*3.4. Performance of the Models for the Residue-Covered Black Soil*

According to Xin et al. [25], *RCFi* was used to fit the infiltration rates of the residue-covered black soil. The performances of the three models were evaluated and the results showed that the Kostiakov model performed poorly. As it did not pass the 1:1 line test for the confidence interval of the slope and intercept of the regressed equation, excluding the numbers 1 and 0, respectively. The Horton and Philip models performed well (Figure 5). As is generally accepted, the performance of the Kostiakov model was robust for many soils over short time periods [31]. In our study, the performance of this model was good for the bare black soil, but it did not perform well after adding the effects of the residue cover in the multiplication form (Equation (1)). The multiplication form underestimated the initial infiltration rate under the high residue coverage scenario, which was in accordance with Almeida et al. [32] who used the Kostiakov–Lewis model for estimation, with the results indicating that the Kostiakov–Lewis model underestimated the infiltration rates at the beginning of the rainfall event and overestimated the rates at the end of the rainfall.

**Figure 5.** Comparison of the observed and fitted infiltration rates obtained with different residue covers (15%, 35%, 55%, and 75%) for the Kostiakov, Horton, and Philip models.

The statistical indexes NSE and RMSE were used for the comparison and are shown in Table 3. The performance of the Philip model was better than the Horton model, as the lower the values of the RMSE and the closer the NSE values were to 1, the better the fitting results were. From the above, the Philip equation was optimal for the infiltration estimation of the black soil under the residue cover conditions. The equation was

$$i(t)\_r = RCF\_i \times \left(1.59 \times t^{-0.5} + 0.290\right) \tag{7}$$

where *i*(*t*)*<sup>r</sup>* is the infiltration rate under the residue cover (mm/min).

**Table 3.** The values of root mean square error (RMSE) and the Nash–Sutcliffe efficiency (NSE) under the Horton and Philip models.


## **4. Discussion**

Four models were compared to evaluate the infiltration of black soil. The GAML model, derived from the Green-Ampt model, demonstrated that infiltration during a steady rainfall event could be simulated. However, the model was not suitable for infiltration estimations of the black soil because of the negative values observed from the hydrological parameters. It might be that the original form was usually applied to initially dry, uniform, coarse-textured soil, such as sands and sand-fraction media [33], whereas the main textural classes of the black soil are silt clay loam and clay loam, according to the USDA (U.S. Department of Agriculture) classification [34]. As with all fine-textured soils, the resistance of soil pores to water flow was higher than in the coarse-textured soils [35]. The permeability of the black soil was poor, which caused the inapplicability of the GAML model.

The infiltration estimations of the Horton and Philip models for the residue-covered black soil performed well, with the Philip model performing better regarding the comparison of the statistical indexes NSE and RMSE. It is worth noting that both models overestimated the initial infiltration rates, especially under high residue coverage.

The average infiltration rates under the four rainfall intensities were used for the model fitting to remove the effects of heavy rain, but only the residue cover was considered, which might have been the reason for the outliers. Considering the physical significance of the Philip model, this derived residue cover infiltration model was suggested for use in estimations of cumulative infiltration amounts.
