Journal of Geophysical Research: Earth Surface

Methodology for reconstructing wind direction, wind speed and duration of wind events from aeolian cross-strata

Authors

  • Erin N. Eastwood,

    1. Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
    2. Now at Shell Oil Company, New Orleans, Louisiana, USA
    Search for more papers by this author
  • Gary Kocurek,

    Corresponding author
    1. Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
      Corresponding author: G. Kocurek, Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, 2275 Speedway, M.S. C9000, Austin, TX 78712, USA. (garyk@jsg.utexas.edu)
    Search for more papers by this author
  • David Mohrig,

    1. Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
    Search for more papers by this author
  • Travis Swanson

    1. Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
    Search for more papers by this author

Corresponding author: G. Kocurek, Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, 2275 Speedway, M.S. C9000, Austin, TX 78712, USA. (garyk@jsg.utexas.edu)

Abstract

[1] A methodology for reconstructing wind direction, speed, and event duration from aeolian dune cross-strata was developed from analysis of crescentic dunes at White Sands, New Mexico, during wind events. Dune lee faces were surveyed, lee-face deposits mapped, deposition rates measured, grain size sampled by stratification type, and winds characterized from meteorological and field data. The spatial distribution of lee-face stratification styles is a function of the incidence angle formed between the wind and the brinkline, with secondary controls by wind speed and dune sinuosity and height. Sets of wind-ripple strata form at incidence angles of 25°–40°, grainfall/grainflow foresets over wind-ripple bottomsets at 40°–70°, and grainflow/grainfall foresets at 70°–90°. Erosional reactivation surfaces form at incidence angles up to 15°; bypass surfaces up to 25°. The total sediment load is fractionated within lee-face stratification types. Wind speed can be reconstructed from relationships between grain size, transport mode, shear velocity and grain-settling velocity. Where the full range of grain transport modes occurs and grain size is limited by shear stress, the shear velocity and grain-size range in each transport mode can be estimated by assuming the coarse fraction in grainflow strata traveled in creep, and the coarse fraction in grainfall traveled in saltation. The minimum duration of a wind event can be estimated using measures of shear velocity, dune height and dune forward migration. Method limitations arise with source-area control on grain size, extremes in wind events, and severe truncation of sets of cross-strata.

1. Introduction

[2] Aeolian dune cross-strata are the most direct stratigraphic record of continental winds and house a climatic record of the wind events that gave rise to the cross-strata. Aeolian cross-strata, which represent dune lee-face deposition, are inherently complex because: (1) most wind regimes are not unidirectional, (2) most dunes are too large to reform with each directional component of the wind regime, (3) the wind is rarely uniform or steady, and (4) the wind (i.e., primary flow) is strongly modified by the dunes themselves (i.e., secondary flow). Despite these complexities, geologists have long used the orientation of cross-strata (i.e., strike and dip) to interpret wind direction and compared these interpretations to models of regional or global circulation [e.g.,Parrish and Peterson, 1988; Loope et al., 2001; Rowe et al., 2007]. In some examples, the types and orientations of cross-strata and bounding surfaces have been used to interpret cyclic components of the wind regime [e.g.,Hunter and Rubin, 1983; Kocurek et al., 1991; Scherer and Goldberg, 2010]. In other examples, the average dip direction of the cross-strata has simply been taken as the wind direction [e.g.,Tanner, 1965; Parrish and Peterson, 1988; Mountney and Jagger, 2004]. As discussed below, this simplifying assumption is correct in only the special case where the total wind regime is unidirectional, and making this assumption may yield an inaccurate and incomplete picture of the wind regime. In addition, the wind speed associated with cross-strata has only rarely been addressed in a quantitative manner [Jerolmack et al., 2006, 2011], and although daily [Hunter and Richmond, 1988] and annual cycles [e.g., Hunter et al., 1983; Hunter and Rubin, 1983; Crabaugh and Kocurek, 1993] have been interpreted in sets of cross-strata, the duration of given wind events has not been explored.

[3] The purpose of this paper is to build upon the existing understanding of sediment transport and airflow over aeolian dunes using data from the White Sands Dune Field in New Mexico to develop a quantified methodology for the reconstruction of wind direction, wind speed, and duration of wind events from sets of aeolian cross-strata. Determination of the wind direction is based upon the spatial distribution of lee-face stratification types. Determination of wind speed is based upon the distribution of grain sizes within stratification types. Determination of the duration of wind events is based upon the volume of sediment transported during a wind event.

2. Theory

2.1. Reconstruction of Wind Direction

[4] Experiments [Rubin and Hunter, 1987; Rubin and Ikeda, 1990], analytical solutions [Werner and Kocurek, 1997] and computer models [Werner, 1995; Bishop et al., 2002] all indicate that the crestlines of aeolian dunes are oriented to be as perpendicular as possible to all constructive wind directions within the total wind regime. This “gross bedform-normal” crest orientation [terminology ofRubin and Hunter, 1987] applies to any bedform where the duration of sediment-transporting flow from a given direction is shorter than the reconstitution time of the bedform, and applies to all but the smallest of aeolian dunes [Rubin and Ikeda, 1990]. In a wind regime that is not unidirectional, therefore, wind directional components of the total wind regime may not strike the dune crestline at right angles. In addition, because most dunes are sinuous, a variety of incidence angles occur along the crestline for any given wind direction.

[5] Current thinking is that secondary flow on the lee face of a dune is primarily a function of the incidence angle (i.e., the angle formed between the primary wind and the local crestline orientation), but also of dune morphology and, to a lesser extent, atmospheric stability [Sweet and Kocurek, 1990; Walker and Nickling, 2003]. For steep dunes (i.e., dunes with slipfaces) during neutral atmospheric conditions that characterize most sand-transporting events [Frank and Kocurek, 1994], secondary flow is thought to be controlled by incidence angle. Based upon a variety of dunes in nature and a rotating experimental dune, Sweet and Kocurek [1990] classified lee secondary flow as a function of the incidence angle: transverse (70–90°), oblique (10–70°), and longitudinal (0–10°). With a longitudinal configuration, the secondary lee flow is attached, undeflected and transport is entirely by tractional processes. As the incidence angle becomes greater (i.e., oblique), the lee flow is deflected to blow alongslope. Flow separation in the form of a vortex with components of alongslope and reversed flow [e.g., Allen, 1982] develops as the incidence angle increases. A 2-D roller with crest-normal return flow occurs as the incidence angle approaches 90°. Wind speed along a lee face is approximately the crestal wind speed times the cosine of the incidence angle: secondary flow speed approaches the primary wind speed at longitudinal incidence angles and approaches zero at transverse incidence angles [Tsoar, 1983]. The general result is the dominance of tractional transport at longitudinal incidence angles, gravity-driven processes at transverse incidence angles, and the co-existence of both gravity-driven and tractional processes at oblique incidence angles.

[6] Lee-face processes and the resultant stratification types result from the secondary flow configurations. The basic aeolian lee-face processes fromHunter [1977] are: (1) grainfall in which grains blown past the dune brink settle to the surface in paths that can be strongly modified by lee turbulence [Nickling et al., 2002]; (2) grainflow in which sediment deposited immediately downslope from the dune brink reaches the angle of initial yield, avalanches and flows down the dune slipface, and (3) wind ripplesin which lee sediments of any origin are incorporated into and transported by the ripples. Grainfall and grainflow are gravity-driven processes and their exclusive presence indicates a transverse flow configuration where there is a general absence of tractional transport. Wind ripples are indicative of a flow configuration where tractional transport dominates, becoming increasingly prominent with decreasing incidence angles. Lee ripples typically have crests oriented parallel to the dip direction of the lee face as a function of alongslope transport and gravity [Howard, 1977]. With oblique flow, both grainfall/grainflow and wind ripples can occur, depending upon the spatial dominance of gravity-driven versus tractional transport. Typically, gravity-dominated processes on the upper lee face yield downslope to ripples migrating alongslope where tractional transport dominates.

[7] In aeolian cross-strata, the stratification types are generally distinct and easily recognized in trenches or outcrops (e.g.,Hunter, 1977, 1981; Kocurek and Dott, 1981). Grainflow cross-strata are tabular, tapering-upward wedges at the angle of repose and typically show inverse grading as a result of sorting during the avalanche process. Grainfall deposits are typically indistinctly laminated and range in dip from horizontal bottomsets to foresets that approach the angle of repose. Wind-ripple deposits are very distinctive, and consist of typically thin (i.e., millimeter scale), inversely graded laminae in which each lamina represents the migration of one wind ripple. In nature a variety of styles in the arrangement of the basic stratification types in sets of cross-strata occurs as a function of the total wind regime, the most common configurations are shown byKocurek [1991].

[8] In summary, the current state of understanding is as follows. Because dune crestline orientation is the product of all constructive primary winds, the average dip direction of cross-strata within a set reflects the overall dune migration direction as measured normal to the generalized crest orientation. Unless the total wind regime is unidirectional, however, this average dip direction alone is insufficient to determine all the constructive primary wind directions that gave rise to the cross-strata. Because any given cross-strata orientation shows the local crestline orientation, a coupling of local crest orientation with stratification style brackets the local incidence angle into broad categories of transverse, oblique and longitudinal configurations. A compilation of pairs of local cross-strata orientation and stratification style all along a set reveals the overall crestline shape and orientation, and the range of incidence angles along the crestline. The correlation between incidence angle and stratification style, however, is known in only the broad categories of transverse, oblique and longitudinal. A primary goal in developing the methodology here is to provide a more precise correlation between incidence angle and style of stratification types, and to examine the extent to which other parameters may impact the distribution of lee-face surface processes.

2.2. Reconstruction of Wind Speed

[9] The three end-member modes of sediment transport by the wind are creep, saltation and suspension, and these arise because of the balance between grain properties and the surface forces that cause motion [Bagnold, 1941]. For sand dunes, saltation is the primary mode of transport and is characterized by grains that rise from the surface in quasi-parabolic arcs to again collide with the surface and eject other grains. Saltating grains, once ejected from the surface, are driven by fluid drag and gravity, with negligible effects from fluid lift by turbulent eddies. The heaviest grains move in creep, characterized by sliding, rolling or short hops, and are driven by the combination of the fluid stresses acting on grains and the kinetic energy transfer associated with impacts from saltating grains. The lightest grains are suspended, carried into the flow when vertical velocities associated with turbulent eddy motions exceed grain settling velocities, and have only rare surface contact. In nature, however, there is significant gradation between the end-member modes of transport, especially betweenpure saltation and pure suspension. This gives rise to motions best described as modified saltation and incipient suspension [e.g., Nishimura and Hunt, 2000; Nino et al., 2003].

[10] Attempts to characterize sediment transport all utilize basic relationships between fluid forces and grain properties. Fluid forces are characterized by the shear stress, τ, exerted on the bed by the flowing fluid. This boundary shear stress is commonly presented as a shear velocity, u*, where

display math

and ρf is the density of the moving fluid. Shear velocity is then typically estimated from a measured velocity profile by application of the “law of the wall”

display math

where uz is the wind speed at height z above the surface, κ is von Kármán's constant (equal to 0.407 in neutral atmospheric conditions), and z0 is the surface roughness height where zero velocity occurs. Neglecting sorting, the transportability of a grain is a function of properties such as volume, shape and density. These grain properties can be characterized by grain settling velocity, ws, and the critical shear velocity to initiate movement, u*c. Bagnold [1941] observed that once grain motion is established, saltation continues and creep begins to occur at a u*lower than that required to initiate motion as a result of momentum transfer from the impact of saltating grains. From wind tunnel data, this critical impact-augmented shear velocity,u*i, is approximately 0.7 u*c [Bagnold, 1941; Nishimura and Hunt, 2000].

[11] Although developed for grains settling in water, the equation by Ferguson and Church [2004], as modified by Jerolmack et al. [2006], can be applied to air:

display math

where inline image is the relative density of sediment where ρs is the sediment density, g is the acceleration due to gravity, d is the nominal grain diameter, v is kinematic viscosity for the fluid, and C1 and C2 are constants with values of 18 and 1, respectively, for natural sand.

[12] We follow Jerolmack et al. [2006] in adopting the equation by Shao and Lu [2000] for u*c, which is based upon data from Iverson and White [1982] for a range of grain sizes that includes most aeolian sand:

display math

[13] Given values for ws, u*c and u*, the range of near-bed conditions associated with the different modes of sediment transport have been described as a function of the ratiosu*/u*c and ws/u*, as summarized in Figure 1a. Values of u*/u*c best serve to address the boundary between creep and saltation, as originally defined by Bagnold [1941], in which grains begin to saltate once u*c is exceeded (i.e., u*/u*c > 1), but creep occurs (and saltation continues) until u*/u*c = 0.7 (Figure 1a). Using high-speed videos,Nishimura and Hunt [2000] found that particle trajectories in saltation begin to be distorted by turbulent eddies when u*/u*c ≥ 1.5. This change in grain paths, although described by Nishimura and Hunt [2000] as the onset of suspension and adopted as such by Jerolmack et al. [2006, 2011], is probably best described as the onset of modified saltation. This change in grain paths would not be ordinarily detectable in the field, and is not a practical definition for suspension. In this study we adopt the relationship that creep occurs when

display math

beyond which saltation occurs with an upper limit that is best characterized by the ratio inline image (Figure 1b).

Figure 1.

Summary diagram of experimentally derived boundaries for grain transport in creep, saltation, modified saltation, incipient suspension and suspension modes. (a) Summary of experimental results defining modes of grain transport by inline image and inline image. Note that modified saltation and incipient suspension are used by different authors to define the same mode of transport positioned between saltation and suspension. (b) Grain-transport boundaries adopted for this study as justified in the text.

[14] Values of inline image are most appropriate to define partitions in the gradation between saltation and suspension because the downward grain settling velocity must be balanced by the upward velocities associated with turbulent eddies, which scale with shear velocity at small distances above the bed [e.g., Bagnold, 1966; Nino et al., 2003]. Attempts to define this gradation in both air and water, summarized in Figure 1a, are subject to differing experimental methods and terminology, as well as making judgmental determinations within a clearly gradational process. The onset of deviations in saltation paths (described above) by Nishimura and Hunt [2000] begins when inline image ≈ 10, with greater values of the ratio reflecting pure bedload. More conservatively, Shao [2000] gives the boundary between saltation and modified saltation as ws/u* ≈ 2, with suspension occurring when ws/u*< 0.5 Using high-speed videos for transport in water,Nino et al. [2003] give the boundary between saltation and incipient suspension at inline image ≈ 2.5, and the boundary between incipient suspension and full suspension as inline image ≈ 1. These values agree with earlier works by van Rijn [1984] and Laursen [1958] where significant numbers of grains are advected into the flow interior by turbulent eddies when inline image ≈ 2.5, and by Bagnold [1966] where a measurable concentration profile of suspended sediment develops at inline image ≈ 1. Laursen [1958] and Smith and Hopkins [1972] argued that the transition to suspension transport is complete when inline image = 0.3.

[15] For field studies, a definition of suspension based upon a measurable sediment concentration profile is the most appropriate definition for the onset of suspension, and we adopt suspension as occurring when

display math

(Figure 1b). All experimental work agrees that the transition from saltation to suspension is well underway in the range of inline image = 2.0–2.5, and we adopt incipient suspension as occurring when

display math

(Figure 1b). Modified saltation would be largely undetectable from saltation in the field, and we combine these modes of transport, using the definition that pure saltation is tied to conditions where

display math

(Figure 1b), whereas Jerolmack et al. [2011] adopt ws/u* ≥ 3.0 for this same boundary.

[16] Given ranges of inline image and inline image associated with the different modes of grain transport, the basis for our approach is the hypothesis that the total grain population traveling over a dune brink is sorted on the dune lee face as a function of lee processes (see section 2.1). Because the preserved aeolian rock record almost exclusively represents the lowermost portions of dune lee faces [Rubin and Hunter, 1982; Kocurek, 1981], we are concerned with the grain-size range in the stratification types that are found there. Although grains traveling in saltation can have trajectories that extend to basal portions of small aeolian dunes, we hypothesize that grainfall that accumulates on the basal lee of larger dunes is enriched in grains that traveled in incipient suspension and is depleted in grains that traveled in creep in comparison to the other lee-face deposits. In contrast, grainflow is hypothesized to be more representative of the entire transport range of grains traveling over the dune. Because lee wind ripples reflect tractional transport of any grain population that has passed the dune brink, we hypothesize that wind ripples possess the least diagnostic distributions of grain sizes, with the exception that coarse grain sizes should be associated with deflationary surfaces.

[17] Our approach in determining wind speed largely follows that of Jerolmack et al. [2006, 2011], also at White Sands, but differs in objectives. Jerolmack et al. [2011] systematically sampled dune stoss, crest and lee face in order to determine the mean grain size in transport, from which the characteristic u*for the “dune-forming wind” could be derived. The dune-forming wind, by a combination of magnitude and frequency, does the most work in dune-field construction [Jerolmack and Brzinski, 2010]. This parameter is important, but because dune grain size is similar throughout the Phanerozoic on Earth [e.g., Kocurek, 1996], significant ranges in wind speeds are most likely to be found in the extremes of the grain-size range for each mode of grain transport as preserved in dune cross-strata. Our methodology is focused, therefore, upon characterization of specific wind events as recorded in lee-face stratification, the most common of which will reflect the typical wind regime.

3. Study Area and Methods

3.1. Study Area Overview

[18] Data for this study were collected from the gypsum dune field within White Sands National Monument, New Mexico (Figure 2a). The White Sands Dune Field is situated within the Tularosa Basin and consists of a core of crescentic and barchan dunes, which is rimmed to the north, east and south by parabolic dunes. To the west the dune field yields abruptly to an extensive gypsum plain, Alkali Flat (Figure 2b). Further to the west, occupying the lowest elevations of the basin, are active playa lakes, the largest of which is Lake Lucero. Analysis of the decades-long wind record recorded at nearby Holloman Air Force Base (AFB) byFryberger [http://www.nature.nps.gov/geology/parks/whsa/] and Jerolmack et al. [2011] yields a transport resultant of 060° and 065°, respectively (Figure 2b). Dominant winds are from the WSW and are strongest during the winter-spring, a second mode of winds from the N-NW occurs during the fall and winter, and a third mode of winds from the S-SE occurs during the spring and summer.

Figure 2.

(a) Location of the White Sands Dune Field in south-central New Mexico, USA. (b) Portion of the dune field within the White Sands National Monument, showing the zone of active crescentic and parabolic dunes, deflationary Alkali Flat, and playa Lake Lucero. The wind resultant toward N65E was determined from wind data recorded at Holloman AFB byJerolmack et al. [2011]. (c) Dunes 1, 2 and 3 monitored in this study and the adjacent Dunes Drive, as indicated in (b). The lines define the brink and top of each lee face for the three studied bedforms.

[19] Aspects of the White Sands Dune Field have been addressed in a number of studies, and a much fuller description and interpretation of its history, geomorphology and sedimentology are given collectively by Kottowski [1958], McKee [1966], McKee and Douglass [1971], Allmendinger [1972], McKee and Moiola [1975], Langford [2003], Jerolmack et al. [2006, 2011], Kocurek et al. [2007], Langford et al. [2009], Ewing and Kocurek [2010], Reitz et al. [2010], Szynkiewicz et al. [2010], and Fryberger [http://www.nature.nps.gov/geology/parks/whsa/].

3.2. Methods

[20] Three crescentic dunes were chosen for this study because of their relatively high sinuosity (Figure 2c). The dunes were similar in height, with average brinkline heights of 10.6 m for Dune 1, 9.7 m for Dune 2, and 9.1 m for Dune 3. The brinkline and lee-face base of each dune were surveyed using a Trimble S3 (2″) Robotic Total Station during calm periods before sand-transporting wind events during March and April 2011. During the surveying process, dowel rods (3 mm in diameter) were set into the dune lee faces at ∼2 m intervals from the base of the lee face to the dune brink, forming transects oriented perpendicular to the brinkline. The lateral spacing of these transects was such that representative segments of the curving dune lee faces were sampled.

[21] Both the March and April wind events were ∼24 hours in duration with winds above threshold speed and significant sand transport. Lee-face deposits were identified and mapped along the entire lee faces at a sub-meter scale for Dunes 1 and 2 after the March wind event, and along Dune 3 after the April wind event. Primary wind directions were determined by the average orientation of wind ripples on the upper stoss slopes of the dunes, and compared to the wind data recorded at Holloman AFB during the same intervals. The weather station at Holloman AFB is located ∼14 km ENE of the study area, and wind data, collected at a height of 10 m, consist of average wind speed and direction over 2 minute intervals and the maximum wind gust during 10 minute intervals.

[22] The incidence angle for each approximately straight-line segment of the lee face was determined based upon the primary wind directions, and lee-face deposits were plotted by incidence angle. Dune sinuosity, s, was calculated based upon the surveys using the definition that s = L / L′, where L is the measured brinkline length and L′ is the straight-line distance. Points of divergence in the lee-face secondary flow field were used as the end points for dune segments for which local brinkline sinuosity was also calculated.

[23] During the April wind event, wind speed was measured over a 2 hour period using robust hot-wire anemometers mounted on a staff at heights of 4 cm, 10 cm, 30 cm and 80 cm above the bed at the crest of Dune 3. This wind profile was subsequently compared to the wind record for the same time interval as recorded at Holloman AFB.

[24] The amount of deposition/erosion that occurred on the lee faces during the wind events was measured off of the dowel rods after the wind events, and these changes in surface elevation were converted to lee-face deposition rates by dividing by the length of time during which the wind was above threshold speed.

[25] Grain-size samples were taken at dowel locations. Care was taken to sample the entire lamina/stratum formed by a given lee-face process, such that the entire thickness of wind-ripple laminae and grainflow tongues were taken. Grainfall deposits were sampled by scraping off and collecting only those grains from the immediate surface. Grain-size analysis was performed using a Retsch Technology CamSizer (www.retsch-technology.com), which digitally images and measures most grains in each sediment sample. Errors associated with measuring grain size using this device are significantly less than those associated with sieving techniques. The grain-size distribution for each sediment sample is composed of 50 bins spaced logarithmically over the diameter range of 0.032–2.5 mm and was plotted by lee-face stratification type. The range in grain size for each mode of grain transport (e.g., creep, saltation, incipient suspension, full suspension) as predicted fromequations (5)(8) was calculated for both wind events.

4. Results

4.1. Primary Wind Direction and Incidence Angles

[26] The primary wind directions determined from the average orientation of wind ripples on the stoss slopes of Dunes 1–3 were 069° for the March wind event, and 068° for the April wind event (Figure 3). These values compare to 061° and 059°, respectively, as recorded at Holloman AFB. The differences in primary wind directions as measured at Holloman AFB compared to those measured within the dune field probably occur because: (1) the weather station at Holloman AFB is situated leeward of the dune field, closer to the Sacramento Mountains, and may not experience exactly the same wind regime as that within the dune field, and (2) dune topography affects the orientation of the near-bed flow. The average orientation of stoss-slope wind ripples is taken as the more accurate indicator of the primary wind within the dune field, especially as it relates to the incidence angle, and is used in our analysis.

Figure 3.

Maps of the lee faces of Dunes 1–3 showing the spatial distribution of styles of lee-face stratification (seeFigure 4) as mapped after the March (Dunes 1–2) and April (Dune 3) wind events. Uncolored areas represent dune segments where the lee face was not defined by a brinkline; these segments were not considered in this study. Primary wind directions were determined by the orientation of stoss-side wind ripples. Local incidence angles along approximately straight-line segments of the brinkline are noted to the left of each segment. Sinuosity for entire dunes is given; local segment sinuosity is shown to the right of the segments, with segments of particularly high sinuosity in red. Black dots mark the location of lee-face traverses where sediment erosion/deposition was measured off of dowel rods, and where grain-size samples were taken.

[27] Calculated dune sinuosity ranges from 1.31 for Dune 3, to 1.44 for Dune 1, to 1.61 for Dune 2 (Figure 3). Given the primary wind directions, local incidence angles for approximately straight-line segments of the brinkline range from 2°–90° (Figure 3). Local brinkline sinuosity, defined by points of divergence in the lee-face secondary flow field, ranges from 1.06–1.47 (Figure 3).

4.2. Lee-Face Processes, Stratification and Incidence Angles

4.2.1. Basic Styles of Lee-Face Processes and Stratification

[28] Seven basic styles of lee-face processes and their resultant stratification were identified and are designated as Styles A–G inFigure 4. Within these basic styles, there was significant variation, which is thought to represent stages of development. For example, grainflow deposits varied from pristine to subdued (“ghosts”) where grainflow tongues had been partly blanketed by subsequent grainfall deposits or partly mantled by wind ripples. The seven basic styles of lee-face stratification represent a distillation that would be recognizable in the rock record.

Figure 4.

Field photos and diagrammatic renderings (used as symbols in Figure 3) of the 7 styles of lee-face stratification recognized on Dunes 1–3 after the March and April wind events. (a) Style A – wind ripples (wr) occurring on net erosional, bypass and depositional surfaces. (b) Style B – wind ripples and grainfall (ga). (c) Style C – wind ripples, grainfall and grainflow (gf). (d) Style D – grainfall only. (e) Style E – grainfall and grainflow with basal wind ripples. (f) Style F – grainfall and grainflow. (g) Style G – grainflow only.

Figure 4.

(continued)

[29] Style A (wind ripples) characterized entire segments of lee faces, ranging from those experiencing erosion to bypass to deposition (Figure 4a). At White Sands, ripples on erosional surfaces, which typically exposed weakly cemented dune cross-strata, were coarser grained than those on surfaces undergoing sediment deposition. Wind-ripple stratification is probably the most common stratification type in the aeolian rock record [e.g.,Hunter, 1981, Figures 3–4; Kocurek and Dott, 1981, Figure 8], and consists of the translatent strata of Hunter [1977]; the very thin subcritically climbing variety referred to as “pin-stripe laminations” byFryberger and Schenk [1988].

[30] Style B (wind ripples and grainfall) occurred on surfaces of bypass to deposition and is characterized by grainfall on the upper lee face passing downward to wind ripples (Figure 4b). These lee faces, therefore, show a mix of gravity-driven and traction-driven processes. Grainfall deposits are largely prevented from building to the angle of initial yield and avalanching by alongslope reworking by the wind ripples. At White Sands, Style B ranged from patchy grainfall deposits on largely rippled lee surfaces to lee surfaces mostly covered by grainfall deposits with minor basal wind ripples. The representation of this stratification style in the rock record is a function of original dune size and preserved set thickness. On small dunes, where grainfall typically reaches the base of the lee face, Style B shows a dominance of grainfall deposits in the upper portion of the set passing downward to interlaminated wind-ripple and grainfall laminae, the former commonly showing a high angle of climb [e.g.,Hunter, 1981, Figures 5a and 6; Hunter and Richmond, 1988, Figure 19; Kerr and Dott, 1988; Figure 3a]. On large dunes or where only the most basal lee face has been preserved, Style B may be indistinguishable from Style A except for the intercalation of some grainfall laminae.

[31] Style C (wind ripples, grainflow and grainfall) typically represented a more depositional surface than Style B and one which was more dominated by gravity-driven processes (Figure 4c). Either higher rates of grainfall or less tractional reworking by wind ripples allowed the grainfall deposits to build to the point of avalanching, yielding grainflow tongues. Wind ripples, however, mantled the entire surface between avalanches, and dominated on lower portions of the lee face. Style C is common in the rock record, and is represented by grainflow cross-strata that both (1) intertongue with bottomsets of ripple laminae, and (2) are intercalated with ripple laminae that extend to the top of the sets [e.g.,Blakey and Middleton, 1983, Figure 11c; Hunter and Richmond, 1988, Figure 21; Mountney and Jagger, 2004, Figure 5a].

[32] Style D (grainfall) is characterized by lee faces showing only grainfall deposits, which may extend as aprons onto the interdune floor (Figure 4d). This stratification style should be inherently ephemeral because the grainfall deposits should build to the angle of initial yield and avalanche (Style F). At White Sands this stratification style occurred along tapering segments of transverse dune terminations. Although not common, cross-strata consisting largely of grainfall laminae have been described [e.g.,Hunter, 1981, Figure 5b; Clemmensen and Abrahamsen, 1983, Figure 6a].

[33] Style E (grainflow, grainfall, and basal ripples) is similar to Style C, with the important difference that wind ripples occur only at the base of the lee face (Figure 4e). Style E, therefore, represents a gravity-dominated slipface except for the basal portion where traction still dominates. In the rock record, this stratification style is identified by grainflow cross-strata that intertongue with bottomsets of ripple laminae [e.g.,Chandler et al., 1989, Figures 3a and 3c; Clemmensen and Blakey, 1989, Figure 11]. Ripple laminae intercalated with the grainflow strata, a characteristic of Style C, are largely absent.

[34] Style F (grainflow and grainfall) is characterized by slipfaces in which grainfall mantles some or much of the surface between avalanches and wind ripples are absent (Figure 3f). The extent to which grainfall is carried down the lee face is a function of dune size, wind speed and turbulence associated with lee eddies. In the rock record, Style F is represented by grainfall laminae intercalated with grainflow cross-strata [e.g.,Kocurek and Dott, 1981, Figures 5–6; Clemmensen and Abrahamsen, 1983, Figure 6b], but it may be indistinguishable from Style G where slipface height or other factors precluded grainfall on the lower lee face.

[35] Style G (grainflow) is characterized by slipfaces where pristine avalanche tongues extended from the lee base to the dune brink (Figure 4g). The difference between Style G and Style F is that although grainfall occurred in Style G, it was confined to the uppermost slipface and the frequency of avalanching in Style G was much greater than in Style F. Style G is common in the rock record and consists of sets of cross-strata composed exclusively of grainflow strata [e.g.,Hunter, 1981, Figure 6d; Kocurek et al., 1991, Figure 10; Loope, 1984, Figure 5b; Taggart et al., 2010, Figure 6a].

4.2.2. Distribution of Styles of Lee-Face Stratification by Incidence Angles

[36] The mapping of the styles of lee-face stratification (Styles A–G) on Dunes 1–3 after the March and April wind events illustrates the diversity of stratification that may form along the lee faces of sinuous dunes during single wind events (Figure 3). The simple plotting of these stratification styles by incidence angle shows a general trend from Style A through Style G corresponding to progressively higher incidence angles (Figure 5). Wind ripples and their stratification where the surface was depositional (Style A) dominate at low incidence angles, and grainflow and grainfall stratification (Styles F and G) dominate at high incidence angles. Between these end-members there is a progression in Styles B–E from the first occurrence of gravity-driven surface processes (grainfall at 16° in Style B and grainflow at 22° in Style C), to the last occurrence of tractional transport (wind ripples disappear at 70° in Style E).

Figure 5.

Styles of lee-face stratification (Styles A–G) plotted by their range of incidence angles on Dunes 1–3, as indicated by data point color. Local dune-segment length over which the lee-face stratification style occurred is shown by data point size. Data points circumscribed by dashed ovals represent lee-face processes that occurred on dune segments with high local sinuosity (marked in red onFigure 3). Note the occurrences of first grainfall, first grainflow, and the last occurrence of wind ripples.

4.3. Characterization of Wind Speed

[37] Wind speed is directly characterized by: (1) the velocity profile measured at the crest of Dune 3 during the April wind event, and (2) wind data recorded at Holloman AFB during both wind events. Wind speed is indirectly characterized by: (3) dune migration rates during the wind events, and (4) the grain-size distributions within the lee stratification types.

4.3.1. Direct Characterization of Wind Speed

[38] The wind velocity profile measured at the crest of Dune 3 during the April wind event shows u* = 0.36 m/s as calculated from the equation (2), with zo = 0.2 mm (Figure 6). Wind data recorded at Holloman AFB during the same interval shows an average wind speed of 6.5 m/s, with an average gust speed of 10.3 m/s (Figure 6). The projection of the velocity profile measured at the crest of Dune 3 to the 10 m height at which data are collected at Holloman AFB yields 9.7 m/s, which is within the gust range recorded at Holloman AFB. Indeed, using the average gust speed at 10 m (10.3 m/s) and zo = 0.2 mm yield u* = 0.38 m/s, which is ∼5% greater than the measured crestal u*. In contrast, the velocity profile for the average gust speed, using the highest 10% of wind speeds measured at the crest of Dune 3, projects well beyond the range recorded at Holloman AFB, and yields u* = 0.59 m/s with zo = 0.8 mm (Figure 6). Note that the increase in the value of zo over the same surface with the increase in u* is expected because of the greater intensity of saltation and momentum extracted from the wind [Owen, 1964; Wiberg and Rubin, 1989].

Figure 6.

Velocity profile (blue) for wind measured by hot-wire probes at 4 cm, 10 cm, 30 cm and 80 cm above the bed at the crest of Dune 3 during the April wind event. Each point represents the average speed for a 2-hour sampling interval, with wind speed measured every 10 sec. The range bars on each mean velocity is +/− one standard deviation. The surface roughness height, zo, is the Y-intercept at 0.2 mm. Usingequation (2), the calculated u* is 0.36 m/s. The measured profile is projected up to a height of 10 m, the height at which wind data is collected at Holloman AFB. For the same period as our measurements, the mean and range for average and gust wind speeds recorded at Holloman AFB are shown (green triangle = average, red square = gust). Note that the projected wind speed at 10 m is most closely approximated by the average gust speed measured at Holloman AFB. In contrast, the velocity profile (red) defined by gust speeds measured at the crest of Dune 3 projects well beyond gusts recorded at Holloman AFB, and yields a calculated u* of 0.59 m/s, with a zo of 0.8 mm. The best fit to each velocity profile is presented in the “law of the wall” (equation (2)) format. The p-value for the regression equation using the average wind data is 5 × 10−4 and for the regression equation using the gust data is 5 × 10−3, indicating a statistically significant relationship between the variables in each equation at the 5% significance level.

[39] Because the primary wind is modified as it travels over the dune topography, including acceleration up stoss slopes and deceleration on the lee slopes, the appropriate dune wind speed to compare to that recorded at meteorological stations is not straight-forward. For the White Sands example, theu* calculated at the dune crest is approximated by the u* calculated using the average wind gust as recorded by meteorological data collected at 10 m, and provides a convenient reference point for characterizing the wind event. The average wind gust speed during the monitoring period (23 hrs) for the April wind event was 12.1 m/s, yielding u* = 0.45 m/s, using zo = 0.2 mm. The average wind gust speed during the monitoring period (14 hrs for Dune 1, 22 hrs for Dune 2) for the March wind event was 9.4 m/s, yielding u* = 0.35 m/s, using zo = 0.2 mm. These values of shear stress are adopted here as approximations that characterize their respective wind events. The “formative shear velocity” u*f = 0.39 m/s for the White Sands Dune Field determined by Jerolmack et al. [2011] falls between the u* values for our March and April events.

4.3.2. Lee-Face Sediment Deposition as a Function of Incidence Angle

[40] Sediment deposition on the dune lee faces during the March and April wind events, as determined from measurements taken off of the dowel rods after each wind event, are not uniform but rather trend with incidence angle (Figure 7). Greatest deposition rates occurred at high (transverse) incidence angles, and deposition rates generally decreased with incidence angle, with examples of bypass (i.e., zero deposition) occurring at incidence angles of ∼15–25° and erosion dominating where the incidence angle is less than ∼15°. This relationship between lee-face deposition and incidence angle occurs because the lee face in transverse configurations is unmodified by alongslope transport, whereas alongslope transport of sediment progressively increases and reworks the lee faces of dunes with decreasing incidence angles characteristic of oblique and longitudinal flow configurations.

Figure 7.

Dimensionless lee-face sediment deposition as a function of local incidence angle for Dunes 1, 2 and 3. First the average amount of sediment deposition measured from dowels (Figure 3) on roughly transverse segments of lee face for Dune 1, 2 and 3 was calculated. Then the value for deposition at each transect site was made dimensionless by dividing it by the appropriate mean transverse value for Dune 1, 2 or 3. Measurements for transects on all three dunes are plotted here. Negative values for deposition represent sites of net sediment erosion from the lee face of a dune. The figure includes two trend lines. The thick solid line is the best fit to the data points. The thinner dashed line depicts the control of incidence angle on dune migration speed as first proposed by Rubin and Hunter [1985, equation 2]. Notice that incidence angle alone (dashed line) does a reasonably good job of predicting the relative amount of lee-face deposition tied to dune migration. However, including a shift of twelve degrees (solid line) provides a better fit to data and captures the lee-face erosion measured at transects with low incidence angles. The p-value for this regression equation is smaller than 10−4, indicating a statistically significant relationship between the sine of incidence angle and dimensionless lee-face sediment deposition.

[41] For the White Sands data the relationship between standardized deposition on the lee face, ϕ, and incidence angle is presented in Figure 7. In order to determine ϕ for all transects on Dunes 1, 2 and 3 (Figure 3) the average amount of sediment deposition measured from the dowels on transverse segments of each dune was calculated, 〈ztrans〉. Then the value for deposition at each transect site, zlocal, was divided by its associated dune value for 〈ztrans〉. Measurements for transects on all three dunes are plotted together in Figure 7. Negative values for deposition represent sites of net sediment erosion from the lee face of a dune. This figure includes two trend lines:

display math

and

display math

where α is incidence angle. Equation (9)describes the control of incidence angle on lee-face deposition and, hence, dune-migration speed as first proposed byRubin and Hunter [1985, equation 2]. In Figure 7, equation (9)does a reasonably good job of predicting the relative amount of lee-face deposition, but over-estimates the observed deposition at lower incidence angles.Equation (10)is the best-fit line to the data set presented inFigure 7. Including a shift of 12° captures both the zone of lee-face bypass and the zone of erosion at low incidence angles. The inclusion of this phase shift inequation (10)indicates the relative amount of sediment deposition on the lee faces dunes is not simply a matter of incidence angle. There is a measurable correction associated with lee-face processes that are not a function of incidence angle alone. Resolving these processes is an important avenue of ongoing and future research.

4.3.3. Indirect Characterization of Wind Speed by Measured Dune Migration Rate

[42] The measured, lee-face deposition rate indirectly characterizes the wind events by providing a measure of the sediment transported during the events. Theu* required to transport this sediment over the duration of the wind event is effectively the characteristic u* of the wind event. Because of the potential for alongslope sediment transport in all but the most transverse flow configurations, those deposition rates occurring within measured incidence angles of 70–90° provide the most accurate measure of the event sand transport rate. The average volume flux of sediment, qs (m2/s), can be estimated for transverse segments of the observed dunes (incidence angles >70°) as

display math

where C is dune forward migration rate, H is dune height (10.6 m for Dune 1, 9.7 m for Dune 2, 9.1 m for Dune 3), and ε is sediment concentration of the bed (1 − porosity). Given the grain size and grain sorting found at White Sands, ε is taken as 0.7 [Beard and Weyl, 1973]. Dune forward migration is the horizontal displacement associated with the lee-face deposition as measured off of the dowel rods. Migration rate is this same horizontal shift divided by the time wind speed was above threshold (u* ≥ 0.29 m/s, assuming ρgypsum = 2320 kg/m3) as measured at Holloman AFB during the wind events. During the March wind event, in which the dowel rods were emplaced in Dune 1 for 14 hrs, yielding qs = 4.2110 × 10−6 m2/s, whereas the dowel rods were emplaced in Dune 2 for 22 hrs, yielding qs = 2.662 × 10−6 m2/s. During the April wind event, dowel rods were emplaced in Dune 3 for 23 hrs, yielding qs = 5.665 × 10−6 m2/s.

[43] A volume flux of sediment can be converted to a mass flux of sediment, Qs, simply by multiplying the former parameter by the appropriate grain density. For this study, Qs = ρgypsum × qs. The characteristic u* can then be calculated from Qs using the White [1979] formulation of the Kawamura [1951] equation, as corrected by Namikas and Sherman [1997]

display math

The calculated characteristic u* for the March event is 0.36 m/s for Dune 1 and 0.34 m/s for Dune 2. The average value of 0.35 m/s is the same as that based upon the average gust speed (Section 4.3.1). The calculated u*for the April event is 0.39 m/s, under-estimating theu* = 0.45 m/s based upon the gust speed by ∼15%.

4.3.4. Indirect Characterization of Wind Speed by Grain Size

[44] Table 1shows a compilation in which the grain-size ranges for: (1) creep (512–1091 μm for March, 874–1801 μm for April) were determined using equation (5), (2) saltation (210–511 μm for March, 252–873 μm for April) were determined using equation (8), (3) incipient suspension (118–209 μm for March, 137–251 μm for April) were determined using equation (7)), and (4) full suspension (≤117 μm for March, ≤136 μm for April) were determined using equation (6) for the March (u* = 0.35 m/s) and April (u* = 0.45 m/s) wind events. These values bracket those of Jerolmack et al. [2011], who used somewhat different definitions (see section 2.2) for the “formative wind” (u*= 0.39 m/s) at White Sands to determine grain-size ranges for suspension (<250 μm), saltation (250–650 μm), and creep (650–1300 μm).

Table 1. Transport Modes for March and April Wind Eventsa
Transport ModeCreep 0.7 ≤ inline image < 1.0Saltation inline image ≥ 2.5 inline image > 1.0Incipient Suspension 1.0 < inline image < 2.5Suspension inline image ≤ 1.0
  • a

    Summary of equations defining the boundaries for grain transport modes of creep, saltation, incipient suspension and suspension. For each mode of transport, the predicted grain-size ranges are given for the March and April wind events. Based upon the grain-size data, the percentages for each grain-size range are given for the total volumetric sediment load and the lee-face processes. Estimates foru* for each wind event were based upon average gust speed at 10 m as recorded at Holloman AFB during each event using equation (2) with zo = 0.2 mm. Estimates of ws were calculated from equation (4). Estimates for u*c were calculated from equation (3).

March Wind Event
u* = 0.35 m/s512–1091 μm210–511 μm118–209 μm≤117 μm
Total Volumetric Sediment Load27.3%64.4%6.9%1.4%
Grainflow Fraction31.2%64.5%3.4%0.8%
Grainfall Fraction15.3%71.6%11.6%1.5%
Wind Ripple Fraction35.9%57.1%5.3%1.7%
 
April Wind Event
u* = 0.45 m/s874–1801 μm252–873 μm137–251 μm≤136 μm
Total Volumetric Sediment Load3.9%76.3%15.5%4.2%
Grainflow Fraction6.0%79.8%10.9%3.3%
Grainfall Fraction0.9%76.0%18.8%4.2%
Wind Ripple Fraction3.0%71.5%19.8%5.6%

[45] Adopting the predicted grain-size ranges for each mode of transport,Table 1also shows the percentages for each transport mode for the total volumetric sediment load and for each stratification type, as based upon grain-size analysis (Figure 8). The differences in the percentage for the modes of transport between the total sediment load and the stratification types demonstrate that the total grain population is sorted by the lee-face processes, and this accounts for the differences in the grain-size curves for the stratification types (Figure 8). As hypothesized, grainfall strata are enriched in the incipient suspension load (12% during the March wind event, 19% during the April event) as compared to the total sediment load (7% for March, 16% for April), and depleted in the creep load (15% in March, 1% in April) compared to the total sediment load (27% in March, 4% in April). Also as hypothesized, wind ripples showed the greatest grain-size variation, which is not surprising given their range from coarser-grained erosional forms at low incidence angles to those incorporating significant grainfall at incidence angle approaching 70°. Although the total sediment load was hypothesized to be best represented by grainflow strata, more correctly it appears that the modes of transport that dominate in a given wind event are best reflected by those stratification types where these modes are concentrated. Although the March event, dominated by saltation (64%) and creep (27%), is best mirrored by grainflow stratification (saltation 64%, creep 31%), the April event, dominated by saltation (76%) and incipient suspension (16%), is best mirrored by grainfall stratification (saltation 76%, incipient suspension 19%). The presence of significant creep load in grainfall strata (15% during March) is surprising, but may reflect (1) the impact of wind gusts and (2) continued creep down the lee face because of grain impact. During the March wind event, wind gusts up to 21 m/s were recorded at Holloman AFB, yieldingu* = 0.91 m/s where zo = 0.8 mm, which is sufficient to put the coarsest grains in the grainfall deposits (∼1 mm) into saltation. Alternately, because of the impact of grains bombarding the lee face and the effects of gravity, slow creep may continue down the lee face.

Figure 8.

Cumulative grain-size curves for deposits occurring at the base of the lee faces of Dunes 1–3 following the March (Dunes 1–2) and April (Dune 3) wind events. (a) Grainflow. (b) Grainfall. (c) Wind Ripples. The curves are portioned into modes of grain transport based upon the empirical relationships shown inFigure 1. Table 1shows the ranges of grain sizes for each mode of transport and their percentage within each lee-face process. Statistics given with each set of curves are mean values for these curves. Sorting is given as the Trask coefficient.

[46] In principle, wind speed could be bracketed from the sediment load using any of the relationships given by equations (5)(8). The suspended load, however, represents a small fraction of the total sediment load and is fairly uniformly distributed across the stratification types (Table 1). The saltation load is not specific to any one stratification type, but rather dominates in all. Wind speed is, therefore, best bracketed by the creep and incipient suspension sediment loads. The creep load is well represented in grainflow strata. The incipient suspension load is best represented by grainfall deposits, but grainfall strata are commonly absent in ancient aeolian cross-strata and the incipient suspension load is also present in grainflow strata, albeit in lesser amounts. Averaged over the grainflow samples, the creep load consists of grain sizes >d69 (i.e., 69% of sediment sample has a smaller nominal grain diameter) for March and >d94for April. Averaged over the grainfall samples, the incipient suspension load is represented by the grain-size range of d2–d13 for March and d4–d23for April. Averaged over the grainflow samples, the incipient suspension load is represented by the grain-size range of d1–d4 for March and d3–d14 for April.

5. Analysis of Results: Methodology Refinement and Limitations

5.1. Parameter Control on the Spatial Distribution of Stratification Styles

[47] Although the plotting of styles of lee-face stratification by incidence angle (Figure 5) shows a general trend (Section 4.2.2), the broad range of incidence angles over which a given style of lee-face stratification occurs suggests that parameters in addition to incidence angle affect this distribution. Parameters of (1) lee-face segment length, (2) segment sinuosity, and (3) wind speed can be explored within the data set.

[48] No distinct trend emerges when segment length, shown by datum point size in Figure 5, is considered. Long segments are common as outliers, and both long and short segments occur within concentrated clusters of points. Segments of local high sinuosity (dashed circles in Figure 5), however, represent outliers, as seen in the low incidence angles for Styles F–G, and the highest and lowest incidence angles for Style E. The sinuosity in these areas ranges from 1.31–1.61 (in red on Figure 3), whereas the sinuosity for other segments ranges from 1.06–1.23. In terms of speculation, the development of a characteristic secondary flow may be retarded where incidence angle is rapidly changing because of dune curvature.

[49] If dune segments of high local sinuosity (i.e., circled outliers in Figure 5) are removed, the range of lee-face processes and the resultant stratification styles form a progression by incidence angle that can be paired with rates of erosion/deposition (Figure 9). Wind-ripple tractional transport in a longitudinal configuration (Style A) occurs exclusively up to incidence angles ≤16°, but this is also the range of lee-face scour (i.e., erosional reactivation surface) and bypass surfaces occur up to incidence angles of ∼25°. For a significant record of cross-strata composed almost entirely of wind-ripple laminae (i.e., Styles A–B where the thickness is greater than a few laminae, which likely represent a lag deposit), an incidence-angle range of 25°–40° is a reasonable assumption. On the other end of the spectrum, although exclusively gravity-driven processes (Styles F–G) can characterize a slipface with an incidence angle as low as ∼45°, most occurrences are at incidence angles ≥60° and the last occurrence of wind ripples is at 70° (Figure 5). For the preserved record of cross-strata composed almost entirely of grainfall and/or grainflow cross-strata, an incidence angle of ≥70° is a reasonable assumption. Between longitudinal and transverse flow is oblique flow, characterized by components of both gravity-driven and alongslope tractional transport, with the “classic” oblique configuration consisting of a well-developed slipface perched upon a plinth marked by wind ripples. Although a fully developed slipface can occur at incidence angles as low as ∼25° and the last wind ripples occurred at 70°, a well-developed oblique configuration (Styles C–E) can be realistically be taken as representing incidence angles of 40°–70°.

Figure 9.

Summary diagram showing the range of incidence angles associated with each style of lee-face stratification (Figure 4) after outliers in Figure 5 have been removed. Note the range of incidence angles for grainflow, grainfall and wind ripples. Ranges of incidence angles for surfaces of erosion and bypass, and deposition are from Figure 7. Rates of deposition continue to increase with incidence angle.

[50] The impact of wind speed on the general ranges of incidence angles given above can be addressed in a general way by comparing stratification formed during the lower-energy March and the higher-energy April wind events. Dune 3 (April wind event) shows an abundance of grainfall and grainflow deposits (Styles E–G), whereas it is poorly represented by stratification styles where wind ripples (Styles A–C) are common (Figure 5). In contrast, Dunes 1–2 (March wind event) yield most of the examples of Styles A–C. Because both the jump length of saltating grains and the proportion of the sediment load transported in incipient suspension increase with wind speed, the intensity and downslope distribution of grainfall increases with wind speed. Conversely, the ability of ripples to rework the lee face decreases as grainfall increases. An increase in wind speed, therefore, is likely to extend Style E (basal wind ripples only) to a lower range of incidence angles, whereas Style C (where ripples rework the entire lee face) is likely to extend into higher incidence angles at lower wind speeds. Both extensions, however, seem likely to occur within the oblique configuration range of 40°–70°. For transverse flow conditions, the presence of grainfall strata within a set dominated by grainflow cross-strata indicates wind-storm conditions [Kocurek, 1991].

5.2. Reconstruction of Wind Speed from Grain Size

[51] A generalization of the approach described in Section 4.3.4entails identifying for both the March and April wind events a common characteristic grain-size percentage that is representative of the (1) incipient suspension load in grainflow strata, (2) incipient suspension load in grainfall strata, and (3) creep load in grainflow strata. As evident fromTable 1, the calculated incipient suspension load in the grainflow strata only overlap at d4 for both the March (203 μm) and April (143 μm) wind events, which from equation (3) yield ws values of 1.20 m/s (March) and 0.77 m/s (April). The calculated incipient suspension load in the grainfall strata for the March and April events overlap at d4–13, and taking the coarsest sediment (d13) yields 209 μm (March) and 190 μm (April), which from equation (3) yield ws values of 1.24 m/s (March) and 1.11 m/s (April). The calculated creep load in the grainflow strata for the March and April events overlap at values ≥d94. Using d95 (998 μm for March, 1028 μm for April) in equation (4) yields u*c values of 0.47 m/s (March) and 0.48 m/s (April).

[52] The above calculated values of ws and u*c provide three points by which to bracket u* for the March and April wind events. For the March wind event, using equation (7) the incipient suspension load in grainflow strata yields 0.48 m/s < u* < 1.20 m/s, whereas in grainfall strata yields 0.50 m/s < u* < 1.24 m/s. Using equation (5), the creep load in grainflow strata yields 0.33 m/s ≤ u* < 0.47 m/s. Combined bracketing for March yields 0.47 m/s < u* < 0.48 m/s, which over-estimates the actual value (u* = 0.35 m/s) by 34–37%. The same procedure for the April wind event yields 0.31 m/s < u* < 0.77 m/s for incipient suspension in grainflow strata, 0.44 m/s < u* < 1.11 m/s for incipient suspension in grainfall strata, and 0.34 m/s ≤ u* < 0.48 m/s for creep in grainflow strata. Combined bracketing for April yields 0.34 m/s ≤ u* < 0.44 m/s, which under-estimates the actual value (u* = 0.45 m/s) by 2–32%. The over- and under-estimations occur because the overlap in grain-size percentages for the modes of grain transport sample high (i.e., coarser grains) in all grain populations for March, whereas the same percentages sample low in all grain populations for April. Exact wind-speed reconstructions would occur using the midpoint in each mode of transport (e.g., d9 and d14 for incipient suspension in grainflow and grainfall strata, respectively, and d97 for creep in grainflow strata for the April event).

[53] The limitation of the approach above is that the ranges of grain sizes traveling in the different modes of transport are not known a priori. A more holistic approach is illustrated in Figure 10, which shows the fields for the modes of grain transport, as defined by equations (5)(8), for a range of values of u* (and the corresponding u10m from equation (2) using zo = 0.2 mm) and grain sizes, with corresponding values for ws and u*c from equations (3) and (4), respectively. Figure 10shows the fields for the modes of grain transport for both gypsum (black lines) and quartz (red lines). Using as examples the grain-size ranges from grainfall and grainflow strata from the March and April wind event, approximations ofu*and the grain-sizes ranges for the different modes of grain transport are given with simple assumptions. Following fromBagnold [1941], assuming that the coarsest sediment traveled in creep and that the size of these particles was limited by u*, placement of the coarse ends of the grain-size ranges at the lower limit for creep yieldsu*and the grain-size ranges for the other modes of transport. Similarly, assuming that the coarsest sediment in grainfall strata traveled in saltation yields a trivial difference in the estimatedu*for the April wind event, but a greater error for the March event with its anomalous coarse-grained grainfall. Following fromJerolmack et al. [2011], assuming that the mean grain size (* in grain-size ranges inFigure 10) represents the middle of the saltation range provides a good estimate of u*for the April wind event, but is significantly off-center for the March wind event. Depending upon the sedimentological context, other assumptions could be made to help bracketu*, as discussed below (Section 5.4).

Figure 10.

Summary diagram in which the fields of the modes of grain transport are plotted by u* and grain diameter or size. For reference, wind speeds at 10 m (u10m) are given for u* values using equation (2) where zo = 0.2 mm. Lines bounding the grain-transport fields are defined byequations (5)(8), showing both gypsum (black lines) and quartz (red lines). The grain-size scale corresponds to values ofws and u*c, as calculated from equations (3) and (4), respectively. Values for gypsum are given along the bottom of the grain-size scale, values for Quartz (in red) are given at the top of the diagram. Two colored horizontal lines define the grain-size ranges from grainflow and grainfall strata for the March and April winds events, and the mean grain size for the grainflow strata is marked by a*. The diagram illustrates the proposed methodology where estimates ofu*can be made by sliding the grain-size range bar up or down according to the interpreted sedimentological context. For the examples shown,u*is well predicted for both wind events by aligning the coarse end of the grain-size range with the lower limit for creep. Assuming that the coarsest sediment in grainfall strata for the April wind event works equally well. Assuming that the mean grain size represents the middle of the saltation range provides a good estimate ofu* for the April wind event, but is significantly offset for the March wind event.

5.3. Reconstruction of Event Duration from Cross-Strata

[54] Where u*and wind speed are approximated from the grain-size distributions, the duration of the wind event can be estimated from the dune migration rate (Section 4.3.3) where dune height can also be estimated and event strata can be identified. Dune height can be measured for modern and some relict Pleistocene/Holocene dunes, whereas set thickness/width or grainflow thickness [Kocurek and Dott, 1981] may constrain dune height in the rock record. Events are defined by stratification representing dune forward migration [e.g., wind storm defined by grainfall strata, cycles of Hunter and Rubin, 1983]. Given u*determined from grain-size distributions, the calculated Qs in equation (12) can be used in equation (11) to evaluate the duration of wind events. This duration necessarily represents a minimum time because it measures only time when wind speed was above threshold values.

5.4. Methodology Limitations

[55] The methodology developed here is based upon data from simple, moderate-sized crescentic dunes during wind events of average intensity in which the primary flow was roughly normal to the dune crestlines with typical dune shape asymmetry. Use of the methodology with other dunes types (e.g., linear or star dunes) was not explored, but there is no reason to believe that it should not apply to crestlines of other simple dune types. For dunes that are not simple, but rather are compound or complex in which dunes are superimposed upon the larger host bedform, the superimposed dunes develop within the secondary flow field of the host bedform and do not reflect the primary windper se. For example, for the common occurrence of dunes migrating alongslope the lee of the host bedform, wind direction for the superimposed dunes can depart markedly from the primary wind direction [e.g., Rubin, 1987]. In addition, the methodology does not address dune behavior during wind reversals, which commonly cause scour of the lee face and formation of reactivation surfaces. Whereas this origin of reactivation surfaces is well known, the White Sands data argues that reactivation surfaces also develop at low incidence angles.

[56] In addition to the impact of high dune sinuosity and fast wind speed in skewing the lee-face distribution of stratification styles (Section 5.1), dune height and degree of truncation of a set of cross-strata may also limit the interpretation. As slipface height increases, grainfall is progressively less able to extend to the base of the slipface and, from momentum considerations, the lee eddy cannot exist as a roller/vortex that extends from the brinkline to the base of the slipface in large dunes. For transverse flow conditions, the net effect should be the convergence from Style F (basal grainfall and grainflow) toward Style G (basal grainflow only), albeit that the interpretation of transverse flow conditions is unchanged. As speculation for oblique flow conditions (Styles B, C, E) on large dunes, grainfall should also not extend to the basal lee face, but otherwise the styles of stratification should remain the same, given that grainfall and grainflow continue on the upper slipface and ripple migration dominates on the remainder of the lee face. Progressive degrees of truncation of a set of cross-strata force interpretations to be made from progressively more basal portions of the lee face. Especially for large dunes where grainfall typically does not reach the base of the lee face, stratification Styles A, B and E are all represented by wind-ripple laminae and would be indistinguishable.

[57] Limitations on the interpretation of wind speed from grain size result from extremes in wind speed and the available grain-size range. The methodology illustrated inFigure 10works best where wind and grain-size conditions are such that the full range of transport modes are present with the uppermost range of creep limited byu*. With high speed-wind events or for very well sorted sediment owing to source-area control or being distal in the dune field, there may be no creep population. Conversely, with low-speed wind events or for coarser sediment proximal to the source area, there may be no incipient suspension population. Grainflow strata may not always contain the full range of grain sizes. On small dunes, grains traveling in incipient suspension may be transported beyond the slipface during high-speed events to exclusively accumulate as bottomset deposits of grainfall. A determination of wind speed from the grain-size distribution within stratification types, therefore, is an interpretation that must be made within the context of the cross-strata and stratigraphic unit.

6. Conclusions

[58] The methodology developed here allows for the reconstruction of wind direction, shear velocity and wind speed, and wind-event duration from sets of aeolian cross-strata, while also recognizing the limitations inherent to dune dynamics that give rise to the cross-strata. The methodology is specifically aimed at reconstruction of specific wind events, and is motivated by the common occurrence of sets of aeolian cross-strata that extend for hundreds of meters or more in the transport direction and that must house the record of a great many wind events.

[59] Lee-face secondary flow is largely a function of incidence angle, and gives rise to lee-face processes that are reflected in sets of cross-strata as styles of stratification. The stratification styles identified at White Sands are common configurations in the aeolian rock record, and their occurrence within ranges of incidence angles (Figure 9) can be used to reconstruct wind direction for sets of cross-strata by pairing of local cross-strata dip with stratification style along the strike of a set of cross-strata. As generalizations, cross-strata composed of wind-ripple laminae characterize incidence angles of 25°–40°. Cross-strata consisting of foresets of grainfall and grainflow strata over bottomsets of wind-ripple laminae characterize incidence angles of 40°–70°. Cross-strata composed entirely of grainflow and grainfall foresets reflect incidence angles of 70°–90.

[60] Secondary parameters that impact the lee-face distribution of stratification styles are: (1) local high brinkline sinuosity, which appears to extend the range of incidence angles over which stratification styles occur, (2) wind speed, in which the production of grainfall is reduced at lower speeds and increased at higher speeds, and (3) dune height, in which the presence of grainfall is decreased as slipface height increases. The stratigraphic record of dunes is also biased by the degree of dune truncation; the preserved basal portion always limits a complete description of lee-face processes, and in some cases (e.g., thin sets of wind-ripple strata) may handicap determination of stratification style. In addition, our analysis has been aimed at simple dunes; where the record is generated by dunes superimposed upon larger bedforms (i.e., compound and complex dunes), the analysis is more complex because the superimposed dunes existed within the secondary-flow field created by the larger bedforms.

[61] Reconstruction of wind speed is based upon empirically-derived relationships (equations (5)(8)), which relate the mode of grain transport to shear velocity, u*, from which wind speed at near-bed heights can be calculated from the law-of-the-wall (equation (2)). Data from White Sands show that the total volumetric sediment load is sorted by the lee-face secondary flow and lee-face processes. As a result, grain-size distributions differ within lee-face stratification types. Given the full range of transport modes, grainfall strata are enriched in grains that traveled in incipient suspension but are depleted in grains that traveled in creep. Grainflow strata typically are most representative of the total transport load. Lee-face wind-ripple strata, which form by alongslope winds, may consist of grains that passed the brinkline in any transport mode, andper se are least diagnostic. Assuming that: (1) the coarsest grains in grainflow strata traveled in creep and grain size was limited by u*, and (2) the coarsest grains in grainfall strata traveled in saltation allow a first-order determination ofu* and the breakdown of modes of transport for the full range of grain sizes (Figure 10). However, because the percentages of grains that traveled in each transport mode within the stratification types are not known a priori, interpretation of wind speed must be done within the sedimentological context of the strata representing whole wind events. Primarily, a creep population may not occur because of source-area supply, position distal to the source area, or during high-speed wind events. Incipient suspension may not occur with low-speed wind events or where the total sediment load is coarser grained.

[62] Lee-face deposition rates increase with incidence angle, and are approximated by the sine of the incidence angle, but trend best with a relationship that shows a 12° shift with incidence angle (equation (10)), suggesting controls on lee deposition beyond incidence angle. Erosional reactivation surfaces, already known to occur with wind reversals, also characterize lee faces up to an incidence angle of ∼15°, whereas bypass surfaces occur at incidence angles up to ∼25°. Given estimations of shear stress from the grain-size distributions, the average transport rate, Qs, for the wind event can be calculated from equation (12)or similar transport equations. Where forward dune migration during the wind event can be measured in preserved transverse segments of the dune cross-strata, a minimum duration of the wind event can be estimated where dune height is known usingequation (11).

Acknowledgments

[63] This research was supported by grants from the National Science Foundation EAR-0921659, the National Park Service as part of the Chihuahuan Desert Network Inventory and Monitoring Program, and from the Jackson School of Geosciences at the University of Texas at Austin. We thank the GEO 380R class, which helped in data collection during the April wind event. We are grateful to David Bustos and Hildy Reiser of the National Park Service for facilitating this study. We appreciate the constructive comments by Alexander Densmore, Eugene Farrell, David Rubin, Douglas Sherman, and an anonymous reviewer in reviewing the manuscript.

Ancillary