4.3 The uncertainty analysis of the C–G model
For calculating evaporation losses, the C–G model can identify relative and absolute error sources. The absolute error of the experiment originates from the error of the measuring instrument itself. The stable isotope composition of water was frequently analyzed in the laboratory, and the errors associated with δ18O and δ2H were found to be ±0.2‰ and ±0.6‰, respectively. When the difference between the maximum analytic uncertainty in the corresponding values and the valid values of two adjacent samples was the greatest (±0.2‰ and ±0.6‰), the uncertainty range caused an increase of 0.4‰ in the difference between the values of δP and δL for δ18O and an increase of 1.2‰ in the difference between those for δ2H. Considering the maximum expected uncertainty in the measured δ value, the maximum difference between the final calculation results of this experiment was 1.67% (f18O)) and 1.35% (f2H)). However, this difference depends on the relative change in the δ value owing to evaporation and impacts the samples that exhibit greater evaporation. It would be worth future research to develop a more accurate method of measuring isotopes.
The relative error of the experiment depended on the uncertainty associated with the parameters in the model calculation. We analyzed the sensitivity associated with each parameter of the model using the control variable method combined with the test data. As shown in Fig. 9, in terms of the sensitivity of the model calculation to a change in a single parameter, parameters such as h, δP, and δL have a greater influence on the calculation. The changes in T, δrain, and other parameters had almost no effect on the calculation of the model. (1) As h varies within the interval (0.5, 1), each 1% change in h results in a change in f of 0.006 to 0.892. As relative humidity increases, f decreases gradually until it reaches a fixed value. The surface soil is more strongly influenced by the atmosphere and its variation is more pronounced. Essentially, relative humidity (h) is the ratio of the actual water vapor pressure in the air to the saturated water vapor pressure at the same temperature, and it reflects how close the atmospheric water vapor pressure is to the saturated water vapor pressure at the current temperature. As the relative humidity increases, the saturation pressure of water vapor in the atmosphere increases, which makes water evaporation more difficult; therefore, evaporation intensity is negatively correlated with relative humidity. (2) As δP(O18) varies within the interval (-10, 0), each 0.5% change in h results in a change in f of 0.006 to 0.892. For each soil layer, f decreases followed by an increase and is then stabilized. The trend of δL(O18) is counter-intuitive to that of δP(O18). As δL(O18) varies within the interval (-10, 0), each 0.5% change in h results in a change in f of 0.019 to 0.462. f increases followed by a decrease and is then stabilized. In essence, the ratio of the difference between the final and limiting isotope values of soil water isotopes to the difference between the initial and limiting isotope values reflects the variation in soil water content. In addition, soil non-stationary evaporation isotopes’ limiting evaporation capacity depends on soil water content and soil medium. In soils with a constant limiting isotopic composition, i.e., when the hydraulic medium of the soil itself is constant, the change in evaporation intensity is determined by changes in soil water content (G.R. Walker, 1988; C.J. Barnes, 1989). As soil water isotopic values become similar to their initial values, it indicates that the soil has changed from a non-steady state evaporation state to a steady state evaporation state. At this point, f describes the evaporation intensity of each soil layer at steady-state. (3) It should be noted that although the controlled variable method can reflect the sensitivity of a certain parameter to the model to a certain extent, it does not consider the synergistic relationship between the parameters. Unsaturated soil water movement is affected by temperature gradients primarily due to saturated water vapor density increasing rapidly with temperature. As the temperature increases with depth, the temperature gradient enhances evaporation. In addition, as the temperature decreases with depth, the temperature gradient reduces evaporation. Thus, a single temperature control does not show evaporation’s response to temperature changes.
In summary, the temperature and relative humidity are the root causes of errors resulting in model calculations. The relative error in the experiment primarily depends on the uncertainty in the temperature and relative humidity.