Published in Soil Sci. Soc. Am. J. 69:30-37 (2005).
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
Division S-1—Soil Physics
Splash Projection Distance for Aggregated Soils
Theory and Experiment
Sophie Leguédoisa,*,
Olivier Planchonb,
Cédric Legoutc and
Yves Le Bissonnaisa
a INRA-Science du sol, B.P. 20619, 45166 Olivet CEDEX, France
b IRD-Lab. BioMCo, Bât. EGER, INRA-INAPG, 78850 Thiverval-Grignon, France
c INRA-UMR INRA/ENSAR Sol, Agronomie & Spatialisation, 65 rue de Saint Brieuc, 35042 Rennes CEDEX, France
* Corresponding author (sophie.leguedois{at}orleans.inra.fr).
 |
ABSTRACT
|
|---|
Splash is an essential process in interrill erosion because it detaches soil fragments from their substrate and transports them. However, splash measurements are difficult to interpret and relatively little is known about the influence of particle characteristics on the spatial distribution of splash. The objective of this work is to study the splash distribution of different size fractions for aggregated soils. We used a recently proposed theory for spatial distribution by splash to interpret experimental data on the radial distribution of soil fragments splashed by simulated rainfall. A laboratory device with five concentric rings was used to determine average splash lengths for 16 fragment size fractions (0.05 to >2000 µm) of four soils. Sieved soil (3- to 5-mm size fraction) was exposed to simulated rainfall at 29 mm h–1 and with a time-specific kinetic energy of 252 J m–2 h–1. We interpreted the measured masses of fragments splashed into the different rings using an approximate solution of the exponential splash distribution theory applied to the experimental design. We demonstrated that the theory is valid for bulk aggregated soil as well as for individual fragment size fractions. The derived average splash lengths ranged from 4 to 23 cm, depending on the fragment size and soil. Splash lengths were greatest for soil fragments of 100 to 200 µm, and decreased for finer and coarser size fractions. Comparison of these findings with physically-based theory suggests that the coarser fragments, 50 to 2000 µm, are transported as single airborne particles, whereas the smaller ones, <50 µm, are transported in groups in splash droplets. This interpretation is consistent with observations reported in the literature.
Abbreviations: FDSF, fundamental splash distribution function
|
INTRODUCTION
|
|---|
RAINDROP IMPACT has long been recognized as a major erosive agent (Ellison, 1944, 1947; Ekern, 1950; Free, 1952). The impact of raindrops on the soil surface leads to the restructuring of the soil surface, for example by aggregate breakdown and crust formation (e.g., McIntyre, 1958; Boiffin, 1984; Moss, 1991; Le Bissonnais, 1996). The impact can also detach and transport soil fragments (e.g., Ellison, 1944; Moss and Green, 1983; Bradford and Huang, 1996). These two phenomenons correspond to a splash event, that is, the simultaneous spatter of water and soil fragments following the impact of a raindrop on the soil surface. A splash event causes soil fragments to move from their initial position at the surface (detachment), with some particles returning to their initial position, and others traveling to a different location (transport).
Splash detachment rate has been related to rainfall kinetic energy, soil type, grain size (De Ploey and Savat, 1968; Quansah, 1981; Sharma et al., 1991) and the thickness of the water layer at the soil surface (Moss and Green, 1983; Kinnell, 1991). Splash transport has been related to slope gradient (Savat, 1981; Planchon et al., 2000), grain size (Poesen and Savat, 1981), and raindrop characteristics (Riezebos and Epema, 1985). Poesen and Savat (1981) show that for noncohesive single grains, the smaller particles are splashed over longer distances than the larger ones. Because of the particle size influence on spatial distribution of splash, experimental results are always ill-defined and experiment-specific (Farrell et al., 1974; Van Dijk et al., 2002). Moreover, it has not been established whether these findings can be extrapolated to natural aggregated soils, where colloidal forces between particles may interfere with the transportation process itself.
Recently, a general theory of sediment redistribution by raindrop splash has been proposed to interpret results obtained with different experimental designs (Van Dijk et al., 2002). On the basis of literature data, the authors hypothesize that the mass transported from a point source by splash decreases exponentially with the distance from the source. To describe this distribution, they used a so-called fundamental splash distribution function (FSDF; Eq. [2]). This equation has only two parameters: the rate of detachment µ (g m–2) and the average splash length 
(m), which describes the range of splash transport. For pragmatic reasons, Van Dijk et al. (2002) defined splash detachment "as the amount of soil that appears to have been detached based on measurements of splash." Theoretical developments based on the FSDF accurately described results obtained with a variety of splash measurement devices (Van Dijk et al., 2002).
Thus the objective of this article is to investigate the splash distribution of aggregated soils using the FSDF. We measured splash transport with a device made of concentric rings for 16 aggregate size fractions from four soils. The experimental data was interpreted using an analytical approximation for the exponential splash theory applied to this nonpoint source experimental design.
|
MATERIALS AND METHODS
|
|---|
Soils
The materials chosen for this study are four cultivated soils with various sensitivities to erosion. Their general characteristics are reported in Table 1. The silt loam was formed from aeolian deposits in the western part of the Paris Basin (Normandy, France), which is a region very sensitive to water erosion. The clay loam was formed from a marly molass of the Basin of Aquitaine (Lauragais, France). The silty clay loam is derived from a cryoclastic limestone found in a region without interrill erosion problems (Beauce, France). The sand is a ferruginous tropical soil from Senegal, poorly aggregated, with high susceptibility to crusting (Valentin, 1994). All the soils were air-dried prior the experiment. After dry sieving, 3- to 5-mm aggregates from each soil were selected for experiments. The choice of this sieved size fraction was driven by a concern of reproducibility and the necessity to have a good surface condition of the source area (a large cover of aggregates and no sealing).
Experimental Device
The amount and the spatial distribution of soil transported by splash were assessed with a splash-ring device. The splash device consisted of a central source area of 4.8-cm diameter surrounded by seven adjacent concentric rings with diameters up to 90 cm (Fig. 1)
. The base of the 18-cm2 source area was made of filter paper to ensure sufficient infiltration and to prevent the formation of a water layer. The data from the first and the last rings were not used because of experimental artifacts. The innermost ring was not perfectly protected from rainfall, so sediments collected there could be broken down or lost during secondary splash. The outermost ring was delimited by a vertical piece of plastic, so soil fragments that would normally be deposited outside the device were collected with the soil fragments of the outer ring.
View larger version (13K):
[in this window]
[in a new window]
|
Fig. 1. Schematic side view of half of the splash sampler. All measurements are in centimeters and their origin is 0, the center of the device.
|
|
The source area was subjected to a simulated rainfall of 28.9 mm h–1 (SD = 2.9 mm h–1). Rainfalls were obtained with an oscillating nozzle. The raindrops were restrained to the source area with an upside-down funnel (Fig. 2)
. The characterization of the rainfall with an optical spectropluviometer (Salles and Poesen, 1999) gave a time-specific kinetic energy of 252 J m–2 h–1, and the raindrop size and velocity distributions (Table 2 and Fig. 3)
. According to Salles et al. (2002), the time-specific kinetic energy of this simulated rainfall corresponds to a natural rainfall event of approximately 10 mm h–1.
The source area was initially filled with about 5 g of 3- to 5-mm air-dried soil aggregates. A first rainfall run was then applied on it. The rainfall led to slow changes of the surface conditions of the source area with a decrease of the stock of aggregates and the potential formation of a water layer due to sealing. To avoid a lack of sediment or a water layer, the duration of the rainfall run was limited. As each soil type has a different susceptibility to rainsplash, each rainfall run has a different duration (Table 1). However, one run was not enough to get a sufficient amount of soil in each ring for size-distribution analysis. So, the source area was replaced by a new one with fresh 5 g of 3- to 5-mm soil aggregates, and then the rainfall restarted for another run. This operation was renewed three to six times depending on the soil (Table 1). For one soil type, each run had the same duration. At the end of these runs, the sediments accumulated in the sampling area were collected. For each soil type, the whole process was iterated three times to obtain replicated data. For each replication, the infiltrated water accumulated in a collector located under the source area was recovered and weighed. This measurement enables us to take into consideration the slight changes in rainfall intensities between the replications and leads to more accurate data for the amount of cumulative rainfall applied on each sample.
Fragment Size Distribution Measurements
The soil fragments collected in each ring were wet sieved at 2000, 1000, and 500 µm (sieve opening diameter). The fraction < 500 µm was analyzed by a laser diffraction sizer which gave the volume distribution of 13 fractions. Both wet sieving and laser diffraction analysis were done in ethanol to prevent breakdown (Concaret, 1967). Then, all the fractions (>2000 µm, 1000–2000 µm, 1000–500 µm, and <500 µm) were oven dried and weighed. The volume fractions issued from laser diffraction analysis were converted into masses by using the same bulk density for each size fraction.
The mass of splashed soil fragments collected in a ring i, mi(li) (g m–2 mm–1), was normalized per unit of ring area and per millimeter of rainfall:
 | [1] |
where Mi (g) is the mass of soil fragments which have been deposited in a ring i of a given width wi (m), at an average radial distance li (m) from the center of the device and for a given amount of rainfall p (mm). As rainfall intensity was approximately constant for all the rainfall simulations, p can also be considered as an expression of time and thus, mi(li) is defined as the measured flux of splash deposition.
Mathematical and Numerical Analysis
Following Van Dijk et al. (2002), we describe the splash flux from a point source mpoint(r) (g m–4 mm–1), that is, the mass per unit source area, per unit target area, per millimeter of rainfall, that arrives at a radial distance r from the source, by
 | [2] |
where (m) is the average splash length, that is, the mass-weighted average radial distance over which the particles are splashed, and µ (g m–2 mm–1, i.e., mass per unit source area per millimeter of rainfall) is the flux of movement initiation. Equation [2] is the FSDF of Van Dijk et al. (2002) where µ, and subsequently the result mpoint(r), are expressed per millimeter of rainfall. As well as for Eq. [1] we consider here cumulative rainfall as a measurement of time and mpoint(r) as a flux.
To determine the splash distribution for a circular nonpoint source, the integration of Eq. [2] over the whole source area is performed. This is done by considering the arc AA' of radius l – a and angle ß (Fig. 4)
. The line integral of Eq. [2] over the arc AA' leads to:
 | [3] |
where marc is the mass per unit source length, per unit target area, per millimeter of rainfall (g m–3 mm–1) originating from AA' and deposited at point O. Integration of Eq. [3] over the cup diameter leads to:
 | [4] |
where mcup is the mass per unit target area per millimeter of rainfall (g m–2 mm–1) collected at point O and coming from the whole cup, and R is the cup radius (m).
View larger version (11K):
[in this window]
[in a new window]
|
Fig. 4. Integration scheme. Flux coming from the source cup (in gray) of radius R and center B, to point O at distance l from B is integrated over length a by considering the arc AA' of angle ß and radius l – a.
|
|
Equation [4] does not appear to have a straightforward analytical solution because ß(a) is dependant of a. However, cups with the same area and the same angle of view from point O should produce similar fluxes of particles toward point O, regardless the details of their shape. Transcribing this intuitive fact into Eq. [4] leads to the approximation of the average value 
in place of ß(a) among the integration interval. This leads to Eq. [5] after has been brought out of the integral:
 | [5] |
where 
cup is an approximation of mcup and is the average value of ß(a) within the integration domain of Eq. [5].
Equation [5] can then be integrated, which yields Eq. [6] after factorizing terms that do not depend on a.
 | [6] |
The next and last step is the calculation of . An approximation is also needed here. We propose Eq. [7], for which we have numerically found a precision better than 1% when R/l > 2.2, and better than 0.1% when R/l > 6.5.
 | [7] |
It may be noticed that arcsin(R/l) is the maximum value of ß/2, which occurs when line AO is a tangent to the source circumference, that is, when angle
is a right angle.
Combining Eq. [6] and Eq. [7] leads to Eq. [8], the analytical approximation of the integration of the exponential FSDF (Eq. [2]) in the case of a splash cup or a circular source of radius R.
 | [8] |
To verify numerically the accuracy of Eq. [8], we developed a numerical integration of Eq. [2] in the case of a circular cup, which is the unique source of splashed sediment. This integration was processed by applying the FSDF equation (Eq. [2]) on the source geometry. We used the Fast Fourier Transform1 technique to perform this convolution. The computation was done on 1-mm cells. The source map and the FSDF equation (Eq. [2]) were evaluated for 0.1-mm subcells. The integration accuracy was 99.9% or better. The results showed that for values ranging from 5 to 10 cm, the maximum error for distances to the cup center of 3 cm and more was 1.1%. When was within 10 to 25 cm and distances to the cup center were 6 cm or more, errors were <0.3%. The range of 5 to 25 cm that we used for was consistent with the literature (e.g., Poesen and Savat (1981), 9–20 cm; Savat (1981), 5–30 cm; Van Dijk et al. (2003), 0.3–15 cm).
Equation [9], which is the logarithm of Eq. [8], is suitable for an ordinary least squares linear regression of the experimental data as computed in Eq. [1]. The is deduced from the slope of the regression.
 | [9] |
where
 | [10] |
and
 | [11] |
and is independent of li. The mi* corresponds to the measured flux of splash deposition mi normalized by the angle arcsin(R/li) at which the source cup is seen at the average radial distance li of the ring i.
|
RESULTS
|
|---|
Splash Measurements
Following Eq. [1], the normalized fluxes of splash deposition were computed from experimental data and fitted to Eq. [9] for both the bulk soils and each of the studied size fractions. The values of three replications have been used, and so there were 15 values for each fit.
For the four soils studied, the spatial distributions of the total measured fluxes of splash deposition fit very well to Eq. [9] (Fig. 5)
. This result has already been suggested by Legout et al. (2005) who found, for these soils, that the mass deposited by splash (g mm–1 cm–1) follows an exponential decrease with an increasing radial distance.
View larger version (23K):
[in this window]
[in a new window]
|
Fig. 5. Radial distribution of the measured flux of splash deposition for four soils. R2 is the coefficient of determination.
|
|
The analysis of the spatial distribution of splash deposition fluxes is not possible for all the studied size fractions. Some size fractions were not collected at all ("nd" in Table 3) or in too small amount ("ns" in Table 3). These size fractions are similar for the four soils included. They are the finest, <0.2 µm, and the coarsest fractions, >2000 µm (Table 3). For the sandy soil, the 1000- to 2000-µm size fraction has also not been collected.
For most of the collected size fractions, the measured radial distribution of splash deposition flux follow Eq. [9], as shown in Fig. 6b
for the silt loam. The determination coefficients of all these fits are summarized in Table 3.
View larger version (24K):
[in this window]
[in a new window]
|
Fig. 6. Radial distribution of the measured flux of splash deposition for some fractions of (a) the sand and (b) the silt loam. The curves are the fitted equations.
|
|
The observed radial distribution is well described by Eq. [9]. The majority of the determination coefficients obtained for these fits are significant and >0.70 (Table 3). Only the size fractions between 0.2 and 20 µm for the sandy soil show a poor fit with determination coefficients under 0.50. Some determination coefficients > 0.70 have also been obtained for the clay loam and the silty clay loam. These poor fits are due to a high deviation of the values of the different replications as shown in Fig. 6a. The very small quantity of soil fragments with the size of clay or silt for the sand is probably the cause of these scattered measurements performed by laser diffraction.
Average Splash Lengths
To analyze the splash spatial distribution of each size fraction, average splash lengths have been computed. The values of average splash length presented here are extracted from the results fitted with Eq. [9]. Arbitrarily, only the fits with a determination coefficient more than 0.65 have been retained.
The computed average splash lengths extend from about 5 to 21 cm (Fig. 7)
. These values are in the same range as the values commonly reported in literature (Poesen and Savat, 1981; Riezebos and Epema, 1985; Poesen and Torri, 1988; Van Dijk et al., 2003). The minimal value corresponds to the minimal value that can physically be measured with our experimental device as explained in the "Mathematical and Numerical Analysis" section.
View larger version (24K):
[in this window]
[in a new window]
|
Fig. 7. Average splash lengths of the four studied soils as a function of size fraction. Only the values from fits with a determination coefficient > 0.65 and standard error < 20% of the value of were used.
|
|
The shape of the curve describing the average splash length as a function of size fraction is similar whatever the soil considered. The size fractions < 50 µm have nearly the same average splash length. For larger fragments, the average splash length increases rapidly with the diameter of soil fragments and reaches a maximum between 100 and 200 µm. In the last part of the graph, the average splash length decreases and reaches a minimum for the coarsest collected size fraction, the 1000- to 2000-µm size fraction.
|
DISCUSSION
|
|---|
Validation of the Fundamental Splash Distribution Function
For total soil masses (Fig. 5) as well as for the aggregate size fractions (Fig. 6b; Table 3), the measured splash radial distributions are in accordance with the theory proposed by Van Dijk et al. (2002). In both cases, the spatial distribution of splashed material fits well to the analytical approximation of the integration of the FSDF for a splash cup (Eq. [8]). Thus, the experimental data supports the FSDF. Van Dijk et al. (2002) have successfully tested their theory with data on well-sorted sediment (Riezebos and Epema, 1985) and loose soil (Savat and Poesen, 1981). Our results extend the validity of the FSDF both to bulk aggregated soils and aggregate size fractions.
Possible Causes for Nonsampling
The masses of some size fractions collected in our splash sampler were negligible or null. This can be attributed to three causes. (i) There were no fragments of this size produced by breakdown in the soil sample. The splash is limited by the composition of the broken down stock. (ii) The splash was not vigorous enough to move these fragments. The detachment is limited by energy. (iii) These fragments were splashed but not far enough to be collected in the rings. The transport is range-limited.
Comparison with Reported Average Splash Lengths
Contrary to most previous studies (e.g., Van Dijk et al., 2002), our results show that the small soil fragments are not splashed over a greater distance than the larger ones. The relationship between average splash distance and size fraction is more complex than expected from the few previous results (Poesen and Savat, 1981; Van Dijk et al., 2003).
Poesen and Savat (1981) investigated nine loose sediments with median grain sizes between 20 and 700 µm. They determined a decreasing relationship between average splash length and median size. This result apparently contradicts ours, as we observed a bell-shaped relationship for this size range (Fig. 7). It should be noted that they computed the average splash length of each sediment without considering the component size fractions separately and these sediments have a large particle-size range: from at least 2 µm to 125 or 2000 µm. In fact, it seems that their sediments were blends of different size fractions with various behaviors. Moreover, there was no framework to interpret the experimental data.
Despite these methodological problems, the behaviors of single particles have been deduced from these results and from other similar ones (e.g., Quansah, 1981) and introduced in numerical models (Poesen, 1985; Wainwright et al., 1995). Our results are likely to provide these models with more accurate parameters, directly computed from the study of single particle behavior.
For median diameters larger than 110 µm, Van Dijk et al. (2003) found a decreasing curve for the function of average splash length vs. aggregate size. They used the theory presented by Van Dijk et al. (2002) to compute average splash length from splash measurements performed under natural rainfall on plots with various slopes and soil covers. The relationship they determined agrees with our results and matches the decreasing part of the curve observed in Fig. 7. However, the values they obtain are smaller than ours (Fig. 8)
. These divergences can be explained by differences in the soil properties (e.g., aggregates density, soil surface structure), the surface conditions (e.g., water layer), and the rainfall characteristics (simulated rainfall vs. natural rainfall).
Effect of Particle Size on Average Splash Length
Two approaches are reported in the literature for the description of transport by rainsplash. Authors like Park et al. (1982) or Planchon et al. (2000) describe the trajectories of individual soil fragments. Others consider the projection of laden droplets (Wright, 1986; Macdonald and McCartney, 1987; Saint-Jean et al., 2004). Splash trajectories, and hence average splash length, are controlled by soil fragments characteristics in the first order, and by the droplets characteristics in the second order. According to physically based models of splash trajectory (Wright, 1986; Macdonald and McCartney, 1987; Allen, 1988; Saint-Jean et al., 2004), the average splash length of an airborne water or soil particle is a function of the density of the particle, its diameter, its initial velocity, and its splash angle, that is, the angle of projection relative to a horizontal plane.
Figure 7 shows that the average splash length is controlled by soil fragment size only for the fractions > 50 µm, the average splash length of the finer fragments being approximately constant whatever the size. The bell shape relationship between fragment size and average splash length indicates that, for the >50-µm fraction, medium-sized droplets are splashed over longer distances than the finer or coarser ones. This result is consistent with models of splash trajectory for droplets (Wright, 1986; Macdonald and McCartney, 1987), and with observations of splash droplets done by Gregory et al. (1959) and Ghadiri and Payne (1988). This behavior is due to the effect of air friction, which is relatively more important for small particles than for big ones. This analysis suggests that the >50-µm fragments are splashed as single particles either dry or with some water. This transport is consistent with the observations of Mouzai and Bouhadef (2003), who noticed single dry splashed particles.
In contrast, fine fragments < 50 µm have size-independent average splash lengths (Fig. 7). For this size fraction, the fragments may be transported in droplets relatively bigger than themselves. In this case, the splash trajectory would be driven by the droplet characteristics. It is highly possible that these small soil fragments are transported in groups inside droplets as observed by Mouzai and Bouhadef (2003) for soil particles and by phytopathologists (Gregory et al., 1959; Huber et al., 1996) for spores.
Thus, the two parts of the curves in Fig. 7 may correspond to two approaches of splash transport found in the literature: a droplet-driven trajectory for soil fragments < 50 µm and a soil fragment-driven trajectory for soil fragments > 50 µm.
Effect of Soil Surface Characteristics on Average Splash Length
The characteristics (splash angle, velocity, and size) of the droplets produced by a splash event depend on the rainfall characteristics and the source surface conditions such as the presence and the depth of a water layer, the nature of the surface, the shear strength, the roughness, and the moisture (e.g., Al-Durrah and Bradford, 1982; Allen, 1988; Range and Feuillebois, 1998; Ntahimpera et al., 1999). The rainfall conditions were held constant for each rainfall experiment but, as shown in Fig. 9
, there was a variability of source surface conditions for the different soil types. The low aggregate stability of the silt loam led to the rapid formation of a structural crust and the initiation of a water layer (Fig. 9a). For the silty clay loam and the clay loam (Fig. 9b and 9c), no structural crust was formed and the soil surfaces were rough and aggregated. This variability of soil surface condition may influence the splash droplets' characteristics and, as a consequence, the average splash lengths of the soil fragments < 50 µm. Thus, the surface condition differences noted for the different soil types may explain the scattered values observed for the left-hand side of the graph in Fig. 7.
View larger version (70K):
[in this window]
[in a new window]
|
Fig. 9. Soil surface conditions at the end of the splash experiments for (a) silt loam, (b) silty clay loam, and (c) clay loam.
|
|
|
CONCLUSIONS
|
|---|
In this article, an approximate solution is derived for the application of the exponential splash theory (Van Dijk et al., 2002) to a nonpoint circular source surrounded by concentric collecting rings. The resulting equation (Eq. [8]) was validated with good agreement by experimental results obtained with a splash sampling device subjected to simulated rainfall.
The spatial distributions of the whole soils, as well as the majority of the size fractions, agreed well with the exponential distribution theory (Van Dijk et al., 2002). The results confirm that the exponential splash distribution theory developed by Van Dijk et al. (2002) is relevant in interpreting splash measurement data for aggregated and cohesive soils, whatever the size fraction considered.
The influence of the size of fragments on the range of their splash spatial distribution, given by the average splash length, is more complex than expected from the few literature data. The aggregate size is a pertinent parameter to describe the splash distribution range, but other factors have to be evoked to explain the observations for the fragments smaller than 50 µm. For the coarser soil fragments, the splash trajectory is well accounted for by a model of airborne particle transfer with air resistance. In contrast, the fine soil fragments do not appear to be transferred as single airborne particles. These two types of splash transport are consistent with the observations of Mouzai and Bouhadef (2003), who noted that soil fragments are transported either in groups inside droplets or as single dry particles. The current models of splash redistribution are based either on the transfer of splash droplets (e.g., Wright, 1986; Saint-Jean et al., 2004) or on the trajectory of single particles (e.g., Planchon et al., 2000), and thus would be unable to predict the fate of the fragments smaller than 50 µm.
These results need to be confirmed by field investigations under natural rainfall as several parameters, particularly the rain properties, are difficult to reproduce in the laboratory. The experimental design presented here is appropriate to investigate the splash distribution in the laboratory, but for field studies a series of splash cups of increasing diameter such the ones used by Poesen and Torri (1988) or Van Dijk et al. (2003) would be more suitable.
The splash is not an effective process of soil transport and exportation at low slopes, but it is the key mechanism of detachment, and thus of sediment production in a sheet erosion event. On heterogeneous surfaces it can lead to microtopographic evolution, as shown by Wainwright et al. (1995) and Planchon et al. (2000). Moreover, when the overland flow is nonspatially homogeneous, splash redistribution is important in predicting the composition and the quantity of sediment provided to the flow. The theory of splash redistribution proposed by Van Dijk et al. (2002) provides an interesting basis for modeling these phenomenons.
|
ACKNOWLEDGMENTS
|
|---|
The authors appreciate the skilled assistance of Bernard Renaux and Loïc Prud'homme for rainfall simulations, Frédéric Darboux for scientific discussion, Hocine Bourennane for statistics, and Stephen R. Cattle and Kristen Feher for English and mathematics corrections.
|
NOTES
|
|---|
1 We used the FFTW library, which is copyright 2003 Matteo Frigo and Massachusetts Institute of Technology. It is distributed as free software under GNU license. See www.fftw.org (verified 27 Sept. 2004) for license details and source downloads. 
Received for publication December 16, 2003.
|
REFERENCES
|
|---|
- Al-Durrah, M.M., and J.M. Bradford. 1982. The mechanism of raindrop splash on soil surfaces. Soil Sci. Soc. Am. J. 46:1086–1090.[Abstract/Free Full Text]
- Allen, R.F. 1988. The mechanics of splashing. J. Colloid Interface Sci. 124:309–316.
- Boiffin, J. 1984. Structural breakdown under rainfall of the soil superficial layers. (In French.) Ph.D. diss., Inst. Natl. Agron., Paris.
- Bradford, J.M., and C. Huang. 1996. Splash and detachment by waterdrops. p. 61–76. In M. Agassi (ed.) Soil erosion, conservation, and rehabilitation. Marcel Dekker, New York.
- Concaret, J. 1967. Study of destruction mechanisms of soil aggregates in contact with aqueous solutes (2). (In French.) Ann. Agron. 18:99–144.
- De Ploey, J., and J. Savat. 1968. Contribution to the study of splash erosion. (In French.) Z. Geomorphology 12:174–193.
- Ekern, P.C. 1950. Raindrop impact as the force initiating soil erosion. Soil Sci. Soc. Am. Proc. 15:7–10.
- Ellison, W.D. 1944. Studies of raindrop erosion. Agric. Eng. 25:131–136, 181–182.
- Ellison, W.D. 1947. Soil erosion. Soil Sci. Soc. Am. Proc. 12:479–484.
- Farrell, D.A., W.C. Moldenhauer, and W.E. Larson. 1974. Splash correction factors for erosion studies. Soil Sci. Soc. Am. Proc. 38:510–514.
- Free, G. 1952. Soil movement by raindrops. Agric. Eng. 33:491–494, 496.
- Ghadiri, H., and D. Payne. 1988. The formation and characteristics of splash following raindrop impact on soil. J. Soil Sci. 39:563–575.
- Gregory, P.H., E.J. Guthrie, and M.E. Bunce. 1959. Experiments on splash dispersal of fungus spores. J. Gen. Microbiol. 20:328–354.[Medline]
- Huber, L., B.D.L. Fitt, and H.A. McCartney. 1996. The incorporation of pathogen spores into rain-splash droplets: A modelling approach. Plant Pathol. 45:506–517.
- Kinnell, P.I.A. 1991. The effect of flow depth on sediment transport induced by raindrops impacting shallow flows. Trans. ASAE. 34:161–168.
- Le Bissonnais, Y. 1996. Aggregate stability and assessment of soil crustability and erodibility: I. Theory and methodology. Eur. J. Soil Sci. 47:425–437.
- Legout, C., S. Leguédois, O. Malam-Issa, and Y. Le Bissonnais. 2005. Splash distance and size distributions for various soils. Geoderma (In press).
- Macdonald, O.C., and H.A. McCartney. 1987. Calculation of splash droplets trajectories. Agric. For. Meteorol. 39:95–110.
- McIntyre, D.S. 1958. Soil splash and the formation of surface crusts by raindrop impact. Soil Sci. 85(5):261–266.
- Moss, A.J. 1991. Rain-impact soil crust. I. Formation on a granite-derived soil. Austr. J. Soil Res. 29:271–289.
- Moss, A.J., and P. Green. 1983. Movement of solids in air and water by raindrop impact. Effects of drop-size and water-depth variations. Austr. J. Soil Res. 21:257–269.
- Mouzai, L., and M. Bouhadef. 2003. Water drop erosivity: Effects on soil splash. J. Hydraul. Res. 41:61–68.
- Ntahimpera, N., J.K. Hacker, L.L. Wilson, F.R. Hall, and L.V. Madden. 1999. Characterization of splash droplets from different surfaces with a phase doppler particle analyzer. Agric. For. Meteorol. 97:9–19.
- Park, S.W., J.K. Mitchell, and G.D. Budenzer. 1982. Splash erosion modeling: Physical analyses. Trans. ASAE. 25:357–361.
- Planchon, O., M. Esteves, N. Silvera, and J.-M. Lapetite. 2000. Raindrop erosion of tillage induced microrelief: Possible use of the diffusion equation. Soil Tillage Res. 56:131–144.
- Poesen, J. 1985. An improved splash transport model. Z. Geomorphol. 29:193–211.
- Poesen, J., and J. Savat. 1981. Detachment and transportation of loose sediments by raindrop splash. Part II: Detachability and transportability measurements. Catena 8:19–41.
- Poesen, J., and D. Torri. 1988. The effect of cup size on splash detachment and transport measurements. Part I: Field measurements. Catena Suppl. 12:113–126.
- Quansah, C. 1981. The effect of soil type, slope, rain intensity and their interactions on splash detachment and transport. J. Soil Sci. 32:215–224.
- Range, K., and F. Feuillebois. 1998. Influence of surface roughness on liquid drop impact. J. Colloid Interface Sci. 203:16–30.
- Riezebos, H.T., and G.F. Epema. 1985. Drop shape and erosivity. Part II: Splash detachment, transport and erosivity indices. Earth Surf. Processes Landforms 10:69–74.
- Saint-Jean, S., M. Chelle, and L. Huber. 2004. Modelling water transfer by rain-splash in a 3D canopy using Monte Carlo integration. Agric. For. Meteorol. 121:183–196.
- Salles, C., and J. Poesen. 1999. Performance of an optical spectro pluviometer in measuring basic rain erosivity characteristics. J. Hydrol. 218:142–156.
- Salles, C., J. Poesen, and S.-T. Daniel. 2002. Kinetic energy of rain and its functional relationship with intensity. J. Hydrol., 257:256–270.
- Savat, J. 1981. Work done by splash: Laboratory experiments. Earth Surf. Processes Landforms 6:275–283.
- Savat, J., and J. Poesen. 1981. Detachment and transportation of loose sediments by raindrop splash. Part I: The calculation of absolute data on the detachability and transportability. Catena 8:1–17.
- Sharma, P.P., S.C. Gupta, and W.J. Rawls. 1991. Soil detachment by single raindrops of varying kinetic energy. Soil Sci. Soc. Am. J. 55:301–307.[Abstract/Free Full Text]
- Valentin, C. 1994. Sealing, crusting and hardsetting soils in sahelian agriculture. p. 53–76. In H.B. So et al. (ed.) Proc. 2nd Int. Symp. on Sealing, Crusting and Hardsetting Soils: Productivity and Conservation, Brisbane, Australia. Austr. Soc. Soil Sci. and ISSCHS, Brisbane.
- Van Dijk, A.I.J.M., L.A. Bruijnzeel, and S.E. Wiegman. 2003. Measurements of rain splash on bench terraces in a humid tropical steepland environment. Hydrol. Processes 17:513–535.
- Van Dijk, A.I.J.M., A.G.C.A. Meesters, and L.A. Bruijnzeel. 2002. Exponential distribution theory and the interpretation of splash detachment and transport experiments. Soil Sci. Soc. Am. J. 66:1466–1474.[Abstract/Free Full Text]
- Wainwright, J., A.J. Parsons, and A.D. Abrahams. 1995. A simulation study of the role of raindrop erosion in the formation of desert pavements. Earth Surf. Processes Landforms 20:277–291.
- Wright, A.C. 1986. A physically-based model of the dispersion of splash droplets ejected from a water drop impact. Earth Surf. Processes Landforms 11:351–367.
TOP
ABSTRACT
INTRODUCTION
