Published in Soil Sci. Soc. Am. J. 68:41-46 (2004).
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
DIVISION S-1—SOIL PHYSICS
Splash–Saltation of Sand due to Wind-Driven Rain
Horizontal Flux and Sediment Transport Rate
Wim M. Cornelis*,
Greet Oltenfreiter,
Donald Gabriels and
Roger Hartmann
Dep. Soil Management and Soil Care, Ghent Univ., Coupure links 653, B-9000 Ghent, Belgium
* Corresponding author (wim.cornelis{at}UGent.be).
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ABSTRACT
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Transport of sediment under wind-driven rains is generally not accounted for in equations for sediment transport by wind. However, the contribution of this rainsplash–saltation process can be substantial. Wind-tunnel experiments, in which horizontal fluxes were measured at four heights above a sand surface, were conducted to study sediment transport under wind-driven rain and rainless wind conditions. It was shown that the horizontal flux could be described by a single exponential equation under both conditions. By integration of the horizontal flux over the height of rainsplash–saltation and saltation, respectively, the sediment transport rate was computed. Hence the obtained data set was used to validate the sediment transport models of Cornelis et al., which were developed from measurements of vertical deposition fluxes under wind-driven rain and rainless wind conditions. The data followed the models very well, which suggests that they are adequate to predict the transport rate of sediment under wind-driven rain and rainless wind.
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INTRODUCTION
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TRANSPORT OF SEDIMENT above dry surfaces as induced by aerodynamic forces and bombardment of saltating sediment particles has been studied in detail. A review of sediment transport models relating the sediment transport rate to a wind-power index is given in Greeley and Iversen (1985) and Shao (2000). Those models enable the prediction of the sediment mass in transport once a threshold shear velocity of the wind is exceeded. If the shear velocity of the wind is below the threshold value for deflation, the sediment transport rate is predicted to be equal to zero.
However, De Ploey (1980), Jungerius et al. (1981), de Lima et al. (1992), and van Dijk et al. (1996) recorded substantial sediment transport on dunes and beaches during rainy days, although the near-surface moisture of the sediment in those studies was probably large enough for the threshold shear velocity to become much larger than the actual measured shear velocities. According to Cornelis et al. (2003), deflation of sediment due to wind ceases once the moisture content exceeds 0.75 times the moisture content at a matric potential of –1.5 MPa. The sediment transport observed in those studies was attributed to a combined action of raindrop impact causing splash of sand particles, and wind, which subsequently transports these particles in saltation (Jungerius and Dekker, 1990) and this phenomenon was referred to as splash–saltation (de Lima et al., 1992). No attempts were made to measure and model the sediment mass transport rates.
To predict the total budget of sediment transported by wind over a given period, it is necessary not only to consider the transport of sediment during periods with no rain, but also to account for the mass of sediment transported during wind-driven rain periods. Wind-blown sediment transport at the point of observation is usually determined by integrating horizontal mass flux profiles, which are obtained from sampling with sediment catchers across height (Wilson and Cooke, 1980; Fryrear et al., 1991; Sterk and Raats, 1996; Goossens and Gross, 2002). However, in literature, the use of a similar methodology to determine sediment transport under wind-driven rain is not reported.
The objective of this study was therefore to measure horizontal sediment fluxes at different heights above a surface with sediment catchers under wind-driven rain conditions, and to find an expression describing the vertical distribution of the horizontal flux. Experiments were carried out in a wind tunnel with a rainfall simulation facility in which detachment was induced from a source zone containing sand and horizontal sediment fluxes were measured at four different heights above the sand surface. Hence the study focuses on the smallest and earliest space and time scale subprocess elements of erosion, detachment, and subsequent transport, rather than on the overall soil loss from a given area. The experiments were performed under different kinetic energies or momentums of the rain and under different shear velocities of the wind, and these conditions are referred to in this paper as wind-driven rain. As a wind-erosion control, experiments were also conducted on dry sand applying different shear velocities only and are referred to as rainless wind. The horizontal sediment flux measured throughout the experiments is defined here as the mass of particles that are captured at a given height above the surface per unit of inlet area of the catcher within a time unit. By integrating the horizontal flux over the height, the sediment transport rate was computed and therefore the obtained data set was used to validate the sediment transport models of Cornelis et al. (2004), which were developed from measurements of vertical deposition fluxes under wind-driven rain and rainless wind conditions. The sediment transport rate is defined as the quantity passing through a plane of unit width and infinite height above the surface, perpendicular to the wind, per unit of time.
Note that the term rainsplash or splash in this study refers to the detachment of particles due to the impact energy of droplets, rather than splash entrainment as used by Shao (2000) for ejection of particles following impact of a saltating particle. Splash–saltation due to wind-driven rain could therefore be referred to as rainsplash–saltation.
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MATERIALS AND METHODS
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Experimental Set-Up
All experiments were performed under laboratory conditions in the wind tunnel of the International Center for Eremology (I.C.E.), Ghent University, Belgium. This closed-circuit blowing-type wind tunnel has a 12-m long, 1.2-m wide, and 3.2-m high test section in which a rainfall simulator is installed (Gabriels et al., 1997). Three pressurized nozzles were used producing raindrops with sizes between 1.53 and 1.63 mm (Erpul et al., 1998).
The material used in this study was the same as used by Cornelis et al. (2004), which was very well-sorted dune sand with a geometric particle diameter of 250 µm. The sand was placed in a 0.95 by 0.40 by 0.05 m tray located at a distance x = 6.45 m downwind from the entrance of the wind-tunnel working section along its centerline (see Fig. 1)
. The tray was perforated at its bottom to allow drainage. The sample surface was smoothed and leveled to the test section false floor by drawing a straight edge across the sand surface. The tunnel floor, windward of the roughness elements, was covered with commercial emery paper with a roughness length similar to that of the sediment. The tray and the tunnel floor had a 0% slope. In case of the wind-driven rain experiments, the samples were prewetted before they were exposed to the rain by spraying, so that the moisture content of the sand exceeded the critical moisture content above which particle entrainment induced by aerodynamic forces does not occur (Cornelis et al., 2003). Consequently, there was no wind-induced particle entrainment at the very beginning of the experiment before the rain wetted the sample surface completely. In the case of the rainless wind experiments, air-dried sand material was used.
The duration time of the wind-driven rain runs was 30 min, and a few seconds after the fan of the wind tunnel that generates the wind was turned on the rainfall simulator was started. The run time of the rainless wind experiments was reduced to 20 min at medium wind shear velocity and to 2 min at the highest wind shear velocity to prevent considerable lowering of the soil surface level in the sample tray. In both the wind-driven rain and the rainless wind experiments, the horizontal flux was measured with an array of four W&C catchers (Wilson and Cooke, 1980), which were slightly modified for the wind-driven rain experiments. The diameter of the inlet and outlet of the modified W&C catchers was 18 mm, which is somewhat larger than the conventional 8-mm wide W&C catchers that were used in the rainless wind experiments. The conventional catchers were not able to catch all rain-splashed sediment, as their inlet was too narrow. The array of W&C catchers was located at x = 7.3 m (see Fig. 1) and the catchers were mounted at heights of 0.03, 0.06, 0.10, and 0.18 m. After each run, the splashed and/or saltated material was washed out of the catchers into aluminum boxes using a water spray. The material was air dried on a heating plate. Each run was replicated thrice.
Since the catch efficiency of the W&C catchers was not 100%, the obtained horizontal mass flux values needed to be corrected. The catch efficiency of the W&C samplers was determined by relating the total amount of transport as determined from integration of the vertical deposition flux values from Cornelis et al. (2004) to the total amount of transport as collected by the W&C catchers. A single relation could be used for all the data, irrespective of the wind shear velocity, and the catch efficiency of the modified W&C catchers appeared to be about 60%. The catch efficiency of the conventional W&C catchers was 51%. A comparable efficiency (49%) has been reported by Sterk (1993) for conventional W&C catchers. Although catch efficiency is likely to decrease to some extent with height, all fluxes were corrected with a single correction term (Sterk and Raats, 1996).
It should be noted that the length of the sample tray, which was 0.95 m, was too short to develop an equilibrium flow of the sand flux and steady-state transport of the sand did not occur. Chepil and Milne (1939) suggested lag distances between 2 and 10 m. However, since the tunnel floor leeward of the sample tray was covered with a 1.65-m long strip of emery paper with the same roughness as the sand used in the experiments, the air-flow and the surface shear stress above the sand surface reached equilibrium conditions.
Determination of the Wind and Rain Erosivity Indexes
The aerodynamic and rainfall conditions were similar to those described in Cornelis et al. (2004). In brief, the boundary layer was 0.6 m thick and was developed by combining a spire array with 36 roughness elements (Cornelis, 2002). The wind shear velocity, which was used as the wind erosivity index in this study, was determined from wind velocity measurements with one 16-mm vane probe (Test, Lenzkirch, Germany), located upwind of the rainfall simulator above the boundary layer, using following empirical equation (Cornelis et al., 2004):
 | [1] |
where u* is the wind shear velocity (m s–1) and uref is the reference wind velocity (m s–1). The u* values used to deduce Eq. [1] were obtained from profiles of wind velocity measured above the sand surface at 12 heights below the boundary layer and using a least-squares fit to the well-known Prandtl–von Kármán logarithmic law. Equation [1] was set up under rainless conditions.
Kinetic energy KE and momentum M, which are the rain erosivity parameters used to model the sediment transport rate in this study, were determined with splash cups, first introduced by Ellison (1947). The mass of sand removed from the cups was related to the erosivity parameter by applying a calibration curve. It was established by correlating the amount of sand that was removed from splash cups to the erosivity of drops vertically falling from a constant height under windless conditions, where the fall velocity was determined from the nomograph of Laws (1941). The previously obtained momentum and kinetic energy are their normal components, rather than their true values exerted by the inclined raindrops. Use of the normal component of erosivity is justified, as it is the normal component of the impact velocity that is responsible for detachment of soil particles by rainsplash (Ellison, 1947; Springer, 1976; Erpul, 2001). The cups were filled with 200- to 500-µm sized prewetted uniform dune sand. The obtained calibration curves were (Cornelis et al., 2004):
 | [2] |
and
 | [3] |
where KEz (J m–2 s–1) and Mz (kg m–1 s–2) are the normal components of respectively kinetic energy and momentum per unit of surface area and unit of time, and S is the mass of rainsplash per unit of surface area per unit of time (kg m–2 s–1). The intercept is actually equal to the threshold Ez needed to initiate the detachment or rainsplash process Ezt, and the slope parameter accounts for the soil-dependent detachability.
Data Analysis
The horizontal flux q was determined by weighing the collected sediment after it was dried on a heating plate. The mass values were divided by the inlet area of the W&C catcher and the duration of each test run. Equations were then fitted to the horizontal flux data as a function of the height above the sand surface.
The sediment transport rate Q (kg m–1 s–1) was calculated from integration of the horizontal flux q (kg m–2 s–1):
 | [4] |
where z is the height above the sand surface (m), and zmax is the maximum height of rainsplash–saltation above the sand surface (m).
All best-fitting procedures were performed by applying least-squares regression. In the case of nonlinear models this was done by means of the quasi-Newton algorithm (Press et al., 1992).
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RESULTS AND DISCUSSION
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Horizontal Flux
The variation of transport flux q with height z above the sand surface for different wind shear velocities u* and kinetic energies KEz (or momentum Mz) is illustrated in Fig. 2a through 2c
for the wind-driven rain case and in Fig. 2d for the rainless wind case. For saltation of sand under rainless conditions, a single exponential equation is generally accepted (Horikawa and Shen, 1960; Williams, 1964; Nalpanis, 1985; Fryrear and Saleh, 1993; van Dijk et al., 1996). A similar equation was fitted to our q vs. z data:
 | [5] |
where a and b are regression coefficients. It appeared that Eq. [5] is valid for wind-driven rain conditions as well. This means that most of the particles that are lifted off due to raindrop impact are splashed over a limited height. The results of fitting this equation and the R2 values are presented in Table 1. In Table 1, the highest standard deviation 
max that was observed for the four horizontal flux values is given as well. This parameter is an indication for the degree of replicability of the experiments, which were conducted in three replicates.
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Fig. 2. Horizontal mass flux q vs. height above the surface z for different combinations of wind shear velocity u* and kinetic energy KEz. The symbols denote the observations.
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Table 1. Best-fitted values of the regression coefficients from Eq. [5], max, and R2 at different wind shear velocities u* and different kinetic energies KEz or momentum Mz.
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The role of u* was not very clear, apart from its strong effect on KEz (or Mz). The b coefficient of Eq. [5] remained more or less constant with increasing KEz or u* and no trend could be observed (see Table 1). This means that at each height, the flux is increasing with a more or less constant factor as KEz increases. This is in contrast with the observations made under rainless wind conditions. In the latter case, b decreases with increasing destabilizing force, which is expressed in terms of u*. This in agreement with findings of Spaan et al. (1991), although Williams (1964) reported that particle shape plays a much more consistent role in changing b than does u*. According to Williams (1964), the average of b at different wind shear velocity for a given particle shape and type is a reasonably good estimate.
When comparing wind-driven rain conditions with rainless wind conditions, the mean of the exponent b is about a factor 2 larger for the rainless wind case (see Table 1). This means that relatively speaking much more sediment will be transported at lower heights in the rainless case, or in other words, the mass distribution of sediment with height is more homogeneous in the case of wind-driven rain. The decay coefficients observed under wind-driven rain are somewhat lower than those reported by van Dijk et al. (1996) who measured vertical mass fluxes of fine beach sand over wet surfaces.
Mass Transport Rates
In Fig. 3
, the sediment transport rate values computed for the wind-driven rain case by combining Eq. [4] with Eq. [5] are plotted against a factor accounting for the effect of kinetic energy or momentum of the rain and the shear velocity of the wind. Based on wind-tunnel experiments in which vertical deposition fluxes were measured, Cornelis et al. (2003b) found that Q was related to KE or M and u* as:
 | [6] |
and
 | [7] |
Equations [6] and [7] are plotted in Fig. 3 as well and it can be seen that the observations follow the models proposed by Cornelis et al. (2004) very well. The good agreement is also well illustrated in the scatter plot shown in Fig. 4
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Figure 5
shows the sediment transport rate values for the wind-driven rain case as a function of different values of a factor accounting for the effect of the shear velocity of the wind. Cornelis et al. (2004) found from wind-tunnel experiments in which vertical deposition fluxes were measured that Q was related to u* as:
 | [8] |
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Fig. 5. The sediment transport rate Q vs. the wind shear velocity u*. The data are derived from rainless wind experiments.
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Again, the observed data seem to agree rather well with the proposed model which is illustrated in Fig. 4.
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CONCLUSIONS
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The horizontal transport of sand particles under both wind-driven rain and rainless wind conditions was well described by a single exponential function relating horizontal mass flux with height above the surface. Under both wind-driven rain and rainless wind conditions, the exponent in the flux-height relationship was more or less constant, which implies that the distribution of the flux with height is independent of the kinetic energy or the momentum of the rain and the wind shear velocity. However, under wind-driven rain the exponent was about twice as low than under rainless wind. This means that relatively much more sediment will be transported at lower heights in the rainless case, or in other words, the mass distribution of sediment with height is more homogeneous in the case of wind-driven rain.
Integration of the horizontal mass flux over height resulted in observed sediment transport rate values that were compared with values predicted with the models of Cornelis et al. (2004) for wind-driven rain and rainless wind conditions respectively. Given that these models were deduced from a set of measurements that were based on measuring a different erosion parameter, that is, vertical deposition flux instead of horizontal flux, very good agreement was observed between observed and predicted sediment transport rates. This suggests that the respective models of Cornelis et al. (2004) adequately describe the sediment transport rate of sand under wind-driven rain and rainless wind conditions.
It further shows that the methodology that is usually applied to determine the sediment transport rate under rainless wind, that is, integration of an exponential horizontal mass flux-height relationship, can also be extended to wind-driven rain conditions. However, if Wilson and Cooke (1980) catchers are used in wind-driven rain experiments, the inlet and outlet should be widened compared with the conventional Wilson and Cooke (1980) catchers used under rainless wind.
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NOTES
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Mention of company names is for the convenience of the reader and does not constitute any endorsement in whatever sense from the authors.
Received for publication June 11, 2002.
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REFERENCES
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ABSTRACT
INTRODUCTION
