2.2.4. Consideration of Vegetation Units in the Time-area Method

Unlike terraces, which can act as a water tank, vegetation does not have a direct storage volume, but it can resist the confluence process of runoff and sediment. Vegetation coverage and canopy density are the main indicators influencing vegetation's impact on water and soil conservation [70–72]. In this study, we chose vegetation cover that was easily derived to incorporate the vegetation module into the time-area method.

Similar to Equation (5), when there are vegetation units occurring in time zone *i*, the outflow *Qi,j* from time zone *i* at time step *j* is as follows:

$$Q\_{i,j} = Q\_{i+1,j-1} + \Delta R\_j \Delta A\_i - \Delta V \epsilon \gchi\_{i,j} \tag{11}$$

where Δ*Vegi,j* is the water or sediment trapped by vegetation units in time zone *i* at time step *j* (m3). Δ*Vegi,j* is calculated as follows:

$$
\Delta V \text{cg}\_{i\dot{\jmath}} = (Q\_{i+1,j-1} + \Delta R\_j \Delta A\_i) \times V \nu\_i \times f(V \text{c\'g}) \tag{12}
$$

$$V\mu\_i = \Delta A\_{V\text{control},i} / \Delta A\_i \tag{13}$$

where *Vui* is the ratio of all the vegetation control area in the time zone *i*; Δ*AVcontrol,i* is the total area of vegetation in time zone *i* (m2); *Veg* is vegetation coverage (%); *f*(*Veg*) is function of *Veg*, it refers to runoff or sediment retention rate of the forestland or grassland with certain vegetation coverage, and *f*(*Veg*) is the average value of runoff or sediment retention rates in the time zone *i*.

Most flume test researches in the Loess Plateau lack the complete information about the runoff and sediment retention rate of grassland and forestland with different cover [73–76]. Xiong et al. [77] systematically deconstructed the experimental data from different slope runoff plots in the Loess Plateau, and summarized benefit indices of runoff and sediment reduction by forestland and grassland of different qualities in years with different runoff and sediment levels [77], as shown in Table 3. This paper refers to the study of Xiong et al. [77]. For the convenience of distributed calculation, we fitted the data in Table 3 to get the runoff and sediment reduction functions of forestland and grassland under different conditions, as shown in Tables 4 and 5, *x* means vegetation coverage (%) and *y* means runoff and sediment reduction rates.

different quality. **Dry Year Normal Year Wet Year**

**Table 3.** The reduction percentage in runoff and sediment generation of forestland and grassland of


**Table 4.** The reduction function of runoff by forestland and grassland.


**Table 5.** The reduction function of sediment by forestland and grassland.


#### 2.2.5. Model Performance Evaluation Criteria

Nash–Sutcliffe efficiency (NSE) was used to evaluate the performance of the simulation:

$$\text{Nash} = 1 - \sum\_{i=1}^{N} \left(\mathbf{O}\_i - \mathbf{E}\_i\right)^2 / \sum\_{i=1}^{N} \left(\mathbf{O}\_i - \overline{\mathbf{O}}\right)^2 \tag{14}$$

where *Oi* is observed data (runoff discharge or sediment discharge); *Ei* is simulated data (runoff discharge or sediment discharge); O is average observed data; *N* is number of values. NSE varies from negative infinity to 1, where NSE closer to 1 indicates a better simulation.

A total of eight isolated storms with observed runoff and sediment yield were selected to calibrate and verify the model. There were five in the 1980s, and three in the 2010s, and each storm was encoded with its start time as Nos. year/day/hour. Among them, Nos. 1981/203/17, 1983/215/22 and 1983/235/16 were used for calibration, while Nos. 1988/199/13, 1989/203/19, 2006/195/5, 2006/224/8 and 2010/263/20 were used for validation.

The runoff and sediment simulation was implemented in four cases: O1—original simulation without considering terrace and vegetation practice; R1—revised with vegetation module; R2—revised with terrace module; R3—revised with vegetation and terrace modules. For the five events in the 1980s, as the terrace data was unavailable and terraces just accounted for a small proportion of the area, only O1 and R1 were simulated. For three events in the 2010s, all four cases were simulated. The terraces in the study area are all level terraces with good quality [78], and we made an assumption that all terraces had an embankment height of 20 cm. For vegetation, the retention functions of runoff and sediment were chosen according to the rainfall amount of each event and the rainfall condition of the two days before each event. Here, for Nos. 1983/215/22, 1983/235/16, 1988/199/13, 2006/224/8 and 2010/263/20 functions of normal period were chosen in Tables 4 and 5, while for Nos. 1981/203/17, 1989/203/19 and 2006/195/5 functions of wet period were chosen.

## *2.3. Data Source*

Input data for the model included hourly precipitation, DEM, land use, vegetation coverage, soil data, and particle size of the sediment. In addition, observed runoff and sediment discharge of hydrological stations were used in the model's calibration and validation.


All data were reproduced at 30 × 30 m spatial resolution and projected to Albers, using the World Geodetic System-84 (WGS84) datum. Data were processed by ENVI5.1 (Harris Corporation, Melbourne, FL, USA), GisNet [80], ArcGIS10.4.1 (Environmental Systems Research Institute, Redlands, CA, USA), or programs written in IDL (Interactive Data Language).
