*2.2. The Residue Cover Factor for Model Validation*

Once the optimal infiltration model was determined for the bare soil, the infiltration under the residue cover could be predicted using a ratio multiplying the function of the bare soil, according to Xin et al. [25]. Therefore, the optimal infiltration model under the residue cover was

$$f(i, t)\_r = R \mathbb{C}F\_i \times f(i, t)\_{b^\star} \tag{1}$$

where *f*(*i*, *t*)*<sup>r</sup>* is the infiltration model under residue cover (mm/min), *i* is the infiltration rate (mm/min), *t* is the corresponding time (min), *RCFi* is the residue cover factor, and *f*(*i*, *t*)*<sup>b</sup>* is the optimal infiltration model of the bare soil. *RCFi* is the ratio of infiltration amounts from the residue cover soil and the bare soil, which was described as

$$RCF\_i = Cl\_r/Cl\_{b\prime} \tag{2}$$

where *CIr* and *CIb* are the cumulative infiltration amount (mm) of the residue cover and bare soil under the rainfall events, respectively. The relationship between the residue cover infiltration factor (*RCFi*) and residue cover was established as

$$RCF\_i = 0.94 \times RC + 1,\tag{3}$$

where *RC* is the residue cover (Figure 2).

The performances of four common infiltration models were compared to evaluate the bare black soil infiltration, including Kostiakov [8], Horton [9], Philip [11], and Mein and Larson (GAML) models (Table 1). The infiltration models were different in terms of mathematical structure and hydrological parameters, but their estimates were all based on the measured water infiltration data for bare soil conditions [26].

**Figure 2.** The relationship between the residue cover infiltration factor (*RCFi*) to predict the infiltration and the residue cover.



Note: *f*(*t*) is the infiltration rate and *t* represents the time.

## *2.3. Accuracy Assessment Methods*

Nonlinear regression was used to determine the values of the parameters in the infiltration models with the rainfall data under the bare soil. The observed values beneath the residue cover and the corresponding predicted values were compared to evaluate the simulations of the models using the 1:1 line method. This method pertains to the t-test method to estimate whether the confidence interval of the slope and intercept of the regressed equation included the numbers 1 and 0, respectively [25]. If included, no difference existed between the regressed curve and the 1:1 line.

The root mean square error (RMSE), the Nash–Sutcliffe efficiency (NSE), and the determination coefficient (*R*2) were used to evaluate the accuracy of the infiltration models [27,28]. The equations of the statistical indexes were as follows:

$$\text{RMSE} = \sqrt{\frac{\sum\_{i=1}^{N} (Y\_i - O\_i)^2}{N}} \,\text{}\tag{4}$$

$$\text{NSE} = 1 - \frac{\sum\_{i=1}^{N} \left(\mathbf{Y}\_i - O\_i\right)^2}{\sum\_{i=1}^{N} \left(O\_i - \overline{O\_i}\right)^2} \tag{5}$$

$$\mathbf{R}^2 = \frac{\sum\_{i=1}^{N} \left( Y\_i - \overline{O\_i} \right)^2}{\sum\_{i=1}^{N} \left( O\_i - \overline{O\_i} \right)^2} \,\mathrm{}\tag{6}$$

where *Oi* is the ith observed value, *Oi* is the average observed value of all of the observed events, *Yi* is the ith predicted value, and *N* is the total number of events. The higher the NSE values were, the better the model performed, as it represented the level of agreement between the observed and predicted values [29]. The values of the RMSE showed the opposite result, namely, the lower the RMSE values were, the better the model performed. The closer to 1 the determination coefficient *R*<sup>2</sup> was, the higher the correlation was. The range of the values of *R*<sup>2</sup> was 0–1, while the range of the values of NSE was (−∞)–1. In the present study, *Oi* represented the observed values and *Yi* represented the predicted values of the infiltration rates.

#### **3. Results**
