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Published in Soil Sci. Soc. Am. J. 68:32-40 (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

Vertical Deposition Flux and Sediment Transport Rate

Wim M. Cornelis*, Greet Oltenfreiter, Donald Gabriels and Roger Hartmann

Ghent University, Dep. Soil Management and Soil Care, Ghent Univ., Coupure links 653, B-9000 Ghent, Belgium

* Corresponding author (wim.cornelis{at}UGent.be).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 RELEVANT SEDIMENT TRANSPORT RATE...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Although transport of sediment under wind-driven rains is generally not accounted for in equations for sediment transport by wind, the contribution of this rainsplash–saltation process can be substantial. Wind-tunnel experiments, in which vertical deposition fluxes were measured at 23 distances from a sand tray, were conducted to study sediment transport under wind-driven rain and rainless wind conditions. It was shown that the vertical deposition flux could be described by a double exponential equation. By integration of the vertical deposition flux over the distance of deposition, the sediment transport rate was computed. A power-law function including both the normal component of the kinetic energy or momentum of the raindrops and the wind shear velocity was presented. However, including the wind shear velocity in the equation increased the model performance only slightly. When comparing the sediment transport rates as determined under the wind-driven rain events with those that were observed when rain was absent, it was shown that in the latter case, the transport rate is much higher at high wind shear velocities. However, at low wind shear velocities and moisture conditions where no motion is predicted by aeolian equations, saltation due to rainsplash is likely to occur and can be predicted with the presented model.


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
RELEVANT SEDIMENT TRANSPORT RATE...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
AN UNDERSTANDING of sediment transport systems is indispensable to predict the on site and off site effects associated with wind erosion. This is not only important for soil conservation and land use studies related to agricultural, ecological, coastal, and environmental issues, but also for modern geomorphology. Many attempts to investigate sediment transport as induced by wind have been reported in literature. 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). Most of this research was, however, performed under rainless conditions above a dry surface. Apart from these wind erosion studies on sediment transport, rainsplash erosion under windless conditions has been investigated in a substantial amount of studies as well (see e.g., Poesen, 1985).

Until now, very little research has been performed on the confluence of water and wind erosion, and more in particular to study the effect of rain on the transport of sediment by wind. 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. It was assumed that this was due 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). This phenomenon was referred to as splash–saltation (de Lima et al., 1992). However, they did not attempt to model the mass transport rate of sediment during wind-driven rains as a function of the lift-off and transporting agents. Soil detachment as induced by the energy of wind-driven raindrops was further studied by Disrud and Krauss (1971), Lyles (1977), and Pedersen and Hasholt (1995). Transport of raindrop-detached soil particles with wind above surfaces with different slopes was reported by Moeyersons (1983), Moss and Green (1983), Moss (1988), Gabriels et al. (1998), and Erpul et al. (2002)(2003).

The objective of this paper was to investigate the combined effects of rain and wind on the detachment and transport of sand. This was achieved by conducting experiments in a wind tunnel with rainfall-simulation facility in which detachment of sand was induced from a source zone and vertical deposition fluxes of the detached sand were measured. Hence, the study focuses on the smallest and earliest space and time scale subprocess elements of erosion, detachment, and subsequent transport and deposition, rather than on the overall soil loss from a given area. The experiments were performed under different kinetic energies or momentum 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 vertical deposition flux measured throughout the experiments is defined here as the mass of particles that settle down at a given distance from the source of detachment per unit of area at the horizontal plane within a time unit. An expression is presented to describe the vertical deposition flux as a function of the distance from the source of rainsplash. By integrating the vertical deposition flux over the distance of deposition, the sediment transport rate was computed for different wind and rain erosivity values. 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. The obtained data set was used to deduce a sediment transport rate model applicable for wind-driven rain and rainless wind conditions. There is a need for such models to predict the total erosion budget over a given period, since rainsplash processes can move sediments in conditions where no motion is predicted by transport rate models traditionally used in wind erosion research, and since transport rates can be substantial during severe storms (Sherman and Hotta, 1990). Notwithstanding this, the sediment transport due to wind-driven rainsplash is generally of secondary importance.

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.


   RELEVANT SEDIMENT TRANSPORT RATE EQUATIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 RELEVANT SEDIMENT TRANSPORT RATE...
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Detachment of Sediment Due to Raindrop Impact
Detachment of soil particles by raindrops is traditionally represented by relating the mass or rate of soil detached by raindrop impact D to an erosivity parameter E by a nonlinear function of the form (Meyer, 1981):

[1]
where Kd is a soil-dependent detachability coefficient and b is an exponent dependent on soil properties. The erosivity parameter E can be expressed in terms of the impact force of a single drop (Ghadiri and Payne, 1977, 1981; Nearing and Bradford, 1985; Nearing et al., 1986), its kinetic energy KE (Al-Durrah and Bradford, 1981, 1982; Morgan, 1985; Sharma and Gupta, 1989; Sharma et al., 1991, 1993), its momentum M (Park et al., 1983; Riezebos and Epema, 1985), and rainfall intensity I (Rose et al., 1983; Govers, 1991). Salles and Poesen (2000) found drop size times momentum to have the highest correlation with D. To account for the threshold kinetic energy or threshold momentum needed to initiate the detachment process, Sharma and Gupta (1989) modified Eq. [1] to:

[2]
where Et is the threshold KE or M.

Transport of Sediment Due to Wind
Transport, and more in particular saltation, of particles under the influence of wind is most often expressed as a function of the wind velocity u or the wind shear velocity u*. Bagnold (1941) presented a third-power relationship to predict the sediment transport rate Q (kg m–1 s–1) as a function of u* (m s–1):

[3]
where C is a proportionality constant accounting for fluid density, gravitational acceleration, and the degree of sorting of the particles (kg m–4 s2). As Eq. [3] tends to zero when u* approaches zero only, a variety of equations which include a threshold wind shear velocity u*t, below which the transport rate is zero, has been reported. A review is given in Greeley and Iversen (1985) and Shao (2000). These equations are in general of the following form:

[4]
where c and c' are two coefficients the sum of which is equal to 3 and c ≥ 1; hence, the transport rate remains a function of the third power of a wind-shear velocity related parameter. However, the exponent 3 as derived by Bagnold is based on the arbitrary assumption that the initial velocity of ejection is linearly proportional to u*. This is in contrast with findings of Ungar and Haff (1987) who found the initial ejection velocity to be constant.

Detachment and Transport of Sediment Due to Wind-Driven Rain
When modeling sediment transport rates under wind-driven rain circumstances, relationships such as Eq. [2] and [4] should be combined. In general, a transport rate model that needs to be applicable under wind and/or rain, should be of the following form:

[5]
where Q' is the transport rate irrespective of whether wind and/or rain occurs, Qr is the transport rate in the case of windless rain events, Qwr is the transport rate in the case of wind-driven rain conditions, and Qw is the transport rate due to rainless wind. The windless rain transport rate can be calculated from equations similar to Eq. [2], the rainless wind transport from Eq. [4], whereas wind-driven rain transport should be predicted from an equation that will be presented in this study. Under windless conditions, transport of particles will occur when Et is exceeded (Q' = Qr). In the case that rain is not accompanied by wind, Q' = Qwr, and Qw = 0 since u*t will not be exceeded. If rain ceases, transport will still occur if u* > u*t.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 RELEVANT SEDIMENT TRANSPORT RATE...
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Experimental Set-up
All experiments were performed under laboratory conditions in the wind tunnel of the International Center for Eremology, 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). The boundary layer in the test section was 0.60 m thick, which was obtained by combining a spire array located at the test section's entrance with a 4.8-m long zone of 36 roughness elements (Cornelis, 2002; see Fig. 1) . The rainfall-simulation facility used for the wind-driven rain experiments consists of one pipe fixed at the tunnel roof along the centerline of the test section. Pressurized nozzles were used rather than drop formers. Tap water was used with an electrical conductivity at 25°C of 0.7 dS m–1. Three operating nozzle pressures were applied. The raindrop sizes obtained under different operating pressures and wind velocities varied from 1.53 to 1.63 mm (Erpul et al., 1998).



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  		Fig. 1. Top view of the experimental set-up to determine the vertical deposition flux.

 
The material used in this study was very well sorted dune sand collected from the Belgian coast. Its geometric particle diameter was 250 µm. Calcium carbonate content was 3.34% and organic matter content was 0%. The electrical conductivity of the sand used was 0.72 dS m–1 at 25°C and the bulk density was 1.7 Mg m–3. The sand was placed in a 0.95 by 0.40 by 0.05 m tray which was 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. As a result, the moisture content of the sand exceeded the critical moisture content above which particle entrainment induced by aerodynamic forces does not occur. For u* = 0.50 m s–1, which is the highest wind shear velocity applied in this study, the moisture content of the test sand should be lower than 0.02 kg kg–1 for deflation to 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 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 vertical deposition flux was measured with an array of 23 troughs located downwind of the sample tray (see Fig. 1). The troughs were 0.14 m wide, 1.00 m long, and 0.07 m high. The centerline of the first trough was at 0.12 m from the sample tray to prevent direct wash out of the sediment from the tray into the trough. After each run, the splashed and/or saltated material was washed out of the troughs into aluminum boxes using a water spray. The material was air dried on a heating plate. Each run was replicated thrice.

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 airflow, and hence, the surface shear stress above the sand surface reached equilibrium conditions.

Shear Velocity of the Wind
Wind velocity uz was recorded electronically at a 1-Hz frequency with a 16-mm vane probe (Test, Lenzkirch, Germany), which was located upwind of the rainfall simulator above the boundary layer. Wind-velocity measurements were not influenced by raindrop impact. To convert this reference wind velocity to wind shear velocities above the sand surface, wind velocity was measured under rainless conditions above the sand at different heights with similar 16-mm vane probes. The sand was wetted to prevent sand transport. Saltating particles, as well as raindrops, carry part of the energy of motion of the fluid to sustain their own motion. The wind shear velocities as used in this study are therefore reference wind shear velocities valid for sediment-free and raindrop-free fluid motion, rather than the actual wind shear velocities during the experiments. Wind velocities that are measured in the field are, however, in most cases not influenced by particle motion (as they are measured at a large height) neither by raindrops (as the anemometers are too inert). The relation between the threshold wind shear velocity u* (m s–1) and the reference wind velocity uref (m s–1) was:

[6]

The shear velocity of the wind u* was determined from the mean of wind-velocity readings obtained at 12 different heights below the boundary layer using a least-squares fit to the well-known Prandtl-von Kármán logarithmic law:

[7]
where is the horizontal component of the mean wind velocity (of a 2-min period) (m s–1) at height z (m), {kappa} is the von Kármán constant ( = 0.4), and z0 is the roughness length (m). Note that the algorithm of Ling and Untersteiner (1974), which forces the profiles to converge into a single roughness length z0, was applied to determine u*. This is illustrated in Fig. 2 .



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  		Fig. 2. Vertical wind-velocity profiles measured at x = 6.0 m and y = 0.6 m at three different free-stream wind velocities u{delta}: wind velocity u as a function of height z. The symbols denote the observations.

 
Preliminary tests were performed to measure wind velocity within the rain. This was done with vane probes as well as pitot tubes. Both types of probes did not seem to be applicable for wind-velocity measurements during a rain event. Impact of raindrops has a mechanical effect on the vane probes in that it accelerates or decelerates the rotating vane, whereas in the case of pitot tubes, raindrops seem to block the openings for total-pressure and static-pressure measurements.

Rainfall Intensity
Rainfall intensity was measured in two replicates by exposing beakers with a height of 0.13 m and a diameter of 0.11 m to the rain for 5 min. The beakers were placed in the same plane as the surface of the sand.

The measured rainfall intensity I ranged from 44 to 103 mm h–1. In Fig. 3 , the measured rainfall intensity I is plotted against wind shear velocity u*. As could be expected, the measured intensity decreased with increasing wind shear velocity. This is to be attributed to the higher angle of inclination of the rain (Sharon, 1980; de Lima, 1990). Although the number of data is rather limited, a slight declination can be observed in the trend line at higher wind shear velocities. This can be explained by the smaller drop sizes that are associated with stronger winds and higher operating pressure on the nozzles (Erpul et al., 1998), and consequently, these lighter drops experience an additional sweep. The I (mm h–1) vs. u* (m s–1) data fitted to a power function of following form:

[8]
in which the coefficients are significant below the 0.005 level. The importance of Eq. [8] is that it illustrates the ‘error’ that can occur when measuring the rainfall intensity under wind-driven rains. The beakers used in our study were of limited size, and it is not sure whether the same relation will hold when using standardized pluviometers under field conditions. Nevertheless, the observations indicate that care should be taken when using rainfall intensity as an erosivity parameter. The measured rainfall intensity should be corrected for the angle of incidence of the raindrops, which depends on the wind shear velocity.



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  		Fig. 3. Measured rainfall intensity I vs. wind shear velocity u* at different operating pressures p on the nozzles. The symbols denote the observations.

 
Kinetic Energy and Momentum of the Raindrops
Since the experiments were conducted at different operating nozzle pressures and at different wind velocities, the fall velocity of the raindrops was unknown. Use of an optical spectro-fluviometer to determine the size and velocity of raindrops is limited to windless conditions, and can lead to severe underestimations when used in wind (Salles et al., 1998). Kinetic energy KE and momentum M, which are the rain erosivity parameters used to model the sediment transport rate in this study, were therefore determined empirically. Splash cups, first introduced by Ellison (1947), were used to determine KE and M during the different runs. Rain erosivity indexes that include drop diameter were not considered here, since the drop-size range varied from 1.53 to 1.63 mm only (Erpul et al., 1998), which is a rather narrow range.

Preliminary single-raindrop tests were executed with a Kinetic Energy of Rain Sensor from Sensit, Portland ND. As it was found that the device showed little replicability, it was omitted in this study. Kinetic energy was determined by means of the more conventional splash-cup technique (Ellison, 1947; Salles and Poesen, 2000; Salles et al., 2000). The cups were filled with 200- to 500-µm sized uniform dune sand. The diameter of the cups was 0.076 m and the height was 0.040 m. They were closed by means of a nylon cloth to allow drainage. After wetting the cups by capillary rise until saturation, they were exposed to rain for 15 min. The cups were then oven-dried at 105°C and the mass of rainsplash was calculated as the mass difference before the experiment and after oven drying. If the mass difference exceeded 16.6 g, which corresponded to a 2.21-mm reduction in height of the sand surface in the cup and hampering rainsplash, the correction equation as proposed by Hudson (1965) was applied:

[9]
where S is the mass of rainsplash per unit of surface area per unit of time (kg m–2 s–1), and S' is the difference in mass of the rainsplash cup before the experiment and after oven drying per unit of surface area per unit of time (kg m–2 s–1). The same procedure was applied during all the experiments performed in this study. Rainsplash was determined in three replicates by using three splash cups, ensuring that the spacing between the cups was large enough to avoid trapping of sediment that was splashed out of one of the other cups.

To convert the measured mass of rainsplash to kinetic energy or momentum, calibration curves were set up. This was performed by correlating the mass of sand that was removed from the splash cups to the kinetic energy or momentum of vertically falling drops under windless conditions (see Fig. 4) , where the fall velocity was determined from the nomograph of Laws (1941). This means that the obtained kinetic energy or momentum is not the true KE or M exerted by the inclined raindrops (with fall velocity vR, which is the resultant of the vertical and horizontal drop velocity vz and vx), but rather their normal components KEz or Mz (with drop velocity vz). For 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), we believe that using splash cups under wind-driven rain is an appropriate technique for KE or M determination, and that their components KEz and Mz are reliable parameters to predict rainsplash–saltation. Furthermore, the mass of sand that is splashed from the cups per unit of cup area and unit of time should be linearly related to the detachment rate of the material that is studied, with an intercept of 0 and a slope coefficient equal to unity if the material in the cups is equal to the material in the sample trays. This is in accordance with typical detachment equations relating detachment rate to KE–KEt or M–Mt, where t denotes the threshold value needed to initiate the detachment process (Sharma and Gupta, 1989). The applied calibration curves were:

[10]
and

[11]
where KEz (J m–2 s–1) and Mz (kg m–1 s–2) are the normal components respectively of kinetic energy and momentum per unit of surface area and unit of time. The intercept is equal to the threshold KE or M needed to initiate the detachment or rainsplash process KEzt or Mzt, and the slope parameter accounts for the soil-dependent detachability.



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  		Fig. 4. Kinetic energy KEz and momentum Mz of vertically falling raindrops vs. the mass of rainsplash S from splash cups.

 
Data Analysis
The vertical deposition flux q was determined by weighing the collected sediment after it was dried on a heating plate. The mass values were divided by the area of deposition per collecting trough (which was its width, 0.07 m, times the width of the sample tray, 0.04 m), and the duration of each test run. Equations were then fitted to the vertical deposition flux data as a function of the distance from the sample tray.

The sediment transport rate Q (kg m–1 s–1) was calculated from integration of the vertical deposition flux q (kg m–2 s–1):

[12]
where {Delta}x is the distance from the sample tray (m), and {Delta}xmax is the maximum distance of rainsplash–saltation from the sample tray (m).

All best-fitting procedures were performed by applying least-squares regression. In the case of non-linear models this was done by means of the quasi-Newton algorithm (Press et al., 1992).


   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 RELEVANT SEDIMENT TRANSPORT RATE...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Vertical Deposition Flux
Figure 5 shows the variation in vertical deposition flux q over the distance {Delta}x windward of the sand tray for different wind shear velocities u* and kinetic energies KEz (or momentum Mz) for the wind-driven rain case (Fig. 5a–c) and the rainless wind case (Fig. 5d). A double exponential function of the following form was fitted to the q vs. {Delta}x data:

[13]
where {alpha}, ß, {chi}, and {delta} are regression coefficients. Since the optimized coefficient values as determined from an iterative nonlinear least-squares procedure can depend on the initial estimates, the best-fit procedure was performed in two steps. First estimates of the coefficients {alpha} and ß were determined by fitting a single exponential curve to the first three data pairs (closest to the sample tray). To determine the first estimates of {chi} and {delta} the other data pairs were used. A similar procedure was followed by Fryrear and Saleh (1993) and Sterk and Raats (1996) in the case of a composed four-parameter model for the horizontal mass flux of wind-blown material. The finally obtained coefficient values and the R2 values are given in Table 1. In Table 1, the highest standard deviation {sigma}max that was observed for the 23 vertical deposition 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. 5. Vertical deposition flux q vs. distance from the sample tray {Delta}x 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. [13], {sigma}max, and R2 at different wind shear velocities u* and different kinetic energies KEz or momentum Mz.

 
A simple exponential equation as proposed by Savat and Poesen (1981) for windless conditions does not hold when considering the complete traveling length of the particles, but is only valid close to the sample tray. The particles that are splashed to a limited height above the soil surface, experience a relatively low impulse, as wind velocity is relatively low at low heights (see Eq. [7]). Hence, the impulse force the particles receive does not exceed particle weight, and as a result, the effect of the wind is minimal. Particles that are lifted by raindrop impact to greater heights encounter higher impulses, and their trajectory is substantially influenced by the wind velocity. This phenomenon explains why a second exponential term is needed when expressing the vertical deposition flux as a function of distance.

When considering the flux values at different wind shear velocities and kinetic energies (or momentum) in Table 1, it seems that the intercept {alpha} + {chi}, which is the vertical deposition flux at zero distance from the tray, increases with increasing KEz (or momentum Mz) as could be expected. Because u* and KEz act simultaneously, the effect of u* as such could not be clearly distinguished. When considering the exponent values ß and {delta}, the effect of the wind is more apparent. Both appear to decrease with increasing KEz, which implies that more particles are splashed to greater heights, and with increasing u*. Furthermore, as KEz and u* are increasing from their lowest to their highest value, {delta} is decreasing with a factor of five, whereas ß is only reduced with a factor of two. Since it is the second term in Eq. [13] that describes the vertical deposition flux at higher distances, this shows once more that the effect of the wind is highest on particles that splash into the zone of highest horizontal wind velocity. This could also indicate that the amount of splashed droplets containing a larger number of particles becomes heavier and increases as KEz increases.

With regard to the rainless wind-driven vertical deposition flux, the effect of an increasing wind shear velocity on both ß and {delta} is less pronounced (see Table 1). On the other hand, the intercept {alpha} + {chi} is clearly increasing with the wind shear velocity. This intercept determines to a high degree the deposition flux.

Sediment Transport Rates
Since the threshold shear velocity of the wind was never exceeded during the wind-driven rain experiments due to the wet sand surface, the observed transport of sediment is therefore likely to be determined primarily by the normal component of the rain erosivity index in those experiments. An equation similar to the detachment model of Sharma and Gupta (1989) (Eq. [2]), was therefore fitted to our experimental data:

[14]
where Kd and b are as in Eq. [1]. The results of fitting Eq. [14] to the transport rate data are compiled in Table 2. The high R2 values indicate that the rain erosivity explains to a high extent the observed variation. Note that the exponent b is very close to the value as observed by Sharma and Gupta (1989), who found b to converge to 1 for windless rain. Refitting Eq. [14] with b = 1, reduced R2 only slightly. To explore whether u* had an additional effect on Q, apart from its influence on the impact velocity of the raindrops, Q was also expressed as a function of both Ez and u*, by using following model with an equal number of parameters as Eq. [14]:

[15]
where c is a wind-power function depending on the soil properties. The results of fitting Eq. [15] to the observed data are presented in Table 2 as well. Including the wind shear velocity u* into the transport rate model, resulted in a somewhat higher model performance (R2 = 0.956), although the exponent c appears not to be significant at the 0.05 level. To examine the model performance graphically, the behavior of Eq. [15] is illustrated in Fig. 6 . The linearized relationship for a wide range of kinetic energies or momentum and wind shear velocities suggests that Eq. [15] adequately describes the transport rate of sand particles under wind-driven rain conditions.


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  		Table 2. Coefficient values of Eq. [14] and [15] where the erosivity index is the normal component of kinetic energy KEz or momentum Mz.{dagger}

 


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  		Fig. 6. The sediment transport rate Q vs. the scaling factor of Eq. [15]. The data are derived from wind-driven rain experiments.

 
As was expected, the effect of the wind shear velocity on the sediment transport rate apart from its influence on kinetic energy or momentum is rather limited. Wind as such cannot detach the sand particles, because the sand surface is too wet and the threshold wind shear velocity for deflation is not exceeded under rainy conditions. The additional effect of wind that can be observed, however, could be due to an extra bombardment of the sand surface by rainsplash–saltating particles, which are entrained in the droplets. As the erosivity of the raindrops increases, the number of particles that are transported per raindrop increases drastically. This is illustrated in Fig. 7 , showing that rainsplash–saltating particles are entrained into splash droplets, and that the number of entrained particles within one droplet, and hence the droplet weight, increases with increasing kinetic energy or momentum. Since an increase of erosivity is, in our study, mainly associated with an increase in wind shear velocity, the impact energy or momentum of a splash droplet will rise accordingly. On the other hand, this phenomenon will be hampered to some extent as the impact angle of the droplets decreases with increasing wind velocity. Furthermore, in sediment-laden flow, part of the energy of motion of the fluid is carried by the grains to sustain their movement. As a result, the shear stress exerted by the wind will be reduced somewhat. Another effect of the wind could be an increase in the transport capacity. As the wind velocity increases, the above-described process will be accelerated. The above observations suggest that wind has an additional effect on transport of particles under wind-driven rains. However, the error caused by discarding the wind shear velocity or using Eq. [14] will be limited, as long as the normal component of kinetic energy or momentum is taken into account.



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  		Fig. 7. Splash droplets with entrapped sand grains as trapped on vaseline-rubbed glass plates when u* was (a) 0.27 m s–1, (b) 0.39 m s–1, and (c) 0.50 m s–1.

 
For the data obtained from the rainless wind experiments, best fits were obtained with following model (see Fig. 8) :

[16]
where Q was calculated similarly as for the wind-driven rain data. The threshold shear velocity u*t was 0.30 m s–1. The ‘new’ form of Eq. [16] as compared with Eq. [4] illustrates once more the difficulty of establishing an appropriate model to fit to transport rate data. This was also concluded by Greeley and Iversen (1985) when reviewing the wide variety of equations that are reported in literature.



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  		Fig. 8. The sediment transport rate Q vs. the wind shear velocity u*. The data are derived from rainless wind experiments.

 
When comparing the transport rates as observed under wind-driven rain circumstances with those from the rainless experiments, the much higher transport rates at high wind velocities above a dry surface when rain is absent are notable. At wind velocities close to the deflation threshold, transport rates are lower than those as induced by wind-driven raindrop impact, even if the wind shear velocities under wind-driven rain conditions were lower than the dry deflation threshold. However, the transport rates that are observed during wind-driven rain events remain relatively low. The highest transport rate observed in this study under wind-driven rain was 2.4 g m–1 s–1, which occurred at KEz = 0.6 J m–2 s–1 and u* = 0.50 m s–1. Applying Eq. [16] for dry conditions, the same transport rate would take place at u* = 0.37 m s–1. On the other hand, when the sand surface is too wet for deflation to occur, movement of sediment can occur once a rainfall event starts. Similarly, when the rain event stops, particle transport will cease, as has been observed on beaches by van Dijk et al. (1996).


   CONCLUSIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 RELEVANT SEDIMENT TRANSPORT RATE...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
The measured rainfall intensity of the wind-driven rain as generated by the rainfall simulator was to a very high degree correlated to the shear velocity of the wind, due to the increasing angle of inclination with increasing wind velocity. Although it was not tested whether the proposed relationship between measured rainfall intensity and the wind shear velocity is valid when using standardized pluviometers under field conditions, care should be taken when using rainfall intensity as an erosivity factor. The effect of the operating pressure on the rainfall-simulator nozzles or the drop size was minimal.

The vertical deposition of sand particles, which are transported under wind-driven rain and rainless wind conditions, was well described by a double exponential function relating the vertical deposition flux to the distance from the source of rainsplash–saltation. The second exponential term needed to be introduced to account for the longer trajectories of particles that are lifted off to greater heights. The higher uplift of particles occurs at higher kinetic energies or momentum of the raindrops in the case of wind-driven rain conditions. These particles encounter an additional effect of the wind, the velocity of which increases with height. This additional effect becomes more pronounced with increasing wind shear velocity, which was reflected in a pronounced decrease of the exponent in the second term. In case of rainless wind conditions, saltation height increases with increasing shear velocity of the wind, and a similar but less pronounced effect was observed.

The transport rate of rainsplash–saltating particles in the wind-driven rain experiments was to a high degree affected by the vertical component of the kinetic energy or the momentum of the raindrops. The wind as such is not able to detach particles from the surface, due to the high threshold wind shear velocity associated with the higher surface moisture content that exists under rainfall events. However, the wind shear velocity could play an additional role as it can induce extra bombardment of the sand surface by rainsplash–saltating particles entrained in the droplets. This implies that impacting droplets exert additional impact energy. Furthermore, wind can increase the transport capacity, accelerating the rainsplash process. The observed variation in transport rate was to a very high degree predicted by a non-linear function of kinetic energy or momentum and wind shear velocity. Notwithstanding this, consideration of kinetic energy or momentum only, will not result in a substantial prediction error as long as the normal component of erosivity is accounted for.

In the absence of rain, the sediment transport rate was much lower at wind shear velocities close to the deflation threshold compared with the sediment transport rates determined from the wind-driven rain experiments at similar shear velocities. However, as wind shear velocity increased, the increase in transport rate was much more pronounced, compared with transport under wind-driven rain. This implies that when predicting transport of particles in general, not accounting for the transport that occurs during rainy periods will only result in minor errors, in the case that heavy winds occur frequently. When heavy winds are not expected to take place regularly, the contribution of rainsplash–saltation in the total soil loss budget will be considerable.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 RELEVANT SEDIMENT TRANSPORT RATE...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
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.


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 RELEVANT SEDIMENT TRANSPORT RATE...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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