**1. Introduction**

Soil erosion and water loss is a serious environmental problem in the Chinese Loess Plateau [1–3]. It can cause soil deterioration and loss of sustainable productivity in croplands [2,4,5]. In addition, sediment yields and chemical loadings associated with soil erosion can cause severe degradation of surface water quality [6–8]. To control soil and water losses, terrace engineering was implemented since the 1980s and the Grain for Green (GFG) project was launched in 1999 [9–12]. Therefore, it is necessary to quantitatively analyze the effect of terraces and vegetation on runoff and sediment in the Loess Plateau.

Slope terracing and vegetation planting are common practices for soil and water conservation on sloped terrain susceptible to water erosion, and have been proven to be effective at retaining water and soil [6,13–20]. Terraces and vegetation can reduce the sediment yield from themselves significantly. Terraces reduce the peak runoff rate by reducing the slope gradient and slope length of the hillside [21,22]. Owing to the topographic slope and the embankment, terraced fields have a certain storage capacity similar to a reservoir, which can intercept surface runoff and sediment and promote runoff infiltration, evaporation, and sediment deposition [23–25]. The vegetation canopy can intercept rainfall directly and influence the rainfall kinetic energy and erosion rates. The stems, roots, and litter layer of vegetation can reduce runoff discharge by promoting infiltration, increasing surface roughness, and slowing down the overland flow and peak runoff. Vegetation also can reduce soil erosion by reducing surface flow volume and increasing sediment trapping through reducing flow velocity [21,26,27]. In addition to this, both terraces and vegetation can intercept the sediment yield from upstream and achieve sediment reduction in the valley by reducing runoff flowing from the slope into the valley [16,24,28,29].

Numerous studies have provided many insights into how terraces and vegetation control water erosion at local scales using observational experiments [20,27]. Terraces could be classified into level terraces, slope terraces, slope-separated terraces, and zig terraces according to their structure [23]. In the Loess Plateau of China, the main terrace type is level terraces. Yao [30] found a terraced field could reduce soil erosion by 92–100% compared with sloped farmland, while Wu [31] found the average benefit of level terraces on soil and water conservation were 86.7% and 87.7%, respectively. Huo and Zhu [32] combined soil water moisture and 137Cs content analysis and found the average soil and water conservation benefit of level terraces was 53%\_ENREF\_18, while Pan and Shangguan [27] reported that grassplots had 14–25% less runoff and 81–95% less sediment yield compared to a bare soil plot. Meng et al. [33] conducted a series of laboratory flume simulation experiments and the results showed that vegetation could reduce the mean velocity by 31–65%\_ENREF\_36. As the effectiveness of terraces and vegetation is limited by many factors, such as climate, soil properties, topography, land use, vegetation type, and spatial patterns, the diversity and natural variability of previously conducted erosion studies limit their potential extrapolation to the catchment scale [23,34–36]. Thus, how to assess the effects of terraces and vegetation on water erosion control at the catchment scale remains a crucial issue.

Estimation of rainstorm-generated sediment yield by means of a hydrological model is an important way to quantitatively evaluate the effect of soil and water conservation measures, such as by using the Soil and Water Assessment Tool (SWAT) model [37–39], the Agricultural Non-Point Source pollution (AGNPs) model [40], and the Agricultural Policy/ Environmental eXtender (APEX) model [41]. In these models, accounting for the impact of terraces and vegetation on runoff and sediment yields has focused on reduction from themselves through adjusting the key input variables, such as the Soil Conservation Service Curve Number (SCS-CN), slope gradient, slope length, Universal Soil Loss Equation (USLE) support practice factor (P-factor), and cover and management factor (C-factor) [11,21,22,25,29,42,43], without considering the roles of water and sediment reduction in the routing process. Then, the runoff and sediment reduction effect of terraces and vegetation is likely to have been underestimated. Therefore, it is necessary to take into account the water and sediment reduction effect of terraces and vegetation in the model's routing process.

Explicitly simulating the interaction between conservation practice and watershed response is difficult. The time-area method, with its inherently distributed concept, explains which parts of a watershed contribute to runoff during a specific period [44]. It provides a simple and useful tool to understand runoff mechanisms and is widely used at the catchment scale [44]. It has also been indicated that the routing of sediment through time-area segments in a catchment produces better results than the conventional routing through a network of cells [45,46]. Her and Heatwole [47] revised the time-area method and considered the upstream contribution for routing sediment, such that the new method provided detailed spatial representation\_ENREF\_15. These studies mainly focused on the effect of surface heterogeneity on routing time or flow velocity [48,49]. Topographic features are delineated through a Digital Elevation Model (DEM), slope gradient, flow direction, and so on. However, the lack of representation of a specific terrace and vegetation process makes it difficult to quantitatively distinguish vegetation and terraced fields and their integrated ability for water and sediment reduction.

Thus, the purpose of this study was to incorporate the effect of terraces and vegetation on runoff and sediment routing in the time-area method and assess their impact in water and sediment reduction. The outflow in each travel time zone was revised in each time step by extracting the watershed of the terrace units and the vegetation units, and calculating the water or sediment stored by the terraces or retained by the vegetation based on their properties.
