Rainfall patterns and landform characteristics are controlling factors of the runoff and soil erosion processes in natural catchments [1
]. Due to climatic change and climatic variability, rainfall events commonly show great temporal variation in intensity, especially in hilly areas [3
] and the peak rainfall rates within an event may dozens of times higher than the mean event rate [1
]. Although the temporal distribution of an individual rainfall event is diverse, some patterns of such distribution in a region can be derived based on historical data (e.g., [6
Previous studies have recognized that the rainfall patterns greatly affect the runoff generation and soil erosion processes (e.g., [8
]). Parsons and Stone [10
] adopted five rainfalls with different patterns but the same total kinetic energy to the soil surface. They found that the soil erosion amount under a constant-intensity storm are reduced by about 25% compared to varied-intensity storms, and that the eroded sediments are coarser under the constant-intensity pattern. An et al. [8
] used the similar rainfall patterns and indicated that, although the total runoff was nearly not affected by the rainfall pattern, the varied intensity patterns yield 1–5 times more soil losses than even-intensity patterns and the rising pattern resulted in a consistently higher soil loss relative to the other four rainfall patterns. Conversely, Dunkerley [3
] performed rainfall simulations of varying intensity profile in a dryland intergrove (runoff source area) and discovered that the late peak events showed runoff ratios that were more than double those of the early peak events and the constant rainfall yielded the lowest total runoff, the lowest peak runoff rate. The reason was inferred to be the reductions in soil infiltration capacity during late rainfall. Zhai et al. [11
] applied a distributed hydrological model at the basin scale, and found that the rainfall patterns have significant impact on the rainfall threshold of flood warning, which the flood rainfall threshold of advanced rainfall is the highest.
However, in most studies on rainfall pattern at plot scale, spatially distributed results of infiltration and soil erosion processes were not carefully considered. The temporal variation of precipitation can lead to corresponding spatial and temporal variations of infiltration, overland flow generation, and further soil erosion. Only considering runoff and soil erosion data at plot outlet, like many previous study did, will miss some important information (e.g., distributed cumulative infiltration or erosion depth) within the study area for comprehensive interpreting the influence of rainfall pattern on runoff and soil erosion processes.
In recent years, many studies on slopes have reported that observed runoff coefficient in Hortonian runoff processes decreases with increasing slope length, and variance of runoff reduces as slope scale increases (e.g., [12
]). A reason was that the runoff generated upslope can infiltrate in downslope areas, which was called the run-on infiltration [14
] or the re-infiltration [15
]. Although rainfall characteristics such as duration were one of the major factors affecting runoff generation at different slope scales (e.g., [16
]), it is still unknown how slope length influences the effect of temporal rainfall pattern on rainfall-runoff and soil erosion processes.
Slope steepness was an important topographic factor of hillslope rainfall-runoff and soil erosion processes. At plot scale, contradictory results were derived regarding slope effects on infiltration (e.g., [17
]) and soil erosion (e.g., [19
]). Besides, some researchers observed that runoff volume and soil loss on slopes increases with increasing slope angle till a critical slope angle of 20°–30° (e.g., [21
]), while others reported that soil erosion is not correlated with slope gradient in tilled fields (e.g., [22
]). However, a majority of the studies focusing on slope steepness neglected the influence of rainfall temporal variation. There is a lack of systematically studies on the effect of slope gradient under different rainfall patterns.
Numerical modelling is an effective approach to reveal spatial and temporal impacts of rainfall patterns on infiltration, overland flow and soil erosion processes at slopes with wide ranges of steepness and length, which can broaden the limitation of the artificial rainfall experiment (e.g., a plot with a few meters long [8
]). Further, strictly controlling factors such as initial condition and soil property, the effect of rainfall patterns can be specifically focused. As a mature hydraulic model, Integrated Hydrology Model (InHM) can quantitatively simulate surface (2D) and subsurface (3D) hydrologic responses to rainfall in a fully coupled approach [23
]. Previously, InHM has been successfully applied in the simulations of hillslope hydrology and slope failure (e.g., [23
]). As this physics-based hydrological model employs fundamental physics laws to describe natural processes [26
], its output results have clear physical meanings and can be used to generalize our understanding of rainfall pattern effects on runoff and soil erosion processes.
The main purpose of this study is to investigate the impact of rainfall temporal patterns on infiltration, runoff generation and soil erosion on slopes with a range of slope lengths and gradients, using a physically based modelling approach. These modelling results are expected to improve the theoretical basis for hillslope runoff and soil erosion prediction, which will be further helpful in soil conservation planning and land management.
In this study, the effect of rainfall pattern on runoff generation and soil erosion processes on slopes were analysed through numerical modelling. The modelling work provides infiltration, runoff and soil erosion differences among five rainfall patterns on wide ranges of slope gradient (5° to 40°) and slope length (25–200 m). The simulation result indicated that the rising-falling rainfall generally had the largest total runoff and soil erosion amount. The constant rainfall did not have the lowest total runoff and soil erosion amount when the projective slope length was over 100 m, which was higher than the falling-rising rainfall. The critical slope of the total runoff was 15°, which was independent of rainfall pattern and slope length. However, the critical slope of the soil erosion amount varied, which decreased with increasing projective slope length from 35° to 25°. And the critical slope for the soil erosion of the constant rainfall was generally 5° larger than that of other rainfalls. The increasing rainfall had the highest peak discharge and erosion rate just at the end of the peak rainfall intensity, while those of the decreasing and rising-falling rainfalls were lower and were several minutes later than the end of peak rainfall intensity.
These findings are helpful to improve the knowledge of the characteristics in runoff generation and soil erosion processes under various rainfall patterns at slopes, and they may be also beneficial for further understanding of hillslope morphology and ecology. Further work will be required for adequate meteorological and hydrological data to gain a more comprehensive understanding of rainfall pattern effects on hydrological processes at larger scale.