Variable power‐law scaling of hillslope Hortonian rainfall–runoff processes

Abstract

Hydrological studies focused on Hortonian rainfall–run‐off scaling have found that the run‐off depth generally declines with the plot length in power‐law scaling. Both the power‐law proportional coefficient and the scaling exponent show great variability for specific conditions, but why and how they vary remain unclear. In the present study, the scaling of hillslope Hortonian rainfall–run‐off processes is investigated for different rainfall, soil infiltration, and hillslope surface characteristics using the physically based cell‐based rainfall‐infiltration‐run‐off model. The results show that both temporally intermittent and steady rainfalls can result in prominent power‐law scaling at the initial stage of run‐off generation. Then, the magnitude of the power‐law scaling decreases gradually due to the decreasing run‐on effect. The power‐law scaling is most sensitive to the rainfall and soil infiltration parameters. When the ratio of rainfall to infiltration exceeds a critical value, the magnitude of the power‐law scaling tends to decrease notably. For different intermittent rainfall patterns, the power‐law exponent varies in the range of −1.0 to −0.113, which shows an approximately logarithmic increasing trend for the proportional coefficient as a function of the run‐off coefficient. The scaling is also sensitive to the surface roughness, soil sealing, slope angle, and hillslope geometry because these factors control the run‐off routing and run‐on infiltration processes. These results provide insights into the variable scaling of the Hortonian rainfall–run‐off process, which are expected to benefit modelling of large‐scale hydrological and ecological processes.

Modeling Soil Erosion With Evolving Rills on Hillslopes

“…The modified WEPP erosion theory is utilized to simulate the interrill and rill erosion processes. The similar form was utilized by WEPP (Flanagan & Nearing, 1995), Liu et al (2006), Tayfur (2007), An and Liu (2009), and Wu et al (2017, 2019). Note that, in the present model, the total widths of the interrill and rill areas are considered to vary along the hillslope, and the length and slope gradient of the representative rills vary accordingly in each longitudinal interval.…”

“…To extend the model to sloping surfaces, the governing equations were further modified by changing the terms depicting the gravity effect (Chen & Young, 2006;Wang et al, 2018;Wu et al, 2018). The detail of the soil infiltration model is showed in Wu et al (2018Wu et al ( , 2019.…”

Sub‐daily rainfall intermittency: Is it really stochastic? A test at two Australian locations

“…Temporal intermittency of rainfall affects processes that influence the partitioning of rain between interception on plant canopies, evaporation, infiltration into soils, overland flow across the land surface, and other pathways. Intermittency influences the continuity of leaf wetness in vegetation communities (Binks et al, 2021), the change in soil moisture levels, and the related recovery of soil infiltrability that commences when rain ceases temporarily (Dunkerley, 2019; Poschlod et al, 2018; Wu et al, 2019), and the recovery of plant canopy interception capacity during intervals when evaporation can dry leaf surfaces and renew the leaf water‐holding capacity (Hadiwijaya et al, 2021; Iida et al, 2017). For estimating infiltration into the soil, it has been shown that the temporal resolution of the input rainfall data is important and that hourly data are only sufficient when the rainfall rate is low and/or the soils have low infiltrability (Fachi et al, 2022).…”