Relevance analysis
Equations (1), (3), (5), (8), and (12) were used to calculate the IR of the HS sample. The measured and calculated values are shown in Fig. 8; the fitting formulas, determination coefficient (\(R\)2), and root mean square error (RMSE) between the measured and calculated values are presented in Table 2. Equations (2)–(5), (8), and (13) were used to calculate the IR of the W-RS sample. For the five models, the \(R\)2 and RMSE between the measured and calculated IRs are listed in Table 3, and the measured and calculated values of IR are shown in Figs. 9–13. The MATLAB Curve Fitting Toolbox was used to solve the KF/PKF, GF/PGF, and FSF water infiltration models with the Levenberg–Marquardt algorithm, Robustness set to LAR, MaxIter=400, and default values of the other parameters. The Optimization Toolbox was used to solve the BF/PBF and GMF water infiltration models, with a genetic algorithm selected for the parameter inversion method, Popsize=50, Generations (MaxIter)=100, Migration Fraction=0.85, Crossover Fraction=0.15, Elite count=5, and default values for the other parameters.
For HS, the BF model gives the largest averageR 2 value, followed by GMF, KF, GF, and FSF in that order; the maximum \(R\)2 value is 0.9464 (BF) and the minimum value is 0.7141 (FSF). The lowest mean RMSE is given by FSF, followed by KF, GF, GMF, and BF in that order; the minimum RMSE value is 0.01178 (FSF), and the maximum value is 0.01636 (BF). For the HS sample, GMF, KF, and GF have relatively good fitting accuracy, whereas GF and FSF provide relatively poor fits. Table 3 shows that the GMF model achieved the highest average\(R\)2 between the measured and calculated IR for the W-RS sample, followed by FSF, PKF, BF, PBF, PGF, and GF in that order. The maximum \(R\)2 is 0.7082 (GMF) and the minimum is 0.5429 (GF). The smallest mean RMSE is given by the GMF model, followed by PKF, FSF, PBF, PGF, and GF in that order. The minimum RMSE is 0.00543 (GMF) and the maximum is 0.01852 (GF). For the W-RS sample, GMF and PKF provide a relatively good fit, FSF and PBF give a reasonable fit, whereas PGF and GF PF are poorly fitted.
The inflection point, which indicates the WR cessation time (Moret-Fernández et al., 2019b), was estimated from the point of intersection of two straight lines, representing the CI relationships for the W-RS and the square root of time (Lichner et al., 2013). From Table 3a (rows 2–4, column 3), we can see that the GF parameter\(\ t_{p}\ \)(581, 352, and 326) is close to the CI inflection point (Fig. 4(b)), which corresponds to the maximum IR (Fig. 5(b)). Compared with the method of using the intersection of two straight lines to estimate the WR cessation time, the GF provides a direct and concise approach.