Simulation of the size distribution and erosivity of raindrops and throughfall drops

This paper presents a model that simulates the size distribution and erosivity of raindrops and throughfall drops. It utilizes existing models of rainfall drop size distribution and fall velocity and combines them with newly collated evidence of throughfall drop size distributions. A sensitivity analysis reveals that the model is sensitive to parameters that are easily measured or estimated: rainfall intensity, the mean volume drop diameter of the intercepted throughfall, canopy cover, and canopy height. The results of the model may be used at two levels. Firstly, to calculate specifically the size and fall velocity of individual drops, parameters that are needed in studies examining the response of soil surfaces to forces applied by rainfall. Secondly, to produce erosivity indices, based on rainfall intensity but which take account of the effects of a vegetation canopy. The paper shows that while the kinetic energy of rainfall (E(0), J mm^?1 m^?2) may be calculated from an equation of the familiar form: the kinetic energy of throughfall under any canopy may be calculated by combining this equation with another that relates the energy of drops under a 100 per cent canopy cover (E(100)) and the canopy height: .     

Interception,drop size distributions and rainfall kinetic energy in four colombian forest ecosystems

Interception losses, rain and throughfall drop size spectra and kinetic energy were studied in four relatively undisturbed tropical forest ecosystems along a transect across the Central Andean Cordillera of Colombia at altitudes between 3000 and 1000 m above sea level. Interception amounts ranged from 11 to more than 20 per cent of the total rainfall and fell within the normal range of interception figures observed in natural tropical forests. Drop size spectra were established using the filter paper method; the drop size distributions of the open field rainfall were unimodal while the throughfall had bimodal distributions, with a higher percentage of the volume of rain falling as large drops. Disturbance of the natural forests, for example by logging activities or cattle grazing, will further increase the throughfall kinetic energy and may lead to higher splash erosion rates inside the forests than in the open field. The kinetic energy of the throughfall was higher than that of the open field rainfall (20-70 per cent), even after correcting for interception losses (4-30 per cent). Splash-cup experiments, conducted both in the field and in the laboratory, indicated that the kinetic energy is a good index of rainfall erosivity. Inside the forests the amounts of sand splashed from the splash-cups was, after correction for interception losses, 2-16 per cent higher than outside the forests.     

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.     

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 shape and erosivity part II: Splash detachment,transport and erosivity indices

The relevance of drop shape for erosivity was tested for different combinations of drop sizes and fall heights. For all test combinations together the introduction of the observed drop shape in erosivity parameters only produces minor improvements in the relation between erosivity and detachment and transport by splash. This result is attributed to the dominance of oblate shapes in high velocity conditions. Using small fall heights and low fall velocities as in many rainfall simulators and drop tests it is shown that prolate drops produce a splash detachment which is 2 to 3 times higher than that produced by drops with an oblate shape at impact. As drop production in rainulators or for aggregate stability drop tests may result in more or less uncontrolled variations of drop shape, it is concluded that in addition to other test conditions drop shape should be specified. Moreover it is noted that the erosive capability of prolate drops can explain partly the high splash erosion amounts below vegetation.     

An evaluation of the use of size distributions of sediment in runoff as a measure of aggregate breakdown in the surface of a cracking clay soil under rain

Two rainfall simulators of different plot sizes were used to test whether sediment in runoff could be used to measure aggregate breakdown in the surface of a cracking clay soil under rain. Plots were prepared with either levelled or furrowed surfaces. Samples of the soil surface under rain were taken from furrow ridges or levelled surfaces, and from areas of deposited sediment. These were compared with samples of sediment in runoff taken at the same times. On both furrowed and levelled plot surfaces and for both simulators, aggregate sizes were significantly finer in sediment in runoff than in samples of the soil surface taken with a spatula. No significant differences in surface aggregate size distributions were found between rainfall simulators, or between furrowed and levelled plot surfaces. Regression lines fitted to the data on size distributions of sediment or of aggregates in the soil surface showed no significant changes through time. The fitted lines showed sediment in runoff to be still significantly finer than aggregates in the soil surface after 50 min rain at 95 mm h^?1, except for levelled plots under the rotating disc rainfall simulator, where extreme variability of data meant that even relatively large differences were not statistically significant. Size distributions of deposited sediment were similar to those of the surface of adjacent furrow ridges exposed to raindrop impact. This provides evidence that sampling the soil surface with a spatula gives a representative sample of the material available for rain-flow transport.     

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     

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.     

The effect of a new zealand beech forest canopy on the kinetic energy of water drops and on surface erosion

Rain and throughfall drops were sampled during rain events in a New Zealand beech forest and the frequency distributions of drop mass and kinetic energy calculated. The kinetic energy of throughfall under the canopy was always greater than that of rainfall in the open, notwithstanding interception losses. During a typical rain event in which 51 mm fell in 36 h, the total kinetic energy of throughfail was 1.5 times greater than that of rainfall, and the mean amount of sand splashed from sample cups was 3.1 times greater under the canopy than in the open. It appears that where mineral soil is exposed at the surface, by animal trampling or burrowing for example, rates of soil detachment by splash under a forest canopy will probably exceed those in the open.     

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.     

Throughfall partitioning by trees

Although we know that rainfall interception (the rain caught, stored, and evaporated from aboveground vegetative surfaces and ground litter) is affected by rain and throughfall drop size, what was unknown until now is the relative proportion of each throughfall type (free throughfall, splash throughfall, canopy drip) beneath coniferous and broadleaved trees. Based on a multinational data set of >120 million throughfall drops, we found that the type, number, and volume of throughfall drops are different between coniferous and broadleaved tree species, leaf states, and timing within rain events. Compared with leafed broadleaved trees, conifers had a lower percentage of canopy drip (51% vs. 69% with respect to total throughfall volume) and slightly smaller diameter splash throughfall and canopy drip. Canopy drip from leafless broadleaved trees consisted of fewer and smaller diameter drops (D_{50_DR}, 50th cumulative drop volume percentile for canopy drip, of 2.24 mm) than leafed broadleaved trees (D_{50_DR} of 4.32 mm). Canopy drip was much larger in diameter under woody drip points (D_{50_DR} of 5.92 mm) than leafed broadleaved trees. Based on throughfall volume, the percentage of canopy drip was significantly different between conifers, leafed broadleaved trees, leafless broadleaved trees, and woody surface drip points (p ranged from <0.001 to 0.005). These findings are partly attributable to differences in canopy structure and plant surface characteristics between plant functional types and canopy state (leaf, leafless), among other factors. Hence, our results demonstrating the importance of drop‐size‐dependent partitioning between coniferous and broadleaved tree species could be useful to those requiring more detailed information on throughfall fluxes to the forest floor.     

Pumped rainfall simulators: the impact of rain pulses on sediment concentration and size

Many pumped rainfall simulators used in soil erosion studies use pulsed rain to control the rainfall intensity. We examined the effect of the rain pulsing on sediment concentration and size using three different pulse cycles with the same rainfall intensity. There was considerable variation in sediment concentration through the pulse cycle: the highest concentration was up to four times that of the lowest concentration. Furthermore, the particle size distribution also varied: the peak median particle size was double the lowest median particle size. The magnitude of differences in sediment concentration and particle size were greater the longer the pulse cycle and these dynamics will vary between rainfall simulators and studies. We suggest the impact of the pulsing on sediment is significant and should be investigated prior to experimentation so that sampling periods are designed to avoid bias introduced by fine temporal scale sediment dynamics. Copyright © 2009 John Wiley & Sons, Ltd.     

A hybrid method for size characterization of coarse subsurface fluvial sediments

This paper introduces and evaluates a novel method for ascertaining the grain‐size distribution of subsurface sediments that involves profoundly less sampling effort than standard methods. It is based on hybrid sampling principles previously applied to the construction of synthetic surface grain‐size distributions. The method is developed from an empirical demonstration of the approximate similarity of surface and subsurface grain‐size distributions when compared over a common range of sizes. Subsurface hybrid models are found to provide good facsimiles of grain‐size distributions de?ned using standard criteria and to yield distribution percentiles with millimetre accuracy. The technique is presented as an expedient alternative to standard methods for large, perennial gravel‐bed rivers. As this is a new technique, prudent application is advised in lieu of further investigation. Copyright © 2004 John Wiley & Sons, Ltd.     

First Results of DSD Measurement by Videodistrometer in the Czech Republic in 1998-1999

The first results of the almost one year drop size distribution (DSD) measurement in the Czech Republic are summarised in this study. The ESA-ESTEC 2D videodistrometer was used to measure the rain drop parameters. The average DSD is shown to be of the gamma type. One minute DSDs were evaluated to test the accuracy of analytical DSD models. Parameters of gamma distribution and exponential distribution functions were evaluated for the whole data set as well as for the various rain rate intervals. Regression technique and the method of moments were applied to estimate the parameters of DSD. It is shown that the parameter value strongly depends on the method of computation as well as on the rain type. Its average value is about 0.59 for the average (smooth) one minute DSD while an average value of un-smoothed DSD is 11.0 (moment method) or 5.4 (regression technique). The Joss's shape parameter and the Tokay-Short's parameter CS estimating roughly the rain type are also discussed (if CS>1, the event should be convective). The tendency of increasing numerical value of the CS parameter with the increasing rain rate was observed (the DSDs were distributed into classes respecting the rain rate value) and thus the idea of the convectivity occurrence bounded with the higher CS parameter value was supported. The study also compares the parameters of the average DSD with the averages of parameter values of all 4 183 one minute DSDs.     

Characterization of differential throughfall drop size distributions beneath European beech and Norway spruce

Forest canopies present irregular surfaces that alter both the quantity and spatiotemporal variability of precipitation inputs. The drop size distribution (DSD) of rainfall varies with rainfall event characteristics and is altered substantially by the forest stand properties. Yet, the influence of two major European tree species, European beech (Fagus sylvatica L.) and Norway spruce (Picea abies (L.) H. Karst), on throughfall DSD is largely unknown. In order to assess the impact of these two species with differing canopy structures on throughfall DSD, two optical disdrometers, one above and one below the canopy of each European beech and Norway spruce, measured DSD of both incident rainfall and throughfall over 2 months at a 10‐s resolution. Fractions of different throughfall categories were analysed for single‐precipitation events of different intensities. While penetrating the canopies, clear shifts in drop size and temporal distributions of incoming rainfall were observed. Beech and spruce, however, had different DSD, behaved differently in their effect on diameter volume percentiles as well as width of drop spectrum. The maximum drop sizes under beech were higher than under spruce. The mean ± standard deviation of the median volume drops size (D50) over all rain events was 2.7 ± 0.28 mm for beech and 0.80 ± 0.04 mm for spruce, respectively. In general, there was a high‐DSD variability within events indicating varying amounts of the different throughfall fractions. These findings help to better understand the effects of different tree species on rainfall partitioning processes and small‐scale variations in subcanopy rainfall inputs, thereby demonstrating the need for further research in high‐resolution spatial and temporal properties of rainfall and throughfall.     

Measuring drop size distribution and kinetic energy of rainfall using a force transducer

The relatively high cost of commercially available raindrop spectrometers and disdrometers has inhibited detailed and intensive research on drop size distribution, kinetic energy and momentum of rainfall which are important for understanding and modelling soil erosion caused by raindrop detachment. In this study, an approach to find the drop size distribution, momentum and kinetic energy of rainfall using a relatively inexpensive device that uses a piezoelectric force transducer for sensing raindrop impact response is introduced. The instrument continuously and automatically records, on a time‐scale, the amplitude of electrical pulses produced by the impact of raindrops on the surface of the transducer. The size distribution of the raindrops and their respective kinetic energy are calculated by analysing the number and amplitude of pulses recorded, and from the measured volume of total rainfall using a calibration curve. Simultaneous measurements of the instrument, a rain gauge and a dye‐stain method were used to assess the performance of the instrument. Test results from natural and simulated rainfalls are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Particle travel distances and bed and sediment compositions associated with rain‐impacted flows

Laboratory experiments were performed with rain of uniform drop size (2·7 mm, 5·1 mm) impacting flows over non‐cohesive beds of uniform sized sand (0·11–0·9 mm) and coal (0·2–0·9 mm) particles with flow velocities (20 mm s^?1, 40 mm s^?1) that were insufficient for the flow to entrain the particles without the aid of raindrop impact. Measurement of particle travel distance under rain made up of 2·7 mm drops confirmed a theoretical relationship between settling velocity and the distance particles travel after being disturbed by drop impact. Although, in theory, a relationship between settling velocity and particle travel distance exists, settling velocity by itself was unable to account for the effect of changes in both particle size and density on sediment discharge from beds of uniform non‐cohesive material. Particle density was also a factor. Further study of how particle characteristics influence sediment discharge will aid modelling of the impact of the soil in process‐based models of erosion by rain‐impacted flow. Copyright © 2001 John Wiley & Sons, Ltd.     

DEVEX-disdrometer evaluation experiment: Basic results and implications for hydrologic studies

Increasing our understanding of the small scale variability of drop size distributions (DSD), and therefore of several bulk characteristics of rainfall processes, has major implications for our interpretation of the remote sensing based estimates of precipitation and its uncertainty. During the spring and summer of 2002 the authors conducted the DEVEX experiment (disdrometer evaluation experiment) to compare measurements of natural rain made with three different types of disdrometers collocated at the Iowa City Municipal Airport in Iowa City, Iowa in the Midwestern United States. This paper focuses on the evaluation of the instruments rather than analysis of the hydrometeorological aspects of the observed events. The comparison demonstrates discrepancies between instruments. The authors discuss the systematic and random effects in terms of rainfall quantities, drop size distribution properties, and the observed drop size vs. velocity relationships. Since the instruments were collocated, the effects of the natural variability of rain are reduced some with time integration, isolating the instrumental differences. The authors discuss the status of DSD measurement technologies and the implications for a range of hydrologic applications from remote sensing of rainfall to atmospheric deposition to soil erosion and sediment transport in the environment. The data set collected during the DEVEX experiment is made available to the research community.     

Leaf Surface Wettability and Implications for Drop Shedding and Evaporation from Forest Canopies

Wettability and retention capacity of leaf surfaces are parameters that contribute to interception of rain, fog or dew by forest canopies. Contrary to common expectation, hydrophobicity or wettability of a leaf do not dictate the stickiness of drops to leaves. Crucial for the adhesion of drops is the contact angle hysteresis, the difference between leading edge contact angle and trailing edge contact angle for a running drop. Other parameters that are dependent on the static contact angle are the maximum volume of drops that can stick to the surface and the persistence of an adhering drop with respect to evaporation. Adaption of contact angle and contact angle hysteresis allow one to pursue different strategies of drop control, for example efficient water shedding or maximum retention of adhering water. Efficient water shedding is achieved if contact angle hysteresis is low. Retention of (isolated) large drops requires a high contact angle hysteresis and a static contact angle of 65.5°, while maximum retention by optimum spacing of drops necessitates a high contact angle hysteresis and a static contact angle of 111.6°. Maximum persistence with respect to evaporation is obtained if the static contact angle amounts to 77.5°, together with a high contact angle hysteresis. It is to be expected that knowledge of these parameters can contribute to the capacity of a forest to intercept water.