Estimating rainfall erosivity by aggregated drop size distributions

Rainfall erosivity is defined as the potential of the rain to cause erosion, and it can be represented by rainfall kinetic power. At first in this paper, the raindrop size distributions (DSD) measured by an optical disdrometer located at Palermo in the period June 2006–March 2014 and aggregated for intensity classes, are presented. Then an analysis of raindrop size characteristics is carried out, and the reliability of Ulbrich's distribution, using both the maximum likelihood and momentum estimate parameter methods, is tested. The raindrop size measurements are used to determine the experimental rainfall kinetic power values, which are compared with the ones calculated by a theoretically deduced relationship. This analysis demonstrates that the kinetic power is strictly related to the median volume diameter of DSD. Finally, the reliability of the simplest Marshall and Palmer exponential DSD for estimating the rainfall kinetic power is demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.     

Drop size distribution and kinetic energy load of rainstorms in Hong Kong

Data on drop size distribution and kinetic energy load of rainstorms are basic for rainfall erosivity indices. A simple and relatively inexpensive instrument was used to asses the instantaneous intensity and kinetic energy load of rainstorms in Hong Kong. Both the drop size and the instantaneous kinetic energy load of rainfall in Hong Kong are greater than in temperate and subtropical climates. The high kinetic energy results from the large size and greater number of raindrops falling per unit time. A high correlation between the kinetic energy of rainfall and the amount of rainfall allows for a convenient estimate of the energy load of storms from the amount of rainfall. Of more significance to the erosion process is the determination that about 74% of the total annual rainfall is erosive, containing about three‐quarters of the total annual energy load of the rains. The variability of rainfall parameters within a rainfall and from storm to storm is shown. The energy–intensity relationship, seasonal and annual distributions of rainfall erosivity are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Establishing a threshold for rainfall-induced landslides by a kinetic energy–duration relationship

Many investigators have attempted to define the threshold of landslide failure, that is, the level of the selected climatic variable above which a rainfall-induced landslide occurs. Intensity–duration (I–d) relationships are the most common type of empirical thresholds proposed in the literature for predicting landslide occurrence induced by rainfall. Recent studies propose the use of the kinetic power per unit volume of rainfall (J m⁻² mm⁻¹) to quantify the threshold of landslides induced by rainfall. In this paper, the relationship between rainfall duration and kinetic power corresponding to landslides triggered by rain was used to propose a new approach to define the threshold for predicting landslide occurrence. In particular, for the first time, a kinetic power per unit volume of rainfall–duration relationship is proposed for defining the minimum threshold needed for landslide failure. This new method can be applied using commonly used relationship for estimating the kinetic power per unit volume of rainfall and a new equation based on the measured raindrop size distribution. The applicability of this last method was tested using the data of rainfall intensity, duration and median volume diameter for 51 landslides in Taiwan. For the 51 landslides, the comparison between the measured pairs' kinetic power–duration and all selected relationships demonstrated that the equation based on the measured raindrop size distribution is the best method to define the landslide occurrence threshold, as it is both a process-oriented approach and is characterized by the best statistical performance. This last method has also the advantage to allow the forecasting of landslide hazard before the end of the rainfall event, since the rainfall kinetic power threshold value can be exceeded for a time interval less than the event duration.     

Drop size distribution and kinetic energy load of rainfall events in the highlands of the Central Rift Valley,Ethiopia

Abstract

Knowledge of rainfall characteristics is important for estimating soil erosion in arid areas. We determined basic rainfall characteristics (raindrop size distribution, intensity and kinetic energy), evaluated the erosivity of rainfall events, and established a relationship between rainfall intensity I and volume-specific kinetic energy KE_vol for the Central Rift Valley area of the Ethiopian highlands. We collected raindrops on dyed filter paper and calculated KE_vol and erosivity values for each rainfall event. For most rainfall intensities the median volume drop diameter (D₅₀) was higher than expected, or reported in most studies. Rainfall intensity in the region was not high, with 8% of rain events exceeding 30 mm h^-1. We calculated soil erosion from storm energy and maximum 30-min intensity for soils of different erodibility under conditions of fallow (unprotected soil), steep slope (about 9%) and no cover and management practice on the surface, and determined that 3 MJ mm ha^-1 h^-1 is the threshold erosivity, while erosivity of >7 MJ mm ha^-1 h^-1 could cause substantial erosion in all soil types in the area.

Editor Z.W. Kundzewicz; Associate Editor Q. Zhang     

Assessing changes in rainfall erosivity in Sicily during the twentieth century

Changes in rainfall erosivity are an expected consequence of climate change. Long‐term series of the single storm erosion index, EI, may be analysed to detect trends in rainfall erosivity. An indirect approach has to be applied for estimating EI, given that long series of rainfall intensities are seldom available. In this paper, a method for estimating EI from the corresponding rainfall amount, h_e, was developed for Sicily. This method was then applied at 17 Sicilian locations, representative of different climatic zones of the region, to generate a long series (i.e. from 1916 to 1999 in most cases) of EI values. Linear and step (step located at 1970) trends in annual and seasonal erosivity were detected by both classical approaches (Mann–Kendall test, Wilcoxon‐Mann‐Whitney rank‐sum test) and a new empirical approach (quantile approach, QA), based on the determination of the erosivity values corresponding to selected probability levels. A power relationship between EI and h_e with a space‐ and time‐variable scale factor and a time‐variable process parameter yielded the most accurate predictions of EI. However, a simpler model, using a time‐variable scale factor and a constant process parameter, yielded reasonably accurate EI estimates. Annual erosivity did not increase in Sicily during the twentieth century. At the most, it decreased at a few locations (three of the 17 considered locations). Significant trends were observed more frequently for winter erosivity (six locations) than for summer erosivity (two locations), suggesting that the erosive storms of winter determined the occasional occurrence of a negative trend in annual erosivity. In general, the QA compared reasonably well with more classical approaches. The QA appears promising since step trends for different return periods may be detected but efforts are needed to statistically formalize the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Characterization of rainfall generated by dripper‐type rainfall simulator using piezoelectric transducers and its impact on splash soil erosion

Rainfall erosivity represents the primary driver for particle detachment in splash soil erosion. Several raindrop erosivity indices have been developed in order to quantify the potential of rainfall to cause soil erosion. Different types of rainfall simulators have been used to relate rainfall characteristics to soil detachment. However, rainfall produced by different rainfall simulators has different characteristics, specifically different relationships between rainfall intensity and rainfall erosivity. For this reason, the effect of rainfall characteristics produced by a dripper‐type rainfall simulator on splash soil erosion (D_s) has been investigated. The simulated rainfall kinetic energy (KE) and drop size distribution (DSD) were measured using piezoelectric transducers, modified from the Vaisala RAINCAP^® rain sensor. The soil splash was evaluated under various simulated rainfall intensities ranging from 10 to 100 mm h^?1 using the splash‐cup method. The simulated rainfall intensity (I) and kinetic energy relationship (I–KE) was found to be different from natural rainfall. The simulated rainfall intensity and splash soil erosion relationship (I–D_s) also followed this same trend. The I–KE relationship was found to follow the natural rainfall trend until the rainfall intensity reached 30 mm h^?1 and above this limit the KE started to decrease. This emphasizes the importance of the I–KE relationship in determining the I‐D_s relationship, which can differ from one rainfall simulator to another. D_s was found to be highly correlated with KE (r = 0·85, P < 0·001), when data produced by the rainfall intensity ranged from 10 to 100 mm h^?1. However, when the threshold rainfall intensity (30 mm h^?1) was considered, the correlation coefficient further improved (r = 0·89, P = 0·001). Accordingly, to improve the soil splash estimation of simulated rainfall under various rainfall intensities the I–KE characterization relationship for rainfall simulators has to be taken into account. Copyright © 2010 John Wiley & Sons, Ltd.     

Application of an optical disdrometer to characterize simulated rainfall and measure drop-size distribution

ABSTRACT

Knowledge of rainfall characteristics such as drop-size distribution is essential for the development of erosion-mitigation strategies and models. This research used an optical disdrometer to elucidate the relationships between raindrop-size distribution, median volume drop diameter (D₅₀), kinetic energy and radar reflectivity (dBz) of simulated rainfall of different intensities. The D₅₀ values were higher for the simulated rain than for natural rain at almost all rainfall intensities, perhaps due to variations in rainfall types and the turbulence in natural rain that breaks up large drops. The kinetic energy ranged from 26.67 to 5955.51 J m^?2 h ^?1, while the median volume drop diameter (D₅₀) was in the range 1.94–7.25 mm, for intensities between 1.5 and 202.6 mm h^?1. The relationship between radar reflectivity (Z) and the intensity (R) of the simulated rain was best described by a power law function (Z = aR^b), with a and b coefficients in the ranges 162–706 and 0.94–2.46, respectively, throughout the range of rainfall intensities (1.5–202.6 mm h^?1).     

Applying the QREI30 index within the USLE modelling environment

The USLE/RUSLE model was designed to predict long‐term (~20 years) average annual soil loss by accounting for the effects of climate, soil, topography and crops. The USLE/RUSLE model operates mathematically in two steps. The first step involves the prediction of soil loss from the ‘unit’ plot, a bare fallow area 22.1 m long on a 9% slope gradient with cultivation up and down the slope. Appropriate values of the factors accounting for slope length, gradient, crops and crop management and soil conservation practice are then used to adjust that soil loss to predict soil loss from areas that have conditions that are different from the unit plot. Replacing EI₃₀, the USLE/RUSLE event erosivity index, by the product of the runoff ratio (Q_R) and EI₃₀, can enhance the capacity of the model to predict short‐term soil loss from the unit plot if appropriate data on runoff is available. Replacing the EI₃₀ index by another index has consequences on other factors in the model. The USLE/RUSLE soil erodibility factor cannot be used when the erosivity factor is based on Q_REI₃₀. Also, the USLE/RUSLE factors for slope length, slope gradient crops and crop management, and soil conservation practice cannot be used when runoff from other than the unit plot is used to calculate Q_R. Here, equations are provided to convert the USLE/RUSLE factors to values suitable for use when the erosivity factor is based on the Q_REI₃₀ index under these circumstances. At some geographic locations, non linear relationships exist between soil loss from bare fallow areas and the Q_REI₃₀ index. The effect of this on the slope length factor associated with the Q_REI₃₀ index is demonstrated using data from runoff and soil loss plots located at the Sparacia site, Sicily. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparing theoretically supported rainfall‐runoff erosivity factors at the Sparacia (South Italy) experimental site

Interpreting rainfall‐runoff erosivity by a process‐oriented scheme allows to conjugate the physical approach to soil loss estimate with the empirical one. Including the effect of runoff in the model permits to distinguish between detachment and transport in the soil erosion process. In this paper, at first, a general definition of the rainfall‐runoff erosivity factor REF_e including the power of both event runoff coefficient Q_R and event rainfall erosivity index EI₃₀ of the Universal Soil Loss Equation (USLE) is proposed. The REF_e factor is applicable to all USLE‐based models (USLE, Modified USLE [USLE‐M] and Modified USLE‐M [USLE‐MM]) and it allows to distinguish between purely empirical models (e.g., Modified USLE‐M [USLE‐MM]) and those supported by applying theoretical dimensional analysis and self‐similarity to Wischmeier and Smith scheme. This last model category includes USLE, USLE‐M, and a new model, named USLE‐M based (USLE‐MB), that uses a rainfall‐runoff erosivity factor in which a power of runoff coefficient multiplies EI₃₀. Using the database of Sparacia experimental site, the USLE‐MB is parameterized and a comparison with soil loss data is carried out. The developed analysis shows that USLE‐MB (characterized by a Nash–Sutcliffe Efficiency Index NSEI equal to 0.73 and a root mean square error RMSE = 11.7 Mg ha^?1) has very similar soil loss estimate performances as compared with the USLE‐M (NSEI = 0.72 and RMSE = 12.0 Mg ha^?1). However, the USLE‐MB yields a maximum discrepancy factor between predicted and measured soil loss values (176) that is much lower than that of USLE‐M (291). In conclusion, the USLE‐MB should be preferred in the context of theoretically supported USLE type models.     

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.     

Comparison of three types of laser optical disdrometers under natural rainfall conditions

ABSTRACT

Optical disdrometers can be used to estimate rainfall erosivity; however, the relative accuracy of different disdrometers is unclear. This study compared three types of optical laser-based disdrometers to quantify differences in measured rainfall characteristics and to develop correction factors for kinetic energy (KE). Two identical PWS100 (Campbell Scientific), one Laser Precipitation Monitor (Thies Clima) and a first-generation Parsivel (OTT) were collocated with a weighing rain gauge (OTT Pluvio²) at a site in Austria. All disdrometers underestimated total rainfall compared to the rain gauge with relative biases from 2% to 29%. Differences in drop size distribution and velocity resulted in different KE estimates. By applying a linear regression to the KE–intensity relationship of each disdrometer, a correction factor for KE between the disdrometers was developed. This factor ranged from 1.15 to 1.36 and allowed comparison of KE between different disdrometer types despite differences in measured drop size and velocity.     

A new procedure to estimate the RUSLE EI30 index, based on monthly rainfall data and applied to the Algarve region, Portugal

One of the best indicators of the potential erosion risks is the rainfall–runoff erosivity factor (R) of the revised universal soil loss equation (RUSLE). Frequently, however, there is not enough data available to compute the R value, and other parameters, such as the modified Fournier index (F_mod), are used instead. But RUSLE is less effective if only the alternative procedures exist. One of the major discrepancies between R and the alternative parameters is time resolution: individual storms are used to calculate R while monthly averages over the year are used to calculate F_mod.

In this study, a multiple linear regression (r²=0.89) involving monthly EI₃₀, monthly rainfall for days with ≥10.0 mm and monthly number of days with rainfall ≥10.0 mm, for the Algarve region, is presented. Twenty-seven years of monthly rainfall erosivity values were computed for the 32 standard daily-read raingauge stations of the Algarve region.     

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.     

Modelling event soil losses using the QREI30 index within RUSLE2

Recently, a USDA Curve Number‐based method for obtaining estimates of event runoff has been developed for use in enhancing the capacity of Revised Universal Soil Loss Equation (RUSLE2) to deal with runoff‐driven phenomena. However, RUSLE2 still uses the EI₃₀ index as the basis for determining the erosivity of the rainfall for sets of runoff producing storms at a location even though the product of the runoff ratio (Q_R) and EI₃₀ index is better at prediction event erosion when runoff is known or predicted well. This paper reports the results of applying the Q_REI₃₀ index using data available from tables within RUSLE2 to predict storm event soil losses from bare fallow areas and areas with continuous corn at Holly Springs, MS, and Morris, MN. In RUSLE2, all rainfall during a calendar year is considered to detach soil material that is flushed from the area if and when runoff occurs. However, the Q_REI₃₀ index is calculated using the EI₃₀ value for the amount of rain in the storm that produces runoff. Consequently, changes were made to the timing of events during the calendar year in order to meet the criteria for using the Q_REI₃₀ index. As a general rule, the peak event soil loss produced using the Q_REI₃₀ index were higher than produced by RUSLE2, and the peak event soil loss for the bare fallow occurred later than for the continuous corn. The results of the work reported here show that the Q_REI₃₀ index may be used to model event erosion produced by a set of storms within RUSLE2 provided that the appropriate mathematical rules upon which the USLE was developed are adhered to. Copyright © 2013 John Wiley & Sons, Ltd.     

Application of piezoelectric transducers in simulated rainfall erosivity assessment

Abstract

Rainfall simulators have often been used to mimic natural rainfall for studies of various land-surface and water interaction processes. The characteristics of the simulated rainfall are the main indicators used to judge the performance of the rainfall simulators. The aim of this study is to investigate the potential of piezoelectric transducers for measuring and evaluating a dripper-type simulated rainfall drop-size distribution (DSD) and kinetic energy (KE). The directly measured KE was significantly correlated with the estimated KE using the drop-size distribution and empirical rain drop fall velocity relationships. This result emphasizes the potential use of the piezoelectric sensor to directly measure and evaluate rainfall kinetic energy. Also, the relationship between rainfall intensity and KE showed good patterns of agreement between simulated rainfall and natural rainfall.

Citation Abd Elbasit, M. A. M., Yasuda, H. & Salmi, A. (2011) Application of piezoelectric transducers in simulated rainfall erosivity assessment. Hydrol. Sci. J. 56(1), 187–194.     

Impacts of annual precipitation extremes on soil and nutrient losses in vineyards of NE Spain

The objective of this research was to characterise annual precipitation extremes in a Mediterranean vineyard region. The number of exceptional events (P > 95th percentile) and annual extreme events (P > 99th percentile), as well as their strength, erosive character and return period were analysed for 2000–2004. The erosive character was evaluated according to the R‐factor (kinetic energy × maximum intensity in 30‐min periods). Soil and nutrient losses caused by these events were evaluated by combining field sampling and a hydrological model to estimate total runoff in a vineyard plot. The results show a clear increase in the number of very wet days and extreme events (P > 95th percentile), which represented up to 88% of annual rainfall. The severity of the extreme events (TS = precipitation event P > 99th percentile) reached values higher than 50 mm almost every year. These values were far exceeded in 2000, when one extraordinary event recorded 50% of the annual rainfall, with TS of 189 mm, about 80% of total rainfall being lost as runoff. Annual erosivity was driven not only by extreme events, but also by short events of less depth but high intensity. During some of the years analysed, rainfall erosivity was two or three times the average in the area. Most soil and nutrient losses occurred in a small number of events: one or two events every year were responsible for more than 75% of the annual soil and nutrient losses on average. Antecedent soil moisture conditions, runoff rates, and events with a return period higher than two years were responsible for the higher erosion rates. Apart from an exceptional event recorded in 2000, which produced more than 200 Mg ha^?1 soil losses, annual soil losses up to 25 Mg ha^?1 were recorded, which are much higher than the soil loss tolerance. Copyright © 2008 John Wiley & Sons, Ltd.     

Spatial variability of rainfall on a sub‐kilometre scale

The variability of rainfall in space and time is an essential driver of many processes in nature but little is known about its extent on the sub‐kilometre scale, despite many agricultural and environmental experiments on this scale. A network of 13 tipping‐bucket rain gauges was operated on a 1·4 km² test site in southern Germany for four years to quantify spatial trends in rainfall depth, intensity, erosivity, and predicted runoff. The random measuring error ranged from 10% to 0·1% in case of 1 mm and 100 mm rainfall, respectively. The wind effects could be well described by the mean slope of the horizon at the stations. Except for one station, which was excluded from further analysis, the relative differences due to wind were in maximum ±5%. Gradients in rainfall depth representing the 1‐km² scale derived by linear regressions were much larger and ranged from 1·0 to 15·7 mm km^?1 with a mean of 4·2 mm km^?1 (median 3·3 mm km^?1). They mainly developed during short bursts of rain and thus gradients were even larger for rain intensities and caused a variation in rain erosivity of up to 255% for an individual event. The trends did not have a single primary direction and thus level out on the long term, but for short‐time periods or for single events the assumption of spatially uniform rainfall is invalid on the sub‐kilometre scale. The strength of the spatial trend increased with rain intensity. This has important implications for any hydrological or geomorphologic process sensitive to maximum rain intensities, especially when focusing on large, rare events. These sub‐kilometre scale differences are hence highly relevant for environmental processes acting on short‐time scales like flooding or erosion. They should be considered during establishing, validating and application of any event‐based runoff or erosion model. Copyright © 2009 John Wiley & Sons, Ltd.     

The non-independence of rainfall erosivity and soil erodibility

Three high erosivity conditions (50 mm hr^?1, 100 mm hr^?1, and 200 mm hr^?1) were generated in a laboratory using a rainfall simulator and coherent soil block samples from fourteen different soil erodibility conditions. The data acquired supports the theoretical contention that soil loss should not increase as a simple linear function of storm intensity. Rather, a variable relationship is caused by the rupturing of surface seals and the changing relative significance of splash, wash and rainwash processes. Slope angle appears to influence soil loss at the higher erosivity conditions of 100 mm hr^?1 and 200 mm hr^?1 on slopes that were either very steep (> 20°) or very shallow (< 3°), but on moderate slopes the relationship is unclear. Examination of the variation of soil loss with erosivity when soil loss for a specific high erosivity condition is known revealed that conversion and power factors are of doubtful value and little generality. A satisfactory predictive equation, a power curve, is seen to be of value only when comparing rainwash soil loss between the higher erosivity conditions. The relationship is most safely considered as soil and site specific. Where the influence of slope and soil erodibility are disregarded, a strong association between soil loss and rainfall intensity is found. That soil loss, and hence, soil erodibility varies non-uniformly with erosivity is clear. The findings indicate caution is required when comparing conclusions drawn from studies based upon different erosivity conditions.     

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.