4. Discussion
4.1 The C–G model reveals the hydrological processes
The non-stationary model of the C–G model is understood as a non-linear model that can be applied to soils with closed isotope systems. The variation of the isotopic composition of input soil water (δP) and the isotopic composition of output soil water (δL) in the C–G model reflects the course of soil water composition in the environment at a given time and temperature and humidity (Fig. 5). In continuous evaporation conditions and at high frequencies of isotope measurements, evaporation exhibits a sinusoidal response for different soil depths at the same time (Fig. 8). Variation of evaporation f indicates that evaporation is not constant throughout the year, and f does not evolve as a simple evaporation process but as a competitive process of evaporation and isotopic mixing of multiple reservoirs (isotopic recharge of upper or lower soil water and evaporation of intermediate soil layers). In addition, the variation in evaporation f in different seasons reflects different isotopic processes - evaporation and mixing - that can be explained by different functions (Fig. 8).
4.2 The accuracy of the C–G model in quantifying soil evaporation
The lysimeter method is the only physical evaluation method that can be used to measure changes in soil moisture fluxes directly. Additionally, it can analyze the soil evaporation pattern of water at various soil depths, for different soil textures, and different crops growing under different climatic conditions (Annelie et al. , 2021; Laura et al. , 2021). However, the set water level in the lysimeter test is fixed, and a deviation results from the natural condition of water level change or the natural state of the water level rising and falling after continuous evaporation. The formula method is based on the observation results produced by the lysimeter; herein, the empirical formula is analyzed, summarized, and then applied to the estimation of soil evaporation without the consideration of associated mechanism problems such as the movement of water during the soil evaporation process; additionally, the result estimated by the experimental formula of evaporation is still different from the actual value (Lehmann et al. , 2019). The location flux method is based on the theory of soil hydrodynamics and involves an analysis of the evaporation process and calculation of the soil evaporation based on the characteristics of the water potential distribution of soil (Xinget al. , 2019; Tingting et al. , 2021). Although the physical interpretation of this method is clear, the applicable conditions are relatively simple and differ significantly from the complex and variable natural conditions; however, the observation requirements for soil water potential are high, and the application of this method is thus limited. The numerical simulation method is based on a large amount of experimental data and combines the principles of ground energy balance and soil hydrodynamics to establish a model for simulating the soil water movement (Ma et al. , 2019; Li and Shi, 2021). The limitation of this method is that more parameters are required for the calculation, and the uncertainty associated with the model is also high. Furthermore, the accuracy of the model in estimating the boundary conditions is limited. In contrast to previous research methods, quantifying soil water evaporation using the C–G model is theoretically applicable to any soil evaporation conditions. Quantification of soil moisture evaporation using the C–G model was similarly validated in the studies of Wei and Yong et al. (Wei et al. , 2015; Yong et al. , 2020). Unlike Wei and Yong et al. We studied a more specific case of soil evaporation estimation under continuous evaporation conditions, which is critical for the study of soil water resources in arid and semi-arid regions. Moreover, in this study, we used soil water content data obtained simultaneously in an experiment as a real measure of soil evaporation. We compared it with the evaluation results of the C–G model, thus validating the accuracy of the model (Fig. 8).
However, soil evaporation is influenced by several factors, such as salinity (C.J. Barnes, 1988), temperature gradients (McDonnell, 1998), soil-water transport mechanisms (Vincent Marc, 2001; Gazis and Feng, 2004), and soil layering (Brent D Newman, 1997). Sofer found that salinity generally reduces equilibrium fractionation, and the degree of reduction is dependent on the type of salt used. Indirectly, salinity affects relative humidity, which reduces kinetic fractionation (Stewart and Friedman, 1975; Z. Sofer, 1975). As Barnes found, temperature affects evaporation of unsaturated soil water primarily by affecting saturated water vapor density, which increases as temperature increases. As a rule of thumb, equilibrium fractionation coefficients, effective diffusion coefficients, and hydraulic conductivities cannot vary more than a few percent per degree Celsius with temperature (C.J. Barnes, 1989). Padilla demonstrated that soil water transport mechanisms produce different isotope profiles that alter soil evaporation calculations. In unsaturated soils, piston flow is dominant when the water content is high, while preferential flow is dominant when the water content is low (Padilla et al. , 1999). Shurbaji found that clay layers possess lower hydraulic conductivity than sand layers, allowing a greater concentration of water to remain in clay layers, decreasing the rate of isotope transport. This resulted in significantly different isotope samples based on different soil layers (A.-R. Shurbaji, 1997). It is still undetermined if these factors affect the calculation of the model and if they can be used to modify the model. Thus, the manner in which the interaction between the parameters affects the model is yet to be determined. These issues should be addressed in a follow-up study.