How do vegetation bands form in dry lands? Insights from numerical modeling and field studies in southern Nevada, USA



[1] Vegetation bands are periodic bands of vegetation, separated by interband spaces devoid of vegetation, oriented parallel to the topographic contour in some gently sloping arid to semiarid environments. Models of vegetation band formation attribute their formation to positive feedbacks among vegetation density, soil porosity/permeability, and infiltration rates. Here we present an alternative model based on field measurements at our study sites in southern Nevada. In this model, interband spaces between vegetation bands form because topographic mounds beneath vegetation bands detain water upslope from vegetation bands, leading to hydrologic and sedimentologic conditions that inhibit the survival of plants in interband spaces. We used terrestrial laser scanning (TLS) to create high-resolution (∼10 cm2/pixel) raster data sets of bare-earth topography and canopy height for four study sites. Analyses of the TLS data, in addition to measurements of soil shear strength and particle size, document the potential for detention in interband spaces and a near-inverse proportionality between band spacing and regional slope. We describe a cellular automaton model (herein called model 1) for vegetation band formation that includes just two user-defined parameters and that generates vegetation bands similar to those at our field sites, including the inverse proportionality between spacing and regional slope. A second model (model 2) accurately predicts the width of vegetation bands in terms of the number and spacing of plants and the geometry of individual plant mounds. We also present a GIS-based analysis that predicts where bands occur within a region based on topographic and hydroclimatic controls.

1. Introduction

[2] Vegetation bands are one of the most striking examples of landscape self-organization on Earth. Vegetation bands (also called arcs) are quasiperiodic bands of vegetation, oriented parallel to topographic contour and separated by bare interband spaces, that form in some gently sloping arid to semiarid environments. Vegetation bands in our study sites in the Mojave Desert of southern Nevada (Figures 1 and 2) are composed of clusters of shrubs, approximately 5–15 individuals wide in the along-slope direction, separated by interband spaces with widths that vary from a few meters to a few hundred meters. Vegetation bands in our study sites form in areas characterized by regional slopes of approximately 0.0003–0.02 m/m, i.e., those characteristic of a low-energy fluvial environment. Vegetation bands sit higher than the interband spaces due to the development of topographic mounds beneath each plant. Water often ponds in the interband spaces, as evidenced by surficial features associated with ephemerally ponded water, including multigenerational closed polygonal mud cracks [Lichvar et al., 2004].

Figure 1.

Aerial photographs of the four study sites in southern Nevada. The slope aspects indicated are approximate because the slope aspect varies somewhat within each study site.

Figure 2.

Field photographs of vegetation bands and interband spaces in southern Nevada. (a) Closed polygonal mud cracks in interband spaces. (b) Vegetation bands (top of image) are characterized by coalescing plant mounds that result in a higher topography than the adjacent interband spaces (bottom of image). Transitions between bands and interband spaces are abrupt. (c) An example of the sediment redistribution that takes place in small (i.e., ∼0.3 m wide) channels located in some vegetation bands. These channels are often sourced from water that spills into the vegetation band from the upslope interband space during high-water conditions. Small tributary channel networks may also exist on the bands that join up with these channels before they exit the downslope end of the band, where they become distributary fans and deposit sediment as shown. (d) Plant mounds are Gaussian shaped with average full width at half maximum height equal to 0.5 to 0.75 m (shadscale (Atriplex confertifolia) shown here). (e) Average distances between bushes are 1.0–1.5 m. (f) To acquire the topographic data, two terrestrial laser scanners were raised to approximately 3.5 m above the ground and moved in tandem in the downslope direction.

[3] Vegetation bands have been described in dry lands throughout the world, including Australia [Mabbutt and Fanning, 1987; Tongway and Ludwig, 1990; Dunkerley, 1997a, 1997b; Dunkerley and Brown, 2002, 1995; Ludwig et al., 1999], Africa [MacFadyen, 1950; Hemming, 1965; White, 1970; Thiery et al., 1995], the Middle East [White, 1969], and North America [Cornet et al., 1988, 1992; Montaña, 1992]. The literature on vegetation bands has grown significantly in the past 20 years due to the potential for vegetation bands to be sensitive indicators of climate change [e.g., Dunkerley, 1997b; Valentin and d'Herbes, 1999; von Hardenberg et al., 2001; Yizhaq et al., 2005] and a growing interest in the origins of self-organized landscape patterns [e.g.,Hallet, 1990].

[4] It should be noted that bands of vegetation can form along paleoshorelines [Wright and Bent, 1968] as well as at larger scales when particular species occur within specific elevation zones in mountain ranges [e.g., Whittaker and Niering, 1975]. The vegetation bands of this paper (Figure 1), which are generated without the need for preexisting banded topography (e.g., pluvial shorelines) and which occur at much smaller scales than vegetation zones in mountain ranges, should not be confused with these other types of banding.

[5] Vegetation bands/interband spaces exhibit several morphological and sedimentological patterns that can be used to test mathematical models for vegetation band formation. First, Eddy et al. [1999]found that the spacing of vegetation bands in Australia is equal to approximately 0.1 m divided by the regional slope. Regional slope in this context refers to the slope calculated at horizontal scales larger than the spacing between vegetation bands. In this paper we document a similar relationship for vegetation bands in southern Nevada. To date, no model of vegetation band formation has been shown to reproduce this inverse relationship between spacing and slope. Second, the width of bands in the along-slope direction, in contrast to the spacing between bands, does not vary significantly with regional slope. Rather, in southern Nevada vegetation bands vary in width over a relatively small range, i.e., from approximately 5 to 15 plants. This range is much smaller than the variation in spacing between bands, which varies over nearly 2 orders of magnitude. Third, soils of interband spaces exhibit higher bulk density and shear strength values compared to soils in vegetation bands. Fourth, vegetation bands do not migrate significantly over interannual to decadal time scales based on analysis of historical aerial photographs [e.g.,Cornet et al., 1992; Montaña, 1992; Couteron et al., 2000].

[6] Vegetation bands are widely thought to form due to positive feedbacks among vegetation density, soil porosity/permeability, and infiltration rates (illustrated conceptually in Figure 3a). In this feedback, locally higher vegetation densities promote greater infiltration in the soil beneath vegetation bands through an increase in soil porosity and permeability (as multiple generations of root growth and decay create macropores through which infiltrating water can be more readily conducted), leading to higher average soil moisture conditions and a greater carrying capacity for vegetation in bands relative to interband spaces [e.g., Dunkerley and Brown, 1995; Lejeune and Tlidi, 2002; Dunkerley, 2002; Rietkerk et al., 2002; Ursino, 2005] (see Borgogno et al. [2009]for an excellent review). In this model, water storage in interband spaces has a positive effect on plant growth in bands via the redistribution of water from interband spaces to bands by runoff. As such, this model predicts that vegetation/biomass density should be greater in vegetation bands (where water use is maximized) than in nearby unbanded areas of similar climate. This conceptual model for vegetation band formation is most often quantified mathematically using coupled reaction-diffusion equations for biomass and soil water availability [e.g.,Borgogno et al., 2009]. In addition to bands, these equations also give rise to patterned vegetation in the form of spots and rings, with the type of pattern that develops dependent on the degree of aridity and other parameters in the model. The standard conceptual model for vegetation bands includes no explicit role for topography, reflecting the fact that most models assume a locally planar slope that does not change with time as vegetation bands become established.

Figure 3.

Schematic diagram contrasting (a) the classic model for vegetation band formation with (b) the new model proposed in this paper based on our study sites. In the classic model, topography does not play an explicit role in controlling vegetation band geometry, and the bands form via positive feedbacks among vegetation density, soil permeability, and infiltration rates. In the new model, the geometry of ephemeral ponds and near-ponded areas between bands controls the spacing of bands, resulting in an inverse proportionality between band spacing and regional slope.

[7] Field-oriented studies of vegetation bands, in contrast, have documented the important role of topography in vegetation band formation. Vegetation growth, for example, leads to the development of plant mounds beneath each plant as multiple generations of roots displace soil upward, as evidenced by the lower bulk density of soils beneath vegetation bands relative to interband spaces. A band of plants oriented parallel to topographic contour can, via the development of plant mounds, lead to water detention in the spaces between bands [Dunkerley, 1997a, 1997b]. Detention in this context refers to the development of ephemerally ponded or near-ponded conditions, i.e., surface water velocities sufficiently close to zero to cause fine sediment deposition. Ephemeral detention may be crucial to the formation of vegetation bands/interband spaces because detention can lead to hypoxic or anoxic conditions, high soil salt contents, and high soil cohesion, all of which make it difficult for plants to become established in interband spaces.

[8] The alternative model proposed and tested in this paper (Figure 3b) is based on the hypothesis that water influences the formation of vegetation band sequences primarily as an inhibitor of plant growth (via water detention) in interband spaces rather than as a promoter of plant growth in bands. To motivate this alternative model, consider the fact that areas of bare ground in many arid to semiarid environments are devoid of vegetation because they receive too much water rather than too little. Playas in the southwestern U.S. occupy the lowest portions of topographically closed or nearly closed basins. They are the wettest areas of these generally water-limited environments yet they have the lowest vegetation density. Ecologists have proposed several explanations for this apparent contradiction. First, studies have suggested that wind erosion of smooth playa surfaces remove seeds before they germinate [Fort and Richards, 1998]. This hypothesis is likely incorrect because it presupposes the existence of a playa and because seeds can be readily deposited in mud cracks of playa surfaces (Figure 2a) where they are protected from wind erosion [e.g., Johnson and Fryer, 1992]. Second, ecological studies have proposed that ponded water creates hypoxic or anoxic conditions that, if sufficiently long in duration, prevent seeds from germinating [Crawford, 1977]. This phenomenon is known in the botany and agriculture literature as soaking injury (see Drew [1997] and Sairam et al. [2008] for reviews). In the case of playas with a sufficiently shallow groundwater table, anoxic conditions may develop even in the absence of surface water [e.g., Dahlgren et al., 1997]. However, in many playa environments where water tables are tens to hundreds of meters below the surface (as is the case in our study region in southern Nevada), hypoxia or anoxia requires surface water detention. Third, water detention can lead to the deposition of fine sediment that leads to soils of sufficient cohesion/shear strength that plant roots cannot become established. Although this mechanism has not been proposed as an explanation for the low vegetation density of playas specifically (to our knowledge), the role of soil compaction in reducing vegetation cover in arid and semiarid environments is well established [e.g., Adams et al., 1982]. Fourth, water detention can lead to the deposition of salts that create conditions inhospitable for the growth of non-salt-tolerant species [e.g.,Schaber, 1994]. Mechanisms two through four together provide a basis for associating ephemeral detention with the inability of new plants to become established.

[9] Of the published studies that have modeled vegetation band development, the approach of this paper is most similar to that of Saco et al. [2007], who were the first to emphasize the importance of topography in controlling vegetation band formation within a modeling framework. The model of Saco et al. [2007]combines the classic coupled reaction-diffusion equations for the ecohydrological interactions within vegetation band sequences [e.g.,Rietkerk et al., 2002] with a landscape evolution model. Our model differs from that of Saco et al. [2007] in several important respects. First, the Saco et al. [2007] model predicts that runoff discharge is maximized in interband spaces because that is where hydraulic roughness is minimized. Here we show that the opposite condition holds in our field sites in southern Nevada. Surface water velocities are either zero (in the case of closed topographic basins) or sufficiently close to zero that fine sediment that silt can be deposited in interband spaces. In contrast, surface water velocities are an order of magnitude faster in vegetation bands. Second, in the Saco et al. [2007] model, variations in slope are due to spatial variations in erosion/deposition by flowing water. In this paper, microtopographic variations that control water detention are due to mounding associated with plant growth in bands. Mounding beneath plants is primarily a result of the increase in porosity (or, equivalently, the decrease in bulk density) associated with the displacement of soil upward by plant roots over multiple cycles of vegetation growth/decay. Third, the model of Saco et al. [2007] predicts sinusoidal variations in biomass between a low but finite biomass in interband spaces and a higher biomass in bands. Here we show that biomass is essentially zero in interband spaces, an observation consistent with our model prediction.

[10] Section 2describes two mathematical models for vegetation band formation. Model 1 illustrates the self-organization of multiple bands from an initially uniform vegetation distribution. Vegetation growth in model 1 is associated with the formation of a topographic mound that enhances the potential for ponding water upslope from the vegetation band if the newly established vegetation has neighbors located in the contour-parallel direction. Model 1 does not have the computational efficiency to resolve individual plants, hence a second numerical model (model 2) is needed to understand why vegetation bands are approximately 5–15 individuals wide. Model 2 resolves individual plants and illustrates how the density and shape of plant mounds control the widths of vegetation bands. Model 2 does not have the computational efficiency of model 1, hence both models are needed (model 1 to understand the large-scale morphology of fields of many vegetation bands, and model 2 to understand the detailed morphology within a vegetation band down to the scale of an individual plant mound).

[11] Section 3describes field work we conducted in four vegetation band/interband sequences in southern Nevada using detailed topographic surveys and other field measurements, including soil particle size analyses, shear strength, and infiltration rates. TLS was used to create high-resolution (∼10 cm2/pixel) maps of bare-earth topography and canopy height for each study site and to test for the potential for water detention in interband spaces. A third numerical model (herein called model 3) was developed to test whether, even in vegetation bands that do not pond water upslope, surface water velocities during floods are sufficiently slow that silt can be deposited, thus leading to soil mechanical properties similar to those associated with ponded conditions. Our TLS data were also used to test whether an inverse proportionality exists between vegetation band spacing and regional slope similar to that of the vegetation bands in Australia studied byEddy et al. [1999]. This relationship is important because, where it exists, it provides a robust pattern that any model of vegetation band formation should honor. Field and laboratory data for soil properties can indicate whether or not young plants face an increased challenge to establishment in interband spaces relative to vegetation bands, due, for example, to the relatively high cohesive/shear strength of soils in interband spaces.

[12] Section 4describes a GIS-based analysis that predicts the occurrence of vegetation band/interband sequences within our study region. In this analysis, vegetation bands are assumed to occur only in areas with slopes between approximately 0.0003 and 0.02 m/m because it is only within that range of slopes that areas of ephemeral water detention are larger than the typical spacing between individual plants and smaller than the maximum width of low-relief areas in or near the valley bottoms in our study region. In order for vegetation bands to form, peak flow depths must also be sufficiently shallow that vegetation bands and their associated mounds are not eroded away over time scales of years to decades. We show that these slope- and flow-depth-based criteria for the formation of vegetation bands are met in most of the small, internally drained basins where vegetation bands are found to occur in southern Nevada. These conditions are rarer elsewhere in the southwestern U.S., thus providing a basis for understanding where vegetation bands do and do not occur in our study region and why vegetation bands are relatively common in southern Nevada but relatively uncommon elsewhere in the southwestern United States.

2. Mathematical Modeling

2.1. Model 1: Mathematical Modeling of Multiple Bands

[13] Model 1 includes three basic elements: a stochastic birth/death process for vegetation, an assumption that vegetation cannot grow in areas susceptible to ponding, and sediment redistribution once a prescribed maximum topographic relief between pixels is exceeded. Vegetation density in the model is characterized by discrete units from 0 to a prescribed maximum value Vmax. To account for mound development underneath plants, each change in the vegetation density up (down) increases (decreases) the local elevation beneath that pixel by a prescribed amount hm/Vmax (nominally equal to 0.1 m), where hm is the height of the mound at maximum vegetation density. For simplicity, the default value for the maximum relief between adjacent pixels before sediment redistribution takes place is set equal to hm/Vmax, so that the maximum difference in vegetation density between adjacent pixels is equal to 1. Model 1 was designed to minimize the number of parameters to just two: the prescribed maximum vegetation density Vmax (default value of 4) and the mound height hm. The output of model 1 depends on just these two parameters, as well as the initial topography and vegetation density.

[14] A unit of vegetation is selected for removal from a random pixel during each time step. A unit of vegetation is added to another randomly chosen pixel if that pixel is not in a ponded domain and if the vegetation density of the pixel is below the prescribed maximum density. When the threshold relief is exceeded, a unit of elevation equal to hm/Vmax is redistributed along the direction of steepest descent until it reaches a pixel where adding that unit of elevation will not result in an oversteepened condition. When it finds that new location, the elevation at that location is raised by an amount equal to hm/Vmax. Locations of ponding are mapped every Nm time steps in model 1 using a recursive algorithm that fills all pits and flats until a spill point is reached [Pelletier, 2008]. In principle, the model should remap zones of ponding after each time step in the model because the birth or death of even one unit of vegetation has the potential to change the map of ponded zones. However, mapping ponded areas is computationally intensive, so we map ponded zones only every Nm time steps, keeping the value of Nm as small as possible, i.e., NmNxNy, where the NxNy is the number of pixels in the model domain. The model was rerun for a smaller value of Nm to check that the model results were not sensitive to the value of Nm.

[15] Figure 4 illustrates representative results of the numerical model with Vmax = 4, hm = 0.5 m, Nx = 50, Ny = 150, and Nm = 100. The initial topography in this case is a plane dipping downward in the figure. The topography is characterized by the total relief, R, of the plane between the upper and lower boundaries of the model domain (2 m in the example illustrated in Figure 4). The example in Figure 4was obtained using periodic boundary conditions in the contour-parallel direction and pseudoperiodic boundary conditions in the along-slope direction. Pseudoperiodic boundary conditions in this context means that the topography on the lower end of the model wraps around to the upper end of the model for the purposes of computing slopes and performing sediment redistribution along paths of steepest descent, but only after the vertical displacement,R, associated with the difference in elevation between the two boundaries is accounted for. Using periodic and pseudoperiodic boundary conditions in this way minimizes finite-size effects in the model.

Figure 4.

Example model output for (a) topography (shown as shaded relief with illumination direction from top to bottom of the image), (b) vegetation density, and (c) ponded water depth for an initially planar topography with 2 m of relief from the upper portion of the grid to the lower portion.

[16] The model self-organizes into a dynamic steady state with vegetation bands spaced proportionally to the mound height divided by the regional slope. In this dynamic steady state, bands change slightly in morphology as vegetation units increase/decrease locally, but the bands themselves are stable over time, i.e., there is no postband configuration. In the example output pictured inFigure 4, the initial vegetation density was assumed to have a uniform value of 2. The number of bands formed in the model is approximately equal to the initial relief divided by half of the maximum mound height, i.e., 2R/hm, or 8 given R = 2 m and hm = 0.5 m. Depending on the random number seed used to generate the pseudorandom number sequence, however, the number of bands can deviate from 8 (as in the example pictured in Figure 4, which has 7 bands). There is no horizontal length scale indicated in the example results of Figure 4 because the model has no horizontal length scale, only a vertical length scale (hm). This fact necessarily implies that the model predicts an inverse proportionality between band spacing and regional slope. If, for example, the pixel width is defined to be 3 m, the length of the model domain would be 450 m and the slope (for the prescribed relief of 2 m between the upper and lower boundaries of the grid) would be 0.00444 m/m. Alternatively, if the pixel size was set to 6 m, the slope length would be 900 m, the spacing between vegetation bands would be twice as large as in the case with 3 m pixels, and the slope would be half as large. Therefore, the spacing of bands in the model is inversely proportional to regional slope in model 1.

2.2. Model 2: Mathematical Modeling of a Band With Individual Plants Resolved

[17] In contrast to the spacing between vegetation bands, the widths of vegetation bands in the along-slope direction (i.e., perpendicular to topographic contour) do not vary systematically with regional slope, i.e., vegetation bands are approximately 5–15 bushes wide in the along-slope direction, irrespective of slope. In order to better understand how ponded conditions arise in interband spaces and how they are controlled by the width of the vegetation band and the geometry of the plant mounds that compose the band, we developed a numerical model, herein referred to as model 2, of a single vegetation band evolving through time via the growth of individual plants and their associated mounds (Figure 5). This second model, distinct from model 1, is needed because we found it computationally unfeasible to model the development of many bands within a vegetation band/interband sequence starting from a uniform initial condition with no assumptions regarding where plants grow (aside from the constraint that vegetation density could not exceed Vmax) and simultaneously model the detailed morphology of individual bands down to the scale of individual plant mounds. Models 1 and 2 are thus both needed and complement one another, i.e., they focus on different scales of the same phenomenon.

Figure 5.

Representative output for the numerical model of a single vegetation band evolving toward a ponded state with the accumulation of Gaussian-shaped plant mounds. The number of plants required before a significant pond is created varies with the ratiowm/λp. For wm/λp = 0.33, approximately 30 plants are needed to create a significant ponded area upslope from the band (Figures 5c and 5f), while for wm/λp = 0.5 the required number is approximately 15 (Figures 5e and 5f). The curves in Figure 5f were obtained by averaging the results of 100 runs together.

[18] Model 2 begins with a single row of plants placed along the center of the grid with spacing equal to a prescribed value λp(default value of 1 m). Each plant has a Gaussian-shaped mound beneath it with a height of 0.1 m and a full width at half maximum value given bywm. New bushes are added to a random location on the grid with a probability proportional to exp (−x/λp), where x is the distance between the new plant and its closest neighbor. In this way, a vegetation band is created with an exponential distribution of plant spacings characterized by a mean value of λp. After the addition of each new plant, zones of potential ponding are mapped.

[19] Figures 5a–5e present color maps of the elevation of plant mounds above the surrounding topography and the depth of ponded water predicted by model 2. Figure 5a illustrates the case with λp = 1 m and wm = 0.33 m after 200 plants have been introduced to an initially planar slope (sloping from the upper to the lower portion of the image) with a gradient of 1%. It is helpful to normalize the number of plants to the width of the model domain and the plant spacing, i.e., math formula = N λp/Nx. After normalizing in this way, math formula represents the average width of the band in the downslope direction in terms of the number of individual plants. Figure 5a shows that the addition of math formula = 5 individuals is sufficient to initiate minor ponding within a small portion of the band. As the value of math formula increases to 15 (Figure 5b) and to 30 (Figure 5c), the size of the zone of ponding grows nonlinearly as the mounds beneath plants develop a sufficiently connected network in the contour-parallel direction to result in significant ponding.Figures 5d and 5e show the corresponding results for the case with wider mounds, i.e., wm = 0.5 m, but the same average spacing between plants. Larger ponds form with fewer individuals in the case with wm = 0.5 m compared to the case with wm = 0.33 m because there is less space for water to flow downslope between plant mounds when the ratio of mound width to average spacing is larger. Figure 5f plots the average ponded width upstream from vegetation bands as a function of the width of the bands (expressed as math formula) for three different values of wm/λp. This plot was made by averaging the results of 100 different realizations of the model with the same parameters but different random number seeds. Due to the stochastic nature of the model and the threshold nature of the development of ponded conditions, individual realizations of the model exhibit stepwise and variable relationships between ponded width and band width. Averaging the results of 100 realizations removes this variability in order to highlight the average trends. Measurements made from the TLS data at our study sites (described in section 3) indicate that the average spacing between individual plants within vegetation bands is approximately 1.0–1.5 m and the average width of plant mounds is approximately 0.5–0.75 m. These values suggest that 0.5 is an appropriate reference value for wm/λp in our study sites. Model results with wm/λp = 0.5 shown in Figure 5f indicate that little or no ponding takes place until bands are approximately 10 bushes wide, i.e., the size of ponds increases nonlinearly (from a ponded width of 0.5 m to 5 m) as the band width increases from math formula = 10 to math formula = 15 in this case. Values of wm/λp that are significantly smaller than 0.5, i.e., 0.33, require bands to be > 25 individuals wide before significant ponding occurs, while those with significantly higher values of wm/λp can create significant ponding with bands that are just a few individuals wide.

3. Field Observations and Measurements

3.1. Study Sites: Climate and Vegetation

[20] Southern Nevada is home to dozens of areas with vegetation bands. Along State Route 95 between Beatty and Goldfield there is an unusually high density of easily accessible sequences of bands and interband spaces. We chose four of these sites for intensive study (Figure 1). In addition to ease of access, we chose these areas because they exhibited a broad range of band spacings both within and between the four sites. The goal of the field work is to test the predictions of the theoretical framework developed in section 2.

[21] Our study region is characterized by many small, internally drained basins, a consequence of the recent (approximately 30–10 Ma) tectonic extension and the relatively arid climate of the region. The climate of the area is characterized by a mean annual precipitation of approximately 150 mm yr−1based on long-term climate data from Beatty, NV (elevation of 1008 m above sea level (asl)). Measurements of groundwater table depths in the study region are sparse, but in Lida Valley (location of sites 2 and 3) and nearby Stonewall Flat (site 4), the depth to the groundwater table is more than 70 m [Lopes et al., 2006]. Vegetation bands in our study sites parallel topographic contour closely and in some cases change orientation by more than ninety degrees over distances of a few hundred meters as the fluvial valleys they occupy change direction. While eolian deposition may contribute to some sediment accretion within bands, the orientations of the bands are unrelated to prevailing wind directions based on available wind gauge data, which follow regional trends and do not change direction significantly over spatial scales of ∼100 m in low-gradient topography.

[22] Site 1 is located in the Saltbush scrub vegetation type. The most common shrubs found at this site were shadscale (Atriplex confertifolia), four-wing saltbush (Atriplex canescens), and greasewood (Sarcobatus vermiculatus). These plant species thrive in moderately alkaline and saline environments [Mozingo, 1987] (moderate given greasewood's inability to tolerate salinity above 1%) [MacKay, 2003]. Sites 2 and 3 are close to one another and significantly higher than site 1 at 1400 m asl. These sites were transitional between the saltbush scrub and shadscale scrub vegetation type based on the plants present. This vegetation type includes species such as spiny hopsage (Grayia spinosa) and winter fat (Krascheninnikovia lanata), yet still includes Sarcobatus and Atriplex species. Shadscale is dominant at these sites, with greasewood, Russian thistle (Salsola tragus), green Molly (Kochia Americana) and bud sagebrush (Artemisia spinescens) also common. The vegetation type at site 4 was also of the shadscale type and the elevation was only slightly higher than sites 2 and 3, i.e., 1440 m asl. The only new species found at site 4 was the Joshua tree (Yucca brevifolia) encroaching on the playas and entering some bands. The most obvious change compared to sites 2 and 3 was the dominance of greasewood and Russian thistle, with many bands composed almost entirely of these two species.

3.2. Topographic Measurements and Analyses

[23] We constructed high-resolution, bare-earth DEMs for each of our study sites using TLS. At each site, two Leica C10 scanners were used to acquire scans along parallel survey lines located approximately 100 m apart. The scanners were raised to approximately 3.5 m above the ground (Figure 2f) to optimize point density and minimize ground occlusion by vegetation. By moving the scanners in tandem in the downslope direction, we were able to acquire approximately 30 scans of each site and cover areas of up to ∼1 km2 a day. A single field of Leica targets (locations shown in Figure 6) was used for the two scanners which, after processing with Leica Cyclone software, made it possible to register data from both scanners into a unified point cloud for each site. Typically four to six targets were surveyed from each scan station to ensure an accurate and robust registration of the point clouds from individual scan stations into a unified point cloud. A subset of the target locations was also surveyed with Real-Time Kinematic Global Positioning System (RTK-GPS) receivers to obtain absolute georeferencing for each unified point cloud.

Figure 6.

(a–d) Shaded relief color maps of the TLS-derived high-resolution, bare-earth DEMs of the study sites. The total relief in each of the study areas is approximately 1 m over horizontal length scales of ∼1 km. Target locations are shown as white crosses.

[24] We used the Terrascan software package to distinguish ground and vegetation points within each point cloud using an iterative algorithm that assumes the lowest points are ground returns. Terrascan iteratively adds additional low points to the cloud of ground points if they result in a sufficiently smooth surface. We created 0.1 m/pixel bare-earth and canopy height raster data sets (Figure 6) of each site using an average of the ground points and vegetation points within each 0.1 m × 0.1 m pixel domain, respectively. We also repeated the analyses of this paper on two alternative bare-earth DEMs constructed from the same TLS-based point cloud, one with resolution of 0.05 m/pixel and the other with 0.1 m/pixel, adopting the lowest point in the portion of the point cloud within each pixel domain as the ground elevation for that pixel, in order to ensure that the results of the bare-earth analyses were not sensitive to the method of point cloud processing or to the resolution of the bare-earth DEM. The bare-earth DEMs exhibit approximately 0.1 m of relief within vegetation bands over spatial scales of 1 m. This value is comparable to topographic relief observed in the field beneath vegetation bands. In contrast, vegetation exhibits relief of 0.3–0.4 m over the same spatial scale. The Leica C10 has an accuracy of less than 0.01 m at a distance of 100 m. Leica Cyclone reports scan-to-scan registration errors in cases where more than three overlapping targets are available between adjacent scans. Maximum errors accrued during scan-to-scan registration reported by the Leica Cyclone software were less than or equal to 0.01 m. As such, the maximum vertical error in the DEMs is less than or equal to approximately 0.01 m.

[25] The classic conceptual model for vegetation bands considers them to be natural water harvesting systems, i.e., runoff from interband spaces infiltrates into the high-permeability soil beneath vegetation bands to support more vegetation than would be possible without water harvesting from interband spaces. The TLS data we collected allows us to test this hypothesis by comparing the vegetation density in unbanded areas to that of vegetation bands. Contrary to the predictions of the classic model, we found vegetation density to be as high or higher on unbanded alluvial fans adjacent to vegetation bands (Figure 7). All else being equal, alluvial fans would be expected to have lower vegetation density compared to the valley bottoms where vegetation band/interband sequences occur because they have steeper slopes and coarser sediments and therefore retain less water in soils. Figure 7illustrates a subset of site 2 that includes a transition from a sequence of bands and interband spaces on the gently sloping valley floor to a significantly steeper alluvial fan located on the southern edge of the study site. To compare the vegetation density on the unbanded fan and fan-playa transition zone to that of the vegetation bands, we constructed a canopy height raster data set at a resolution of 0.1 m/pixel within the portion of the study area that includes the transition from the banded area to the adjacent unbanded alluvial fan. The average canopy height was computed by averaging the 0.1 m/pixel canopy height data within 5 m × 5 m pixels. Averaging the canopy height over a 5 m length scale ensures that the effects of both variable plant height and density are accounted for (i.e., a lower density of individuals may yield a higher average canopy height if the plants in that area are sufficiently tall to offset their lower density) in order to arrive at a metric that is related to biomass density or vegetative carrying capacity. Data from the color map of average canopy height (Figure 7) were averaged in E-W transects (excluding interband spaces) to obtain a plot of the variation in average canopy height in vegetated areas along a N-S direction (plotted in the lower right corner ofFigure 7). These data show that vegetation density is the same or slightly higher on the unbanded fan compared to the vegetation bands. At all of our sites, this pattern is consistent with anecdotal observations that vegetation density is as high or higher on the fans surrounding vegetation bands (where no water ponds) than on the vegetation bands themselves. Portions of each study site that have the potential for ponding water were identified using the same recursive filling algorithm used in the mathematical model (e.g., Figure 4c) with the bare-earth DEMs shown inFigure 6 as input. Figure 8shows the portions of each site (in black) that have the potential for ponding water during flood events. This figure demonstrates that many interband spaces, the largest ones in particular, pond water ephemerally. Interband spaces that do not pond water are still, on average, topographically lower than the adjacent vegetation bands, but they are bounded by one or more incised channels that connect one interband space to the next interband space downslope. Channels that drain interband spaces through a vegetation band may have developed contemporaneously with that of the band/interband sequence, or they may postdate the development of the sequence by having formed as erosional features by the breaching of a previously ponded interband space during high-flow conditions.

Figure 7.

Comparison of average canopy height in bands compared to surrounding unbanded areas. (a) Aerial photograph of a portion of site 2 where the sequence of vegetation bands/interband areas grades into an alluvial fan. (b) Color map of the bare-earth DEM. (c) Color map of average canopy height in 5 m × 5 m pixels. Canopy height averaged along E-W swaths (interband areas excluded) is shown as a function of N-S distance at the bottom right. The average canopy height is slightly lower in the vegetation bands compared to the distal margin of the alluvial fan.

Figure 8.

(a–d) Maps of topographically closed areas (shown in black) where water-ponded conditions may occur for each of the study sites.

[26] To test for the presence of near-ponded conditions in the portions of our study sites that are not topographically closed and hence do not pond water, we used the 2D hydraulic model FLO-2D [FLO Engineering Inc., 2006] to estimate the surface water velocities. We refer to this model as model 3 to distinguish it from models 1 and 2 of section 2. For model 3 we chose the central portion of site 3 (Figure 9a) as representative of areas in our study sites that have well-developed bands but are not topographically closed based on the results of the recursive filling algorithm illustrated inFigure 8c. The FLO-2D model solves the full shallow-water equations using a Manning-type drag formulation (with an assumed Manning'sn value of 0.03). A depth of water equal to 0.1 m was introduced into the model at its upstream boundary and no infiltration was assumed to occur. As such, the model conserves the total volume of water and the momentum of the flow as it is routed. The model predicts that peak flow velocities in interband spaces are approximately 0.03 m s−1 (Figure 9c), increasing to approximately 0.3 m s−1 as surface water flow is focused into the channels that drain one interband space to the next through vegetation bands. According to the Hjulström diagram [Hjulström, 1935], velocities of ∼0.01 m s−1are sufficiently slow that coarse silt can be deposited (contributing to soils with high cohesive/shear strength in interband spaces). Our model-predicted, peak flow velocities are slightly faster than 0.01 m s−1, but given that 0.03 m s−1 represents a peak flow velocity for this representative flood event it is reasonable to conclude that in the waning stages of such a flood the flow would achieve velocities ∼0.01 m s−1, resulting in coarse silt deposition and hence the development of soils with a high cohesive/shear strength.

Figure 9.

Maps of (b) peak flow depth and (c) peak flow velocity predicted by the FLO-2D model for the central portion of site 3 where the results inFigure 8 indicate that ponded conditions do not occur. (a) Input topography. The model predicts that flow velocities are approximately 10 times lower, i.e., 0.03 compared to 0.3 m s−1 for interband spaces compared to incised channels within bands.

[27] In the conceptual model of this paper (Figure 3b), all plant mounds are assumed, for simplicity, to have the same height (hm) measured between the base of the mound and the spill point that separates one interband space from another. Based on that assumption, the spacing between bands, λ, should be approximately equal to the mound height, hm, divided by the regional slope, S. This suggests a simple test of the conceptual model of this paper: band spacing should vary in inverse proportion to the regional slope.

[28] In seeking to test the inverse proportionality between band spacing and regional slope, we faced a choice of how best to use the high-resolution, bare-earth topographic data we constructed. The simplest approach is to pick points near the center of each band and measure the vertical and horizontal spacings between those points on adjacent bands using our TLS-derived bare-earth DEMs. This approach is problematic for two reasons. First, the spacing between bands varies significantly in the contour-parallel direction, and second, the slope also varies depending on the spatial scale of the slope measurement and the position from which the elevation differences are measured. Given the relatively small number of vegetation bands we have data for (∼20) and the dense topographic data collected for each site, it is better to use all of the bare-earth topographic data for each site in the analysis. To do this, each bare-earth DEM was first analyzed to create a map of bands and interband spaces using threshold absolute values of curvature and slope. Interband spaces have both very low slopes (typically less than 0.05 m of relief over 50 m) and curvatures. In contrast, slopes within the vegetation bands can vary from 0 to 0.5 over distances of less than a meter. Once the vegetation bands and interband spaces are identified, the analysis treats each pixel-wide transect in the regional along-slope direction separately. For each transect, the analysis identifies the upslope and downslope ends of each interband space. The distance between these points is the local band spacingλ. The average position between the upslope and downslope ends of each interband space is used to identify the center point of each interband space in the regional along-slope direction. The slope is calculated as the ratio of the vertical and horizontal distances between the center of that interband space and the center of the adjacent interband space in the upslope (downslope) direction. A centered slope is calculated for each interband center point using the average of the slopes in the upslope and downslope directions. Calculating the slopes at the centers of each interband space has the advantage that slope values are least variable in these areas. In contrast, slope values computed between vegetation bands are highly variable according to differences in mound height which may be greater than the change in average or regional elevation over horizontal length scales of ∼100 m. This analysis yields thousands of pairs of values forλ and S. Values for λ were averaged using a geometric mean in logarithmically spaced bins of S (Figure 10). Although this analysis procedure is complex, it has the advantage that it includes all of the data in the DEM, as opposed to using data from only one transect or portion of the band/interband sequence, and it is robust because it computes slopes using portions of the landscape that are most representative of the slope at a spatial scale that averages over the variations between bands and interband spaces. As Figure 10 shows, three of the four sites exhibit a significant inverse relationship between average spacing and slope. Least squares linear regressions to the logarithms of the data in Figure 10 constrain average band spacing to be a power law function of slope with exponents −0.72 ± 0.04, −0.65 ± 0.05, −0.16 ± 0.05 and −0.53 ± 0.03 for sites 1–4, respectively. The model prediction follows the straight line in Figure 10 corresponding to λ = cS−1 where c = 0.05 m. Error bars shown in Figure 10 were obtained by decreasing the bin width by a factor of 2 and using the variation in bin averages within each of the larger bins as an estimate of uncertainty. Site 3 is anomalous in that it shows a less significant inverse relationship between band spacing and slope. This site also exhibited the least variability in band spacing and was the smallest of the four sites we studied.

Figure 10.

Plots of average band spacing versus regional slope. The model predicts an inverse relationship (shown as straight line) if the mound height is uniform across a study site. Data for sites 1, 2, and 4 show an inverse relationship close to the model prediction. Site 3 does not show as significant an inverse relationship between band spacing and regional slope compared to the other sites. Error bars represent one standard deviation from the mean.

3.3. Soil Measurements and Laboratory Analyses

[29] Soil samples and field measurements were acquired at two locations each within sites 1, 2, and 4. At each of the two locations within each site, samples and measurements were collected at four different positions along the interband-to-band continuum, i.e., near the centers of interband spaces (called playa), on interband spaces within 2 m of a vegetation band (called playa in band), within the vegetation band near a mound with no plant present (called mound), and within the vegetation band near a plant (called mound at veg), resulting in a total of twenty four samples. This sampling scheme was used to characterize differences in the upper 0.05 m of soil between vegetation bands and interbands.

[30] Visually, there was no indication of significant salt accumulation in the soils of the interband spaces. In the field we attempted to use an electrical conductivity meter to measure the salt content of the soils but obtained values too low for consistent positive readings. The salinity of our drinking water was higher than the salinity in the soils of the interband spaces we studied, hence these are not especially saline environments.

[31] Field measurements included soil shear strength and infiltration rate/unsaturated hydraulic conductivity, K.Soil shear strength was measured in three repeat measurements at each microtopographic location with a standard-sized, Humboldt soil–shear strength vane. Infiltration rate into the soil surface was measured using a Decagon minidisk infiltrometer set at a suction of 0.5 cm. Water volume was recorded at 30 s intervals for 5 min. Infiltration data were compiled and used to calculateK using the Decagon instruction manual that follows the methodology of Zhang [1997].

[32] Two field samples were collected at each microtopographic location at each site with a 66.4 cm3 soil ring sampler. Bulk density calculations were completed by measuring the mass of the sample after a 36 h drying time at 50°C to remove all water from the sample. Water content was less than 2% by volume for all samples. A second sediment sample collected at each sampling location was used for particle size analysis on a Malvern Mastersizer 2000 diffractometer (or laser particle size analyzer). Each field sample was manually mixed to insure a homogenous sample and representative grain size distribution. An approximately 10 cm3 subsample from each field sample was placed in a centrifuge tube where approximately 30 ml of deionized (DI) water was added to disperse the soil. Samples were allowed to settle for 3 days and supernatant and floating organic material was decanted off without any loss of sediment. Samples were put in a 40°C water bath and 30% H2O2 was added in 1 ml aliquots until no reaction was observed. Samples were rinsed and centrifuged three times for three minutes at 3500 rpm to remove any nonreacted H2O2. Samples pretreated in this way were run on a Malvern Mastersizer 2000 diffractometer following the methodology of Sperazza et al. [2004]. The material refractive index was set at 1.52 and the absorption set at 0.1 to represent the mostly silica sand and silt composition of the samples. Samples were measured in three consecutive measurements and the average was taken as the final result.

[33] Results from the soil sample analyses indicate that surface soils within the vegetation bands (mound and mound at veg microtopographic locations) are significantly different than those in interband spaces (playa and playa in band microtopographic locations; Table 1). In general, surface soils in the interband spaces have higher bulk densities and shear strengths than those in the vegetation bands. Also, surface soils within the interband spaces include more clay and silt than soils within the vegetation bands, while soils within vegetated bands have higher mean grain sizes and higher sand percentages. Values of K follow the grain size and shear strength data (Table 1), i.e., lower K values and higher Kvalues correspond to stronger and finer interband soils and weaker and coarser vegetated band soils, respectively. It should be noted that the bulk densities reported for sites within the vegetation bands are maximum estimates because these soils have many low-bulk-density areas (void spaces formerly occupied by plant roots, animal burrows, etc.) that cannot be accurately sampled because emplacing the sampling ring into the soil caused the soil to collapse.

Table 1. Bulk Density, Mean Shear Strength, Mean Grain Size, Percent Texture Classes, and Unsaturated Hydraulic Conductivity for Soil Samples Collected From Different Microtopographic Locations at Each Site
SiteLocationBulk Density (g/cm3)Mean Shear Strength (kPa)Mean Grain Size (μm)Percent ClayPercent SiltPercent SandTexture ClassaKb (cm/d)
  • a

    Texture class based on soil texture ternary diagram with clay, silt, and sand defined as grains <2 μm, grains 2–50 μm, and grains >2000 μm.

  • b

    Unsaturated hydraulic conductivity (K) calculated using Zhang's [1997] methodology. Analyses with a negative slope of the cumulative infiltration curve are prescribed a K value of <0.1 cm/d.

Band 1
Site 1playa1.2740.6737.26166816silt loam3.60
 playa in band1.3216.33151.6673459sandy loam17.28
 mound1.2112.33123.2273954sandy loam4.32
 mound at vegetation1.138.33341.8321385loamy sand48.96
Site 2playa1.5041.3323.00167113silt loam0.24
 playa in band1.2431.3336.65166321silt loam<0.1
 mound1.1610.00108.2083755sandy loam45.36
 mound at vegetation0.978.33127.9973063sandy loam36.72
Band 2
Site 1playa1.2556.0024.06157213silt loam<0.1
 playa in band1.2756.6742.97155530silt loam0.24
 mound1.2210.33143.3741680loamy sand95.04
 mound at vegetation1.329.67248.9452471sandy loam49.68
Site 2playa1.5235.0030.68167014silt loam1.20
 playa in band1.6315.33105.76113158sandy loam<0.1
 mound1.5819.33130.9182270sandy loam4.32
 mound at vegetation1.1513.6798.8283953sandy loam58.32
Band 4
Site 1playa1.5474.6740.11145828silt loam<0.1
 playa in band1.5468.0026.08186715silt loam14.40
 mound1.238.00118.8062272sandy loam30.24
 mound at vegetation1.3418.00134.0921286loamy sand118.08
Site 2playa1.2669.3320.5212808silt loam4.80
 playa in band1.2289.6736.2997021silt loam<0.1
 mound1.1717.6748.98106228silt loam15.60
 mound at vegetation1.0135.33103.0642472sandy loam28.08

4. GIS-Based Analysis of Vegetation Band Occurrence

[34] Any model of vegetation band formation should provide some predictive understanding of where vegetation bands occur. In this section we describe a GIS-based analysis using threshold slope and flow depth criteria to predict where vegetation bands do and do not occur within our study region in southern Nevada.

[35] The conceptual model illustrated in Figure 2 suggests that vegetation bands are unlikely to form when the slope is outside of a particular range. When the regional slope is too large, the length of the zone of ponding upslope from the vegetation band is too small to form an interband space that is significantly larger than the typical spacing between bushes. Given a mound height of 0.05 m and a minimum spacing of approximately 3 m for an interband space to be distinguishable from its adjacent vegetation bands (where plant spacing is approximately 1.0–1.5 m), the relationship λ = cS−1, where c = 0.05 m and λ = 3 m, suggests that the regional slope must be less than approximately 0.02 in order for a sequence of vegetation bands/interbands to form. At the other extreme, slopes less than approximately 0.0003 will form bands spaced by approximately 200 m or more. In order for a field of several vegetation bands to form with such large spacings, the topography on which those bands form must have slopes that are approximately equal to 0.0003 m/m over a distance of ∼1 km. Basins in our study sites are ∼10 km wide and are occupied predominantly with prograding alluvial fans with slopes greater than 0.02 m/m. As such, these basins lack the sufficiently broad areas with slopes in the range of 0.0001 to 0.0003 m/m that would be needed to form vegetation bands with spacing greater than 200 m. Instead, the bottommost portions of basins and fluvial valleys tend to form a single large area of ephemerally ponded water (i.e., a playa) or a field of vegetation bands with spacing less than 200 m. Model 1 does not produce vegetation bands when the regional slope, defined by R/Ny, is greater than the mound height, hc, because the domain of detention upslope from an incipient vegetation band does not extend for more than 1 pixel. Conversely, when the slope is very low, multiple bands also do not form because any incipient vegetation band tends to flood the entire model domain, forming a single playa.

[36] In addition to the regional slope control, vegetation bands likely form only in areas subject to peak flow depths of less than approximately 0.3 m. Slopes between 0.0003 and 0.02 m/m are relatively common in valley floor channels of the western U.S., yet vegetation band development is the exception rather than the rule. This rarity may be explained by the fact that many of the valley floor channels with slopes in the range of 0.0003 to 0.02 m/m convey flows with sufficient bed shear stresses to erode any vegetation bands that might otherwise be present. Flows that are significantly deeper than the height of a vegetation band would likely erode the soft, bioturbated sediments. As such, vegetation bands are likely to form only in areas where peak flow depths are less than 0.3 m. Peak flow depths are controlled by basin area (with smaller basins yielding lower flow depths), precipitation intensity (more arid climates yielding lower flow depths), channel geometry (less incised channels with larger width-to-depth ratios yielding lower flow depths), hydraulic roughness, and the permeability of soils and sediment (with higher permeability values yielding lower flow depths).

[37] Figure 11illustrates the results of the GIS-based analysis designed to test the hypothesis that vegetation bands form only in areas where regional slopes and peak flow depths are within appropriate ranges.Figure 11a illustrates where sequences of vegetation bands and interband spaces occur in the study region based on 1 m/pixel aerial imagery. The best DEM available for this type of analysis is the 10 m/pixel or 30 m/pixel DEMs of the U.S. Geological Survey National Elevation Database (NED). This data set defines the topographic variations of steep upland landscapes relatively well compared to gently sloping piedmonts, where elevation values are interpolated from widely spaced contours. Contour interpolation often results in unrealistically steep slopes near the locations of contours in the original topographic maps and unrealistically low slopes elsewhere. One way to minimize such slope artifacts is to average slope values over larger areas. Figure 11b illustrates a slope map created by spatially averaging all areas with slopes less than 0.01 m/m over a 1 km × 1 km moving window. This approach does nothing to modify slopes steeper than 0.01 m/m but helps to mitigate slope artifacts associated with gentler slopes.

Figure 11.

Comparison of (d) predicted versus (a) actual vegetation bands in southern Nevada using the slope- and flow-depth-dependent criteria described insection 4. (b) Slope map and (c) flow depth map used in the analysis.

[38] The first step toward mapping peak flow depths over such a large region is to map the unit contributing area in each pixel. Such mapping requires a hydrologically correct DEM, i.e., one in which each pixel has a pixel in the downslope direction so that flow that enters each pixel can be routed downslope. Hydrological correction typically involves recursively filling in the small pits and flats in a DEM so that all of the pixels drain to the boundaries of the grid. Southern Nevada has many internally drained basins, however, that, if hydrologically corrected, would raise the elevation of those basins by tens of meters until they spill over into neighboring basins. To prevent this behavior and retain internal drainage where it occurs naturally, we ran a hydrological correction algorithm that flagged the lowest pixel in each internally drained basin as a sink to be retained. Such flagged pixels are not incremented and the model allows those sites to be locally closed basins. All other pixels must drain to the boundaries of the grid or to one of the flagged low spots where internal drainage is allowed. The contributing area is calculated using the multiple-flow direction (MFD) algorithm ofFreeman [1991]. Of the standard flow methods, including D8 and D∞, the MFD method is the one most appropriate for computing contributing areas in distributary topography [Pelletier, 2008]. Once the unit contributing area, a, is calculated for each pixel, the peak flow depth is estimated according to the relationship h = fab where b = 0.73 and hw is the peak flow depth. This b value follows from the assumption that peak flow depth is proportional to unit discharge and that measured unit discharges in stream channels of the southwestern U.S. scales with unit contributing area to the 0.73 power [Baker, 2006]. The value of f was estimated by a least squares fit to average peak annual flow depth data for gage stations available in NWIS. The resulting peak flow depth map is illustrated in Figure 11c. It should be noted that accurate contributing area maps, particularly those in gently sloping environments, require that channels be well resolved in the input DEM data. NED data do not resolve all channels accurately, particularly on low-relief topography. The result is that in some cases channel flow that should be confined is predicted to be unconfined inFigure 11c and vice versa. Nevertheless, Figure 11c represents the best possible flow depth map obtainable using currently available topographic data for this large region.

[39] Figure 11d illustrates the predicted locations of vegetation bands based on the criteria 0.0003 < S < 0.02 and h < 0.3 m. The map does a reasonably good job at predicting where vegetation bands occur and their relative rarity in the study region. As such, the similarity between Figures 11a and 11dadds confidence to the conceptual model of this paper and provides a preliminary basis for using slope and flow-depth-based criteria to understand where vegetation bands do and do not occur regionally within the southwestern U.S. There are a few locations inFigure 11where bands are predicted to occur but where playas or well-vegetated fluvial valleys occur instead. These discrepancies may occur due to DEM data of limited accuracy and/or controls on vegetation band development besides slope and flow depth.

5. Discussion and Conclusions

[40] The models of this paper reproduce the four major patterns observed in vegetation bands. Model 1 and the conceptual model (Figure 3b) reproduce the inverse relationship between spacing and slope documented here for vegetation bands in southern Nevada and by Eddy et al. [1999] for bands in Australia. The exponents characterizing the inverse relationship between band spacing and slope in the data of Figure 10 deviate significantly from the model prediction of −1, however. As such, more work is needed to understand the controls on band spacing and why they deviate from −1. Model 2 reproduces the observation that vegetation bands vary in width over a relatively small range, i.e., from approximately 5 to 15 plants.

[41] In the conceptual model of this paper, topographic mounding occurs in vegetation bands, a process consistent with the lower bulk density measured in soils of vegetation bands compared to interband spaces documented in this paper for our study sites and by Dunkerley and Brown [2002] for vegetation bands in Australia. The correlation between soil properties and topographic location was hypothesized by Dunkerley and Brown [2002] to be related to hydrologic pathways and the deposition of finer materials such as clay and salts in interband spaces. Ephemeral water ponding within interband spaces is evidenced by the high soil cohesion/shear strength and low Kvalues indicative of soil surface sealing due to the deposition of silt- and/or clay-sized particles. Water detention can cause soaking injury to seeds [e.g.,Crawford, 1977; Drew, 1997; Sairam et al., 2008], limiting the growth of vegetation and resulting in effectively bare interband spaces. The high silt and clay percentages that pose a mechanical impediment to the establishment of young plant roots were found in interband locations but not found in vegetation band locations. The median grain size measured in interband spaces is consistent with hydraulic model results indicating velocities ∼0.01 m s−1in interband locations. Faster velocities and concentrated flow within the vegetation bands preclude the deposition of the silt- and clay-sized particles; larger grain sizes (sand) dominate in these locations.

[42] Model 1 of this paper is consistent with the observation that vegetation bands do not migrate significantly over time scales of years to decades, i.e., the stochastic nature of plant birth and death in the model gives rise to some variations in band shape and size over time once bands form but the bands themselves do not migrate significantly, even over many generations of plant births and deaths. Many coupled reaction-diffusion models of vegetation band development predict migration rates on the order of meters per year or greater, rates that are tens to hundreds of times larger than the maximum rates of migration inferred from field studies [e.g.,Thompson and Katul, 2009, and references therein]. Recent papers [e.g., Pueyo et al., 2008; Thompson and Katul, 2009] have proposed specific seed dispersal mechanisms as solutions to this paradox. The model of this paper suggests that including the details of seed dispersal may not be necessary in order to obtain a model consistent with the observed stationarity of vegetation bands in nature.

[43] The standard model of quasiperiodic vegetation patterns in dryland environments, including bands as well as other patterns not considered here such as spots and rings, is that they arise from a common set of ecohydrological feedbacks (in which increased water availability leads to higher biomass) quantifiable with coupled reaction-diffusion equations for biomass and soil water availability [e.g.,Borgogno et al., 2009]. The model of this paper, taken together with recent research highlighting the importance of eolian processes in the formation of spots and rings in the Mojave Desert [Ravi et al., 2008], suggests that, in the Mojave Desert at least, bands may be sufficiently different from rings that both patterns cannot be viewed as minor variations of the same fundamental reaction-diffusion pattern-forming mechanism. Our model was motivated by observations and measurements at our study sites in southern Nevada, therefore it is important to emphasize that the conceptual and mathematical models we propose may not hold for other fields of vegetation bands. Nevertheless, the inverse relationship between band spacing and regional slope is not unique to southern Nevada [i.e.,Eddy et al., 1999], hence the model may be applicable to other vegetation band/interband sequences.

[44] The conceptual and numerical models of this paper adopt a binary approach to the relationship between water detention and the inability of plants to become established in interband spaces. Ideally, the ecology literature would have established quantitative estimates of the depth and duration of detention necessary to prevent the establishment of plants and our model would use this information explicitly as criteria for determining plant survival or death. However, to our knowledge, the ecology literature has not quantified the threshold conditions for when soaking injury and/or fine sediment/salt deposition makes it impossible for plants to become established. Even if such conditions had been quantified, they would likely vary significantly by species. As such, we are unable to specify how often or how long detention must occur in order to prevent the establishment of young plants in our study sites. More research is needed on this aspect of the problem.


[45] We thank the Department of Geosciences at the University of Arizona, via the generous donors to the William R. Dickinson Fund, for support of the field work involved in this project. We also thank UNAVCO, with support from the National Science Foundation (NSF) and NASA under NSF cooperative agreement EAR-0735156, for loaning us one of the two scanners used in this study. Field work and field equipment were also partially funded by the Philecology Foundation of Fort Worth, Texas. We thank Travis Huxman and Bob Webb for helpful communications on the role of water detention in inhibiting plant growth in dryland environments. We also thank editor Alex Densmore, the associate editor, and three reviewers (Taylor Perron and two anonymous reviewers) for helpful comments that greatly improved the paper.