*2.2. Methods*

The serious soil and water loss in the Loess Plateau has always occurred because of the surface runoff caused by heavy rains. In this paper, runoff generation was simulated based on the Land Catchment Model (LCM), which is a flood event forecasting model that was developed through more than 300 artificial rainfall experiments in the Loess Plateau [51,52]. The model has been modified into a distributed model [53–55]. The Modified Universal Soil Loss Equation (MUSLE) was chosen to estimate the sediment yield of individual heavy rainfall events [56], and numerous studies had proven its applicability to estimate the sediment yield in the Loess Plateau [57–59]. The main functions of LCM-MUSLE model are listed in Tables 1 and 2. The reader is referred to Luo et al. [59] for a detailed description of the LCM-MUSLE model, which is not described here. Runoff and sediment generation from sub-catchments was routed to the outlet by considering overland flow and stream channels. Time-area method was used for overland routing [49] and Muskingum method was used for channel routing [60,61].


**Table 1.** Functions and parameters related to runoff generation in the Land Catchment Model-Modified Universal Soil Loss Equation (LCM-MUSLE) model.

Annotation: *Sv*: interception (mm); *Vf*: vegetation coverage (%); *Smax*: canopy storage capacity (mm); η: a correction coefficient; *P*: precipitation (mm); *LAI*: leaf area index; *Qd*: surface runoff (mm); *P* : effective rainfall (mm); *f*: infiltration (mm); *R* and *r*: both infiltration coefficient; *La*: interflow coefficient; *Ws*: unsaturated soil moisture storage (mm); *Wsm*: maximum soil moisture storage capacity of the soil layer (mm); *Ql*: interflow (mm); *Qb*: base flow (mm); *Kb*: base flow coefficient; *GWs*: groundwater storage (mm); *REC*: groundwater recharge (mm); *Rc*: groundwater recharge coefficient.

**Table 2.** Functions and parameters related to sediment yield in the Land Catchment Model-Modified Universal Soil Loss Equation (LCM-MUSLE) model.


Annotation: *Sed*: sediment yield (t); *Rs*: surface runoff (mm); *qpeak*: peak runoff rate (m3/s); *Apixel*: area of the grids (ha); *<sup>K</sup>*: soil erodibility factor (0.013·t·m2·h/(m3·t·cm)); *<sup>C</sup>*: cover and management factor; *<sup>P</sup>*: support practice factor; *LS*: topographic factor; *CFRG*: coarse fragment factor; α*tc*: fraction of rainfall that occurs during the time of concentration (for event modeling the value of α*tc* is 1); *tconc*: the time of concentration for the grid; *Sd*: percent sand content (%); *Si*: percent silt content (%); *Ci*: percent clay content (%); *C*: percent organic carbon content of the layer (%); *Lslp*: slope length (m); θ: gradient of the slope (◦); *cv*: vegetation coverage (%); *rock*: percent rock in the top soil layer (%).

With the purpose of simulating the influence of terrace and vegetation units on water and sediment reduction at confluences, as the critical hydrologic process, both terrace and vegetation modules were added to the time-area method. In the time-area method, the catchment is divided into a number of travel time zones via isochrones [67]. By extracting the watershed of terrace units and vegetation units, and calculating the water stored by the terraces or intercepted by vegetation, the runoff yield and the outflow in each travel time zone are revised. This represents the spatiotemporally varied flow in the routing simulation. Sediment reduction was achieved in a similar way.

The integrated structure of the model is shown in Figure 2. Specific equations and methods are discussed in the following sections. The integrated model can represent landscape heterogeneity in detail, if a higher spatial resolution DEM is used.

**Figure 2.** Framework of revised integrated model. *Ti,j* is the amount of stored water or sediment in all terraces in travel time zone *<sup>i</sup>* at present time step *<sup>j</sup>* (m<sup>3</sup> or t); *Ti*,*j*−<sup>1</sup> is the amount of stored water or sediment in all terraces in *i* at previous time *j* <sup>−</sup> 1 (m3 or t); and *Tci* is water storage capacity of all terraces in *i* (m3).
