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EARTH SURFACE PROCESSES AND LANDFORMS, VOL. 20,207-218 (1995) SURFACE STONE COVER ON DESERT HILLSLOPES; PARAMETERIZING CHARACTERISTICS RELEVANT TO INFILTRATION AND SURFACE RUNOFF D. L. DUNKERLEY Department of Geography and Environmental Science, Monash University, Clayton, Victoria 3168, Australia Received 25 October 1993 Revised 27 April 1994 ABSTRACT Surface stones are a common feature of desert hillslopes. They influence slope processes ranging from the interception and partitioning of rainwater to the dislodgement and transport of regolith particles. The aspects of a stone mantle which relate to these various influences are diverse, and include surface cover fraction, dimensions of the infiltration annulus, and geo- metric and packing effects. Analyses of the characteristics of stone cover at two study sites were made using photographic methods and are used to evaluate different means of reporting mean stone sizes. It is found that mean diameter based on weight, as conventionally employed in sieve analysis, is insensitive to important stone cover characteristics and may be influenced greatly by uncom- mon, large stones. Similarly, mean diameters based on count become inappropriate if large numbers of small stones dom- inate the calculated mean, concealing other site-to-site differences in stone cover. As a more appropriate parameterization of stone geometry, the use of mean diameters weighted by stone surface area and perimeter length are proposed. These weighting factors have the advantage that they relate closely to stone characteristics relevant to slope hydrology and erosion processes. KEY WORDS stone mantle; grain size; mean diameter; infiltration INTRODUCTION Desert hillslopes are often mantled by stony debris, the character of which may be partly or largely relict from slope transport under previous environments. Whether relict or related to contemporary slope trans- port, the character of stone mantles may nonetheless vary systematically with position on the hillslope. Upslope, near to an outcrop source, rock debris may be coarse and cover most of the slope surface to some depth, forming a rubble slope or scree. Distally, stone size may decline and the mantle may provide a lower cover percentage and a thinner (perhaps monolayer or veneer) structure. These spatially varying stone covers influence many aspects of the hydrologic and erosional behaviour of slopes. They may do this through the role of stones as impervious surfaces that shed water, absorb raindrop impact energy, and provide a microhabitat for algae and other organisms, or through the influence of the stones as obstacles modifying the depth, velocity and flow path of surface runoff. A multitude of such mechanisms has been envisaged in the literature. Since the character of the stone mantle may vary with land- scape position, as noted above, then so too may it s hydrologic and erosional effects. Consequently, descrip- tions of stone cover relevant to hydrologic and erosional investigations must be sensitive to spatial variability in the important aspects of that stone cover. The use of a simple cover percentage, for example, without regard to sorting or size, will probably prove unsuitable: two sites displaying the same cover fraction might display different size and sorting characteristics with different impacts on sheetflow behaviour. The work reported here seeks to examine the issues involved in making more appropriate descriptions of surface stone CCC 0197 -9337/95/030207-12 0 1995 by John Wiley & Sons, Ltd

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Page 1: Surface stone cover on desert hillslopes; parameterizing characteristics relevant to infiltration and surface runoff

EARTH SURFACE PROCESSES AND LANDFORMS, VOL. 20,207-218 (1995)

SURFACE STONE COVER ON DESERT HILLSLOPES; PARAMETERIZING CHARACTERISTICS RELEVANT TO

INFILTRATION A N D SURFACE RUNOFF

D. L. DUNKERLEY

Department of Geography and Environmental Science, Monash University, Clayton, Victoria 3168, Australia

Received 25 October 1993 Revised 27 April 1994

ABSTRACT

Surface stones are a common feature of desert hillslopes. They influence slope processes ranging from the interception and partitioning of rainwater to the dislodgement and transport of regolith particles. The aspects of a stone mantle which relate to these various influences are diverse, and include surface cover fraction, dimensions of the infiltration annulus, and geo- metric and packing effects.

Analyses of the characteristics of stone cover at two study sites were made using photographic methods and are used to evaluate different means of reporting mean stone sizes. It is found that mean diameter based on weight, as conventionally employed in sieve analysis, is insensitive to important stone cover characteristics and may be influenced greatly by uncom- mon, large stones. Similarly, mean diameters based on count become inappropriate if large numbers of small stones dom- inate the calculated mean, concealing other site-to-site differences in stone cover. As a more appropriate parameterization of stone geometry, the use of mean diameters weighted by stone surface area and perimeter length are proposed. These weighting factors have the advantage that they relate closely to stone characteristics relevant to slope hydrology and erosion processes.

KEY WORDS stone mantle; grain size; mean diameter; infiltration

INTRODUCTION

Desert hillslopes are often mantled by stony debris, the character of which may be partly or largely relict from slope transport under previous environments. Whether relict or related to contemporary slope trans- port, the character of stone mantles may nonetheless vary systematically with position on the hillslope. Upslope, near to an outcrop source, rock debris may be coarse and cover most of the slope surface to some depth, forming a rubble slope or scree. Distally, stone size may decline and the mantle may provide a lower cover percentage and a thinner (perhaps monolayer or veneer) structure.

These spatially varying stone covers influence many aspects of the hydrologic and erosional behaviour of slopes. They may do this through the role of stones as impervious surfaces that shed water, absorb raindrop impact energy, and provide a microhabitat for algae and other organisms, or through the influence of the stones as obstacles modifying the depth, velocity and flow path of surface runoff. A multitude of such mechanisms has been envisaged in the literature. Since the character of the stone mantle may vary with land- scape position, as noted above, then so too may it s hydrologic and erosional effects. Consequently, descrip- tions of stone cover relevant to hydrologic and erosional investigations must be sensitive to spatial variability in the important aspects of that stone cover. The use of a simple cover percentage, for example, without regard to sorting or size, will probably prove unsuitable: two sites displaying the same cover fraction might display different size and sorting characteristics with different impacts on sheetflow behaviour. The work reported here seeks to examine the issues involved in making more appropriate descriptions of surface stone

CCC 0197 -9337/95/030207-12 0 1995 by John Wiley & Sons, Ltd

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208 D. L. DUNKERLEY

cover, using a desert field site as the test case. The problem of description and parameterization is considered in the context of the erosional and hydrologic functioning of hillslopes carrying surficial stones.

HYDROLOGIC AND EROSIONAL ROLE O F SURFACE STONE MANTLES

Hydrology and rainfall partitioning Stone cover affects the hydrologic behaviour of slopes through influences on rainfall partitioning, areal

extent of seal development, rapidity and areal extent of infiltration, and consequent runoff development. Interception of rain by surface stones was studied by El Boushi and Davis (1969) in a series of laboratory

experiments on rock rubble. They found that in assemblages of stones smaller than about 30 mm. most water was retained in droplets of up to 0.18ml held at contact points where stones touched. For larger stones (> l00mm diameter), most water was held as puddles on the rock surface. These authors examined only simple geometries of rock rubble and did not consider the properties of mixed sizes, for example. Their results nonetheless emphasize that a simple parameter such as surface rock detention storage (in millimetres of water depth) will vary significantly with factors including stone size, sorting and rubble depth.

Field studies of the role of stone cover in influencing infiltration and runoff generation (e.g. Epstein rt al., 1966; Roy and Jarrett, 199 1 ; Abrahams and Parsons, I99 1 a; Valentin and Casenave, 1992) have produced a diversity of results. In much of this literature, interpretation of results is diffcult because the investigators only partially consider the geometry of the stone cover, and define coarse particles in different ways. Abra- hams and Parsons (1991a), for example, reported only that the stone cover at sites studied in rainfall simula- tion experiments had a mean size of 16.2 mm, with a stone cover percentage in the range 0-84 per cent across a set of trial plots. Whether their results have other than local significance depends upon how the unreported properties of the stone cover match those of other desert areas. The role of certain other aspects of the surface stone cover has been illustrated in studies such as those of Poesen et al. (1990) and Valentin and Casenave (1992), with soils that were structurally unstable. On soils of this type, raindrop impact produces a surface seal or crust (McIntyre, 1958). Sealed surfaces locally restrict infiltration and promote surface run- off. Stone cover is also essentially impermeable, so that the covered fraction of the surface is also unavailable for infiltration. Thus a stone-covered, crusted soil offers only one major site for water entry and reciprocal escape of soil air: the margins of the stones, especially where overhanging margins protect the regolith sur- face from droplet impact and seal development. Along the stone margins, water entry appears to exceed air release, so that positive air pressures are generated beneath the stones and the sealed surfaces. This results in the development of gas-filled vesicles (Springer, 1958; Evenari et al., 1974). The developmeiit of such pres- surized vesicular structures presumably acts to reduce further the permeability of the regolith. There is as yet no information on how the size and mass of stones relates to the air pressure developed beneath them. It seems reasonable to presume that very small stones will generate negligibly small or no infiltration annuli, and that they would not be associated with the development of positive pressures in the soil air. At the other end of the size range, very large stones may cover a sufficiently large volume of regolith that the region under the centre of the stone is not fully wetted even in major storms, so that vesicle development might be restricted to a zone around the stone perimeter. The width of such a zone might well vary with stone size and position on or in the regolith surface, as well as with storm characteristics such as intensity and dura- tion, in ways that are yet to be investigated. Here again it is evident that a simple cover percentage may not provide sufficient information for the understanding of slope hydrological processes.

Because the stone perimeter may be a key site for infiltration of water and of air escape, the nature of this parameter must often be studied in hydrologic studies of stone-covered surfaces. In experiments with simu- lated rain and soils prone to seal development, Poesen et al. (1990) and Valentin and Casenave (1992) have highlighted the significance of stone position, which they treated as being either loose (resting on the surface) or embedded. Experimental plots with loose surface stones showed increased infiltration of water with increasing cover percentage (Poesen et al., 1990). On the other hand, when the stones were embedded in the surface, increasing cover amount simply represented an increase in non-absorbing surface and hence a decrease in infiltration.

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SURFACE STONES ON DESERT HILLSLOPES 209

These studies are again somewhat difficult to compare owing to their treatment of stone size. Valentin and Casenave (1992), working with natural stone cover in the field, treated grains > 2mm diameter as coarse fragments. The laboratory experiments of Poesen et al. (1990) used only well-sorted stones of about 6cm diameter. It is not clear whether the results obtained in the latter case would still apply if the cover per- centage were composed of many smaller grains, or a poorly sorted mixture of many sizes, because of the size-related annulus effects already referred to. Further experimental data relevant to this point were pre- sented by Koon et al. (1970), who studied the behaviour of soils carrying square and rectangular tiles arranged in various ways. Their essentially planar cover of tiles may not, however, have simulated the effects that arise in a natural poorly sorted stone cover, whzre obstacle height is not fixed and where complex wake and turbulence effects may therefore arise in sheetflow (see Bunte and Poesen, 1993). These frictional effects in surface flow might once again exert an important influence on flow speeds and depths, and hence on seal development, surface scour and infiltration behaviour.

Surface erosion Stone cover affects the erosional behaviour of slopes through the absorption of droplet impact energy, by

roughening the surface, and by increasing the tortuosity of overland flow paths with, presumably, a conse- quent reduction in velocity and an increase in flow depth. An increased depth of water over the regolith sur- face can result in a diminished efficacy of splash detachment through impact cushioning effects (Moss and Green, 1983; Proffitt and Rose, 1991). With deeper flow films, much of the impact energy is dissipated by shear within the water column, resulting in a lowering of the shear forces actually generated at the surface of the regolith. This effect suggests that the influence of stone cover on splash detachment cannot be identi- fied independently of an understanding of overland flow depths and of the sizes of droplets striking the sur- face. There appear to be no field or laboratory data that quantitatively assess the significance of the absorption of drop energy at stone surfaces or in the stone-modified surface water flow.

There are several studies of stone cover as a factor affecting the roughness of the surface and the tortuosity of overland flow paths (e.g. Abrahams and Parsons, 1991b). These suggest that geometric considerations (including stone spacing and shape) have important effects on friction factors, overland flow speeds and, by inference, erosion processes.

In summary, sufficient experimental results now exist to demonstrate that adequate descriptions of surface stone cover configuration are essential in studies of runoff and erosion on desert and other rocky surfaces. Stone covers developed in the field display complex structures and pose severe difficulties for analytical description. Given that some stones rest loosely on the regolith surface, others are partially embedded in it and yet other stones may lie just covered by a thin veneer of fines, the definition of slope surface becomes problematic. A description based upon a gradational downward increase in the percentage of fines, rather than on a discrete and definable ‘surface’, actually seems more appropriate but is operationally very diff- cult. Additionally, the description of rocky rubble as commonly developed on desert hillslopes encounters all of the severe sampling problems that have been examined in the context of river gravels and other coarse clastic sediments (Dunkerley, 1994). The brief review above is sufficient, however, to demonstrate that con- ventional cover percentage and size distribution by sieve analysis fail adequately to convey information that is relevant to slope hydrology and slope erosion processes. The importance of other parameters, such as stone perimeter length, is now well demonstrated. Thus it is now incumbent upon geomorphologists to develop adequate descriptive procedures. A choice of stone cover parameters to be employed in models which seek to relate infiltration behaviour, for example, to stone cover must be guided by a functional analysis of the role of the stones. The present work is an attempt to quantify some alternative parameters describing the surface for natural stony hillslopes in desert environments of Australia. A major goal is to investigate the relative importance of stones in different size classes to the overall site value of cover per- centage or stone edge length.

THE FIELD SITE

The field area is located on the Fowlers Gap Arid Zone Research Station in arid western New South Wales,

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210 D. L. DUNKERLEY

Figure 1 . Image of South Sandstone site, with significant rounding of stones evident. Scale bar is marked in centimetres

Australia. Rocky strike ridges in this area evolve from very durable quartzites. Ridge crests often carry little regolith, and consist of outcropping bedrock undergoing breakdown into angular blocks. These apparently disintegrate slowly and cascade down the adjacent hillslopes, producing a mantle of stone whose typical grain size declines downslope as gradient flattens. The stone cover on lower slopes often consists of a thin mantle overlying deep clay-rich regolith. The stone mantle on steep slopes is chaotically distributed, and large blocks may be partially embedded in pockets of regolith. On footslopes of lower gradient, stones are often sorted into patches as well as being of smaller diameter. The patches are separated by essentially stone-free areas, a distribution that may relate to gilgai processes arising from the wetting and drying of the underlying deep regolith (Dunkerley and Brown, in press).

The area now receives an annual rainfall of about 190mm. Summers are hot, and surface water is absent. Vegetation consists of chenopod shrublands (most commonly the saltbush Atriplex vesicaria) and native grasslands, with occasional small trees (Acacia spp. and Casuarina spp.) on rocky slopes.

Two study sites are described here. One is a typical steep (about 14") upper slope site with a blocky, dis- ordered stone cover. This is termed the Homestead Creek site. The second is a typical stone monolayer of somewhat smaller size and greater stone roundness, lying on a low gradient footslope (about 3"). This is the South Sandstone site. In both cases, the surface not covered by stones consists of a fine sandy matrix, sometimes colonized by cryptograms (algae, lichens and bacteria). At Homestead Creek, small shrubs, grasses and some plant litter are also present. Both study sites are located in areas grazed at very low stock- ing rates by sheep. Native marsupial herbivores (dominantly kangaroos and euros) also use the area. Their saltatory locomotion probably contributes to the periodic downslope motion of stones. The two sites repre- sent end-members in the array of stone characteristics that is generally represented in the study area; these characteristics vary with slope position, as noted earlier. Photographs of the surfaces of the two sites are presented in Figures 1 and 2.

FIELD DATA COLLECTION

In order to describe stone mantles at the study sites, coloured photographs of the sites were taken with a

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SURFACE STONES ON DESERT HILLSLOPES 211

Figure 2. Image of Homestead Creek site, displaying common large, angular blocks. Scale bar is marked in centimetres

camera mounted on the end of a hand-held boom. The camera was suspended 3-4 m above the surface, and the optical axis remotely tilted to be orthogonal to the local slope surface (this was judged by an assistant standing to one side). This method has the advantage that many sites may be recorded in the field in a short time, each involving perhaps thousands of stones. More importantly, information subsequently gleaned from the images relates to the stone cover in the condition in which it receives rain and carries runoff. It is therefore possible to record the surface area of non-spherical stones as they were exposed to drop impact and to extract spatial geometric data, such as descriptions of size-related clustering in the stone cover. A photographic image does not, however, facilitate the measurement of true stone diameter, since only plan features are displayed. Stones may also be partially embedded in the regolith surface. However, it can be argued that diameters as conventionally measured in grain size work need not be of direct concern in the context of hydrology and slope erosion, since it is the surface character that is important.

In the laboratory, the site photographs were projected from coloured slides directly onto a large digitizing tablet. Image scale was generally close to 1:1, and clasts as small as 1 mm could be readily identified. The images typically covered a ground area of 0.5 m2. Within this area, each visible stone was individually digi- tized to determine surface area and perimeter length. Typically more than 1000 stones were digitized from each image.

Since stones are generally not exactly spherical (and hence not circular in planimetrc view), a means to record diameter had to be adopted. This was done by calculating the diameter of a circle having the same area as that digitized for each stone.

Where stones overlapped, the form of the partly hidden clast was extrapolated to complete its outline. Imprecision in the data arises from the possibility that some stones or parts of stones were actually covered by a very thin veneer of the fine regolith, sufficient to conceal the presence of stones immediately below the surface. In this case, observation records that part of the surface as permeable and a potential site for infil- tration, when in fact this is not the case. This situation is very difficult to assess in a rigorous quantitative way. Many large stones might be partially embedded in the surface and a better description of such a site would be a three-dimensional one, based perhaps on layer-by-layer excavation and mapping, rather than simple planimetry as employed here. The great bulk of stones in the two particular sites described here

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212 D. L. DUNKERLEY

are, however, clearly exposed at the surface, but a small fraction of the surface fines may indeed be underlain by stones.

Stones resting loosely upon the surface, rather than embedded in it, may permit water to flow down- slope beneath overhanging margins, and hence may not provide such large obstacles to flow as planimetry might suggest. This was investigated at the field sites by removing by hand all stones that could be lifted away from the surface with little or only gentle effort. A second photograph was then taken, and the statistics collected before and after stone removal were compared. For the two sites studied here, only small numbers of such stones were involved. However, this kind of analysis is potentially important because on upper, rocky slopes there are often large, loose blocks, and the loss of just one or two of these stones greatly alters the grain size data calculated by weight and in other ways outlined below. Down- slope, where the stone mantle is better sorted and approaches a monolayer, the significance of this effect is probably much reduced. Failure to account for stones resting loosely above the surface potentially intro- duces an error which is topographically modulated, and which might result in serious error in slope hydro- logic modelling.

An estimate of the volume (and hence mass) of each stone was calculated from the measured diameter. This involved an untested extrapolation of the planimetric data into the third dimension. Stones which had large buried extensions would clearly be misrepresented in the derived volume data. This effect may indeed arise with larger stones, but seems unlikely to be a significant problem for the numerous smaller stones that sit embedded in (or sometimes loosely upon) the regolith surface. The results of the photographic analyses can be compared with an approximation to the results that would be derived from conventional sieve analysis of exactly the same particles, and so reveal the relative utility of the two methods. The results presented here are not exactly those that would be obtained from sieve analysis, since that procedure involves grouping of data into classes of typically 0.5 phi width, with some resulting loss of information. All of the data analysed here were employed in ungrouped form.

The data derived by digitizing were described by standard statistical procedures. Values of hydrologically and erosionally important variables (stone perimeter length and surface area) were cross-tabulated against stone diameter to reveal the relative contributions to the site aggregate values of these parameters by stones of different sizes.

The use of mean diameters Distributions of weathered particles by number (frequency distributions) or by weight (weight-size

distributions) often reveal strong positive skew, perhaps roughly log-normal (e.g. Ibbeken, 1983). Arithmetic means in this situation are not ideal measures of location. They do retain the useful prop- erty, however, that the arithmetic mean of a variable (e.g. particle weight), when multiplied by the sample size, yields the total weight of the sample. This enables the distribution to be represented by a single number, but one that would have greater utility if the distribution were monosized or normally distributed.

We can observe that the arithmetic mean diameter, geometric mean diameter, etc., can be calculated on the basis of particle frequency (count), volume, weight, surface area, density, manganese content, or any other scalable property. In conventional sieve analysis by weight, the weighted mean is calculated across all the phi classes from:

C(diam. x class weight) C( sample weight)

Mean diameter =

The widespread use of weight-based statistics, as in traditional sedimentology, is most suited to work on sediment transport and need not be adopted in studies of infiltration and runoff on slopes. Rather, in slope hydrology studies, we can usefully weight data by significant properties such as exposed surface area and perimeter (edge) length. This procedure is adopted here and leads to the determination of mean diameters expressed in millimetres but based on the size-related distributions of surface area or edge length. The utility of these results is then compared with traditional analyses employing volume or mass weighting to derive

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SURFACE STONES ON DESERT HILLSLOPES 213

Table I. Summary of stone cover characteristics and calculated mean grain diameters, South Sandstone and Homestead Creek study sites

Parameter Homestead Creek South Sandstone

Quadrat area (m2) Stone cover (%) Edge length mm-’)

Maximum diameter (mm) Minimum diameter (mm) No. of particles Arithmetic mean area (cm’) Arithmetic mean edge length (cm) Arithmetic mean volume (cm3)

Mean diameters (mm) Perimeter-weighted Area-weighted Volume-weighted Arithmetic Geometric Surface area Perimeter Volume Surface area/edge length

Mass (kgm- 1 ) 0.55

31.8 99.5 48.1

119.1 1.52

2.25 3.92 7.28

1400

0.47 67.5 94.5 14.4 52.1

1.96

1.58 3.99 2.33

I104

26- 1 46.8 68.0 11.4 8.3

17-3 11.4 24.1 20.5

16-9 22.0 26.9 11.9 9.9

14.2 11.9 16.4 13.3

mean sizes. The formulae employed are exactly like the one above, namely:

C(diam. x surface area) C(samp1e surface area)

C(diam. x edge length) C (sample edge length)

Mean diameter = or

Mean diameter = (3)

but in the present study were employed with data on individual grains, rather than data grouped by surface area or edge length. When employed with ungrouped data, these relationships may be determined easily from simple powers of the grain diameters, as follows:

Ed4 Ed

Volume (or weight) weighted mean diameter: (4)

( 5 ) E d 3 Cd

Surface area weighted mean diameter:

Ed2 Edge length weighted mean diameter: -

Cd The weighted mean diameters must be distinguished from simple mean diameters such as the mean volume

diameter:

Mean volume diameter: E - (7)

which is simply the hypothetical diameter which, if multiplied by the number of grains, yields the total volume of the sample. (Useful reviews of the many kinds of mean diameter that might be calculated are con- tained in standard works such as those by Herdan (1960), Orr (1966) and Allen (1974).)

The two principal stone characteristics treated here, surface area and edge length, might be described for a site by employing two separate means. However, in seeking a single site descriptor which might be employed

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214 D. L. DUNKERLEY

Line Chart for columns: XlYl ... X i Y 4 A% area 0% count 0% edge length

Figure 3. Cumulative plots of stone cover characteristics, South Sandstone site

as a kind of latent variable underlying the hydrologic response of the surface, it is possible to combine these two properties into a single term. This is done below by examining factors such as the mean diameter based upon the surface area to edge length ratio.

RESULTS

Results for the two sample plots are presented in Table I and Figures 3 and 4. Stone cover percentage was determined by summing the digitized surface areas of stones within the sample

quadrats and expressing this as a fraction of the total quadrat area. For Homestead Creek (n = 1400 stones) the value was 32 per cent and for South Sandstone (n = 1104 stones), 68 per cent.

Line Chart for columns: X1Y1 ... X1Y4 0% count 0% edge length A% area

Figure 4. Cumulative plots of stone cover characteristics, Homestead Creek site.

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The descriptive data may conveniently be expressed as standardized to a unit area of slope surface, for comparison with results derived elsewhere. Using this method, stone cover amounts to 0.32m2 mp2 at Homestead Creek and 0.68m2m-2 at South Sandstone. Stone edge length at these two sites amounts to 99.5 m mP2 and 94.5 m mP2, respectively. Stone masses, based on a conversion at 2.6 g cm-' , are 48.1 kgmP2 and 14.4kgmp2. The magnitude of the edge length totals, approaching 100mmp2, is striking. However, it is more informative to break the results down according to grain size and assess the contribu- tions of stones of different sizes to these aggregate results.

Distribution churacteristics Frequency distributions of all measured parameters were inspected for normality prior to further analysis.

All displayed positive skewness and were leptokurtic: values ranged up to 12 for skewness and up to 188 for kurtosis. Distributions of perimeter length, being proportional to diameter, displayed similar characteristics to those of stone diameter. Since the frequency distribution of stone sizes was skewed, distributions of vari- ables relating to higher powers of the diameter (i.e. in the order area (co d2) and volume (00 d3)) were increas- ingly skewed and leptolurtic. This suggests a need to consider parameters other than arithmetic means as measures of location. Variables were therefore log transformed, and means calculated in log space. After transformation, South Sandstone data were slightly platykurtic and almost symmetrically distributed; Homestead Creek data were slightly leptokurtic and slightly positively skewed. All values of skewness and kurtosis at both sites after transformation were < 1 (often < O.l ) , and the transformation appeared to yield acceptable distributions. It must be emphasized, however, that even with the significant sample sizes available here, the distributions cannot exactly be described by smooth probability density functions. This seems intuitively reasonable given the steep slopes, on which a coarse particle from unslope may be moved by chance events to lie among finer materials lower down.

When converted to density distributions of the variables of interest (surface area, edge length, volume), cross-tabulated by grain diameter, the distributions were significantly modified. In the case of distributions of surface area and volume, which depend on higher powers of diameter, the dominant contribution made by small stones on a count basis vanished and the distributions became much more symmetrical. In the case of the Homestead Creek site, where a few very large individual grains were present, the distribution of volume by diameter actually became negatively skewed, with a single large grain contributing nearly 9 per cent of the total stone mass on the study plot.

At both sites, the arithmetic and geometric mean diameters lay in the range 8-12mm. In fact, the two arithmetic means by count (1 1.9 mm at Homestead Creek and 11-4mm at South Sandstone) were very similar and disguised the evident differences in stone cover between the two sites. This occurred because of the enormous abundance of small stones at each site, which dominated the frequency-weighted statistics.

The mean diameters weighted by stone volume or weight, providing values similar to those that would have been obtained by conventional sieve analysis, were very different. The large stones present at the Home- stead Creek site raised the mean diameter there to 68.0 mm. At South Sandstone the mean was 26.9 mm. These means were thus able to distinguish between the two sites. However, they reflected the influence of large stones which are not necessarily the most significant in terms of infiltration and runoff generation. To examine this question, the cross-tabulated data on surface area and edge length in relation to stone diameter must be examined.

At the Homestead Creek hillslope site (the debris-mantled upper hillslope), about 80 per cent of stones had diameters lying below the arithmetic mean. These grains contributed about 15 per cent of the total surface area, 47 per cent of the total edge length, but less than 2 per cent of the total mass. Grains smaller than the mean diameter based on weight (68 mm) amounted to 99 per cent of the count, and contributed 76 per cent of the surface area, 92 per cent of the edge length and 56 per cent of the weight.

Results for the South Sandstone site were somewhat similar. About 62 per cent of stones had diameters below the arithmetic mean by count (1 1.9 mm). These grains contributed 18 per cent of the total surface area, 36 per cent of the edge length, and only 7 per cent of the mass. Mass (or volume) was dominated by the large grains, a single large grain (d = 1 19.5 mm) contributing nearly 9 per cent of the total sample mass. The 95 per

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216 D. L. DUNKERLEY

cent of grains smaller than the mean diameter based on weight (26.9 mm) contributed 73 per cent of the sur- face area, 88 per cent of the edge length, and 58 per cent of the weight.

The conclusion reached from this analysis is that neither arithmetic mean nor conventional weight-based mean diameter represents the hydrologically significant aspects of the stone cover at all well. They do not provide suitable measures of location for area or edge length. This should not be surprising, since neither measure is weighted by either of the hydrologically significant variables.

The mean diameter weighted by surface area was 46.8mm at Homestead Creek and 22.0mm at South Sandstone. The corresponding values for the mean diameter based on edge length were 26.1mm and 16.9mm. Both values successfully distinguish between the two sites. Both values lie between the simple mean diameters by count and those weighted by stone volume or mass for the site concerned. Each would therefore be more appropriate in a site description designed to be meaningful in a hydrologic context.

Finally, it can be noted that the diameters based upon surface area to perimeter ratio, of 20.5mm at Homestead Creek and 13.3 mm at South Sandstone, also distinguished successfully between the two sites. These are again intermediate between simple unweighted means and those weighted by volume, and could also serve as valuable site descriptors. Their particular value is that, as single numerical values, they none- theless contain information on two key stone cover parameters of relevance to slope hydrology and erosion.

DISCUSSION AND CONCLUSIONS

Many studies of stone cover in relation to infiltration, runoff and erosion appear to have adopted incomplete descriptions of the stone cover. Epstein et al. (1966) defined as stones all particles coarser than 6.4mm diameter (equivalent to 0.25 in). They used photographs of 930cm’ (1 f’) areas projected at 1:l scale with surface cover percentage estimated by grid intersection counting. However, size distributions were reported in four classes on the basis of sieving and weighing. In a study of the role of slaty stone fragments in surface erosion, Box (198 1) used coloured slides projected onto a grid to assess cover percentage, but then again used sieve methods to determine a mean particle size. He gave the total stone weight per square metre assessed in seven sieve classes. These authors thus had planimetric data available but elected not to employ them in representing grain size. Abrahams et al. (1985) used samples of 50-200 particles with arithmetic mean diameter based upon a grid intersection sampling method. The resulting data are thus frequency distribu- tions of size (linear diameter) based upon count. They adopted this measure of size because of its relatively good correlation with slope inclination at their study sites. Abrahams and Parsons (1991a) used a similar grid-based sample, but of only 25 particles. The mean size that they reported again appears to be an arith- metic mean size based upon frequency. Elsewhere (Abrahams and Parsons, 1991b) these authors used samples of 56-70 particles and again reported arithmetic mean size by frequency. Abrahams et al. (1988) employed a grid-based sample of 200 particles, but reported the geometric mean size by frequency. In no case did these authors report the shape of the frequency distribution to be represented by these means. Valentin and Casenave (1992) employed a grid sample derived from a photograph of the study surface. They employed a weighted measure of surface stone size based upon the fraction of a study plot covered by stones grouped into three classes by diameter. This method is somewhat akin to that reported here, but involves greater pooling of the data. Again, these authors did not comment upon the nature of the distributions of frequency, area, weight or any other measure of the surface stone population that they represented by mean values.

These citations demonstrate that no uniform procedure for stone cover description has yet evolved. More importantly, mean sizes based upon frequency or weight appear to be commonly adopted, when it seems clear from the results presented earlier that an area or edge length weighting would be functionally more appropriate in the light of a knowledge of slope processes.

The data derived from the present study show that frequency distributions of all stone characteristics estimated (count, surface area, edge length, and volume or mass) are strongly skewed. They are dominated by greatest frequencies at small values of each variate. When transformed to distributions by grain diameter, skewness becomes less severe. Even then, and especially at the rocky Homestead Creek site, the data did not lend themselves to suitable representation by any particular regular distribution. However, the

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SURFACE STONES ON DESERT HILLSLOPES 217

determination of means by incorporating weighting by an appropriate variate permitted the distributions to be described satisfactorily.

An analysis of distributions of each descriptive variable against grain diameter shows that conventional sieve size analysis yields results inappropriate to research on slope hydrology and erosion. This is because the mean diameter based on particle weight lies well above the diameter representative of the distributions of surface area and edge length. It is insensitive to wide fluctuations in the population of smaller grains, whose contribution to surface area and edge length values is of vital importance. Additionally, weight-based data are subject to considerable influence by rare large stones which alter the weight-based mean diameter but which have much less effect on the hydrologically important character of the stone mantle. Finally, the argument raised earlier about the greater significance of a description of the slope surface planimetry incor- porating undisturbed stone orientation must be recalled. Taken together, these limitations of weight-based mean diameters amount to a cogent argument for abandoning their use in many studies of slope hydrology and erosion processes. Likewise, mean diameters based upon count are evidently prone, at least at sites like those studied here, to be influenced unduly by numerous very small clasts, which are not necessarily those displaying prominent infiltration annulus effects or large aggregate surface area.

However, the simplest descriptive procedure that will permit us to discover how hydrologic processes operate in the field is the most efficient to adopt. It remains to be seen whether the apparently more appro- priate, but more exacting, site descriptions advocated here will yield higher levels of explanation in experi- mental studies of infiltration and surface runoff production.

ACKNOWLEDGEMENTS

The author thanks the University of New South Wales for support at its Fowlers Gap Arid Zone Research Station. The field assistance of Kate Brown is also gratefully acknowledged.

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