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.