Modelling raindrop impact and splash erosion processes within a spatial cell: a stochastic approach

A new approach is proposed to simulate splash erosion on local soil surfaces. Without the effect of wind and other raindrops, the impact of free‐falling raindrops was considered as an independent event from the stochastic viewpoint. The erosivity of a single raindrop depending on its kinetic energy was computed by an empirical relationship in which the kinetic energy was expressed as a power function of the equivalent diameter of the raindrop. An empirical linear function combining the kinetic energy and soil shear strength was used to estimate the impacted amount of soil particles by a single raindrop. Considering an ideal local soil surface with size of 1 m × 1 m, the expected number of received free‐falling raindrops with different diameters per unit time was described by the combination of the raindrop size distribution function and the terminal velocity of raindrops. The total splash amount was seen as the sum of the impact amount by all raindrops in the rainfall event. The total splash amount per unit time was subdivided into three different components, including net splash amount, single impact amount and re‐detachment amount. The re‐detachment amount was obtained by a spatial geometric probability derived using the Poisson function in which overlapped impacted areas were considered. The net splash amount was defined as the mass of soil particles collected outside the splash dish. It was estimated by another spatial geometric probability in which the average splashed distance related to the median grain size of soil and effects of other impacted soil particles and other free‐falling raindrops were considered. Splash experiments in artificial rainfall were carried out to validate the availability and accuracy of the model. Our simulated results suggested that the net splash amount and re‐detachment amount were small parts of the total splash amount. Their proportions were 0·15% and 2·6%, respectively. The comparison of simulated data with measured data showed that this model could be applied to simulate the soil‐splash process successfully and needed information of the rainfall intensity and original soil properties including initial bulk intensity, water content, median grain size and some empirical constants related to the soil surface shear strength, the raindrop size distribution function and the average splashed distance. Copyright © 2007 John Wiley & Sons, Ltd.     

A simulation study of the role of raindrop erosion in the formation of desert pavements

A simple model of raindrop erosion—the combined effects of the detachment of sediment by raindrops and its transport by splash or by overland flow—is developed to examine the role of this process in the formation of desert pavements. Application of the model to soils in areas of existing pavement initially simulates the formation of pavements, but the changing sediment size distributions lead to the subsequent destruction of these modelled surfaces. An improved model that accounts for the feedback effects of the changing size distributions on infiltration and microtopography is then developed. Incorporating these effects allows simulated pavements to be maintained over longer periods. The model yields desert pavements whose particle size compositions differ in response to differences in initial soil characteristics, slope and rainfall intensity. This model is tested against empirical data from a site where there is intershrub pavement and associated mounds of fines beneath desert shrubs. The results successfully predict the accumulation of fines under shrubs but underestimate the development of the pavement between shrubs. These findings suggest that the raindrop erosion mechanism on its own cannot account for the development of the pavement and that some other mechanism leading to the surface concentration of coarse particles must also be operating.     

Number and volume raindrop size distributions in Taiwan

Knowledge of rainfall characteristics is very important for the accurate estimation of rainfall kinetic energy and prediction of soil erosion. In this study, a reliable and efficient data collection and analysis system was developed to analyse the natural raindrop data collected in subtropical Taiwan. Both raindrop size distributions by number and volume were carefully analysed. The seasonal variations of the rainfall erosivity factor R, which is an index of the erosive potential of rainfall and a function of rainfall kinetic energy, was also discussed. An isoerodent map of Taiwan was also developed based on the rainfall data recorded by 158 automated rainfall‐measuring stations within 26 years. Copyright © 2007 John Wiley & Sons, Ltd.     

Raindrop‐impact‐induced erosion processes and prediction: a review

Raindrop‐impact‐induced erosion is initiated when detachment of soil particles from the surface of the soil results from an expenditure of raindrop energy. Once detachment by raindrop impact has taken place, particles are transported away from the site of the impact by one or more of the following transport processes: drop splash, raindrop‐induced flow transport, or transport by flow without stimulation by drop impact. These transport processes exhibit varying efficiencies. Particles that fall back to the surface as a result of gravity produce a layer of pre‐detached particles that provides a degree of protection against the detachment of particles from the underlying soil. This, in turn, influences the erodibility of the eroding surface. Good understanding of rainfall erosion processes is necessary if the results of erosion experiments are to be properly interpreted. Current process‐based erosion prediction models do not deal with the issue of temporal variations in erodibility during a rainfall event or variabilities in erodibility associated with spatial changes in dominance of the transport processes that follow detachment by drop impact. Although more complex erosion models may deal with issues like this, their complexity and high data requirement may make them unsuitable for use as general prediction tools. Copyright © 2005 John Wiley & Sons, Ltd.     

Effects of hydrophobicity on splash erosion of model soil particles by a single water drop impact

Raindrop impact can be a major contributor to particle mobilization for soils and other granular materials. In previous work, water repellent soils, comprised of hydrophobic particles, have been shown to exhibit greater splash erosion losses under multiple drop impact. However, the underlying principle differences in splash behavior between hydrophobic and hydrophilic granular surfaces have not been studied to date. In this study the effects of particle hydrophobicity on splash behaviour by a single water drop impact were examined using high‐speed videography. Water drops (4 mm in diameter) were dropped on beds of hydrophilic and hydrophobic glass beads (sieved range: 350–400 µm), serving as model soil particles. The drop velocity on impact was 2.67 m s^‐1, which corresponds to ~30% of the terminal velocity of a raindrop of similar size. The resulting impact behaviour was measured in terms of the trajectories of particles ejected from the beds and their final resting positions. The response to the impacting water drop was significantly different between hydrophilic and hydrophobic particles in terms of the distance distribution, the median distance travelled by the particles and number of ejected particles. The greater ejection distances of hydrophobic particles were mainly the result of the higher initial velocities rather than differences in ejecting angles. The higher and longer ejection trajectories for hydrophobic particles, compared with hydrophilic particles, indicate that particle hydrophobicity affects splash erosion from the initial stage of rainfall erosion before a water layer may be formed by accumulating drops. The ~10% increase in average splash distance for hydrophobic particles compared with hydrophilic particles suggests that particle hydrophobicity can result in greater net erosion rate, which would be amplified on sloping surfaces, for example, by ridges in ploughed agricultural soils or hillslopes following vegetation loss by clearing or wildfire. Copyright © 2012 John Wiley & Sons, Ltd.     

The increase of rainfall erosivity and initial soil erosion processes due to rainfall acidification

The drastic growth of population in highly industrialized urban areas, as well as fossil fuel use, is increasing levels of airborne pollutants and enhancing acid rain. In rapidly developing countries such as Iran, the occurrence of acid rain has also increased. Acid rain is a driving factor of erosion due to the destructive effects on biota and aggregate stability; however, little is known about its impact on specific rates of erosion at the pedon scale. Thus, the present study aimed to investigate the effect of acid rain at pH levels of 5.25, 4.25, and 3.75 for rainfall intensities of 40, 60, and 80 mm h^?1 on initial soil erosion processes under dry and saturated soil conditions using rainfall simulations. The results were compared using a two‐way ANOVA and Duncan tests and showed that initial soil erosion rates with acidic rain and non‐acidic rain under dry soil conditions were significantly different. The highest levels of soil particle loss due to splash effects in all rainfall intensities were observed with the most acidic rain (pH = 3.75), reaching maximum values of 16 g m^?2 min^?1. The lowest levels of particle losses were observed in the control plot where non‐acidic rain was used, with values ranging from 3.8 to 8.1 g m^?2 min^?1. Similarly, under saturated soil conditions, the lowest level of soil particle loss was observed in the control plot, and the highest peaks of soil loss were observed for the most acidic rains (pH = 3.75 and pH = 4.25), reaching maximum average values of 40 g m^?2 min^?1. However, for saturated soils with acidic water but with non‐acidic rain, the highest soil particle loss was observed for the control plot for all the rainfall intensities. In conclusion, acidic rain has a negative impact on soils, which can be more intense with a concomitant increase in rainfall intensity. Rapid solutions, therefore, need to be found to reduce the emission of pollutants into the air, otherwise, rainfall erosivity may drastically increase.     

Pressure and shear stress caused by raindrop impact at the soil surface: Scaling laws depending on the water depth

Raindrop impact is an important process in soil erosion. Through its pressure and shear stress, raindrop impact causes a significant detachment of the soil material, making this material available for transport by sheet flow. Thanks to the accurate Navier–Stokes equations solver Gerris, we simulate the impact of a single raindrop of diameter D, at terminal velocity, on water layers of different thickness h: , , D, 2D, in order to study pressures and shear stresses involved in raindrop erosion. These complex numerical simulations help in understanding precisely the dynamics of the raindrop impact, quantifying in particular the pressure and the shear stress fields. A detailed analysis of these fields is performed and self‐similar structures are identified for the pressure and the shear stress on the soil surface. The evolution of these self‐similar structures are investigated as the aspect ratio h/D varies. We find that the pressure and the shear stress have a specific dependence on the ratio between the drop diameter and the water layer thickness, and that the scaling laws recently proposed in fluid mechanics are also applicable to raindrops, paving the road to obtain effective models of soil erosion by raindrops. In particular, we obtain a scaling law formula for the dependence of the maximum shear stress on the soil on the water depth, a quantity that is crucial for quantifying erosion materials. Copyright © 2016 John Wiley & Sons, Ltd.     

Rain properties controlling soil splash detachment

Laboratory experiments have been conducted to study the effects of various rain properties on sand detachment resulting from raindrop impact. Splash cups were exposed to simulated rainfall intensities ranging between 10 and 140 mm h⁻¹. The detached sand was collected and weighed whereas rain intensity, equivalent drop diameter and fall velocity of raindrops were measured with an optical spectro‐pluviometer (OSP). The properties of the simulated rain (i.e. median volume diameter and kinetic energy) were compared with those observed in natural conditions. Statistical analyses have been undertaken in order to evaluate which rain variable best predicts the mass of sand detached. Linear and non‐linear correlations between the mass of detached sediment and the product of drop size (d) by drop velocity (v), i.e. D^αV^β, with values of α varying between 1 and 6 and β between 0 and 3, have been computed. The results indicate that the coefficient of determination (R²) for α ranging between 3 and 5 and β lower or equal to 2 are satisfying. Although kinetic energy (D³V²) described splash detachment relatively well, the product of momentum by drop diameter (D⁴V) was slightly superior in describing splash detachment. Therefore, the momentum multiplied by the drop diameter is recommended as the best rain variable to describe splash detachment. Copyright © 2000 John Wiley & Sons, Ltd.     

Mechanics of interrill erosion with wind‐driven rain

The vector physics of wind‐driven rain (WDR) differs from that of wind‐free rain, and the interrill soil detachment equations in the Water Erosion Prediction Project (WEPP) model were not originally developed to deal with this phenomenon. This article provides an evaluation of the performance of the interrill component of the WEPP model for WDR events. The interrill delivery rates were measured in the wind tunnel facility of the International Center for Eremology (ICE), Ghent University, Belgium with an experimental setup to study different raindrop impact velocity vectors. Synchronized wind and rain simulations with wind velocities of 6, 10 and 14 m s^–1 were applied to a test surface placed on windward and leeward slopes of 7, 15 and 20%. Since both rainfall intensity and raindrop impact velocity varied greatly depending on differences in the horizontal wind velocity under WDRs, the resultant kinetic energy flux (KE_r, in J m^–2 s^–1) was initially used in place of the WEPP model intensity term in order to incorporate the effect of wind on impact velocity and frequency of raindrops. However, our results showed only minor improvement in the model predictions. For all research data, the model Coefficients of Determination (r²) were 0·63 and 0·71, when using the WEPP and the KE_r approaches, respectively. Alternately, integrating the angle of rain incidence into the model by vectorally partitioning normal kinetic energy flux (KE_rn, in J m^–2 s^–1) from the KE_r greatly improved the model's ability to estimate the interrill sediment delivery rates (r² = 0·91). This finding suggested that along with the fall trajectory of wind‐driven raindrops with a given frequency, raindrop velocity and direction at the point of impact onto the soil surface provided sufficient physical information to improve WEPP sediment delivery rate predictions under WDR. Copyright © 2012 John Wiley & Sons, Ltd.     

Shear strength of compacted soil: effects on splash erosion by single water drops

The persistence of soil compaction, caused by farmers' vehicles (tractors wheelings) during the dry season, can affect splash distribution and soil erosion so that surface flow starts at an earlier stage than between the wheelings. To investigate the effects of soil compaction on splash distribution, a dry clayey agricultural soil was compacted in steel cups with a hydraulic piston, and the shear strength was measured with a fall‐cone penetrometer. Two cups were compacted in the same manner, using one to measure the shear strength and the second for splash erosion measurements. A laboratory splash board of 1 m radius, divided into 13 concentric compartments, was used to collect the splashed particles. The water drop diameter used was 4·9 mm falling onto a soil splash cup of 50·2 cm² area from 8 m height with a terminal velocity of 8·8 m s^?1. The spatial distribution of the splashed particles, for different soil compactions, fitted the fundamental splash distribution function (FSDF) model better than the exponential function. The shapes of the curves of this function demonstrated the importance of the source area size; the smaller the cup diameter the better the spatial distribution is expressed by an exponential function. In addition, variability in soil surface conditions contributes to variation in splash characteristics. Detachment rates and average radial distance followed second degree relationships in terms of shear strength. Copyright © 2010 John Wiley & Sons, Ltd.     

The influence of rain intensity on raindrop diameter and the kinetics of tropical rainfall: case study of Skudai,Malaysia

ABSTRACT

The modelling of soil loss and investigation of urban hydrology and wet weather pollution in Malaysia requires the definition of rainfall parameters for the region. In this study, an inexpensive method was applied to establish the influence of raindrop diameter on kinetics and rain intensity in Skudai, Peninsular Malaysia, as a prelude to wider regional research. Raindrop sizes vary from less than 1.2 mm to as big as 7.0 mm, with median raindrop diameters of 2.51 mm and a mean diameter of 2.56 mm. The median raindrop diameter–intensity relationship correlates strongly using power and exponential equations, with coefficients of determination of 0.75 and 0.73, respectively. The kinetic energy–intensity relationship fits an exponential function and also a linear equation with R² values of 0.49 and 0.34, respectively. An average rain kinetic energy of 30 J m^-2 mm^-1 was recorded. This research leads to an objective reclassification of rainfall intensities in the region.

Editor Z.W. Kundzewicz; Associate editor not assigned     

The impact of slope length on the discharge of sediment by rain impact induced saltation and suspension

Simulations using a mechanistic model of raindrop driven erosion in rain‐impacted flow were performed with particles travelling by suspension, raindrop induced saltation and flow driven saltation. Results generated by both a high intensity storm, and a less intense one, indicate that, because of the effect of flow depth on the delivery of raindrop energy to the bed, there is a decline in sediment concentration, and hence soil loss per unit area, with slope length when particles are transported by raindrop induced saltation. However, that decline is reversed when the critical velocities that lead to flow driven saltation are episodically exceeded during an event. The simulations were performed on smooth surfaces and a single drop size but the general relationships are likely to apply for rain made up of a wide range of drop size. Although runoff is not always produced uniformly, as a general rule, flow velocities increase with slope length so that, typically, the distance particles travel before being discharged during an event increase with slope length. The effect of slope length on soil loss per unit area is often considered to vary with slope length to a power greater than zero and less that 1·0. The simulations show that effect of slope length on sediment discharge is highly dependent on the variations in runoff response resulting from variations in rainfall duration‐intensity‐infiltration conditions rather than plot length per se. Consequently, predicting soil loss per unit area using slope length with positive powers close to zero when sheet erosion occurs may not be as effective as commonly expected. Erosion by rain‐impacted flow is a complex process and that complexity needs to be considered when analysing the results of experiments associated with rain‐impacted flow under both natural and artificial conditions. Copyright © 2009 John Wiley & Sons, Ltd.     

Field and computer simulation experiments on the formation of desert pavement

A series of rainfall simulation experiments was carried out at the Walnut Gulch Experimental Watershed, Tombstone, Arizona (31° 43′N, 110° 41′W), to observe the speed at which desert pavement surfaces could be re-established following disturbance. The results of these experiments, which consisted of repeated, 5 min rainfall events, demonstrate that pavements can reform within 10 events, which is compatible with observations of the recovery of surfaces under natural rainfall on an annual cycle. A model for the development of pavements by raindrop erosion processes had previously shown the importance of these processes. The rainfall simulation experiments were used to test the general applicability of this model. The model was able to reproduce the general characteristics of the regenerated surfaces and the timing of their development. However, details of the particle size fractions produced were less well simulated by the model. Testing of the sensitivity of the model to the sediment transport parameters suggests that this problem is not related to the soil characteristics, but is more likely to be an indication of a poor understanding of all the feedbacks operating in the raindrop erosion processes. Copyright © 1999 John Wiley & Sons, Ltd.     

Effects of rainfall,overland flow and their interactions on peatland interrill erosion processes

Interrill erosion processes on gentle slopes are affected by mechanisms of raindrop impact, overland flow and their interaction. However, limited experimental work has been conducted to understand how important each of the mechanisms are and how they interact, in particular for peat soil. Laboratory simulation experiments were conducted on peat blocks under two slopes (2.5° and 7.5°) and three treatments: Rainfall, where rainfall with an intensity of 12 mm h^?1 was simulated; Inflow, where upslope overland flow at a rate of 12 mm h^?1 was applied; and Rainfall + Inflow which combined both Rainfall and Inflow. Overland flow, sediment loss and overland flow velocity data were collected and splash cups were used to measure the mass of sediment detached by raindrops. Raindrop impact was found to reduce overland flow by 10 to 13%, due to increased infiltration, and reduce erosion by 47% on average for both slope gradients. Raindrop impact also reduced flow velocity (80–92%) and increased roughness (72–78%). The interaction between rainfall and flow was found to significantly reduce sediment concentrations (73–85%). Slope gradient had only a minor effect on overland flow and sediment yield. Significantly higher flow velocities and sediment yields were observed under the Rainfall + Inflow treatment compared to the Rainfall treatment. On average, upslope inflow was found to increase erosion by 36%. These results indicate that overland flow and erosion processes on peat hillslopes are affected by upslope inflow. There was no significant relationship between interrill erosion and overland flow, whereas stream power had a strong relationship with erosion. These findings help improve our understanding of the importance of interrill erosion processes on peat. Copyright © 2017 John Wiley & Sons, Ltd.     

Dependence of shrub canopy water storage on raindrop size in revegetated desert

Abstract

The aim of this study was to evaluate canopy water storage (CWS) of the co-dominant shrubs in the revegetation of sand dunes in northwest China. Our results indicated that CWS differed among the xerophyte taxa studied. The average CWS increased exponentially with decreased raindrop size. The time course of CWS in terms of leaf area indicated that Artemisia ordosica attains its peak value of 0.48 mm within 170 min. The corresponding values for Caragana korshinskii and Hedysarum scoparium were 0.38 mm and 178 min, and 0.32 mm and 161 min, respectively, implying that A. ordosica had a higher CWS than C. korshinskii and H. scoparium. Dry biomass was a desirable predictor for estimation of CWS for C. korshinskii and H. scoparium, and shrub volume for A. ordosica. Our results show that the dependence of CWS on raindrop size varied in accordance with the shrub canopy structure.

Editor Z.W. Kundzewicz     

A methodology to study rain splash and wash processes under natural rainfall

The complex interactions between rainfall‐driven erosion processes and rainfall characteristics, slope gradient, soil treatment and soil surface processes are not very well understood. A combination of experiments under natural rainfall and a consistent physical theory for their interpretation is needed to shed more light on the underlying processes. The present study demonstrates such a methodology. An experimental device employed earlier in laboratory studies was used to measure downslope rain splash and ‘splash‐creep’, lateral splash, upslope splash and rainfall‐driven runoff transport (wash) from a highly aggregated clay‐rich oxisol exposed to natural rainfall in West Java, Indonesia. Two series of measurements were made: the first with the soil surface at angles of 0°, 5°, 15° and 40°; and the second all at an angle of 5° but with different tillage and mulching treatments. A number of rainfall erosivity indices were calculated from rainfall intensity measurements and compared with measured transport components. Overall storm kinetic energy correlated reasonably well with sediment transport, but much better agreement was obtained when a threshold rainfall intensity (20 mm h^?1) was introduced. Rain splash transport measurements were interpreted using a recently developed theory relating detachment to sediment transport. Furthermore, a conceptually sound yet simple wash transport model is advanced that satisfactorily predicted observed washed sediment concentrations. The lack of replication precluded rigorous assessment of the effect of slope and soil treatment on erosion processes, but some general conclusions could still be drawn. The results stress the importance of experiments under conditions of natural rainfall. Copyright © 2002 John Wiley & Sons, Ltd.     

Splash detachment of sand particles under varying contact stress field of wind-driven raindrop impact

The effects of wind-driven rain (WDR) on sand detachment were studied under various raindrop obliquities. Results suggested a significant reduction in compressive stress on sand surfaces for a two-dimensional experimental set-up in a wind tunnel. During experiments, sand particles in splash cups were exposed to both wind-free rain (WFR) and WDR driven by horizontal winds of 6.4, 8.9 and 12.8 m s⁻¹ and rainfall intensities of 50, 60, 75 and 90-mm h⁻¹ to assess the sand detachment rate (D, in g m⁻² s⁻¹). The effects of sand moisture state (dry and wet) on the detachment of different-sized particles (0.20–0.50 and 0.50–2.00 mm, respectively) were also tested. Factorial analysis of variance showed that shear and compressive stress components evaluated by horizontal and vertical kinetic energy flux terms (KE_x and KE_y, respectively, in J m⁻² s⁻¹) along with their vector sum (KE_r, in J m⁻² s⁻¹) explained the variation in D. Neither sand size nor sand moisture was statistically significant alone although binary interactions of KE_r, KE_x and KE_y with the sand size and three-way interaction of KE_x, sand size and moisture were statistically significant. These results can be explained by size-dependent variation in sand compressibility and surface friction related to the total stress field developed by a given partition of shear and compressive stresses of wind-driven oblique raindrops (KE_x/KE_y). Further analysis of the variation of the unit sand detachment rate (D_u = D/KE_r = g J⁻¹) with rain inclination (α, in degrees) better revealed the effect of WDR obliquity on D_u that further changed with sand size class and moisture state. Finally, the difference in the resulting stress field differentiable by the oblique raindrop trajectories of the experiment over sand surface significantly affected the non-cohesive particle detachment rates, to some extent interacted with size-dependent compressibility and interface shear strength of sand grains.