Effect of soil crusting on the emission and transport of wind-eroded sediment: field measurements on loamy sandy soil

Effect of soil crusting on the emission and transport of wind-eroded sediment: field measurements on loamy sandy soil

Geomorphology 58 (2004) 145 – 160 www.elsevier.com/locate/geomorph Effect of soil crusting on the emission and transport of wind-eroded sediment: fie...

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Geomorphology 58 (2004) 145 – 160 www.elsevier.com/locate/geomorph

Effect of soil crusting on the emission and transport of wind-eroded sediment: field measurements on loamy sandy soil Dirk Goossens * Erosion and Soil and Water Conservation Group, Wageningen University and Research Centre, Nieuwe Kanaal 11, NL-6709 PA Wageningen, Netherlands Laboratory for Experimental Geomorphology, Katholieke Universiteit Leuven, Redingenstraat 16 bis, B-3000 Leuven, Belgium Received 29 June 2002; received in revised form 21 April 2003; accepted 9 May 2003

Abstract Field data are reported for the horizontal and vertical flux of wind-eroded sediment on an agricultural field in northern Germany. Measurements were made during a windstorm that hit the region on 18 May 1999. The magnitude of both fluxes was significantly affected by the presence of a surface crust covering the test field. Measuring the physical crust strength at 45 locations with a torvane, the relationships between crust strength (s) and the horizontal ( Fh) and vertical ( Fv) sediment fluxes were investigated. Both fluxes decreased as the surface crust became stronger. The decay behaved as an exponential function for both types of flux. The horizontal sediment flux over a crusted surface can be accurately predicted by completing Marticorena and Bergametti’s [Journal of Geophysical Research 100 (1995) 16415] erosion model with a crust function. The vertical particle flux over crusted soil can be calculated by adding a similar function to Alfaro and Gomes’s [Journal of Geophysical Research 106D (2001) 18075] dust production model. The study also suggests that the gradual bombardment of a surface crust by impacting particles does not immediately result in a decay of the crust’s protective effect, provided that the crust has a minimum thickness. However, once the crust becomes perforated, its protective effect disappears very quickly, leading to much higher horizontal and vertical sediment fluxes than predicted for undamaged crusted soil. D 2003 Elsevier B.V. All rights reserved. Keywords: Horizontal sediment flux; Vertical sediment flux; Surface crust; Crust strength; Wind erosion

1. Introduction Crusts are a major structural feature of surface soils and sediments (Guthrie, 1982). This is especially true in the arid and semiarid regions, but also in agricul* Laboratorium voor Experimentele Geomorphologie, Katholieke Universiteit Leuven, Redingenstraat 16 bis, 3000 Leuven, Belgium. Tel.: +32-16-32-64-36; fax: +32-16-32-64-00. E-mail address: [email protected] (D. Goossens). 0169-555X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0169-555X(03)00229-0

tural areas in moderate climates. It is well known that soil crusting is a significant factor in the susceptibility of surface particles to be entrained by wind (Lyons et al., 1998). The presence of a crusted surface layer significantly reduces the amount of material eroded by the wind compared to surfaces consisting of unconsolidated material (Gillette et al., 1982; Zobeck, 1991a,b; Rice and McEwan, 2001). The fine particle fraction of the soil plays a very important role in the process of crust formation. Particles smaller than 50 – 60 Am usually act as

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‘‘cement’’ between larger particles. Any increase in the fine particle soil content is likely to increase the cohesion of the topsoil, leading to an increase of the crust strength (Diouf et al., 1990; Skidmore and Layton, 1992). As pointed out by Smalley (1970), the cohesion between soil particles is a major factor in their erodibility. Two major types of soil crust occur in the natural environment: physical crusts and biological crusts. Crusts of the first type form as moisture evaporates from a soil. A high content in clay, sodium salt and/or calcium carbonates enhances the formation of such crusts (Gillette et al., 1980, 1982). Biological crusts (also known as microphytic, microbiotic or cryptogamic crusts), on the other hand, form as algal filaments, bryophytes, cyanobacteria and fungal mycelia intermesh with the soil particles, thereby creating a resistant layer. Organic secretions, such as polysaccharides and mucilage, may provide extra ‘‘cement’’ in such crusts (McKenna Neuman et al., 1996; McKenna Neuman and Maxwell, 1999; Rice and McEwan, 2001). With respect to wind erosion, the exact type of crust (physical or biological) is not the dominant factor; it is mainly the strength of the crust that is important. There are a few distinctions that deserve attention, however. First, physical crusts form much faster than biological crusts. A few days, or even a few hours, may be sufficient to create a strong physical crust. The development of a biological crust requires much more time, ranging from several months to several years (see Belnap and Gillette, 1998). This is important for wind erosion, because crusts of the former type provide an adequate protection against wind shortly after the evaporation of the top layer has started. Biological crusts, on the other hand, may be more durable than physical crusts. Local damage caused by, for example, impacting grains does not necessarily lead to a complete breakdown of the crust’s protection against wind erosion. In the case of physical crusts, weak bonds between the surface grains may be easily broken by such bombardment of saltating grains (Rice et al., 1999). As cohesion is reduced, the surface material becomes more susceptible to entrainment (Rice and McEwan, 2001). However, biological crusts are also susceptible to rupture by particle impact (McKenna Neuman et al., 1996), although in many of such crusts, the surface particles are well bonded by the biotic

elements. Surface strength, though, is normally lower for biological crusts than for physical crusts (Rice and McEwan, 2001). Various methods have been used to quantify the role surface crusts play in the reduction of wind erosion. Indirect techniques have been applied, such as describing (in quantitative terms) the soil’s type and composition (Rice and McEwan, 2001) or using the percentage of clay in the soil to develop a soil crust factor to be included in existing wind erosion models (Fryrear et al., 1996; Fryrear, 1998). Direct techniques, on the other hand, focus on the measurement of the physical strength of the crust. Various methods for measuring crust or aggregate strength have been adopted: the modulus of rupture test (Richards, 1953), aggregate stability tests (Skidmore and Powers, 1982), penetration tests using needle penetrometers (Bengough and Mullins, 1990) or fall cone or cone penetrometers (Bradford and Grossman, 1982; Campbell and O’Sullivan, 1991), torvane measurements (Govers and Poesen, 1986), the use of soil crushing energy meters (Skidmore and Powers, 1982; Boyd et al., 1983; Hagen et al., 1995). However, several of these techniques are not really applicable in the field (i.e., to undisturbed samples), which puts severe constraints on their usefulness when investigating natural crusts. Various studies on the relationships between surface crusting and wind erosion have appeared in the last few years. Fryrear et al. (1996) and Fryrear (1998) introduced a soil crust factor to be included in physical wind erosion models. Leys and Eldridge (1998) examined the effect of biological crust disturbance on wind erosion of sand and loam rangeland soils. McKenna Neuman et al. (1996) and McKenna Neuman and Maxwell (1999) investigated the effect of biological crusts on aeolian sediment transport. Rice et al. (1996, 1997, 1999) explored the relationship between crust strength, saltating particles and initial rates of erosion. Offer and Goossens (2001) studied the effects surface crusts exert on aeolian dust dynamics in arid regions. Nickling (1984) investigated the stabilizing role of soluble salts in soil crusts exposed to the wind. Chepil (1953, 1958), Gillette et al. (1980, 1982), Hagen (1984), Zobeck (1991a,b), Williams et al. (1995) and Belnap and Gillette (1997, 1998) have published other important studies on soil crusts and wind erosion.

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Despite the extended list given above, few studies directly quantify the effects soil crusts exert on the wind-induced emission (and subsequent transportation) of soil particles in the field. Field measurements are very important because any simulation executed under laboratory conditions (for example, wind tunnel tests) necessarily implies a simplification of the environmental conditions. In the study presented here, field data relating to the vertical and horizontal transportation fluxes of soil particles eroded from an agricultural field in northern Germany are studied as a function of the strength of the surface crust occurring in the field during the windstorm. The aim of the study is twofold: one aim is to quantify the relationship between crust strength and the emission and transportation of the eroded sediment, and the second is to incorporate crust strength, as a numerical parameter, in a numerical wind erosion model developed recently for European soils. In many current wind erosion models, soil crusting remains an insufficiently known parameter (Lyons et al., 1998; Potter et al., 1998). This paper aims to provide more information on how to fill this gap.

2. Test field, methods and instrumentation 2.1. Situation and description of the test field The measurements were made on an agricultural field in Gro¨nheim, Lower Saxony, Germany, about 14 km west of the town of Cloppenburg (Fig. 1). The size of the field is approximately 320  230 m. The landscape in this part of Germany is nearly flat, with a slightly undulating microtopography of slopes usually < 2% (Fig. 2A). The northern and southern parts of the field have a relief of only a few decimeters. Small valleys approximately 1.5 m deep occur in the northwestern and southeastern corners of the field. In general, the test field is situated at approximately 34 m above sea level. Characteristics of the topsoil (upper 5 cm) are given in Fig. 2B – D. Parameters shown in the figure were measured at 45 sites, marked in Fig. 2A. Fig. 3 shows that the topsoil is predominantly sandy; silt and clay nearly always total >15% and reach >20% in the northern half of the field. The sand is very fine

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Fig. 1. Situation of the Gro¨nheim site.

(median diameter around 125 Am) and well sorted. It is mainly of fluvioglacial origin. In the southern part of the field, and particularly in the southern corner, very small (2– 5 mm) rock fragments occur in the sand; their cover percentage is < 1%. Large, erratic granite boulders are found all over the field, but the farmers have removed most of them from the land. Organic matter content in the topsoil is between 1% and 6% (Fig. 2D). The highest values are near the southern and western corners. Average annual rainfall at Gro¨nheim is 750 mm. There are no especially dry or wet periods in the year, although the wettest months are normally in summer (July, August). The episodes of wind erosion are normally in spring (April –June) and autumn (October – November), when the fields have been tilled and protective vegetation is absent or very sparse. The dominant wind directions during wind erosion events are NW and E. 2.2. Horizontal and vertical sediment flux models used in this study 2.2.1. Horizontal sediment flux The horizontal flux of the emitted soil particles was calculated using a theoretical model developed by

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Fig. 2. Characteristics of the test field. (A) Topographical map showing the 45 test plots; (B) median particle diameter D50; (C) mass percentage of the silt + clay fraction; (D) mass percentage of organic matter.

Marticorena and Bergametti (1995), denoted below as MB95. From a relatively simple description of the soil characteristics and of the wind conditions, MB95 allows determination of the emission source locations and a calculation of the horizontal flux ( Fh) of the airborne soil particles (aggregates as well as individual grains). The model makes it possible to calculate Fh for individual grain-size classes. Summing up Fh for all classes, the total horizontal sediment flux can also be calculated. The input parameters for MB95 are 1. A description of the size distribution of the soil’s erodible fraction. It is assumed that the erodible particles can be granulometrically sorted into three lognormally distributed modes (or populations). The description is then quantified by means of

three variables: the proportion of each population in the total sediment mass, the median diameter of each population and the geometric standard deviation of each population. These variables can be calculated by means of an iterative procedure based on a least square routine, where the results of a simple grain-size analysis of the topsoil serve as input parameters. 2. The particle (or aggregate) density of the soil (qp). 3. The aerodynamic roughness length of the surface (z0). 4. The friction velocity of the wind (u*). The output parameters of the model are 1. The mass size distribution of the transported particles.

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possible to calculate the vertical sediment flux Fv. The SA98 model is only applicable to the particle fraction < 20 Am (or PM20); the values of Fv calculated by the DPM thus refer to the PM20 fraction only. The calculation, by SA98, of a is based on the following steps. Analogous to MB95, it is first assumed that the aerosol particles released from the soil can be granulometrically sorted into three lognormally distributed modes (or populations). Next, the kinetic energy flux ( Fkin) of the saltating particles is calculated. Subsequently, the fraction Fi (of the kinetic energy flux) that is available to release particles from the ith aerosol mode is calculated. Then the binding energy ei, which is the kinetic energy necessary to release one particle of the ith aerosol mode, is determined via wind tunnel experiments. The ratio Fi/ei then gives the number of particles (of mode i) that are released from the soil. It is then possible to calculate the vertical flux Fvi of the particles of mode i: Fig. 3. Typical grain-size distribution curve for the Gro¨nheim topsoil.

2. The horizontal flux of the particles, for various grain-size classes. 3. The threshold friction velocity (deflation threshold). Summing up the horizontal fluxes for all grain-size classes, the total horizontal sediment flux Fh can be calculated. Fh is expressed in mass per unit length per time, for example, in g cm 1 s 1. For more information about MB95, see the original publication (Marticorena and Bergametti, 1995). 2.2.2. Vertical sediment flux The vertical flux of the soil particles at the surface was calculated using a theoretical dust production model developed by Alfaro and Gomes (2001), denoted below as DPM. The DPM combines MB95 with a sandblasting model developed by Alfaro et al. (1997, 1998), denoted below as SA98. The SA98 model calculates the sandblasting efficiency (a), which is defined as the ratio Fv/Fh, where Fv and Fh are the vertical and horizontal sediment fluxes. Since Fh can be calculated by MB95, it is

  Fi Fvi ¼ ðdi Þ 6 ei p

3

ð1Þ

whereby the particles are assumed spherical and di is the particle diameter. Summing Fvi for all three aerosol modes and dividing the sum through the horizontal sediment flux Fh (calculated via MB95) produces the sandblasting efficiency a. The input parameters for the DPM are identical to those of MB95, completed by the binding energy ei (which is determined by means of wind tunnel experiments). The output parameters of the DPM are 1. The sandblasting efficiency (a) 2. The grain-size distribution of the released aerosol particles 3. The threshold friction velocity (deflation threshold). Recall that Fv, as calculated by the DPM, only refers to the PM20 fraction of the emission (not to the total particle or aggregate emission). Fv is expressed in mass per unit surface per time, for example, in g cm 2 s 1. For more information about the DPM model, see the original paper by Alfaro and Gomes (2001).

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2.3. Instrumentation, field methods and field conditions 2.3.1. Instrumentation To measure the horizontal and vertical sediment fluxes, 45 sites, distributed fairly uniformly over the field (Fig. 2A), were selected from the topographical map. A vertical mast carrying a set of seven or eight sediment traps (Fig. 4) was erected at each site. The traps consisted of modified Wilson and Cooke (MWAC) bottles 9.4 cm long and 4.8 cm in diameter, with glass inlet and outlet tubes of inner diameter 0.75 cm. Further details are given by Goossens and Offer (2000). For the wind erosion event investigated, the efficiency of the trap was between 90% and 103% for the dust fraction and between 98% and 102% for the sand fraction (Goossens and Offer, 2000, Fig. 9; Goossens et al., 2000, Fig. 10). Thirty-three masts were 140 cm high and the remaining 12 were 240 cm high. The MWACs were installed at the following heights above the soil surface (values refer to the centre of the inlet tubes): 5, 12, 19, 26, 45, 70 and 100 cm. A further MWAC was attached to the 240-cm

masts at a height of 200 cm, but the amount of sediment collected by these upper MWACs was too small to be analysed, so the results refer only to the sediment flow up to 100 cm above the soil surface, and no distinction is made between the 140- and 240cm masts in Fig. 2A. The sediment caught by each MWAC was weighed to 0.001 g after the storm. During the windstorm investigated, a surface crust was present all over the test field. The strength of the crust was measured at each site with a torvane. This instrument measures the shear strength of the crust (see Govers and Poesen, 1986). Between five and seven measurements were made at each site, the values used later in this paper refer to the average of these measurements (but there was only a little variation within each plot). Wind speed and direction were measured from a meteorological tower located near Site 10 (Fig. 2A). Wind speed was measured with cup anemometers at heights of 1, 2, 5 and 10 m. Wind direction was measured at 10 m only. Wind data were recorded every 10 s and stored as 10 min averages. Maximum speed for each 10-min interval was also recorded. Using the WASP model (Troen and Petersen, 1990; Mortensen et al., 1993), wind speeds (u), wind profiles, friction velocities (u*) and roughness lengths (z0) were calculated for each plot. Average horizontal sediment flux and average sediment concentration during the storm were then calculated for each trap. 2.3.2. Calculation methods The vertical (upward) dust flux at the surface Fv was estimated by calculating the dust flux Fvz at each trap height z and extrapolating the flux curve to zero level. Fvz can be calculated from Fvz ¼ KA

Fig. 4. Mast with the modified Wilson and Cooke traps.

BC Bz

ð2Þ

where KA is the exchange coefficient for particles, C the airborne dust concentration and z the height (Sundborg, 1955). For particles of the order of 30 Am or less, KA can be replaced by KM, the eddy viscosity for momentum transport (Chamberlain, 1967). At wind speeds above 7 m s 1 (such as in the windstorm investigated here), the atmosphere may be considered thermally neutral and KM = ku*z, where k is von Karman’s constant, equal to 0.4. Substituting KA by KM in Eq. (2) and taking into account that for

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aeolian dust, C = azb (Nickling, 1978), where a and b are empirical constants, Fvz can be calculated as Fvz ¼ ku abzb *

ð3Þ

The horizontal sediment flux at height z, Fhz, is defined as the product of airborne particle concentration and wind velocity at height z. Airborne particle concentration was calculated as f  1GL 1, where f is the trap efficiency, G the amount of sediment caught by the trap and L the air volume passing through the trap. The total horizontal sediment flux Fh was then calculated by integrating the Fhz values over the first 100 cm of the atmosphere. The 100-cm interval was chosen because more than 95% of the sediment was transported in this layer at all field plots (89% and 87% for the plots No. 2 and 7, respectively). 2.3.3. Field conditions Small ( < 10 cm) maize plants sown in rows about 80 cm apart were present in the field during the experiment. Near the MWAC sites (first 50 cm), they had been locally removed 2 weeks before the storm. Since the configuration of the maize roughness was identical at all sites, it is reasonable to assume that it did not have any substantial effect on the vertical and horizontal sediment flux. Apart from the maize, no roughness elements were present in the field during the storm. Micro-roughness of the soil surface was very low since nearly all soil clods were mechanically destroyed when the maize was sown. During the storm, the topsoil was completely dry because there had been no rain in the week prior to the storm, and there was none during the storm. As stated above, a surface crust covered the field at the time the storm started.

3. Experimental results 3.1. Meteorology of the storm The measurements were made during a windstorm that hit northern Germany on 18 May 1999. Fig. 5 shows the wind data recorded by the meteorological tower. The storm started around 0800 and terminated around 1900. During these 11 h, wind blew predominantly from the SE, varying between E and SSE. The

Fig. 5. Wind characteristics during the 18 May 1999 erosion event.

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10-min wind speed (at 10-m standard height) was constantly around 9 m s 1, with peaks of 10 m s 1 or more. The 10-min maximum speed was around 12 m s 1. Friction velocity (also calculated as a 10-min average) was around 0.60 m s 1, which is substantially above the deflation thresholds for sand (Pye and Tsoar, 1990) and dust (Goossens, 2001). However, the friction velocity values in Fig. 5 should be interpreted with care, since they are 10-min averages and therefore less than the values that occurred during the gusts of effective wind erosion (see Stout, 1998). No rain occurred during the storm. 3.2. Crust strength and the horizontal sediment flux Fig. 6 shows the horizontal sediment flux measured in the field, Fh, as a function of the crust strength (expressed in kPa). The figure shows the results for all 45 field plots, except the plots No. 16, 24 and 34, which cannot be used in this study. The reason is that at these three plots, wind erosion was so severe that the surface crust was entirely destroyed a few hours after the windstorm had started. Thus, during the remaining part of the storm, no surface crust was present on these plots. Because the crust strength measurements were made at a time when the crust was still intact (i.e., well before the next windstorm occurred), the crust strength values measured at the plots 16, 24 and 34 are not representative for the storm event as a whole. At all other

42 plots, the crust survived the erosion event, at least partly, which means that their data can be used in this study. The reason why the erosion was so severe at the plots No. 16, 24 and 34 is the topographic location of these plots (see Fig. 2A, and recall that during the 18 May 1999 windstorm, the wind blew from the SE direction). We now return to the picture shown in Fig. 6. Although there is some experimental noise in the data, the general trend is clear; the stronger the crust, the smaller the horizontal sediment flux. This agrees with previous experimental work (see, for example, Leys and Eldridge, 1998). Fig. 6 also shows that the decay of horizontal sediment flux with increasing crust strength occurs more or less exponentially. Although interesting, Fig. 6 is somewhat limited, as it does not show data for ‘‘weak’’ and ‘‘very weak’’ crusts. The minimum crust strength during the Gro¨nheim experiment was 12 kPa; there are no data available for the interval 0– 12 kPa. Extrapolation, to low crust strength values, of the decay curve in Fig. 6 is somewhat dangerous because of the exponential character of the decay. The horizontal sediment flux at s = 0 (where s stands for the crust strength) cannot be derived with an acceptable precision from the figure. This is important because Fh at s = 0 represents the flux in the absence of a crust, and this value is required for the calculation of the normalised relationship between Fh and s.

Fig. 6. Horizontal sediment flux measured in the field as a function of crust strength.

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Fig. 7. Horizontal sediment flux as a function of crust strength: ., horizontal sediment flux predicted by Marticorena and Bergametti’s (1995) model; E, horizontal sediment flux measured in the field.

The rapid increase of horizontal sediment flux for a crust strength below 15 kPa could be interpreted in terms of a threshold. When s is smaller than 15 kPa, crust strength would no longer be a limiting factor with respect to the horizontal sediment flux. However, Gillette et al. (1982) showed that even very weak crusts reduce the rate of erosion, thus affecting the horizontal flux. To estimate Fh at s = 0, we calculate the Fh values for the Gro¨nheim storm with the MB95 model (see Fig. 7, upper data set). Fh appears to be constant as a function of s, which is what could be expected since

MB95 assumes that the topsoil is uncrusted, i.e., s = 0. Next, the Fh values measured during the Gro¨nheim storm are plotted in the same figure (Fig. 7, data set below). The increase of Fh with decreasing crust strength is obvious in the figure. Fitting a curve through the data points and extrapolating this curve to the region of very weak crusts, it becomes clear that both data sets will intersect at s = 0. This means that the MB95 model operates very well; it predicts correctly the horizontal sediment flux at s = 0, i.e., when the topsoil is devoid of a surface crust.

Fig. 8. The ratio FhMB95/FhGro¨nheim as a function of crust strength.

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Fig. 9. Horizontal sediment flux predicted by Marticorena and Bergametti’s (1995) model versus the horizontal sediment flux measured at the Gro¨nheim site. (a) Predictions without crust correction; (b) predictions when Eq. (5) is incorporated in the model.

It is now possible to calculate a normalised expression describing the decay of the horizontal sediment flux as a function of crust strength. In Fig. 8, the ratio FhMB95/FhGro¨nheim is plotted as a function of s ( FhMB95 is the Fh calculated by MB95, FhGro¨nheim is the Fh measured during the Gro¨nheim storm). We now search for the optimum curve fitting through the data points and containing the point (0,1). The optimum course of the curve in the interval 12 kPa V s V 37 kPa is calculated via regression analysis, whereby the bisector of both regression lines is taken as the reference (Fig. 8 shows that in the interval in question, the relationship between both variables is

more or less linear). Next we look, by trial and error, for a curve that approaches the bisector as closely as possible and also runs through the point (0,1). The curve shown in Fig. 8 shows the final result of this procedure. Its mathematical expression is  s 6  s 5 Fh MB95 ¼ 5:2 55:0 Fh Gro¨ nheim 10 10  s 4  s 3 þ 201:6 300:6 10 10  s 2 s þ 255:2 15:8 þ1 10 10

ð4Þ

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or in a modified form, Fh crusted surface ¼ ðKh1 ÞðFh uncrusted surfaceÞ ð5Þ where  s 6  s 5  s 4 55:0 þ201:6 10 10 10  s 3  s 2 s  300:6 þ255:2 15:8 þ1 10 10 10

Kh ¼ 5:2

s = crust strength, measured with a torvane. Eq. (5) shows how the strength of a surficial crust affects the horizontal sediment flux above the surface. Fig. 9 shows, in the abscissa, the Fh values measured during the Gro¨nheim storm. The ordinate shows the Fh values as predicted by MB95. The upper figure shows the predictions without a crust correction, the figure below the predictions when Eq. (5) is incorporated in the MB95 model. As can be seen in the figure, inclusion of Eq. (5) in the model leads to good results for a large majority of the field plots. 3.3. Crust strength and the vertical dust flux Fig. 10 shows the vertical sediment flux measured in the field, Fv, as a function of the crust strength s. Recall that all Fv values are for the PM20 fraction only. As already explained earlier, the

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results of the plots No. 16, 24 and 34 are not shown in the figure. Similar to Fig. 6, the vertical dust flux shows a decreasing trend as the crust strength increases. Fig. 10 shows that the decay occurs more or less exponentially, which was also the case for Fh. When calculating the normalised relationship between Fv and s, we face the same problem as in the case of Fh. Extrapolation of the curve in Fig. 10 to weak crusts is dangerous because of the exponential character of the decay function, and the vertical dust flux at s = 0 cannot be derived with an acceptable precision. To solve this problem, we apply a similar technique as used earlier for Fh. First, we calculate the Fv values for the Gro¨nheim storm with the DPM model. To operate the DPM, it is necessary to know the numerical value of ei (binding energy) for the Gro¨nheim soil. Direct ei data for Gro¨nheim are not available however; hence, they have to be derived indirectly. For each field plot, statistics were used to find the optimum ei value for which the calculated flux matches with the measured flux at s = 0. The differences between the plots were small however; an ei of 0.07 g cm2 s 2 (which is a rather low value, see Section 4) leads to a good agreement for all field plots. In Fig. 11, the upper data set shows the Fv values calculated by the DPM (with ei = 0.07 g cm2 s 2). The data set below shows the Fv values measured during the Gro¨nheim storm. Similar to Fig. 7, fitting a curve through the data points and extrapolat-

Fig. 10. Vertical dust flux measured in the field as a function of crust strength.

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Fig. 11. Vertical dust flux as a function of crust strength: ., vertical dust flux predicted by the model of Gomes et al. (2003); E, vertical dust flux measured in the field.

ing this curve to the region of weak crusts leads to an intersection of both data sets at s = 0. The correction term (for crust) that should be added to the vertical dust flux prediction by the DPM can now be derived in a similar way as for the horizontal sediment flux Fh. First, we plot the ratio F v DPM/F v Gro¨ nheim as a function of the crust strength s (see Fig. 12). Next, we search for the optimum curve fitting through the data points and containing the point (0,1). Also here, the optimum course of the curve in the interval 12 kPa V s V 37

kPa is calculated via regression analysis. The final curve (shown in the figure) has the following mathematical expression:  s 6  s 5 Fv DPM ¼ 0:03 þ0:42 Fv Gro¨ nheim 10 10  s 4  s 3  2:17 þ4:88 10 10  s 2 s  3:35 þ0:85 þ1 10 10

Fig. 12. The ratio FvDPM/FvGro¨nheim as a function of crust strength.

ð6Þ

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or in a modified form, Fv crusted surface ¼ ðKv1 ÞðFv uncrusted surfaceÞ ð7Þ where  s 6  s 5  s 4 þ0:42 2:17 10 10 10  s 3  s 2 s þ 4:88 3:35 þ0:85 þ1 10 10 10

Kv ¼ 0:03

s = crust strength, measured with a torvane.

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Eq. (7) shows how the strength of a surficial crust affects the vertical sediment flux (only PM20) above the surface. Fig. 13 shows, in the abscissa, the Fv values measured during the Gro¨nheim storm. The ordinate shows the Fv values as predicted by the DPM. The upper figure shows the predictions without a crust correction, the figure below the predictions when Eq. (7) is incorporated in the model. As can be seen in the figure, inclusion of Eq. (7) in the model leads to acceptable results for most of the field plots.

Fig. 13. Vertical dust flux predicted by the model of Gomes et al. (2003) versus the vertical dust flux measured at the Gro¨nheim site. (a) Predictions without crust correction; (b) predictions when Eq. (7) is incorporated in the model.

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4. Discussion An important result of this study, especially for practical applications, is that Marticorena and Bergametti’s (1995) saltation model predicts correctly the horizontal sediment fluxes that were measured during the Gro¨nheim wind erosion event. The MB95 model thus seems to operate well, on the condition that a crust term is added to the model. It is true that the ordinate axis in Fig. 7 is logarithmic, but the predicted Fh at s = 0 is of the right order of magnitude. Whether the SA98 model (and thus the DPM model) operates equally well cannot really be derived from this study since the exact binding energy value (ei) for the Gro¨nheim soil was unknown. The value of 0.07 g cm2 s 2, which was derived statistically, is rather low compared to previously reported ei values for other soils. Alfaro et al. (1998), for example, mentioned ei values between 3.46 and 3.76 g cm2 s 2 for a soil in northern Spain. Gomes et al. (2003) reported lower values for a soil in Niger; here, ei was of the order of 1.2 g cm2 s 2. Both values are more than one order of magnitude higher than the statistically derived value for the Gro¨nheim soil. Since binding energy is a basic parameter in the SA98 model (and thus in the DPM), great care should be taken in its correct determination. More experimental work is needed to determine ei for a large number of soils, so that the Gro¨nheim value of 0.07 g cm2 s 2 can be evaluated more reliably. Eqs. (5) and (7) quantify the effect crust strength exerts on the horizontal and vertical sediment flux. These relationships are not a function of the specific size distribution of the soil, for size distributions (and also the aggregate mass density) are input parameters of the MB95 and DPM models. It is true that both models assume that the top layer of the soil is air dry. For topsoil that are not fully air dry, ei will be high and the SA98 and DPM models should be applied with care. This is especially true for very fine-grained topsoil, because in such soils evaporation occurs much more slowly than in coarser grained (for example, sandy) soil. Another limitation in the present study is that the crust correction terms that have been derived for Fh and Fv have been derived for the crust strength interval 0 kPa V s V 37 kPa only. Crusts with a s value of 37 kPa are relatively strong; walking over them normally does not lead to a destruction of the crust, although the

frequency of disruption is an important parameter. In the case of a very high clay content, or a high carbonate or salt content, the value of s can mount to well over 50 kPa and more. For such very resistant crusts, the validity of Eqs. (5) and (7) has not been tested in this study. An important problem with respect to sediment flux predictions is that weak crusts will quickly disappear (or at least become seriously damaged) during heavy wind erosion. Such crusts can only temporarily protect the soil from erosion. This is what happened at the plots No. 16, 24 and 34 in the Gro¨nheim experiment. When the crust disappears during the erosion event itself, it is no longer possible to apply Eqs. (5) and (7) to the entire event. For evident reasons, the Fh and Fv values measured in the field will be considerably higher than those predicted by MB95 and the DPM. As long as the crust remains present, both equations should remain valid, however. It is currently unknown whether the progressive injury to a crust (due to impacting grains) during the first phases of an erosion event will affect Eqs. (5) and (7), although the measurements in Gro¨nheim suggest that the equations remain valid as long as the crust has not disappeared completely. The fact that the s values that were measured prior to the storm allowed accurate predictions of the horizontal and vertical sediment fluxes during the storm is a good argument for this assumption. Another point is that normally, the rupture of a crust is more or less an instantaneous rather than a gradual process; once impacting particles have pierced the crust, subsequent destruction of the crust will take place quickly. Future research on the relationships between crust strength and sediment fluxes is required to confirm (or deny) the assumptions made above.

5. Conclusions Field experiments have been conducted to investigate the relationships between crust strength and the horizontal and vertical sediment flux during wind erosion. Crust strength, which was measured with a torvane in this study, significantly affects the horizontal and vertical sediment fluxes. Both fluxes decrease as the surface crust becomes stronger. The measurements also show that the decay occurs exponentially, both for Fh and Fv.

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The MB95 model accurately predicts the horizontal sediment flux when the topsoil is devoid of a crust. For topsoil with a surface crust, incorporation of Eq. (5) in MB95 allows accurate predictions of the horizontal sediment flux provided that the crust does not disappear in the course of the erosion event. For calculations of the vertical sediment flux, the DPM model completed by Eq. (7) can be used. Also here, the restriction appears that the crust may not disappear during the erosion event. A further restriction for the DPM is that it only calculates the vertical sediment flux for the PM20 fraction of the soil erodible fraction. Total vertical flux is thus not calculated by the DPM. Further research is needed to extend the DPM to coarser particle fractions. It is also desirable that Eqs. (5) and (7) be tested for larger crust strength intervals and for a wider range of topsoil than in the present study. This would provide more evidence for the universal validity of these equations. Acknowledgements The author is very grateful to S. Alfaro (Laboratoire Interuniversitaire des Syste`mes Atmosphe´riques, Universite´ de Paris 12, France) for providing the electronic version of the DPM model, for doing a few grain-size analyses and for fruitful discussions. Thanks are also expressed to J. Gross (Niedersa¨chsisches Landesamt fu¨r Bodenforschung, Bremen, Germany) and J. Bo¨hner (Geographisches Institut, Georg-August-Universita¨t Go¨ttingen, Germany) for additional grain-size analyses and for providing the aerodynamic data for the 18 May 1999 wind erosion event. References Alfaro, S.C., Gomes, L., 2001. Modeling mineral aerosol production by wind erosion: emission intensities and aerosol size distributions in source areas. Journal of Geophysical Research 106D, 18075 – 18084. Alfaro, S.C., Gaudichet, A., Gomes, L., Maille´, M., 1997. Modeling the size distribution of a soil aerosol produced by sandblasting. Journal of Geophysical Research 102D, 11239 – 11249. Alfaro, S.C., Gaudichet, A., Gomes, L., Maille´, M., 1998. Mineral aerosol production by wind erosion: aerosol particle sizes and binding energies. Geophysical Research Letters 25, 991 – 994. Belnap, J., Gillette, D.A., 1997. Disturbance of biological soil

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