaller. Tr and An tend to be synchronized because they share common environmental constraints and drivers, and stomatal regulation regulates both processes [24; 25]. For example, under conditions of high atmospheric drought, i.e., VPD, stomata nearly inhibit water loss. Under extremely high temperatures and VPD conditions, it was found that even when photosynthetic activity was reduced to near zero, plants continued to evaporate as long as soil water was sufficiently available [26; 27].