Modelling palaeosol preservation in aeolian dunes

EARTH SURFACE PROCESSES AND LANDFORMSEarth Surf. Process. Landforms (2014)Copyright © 2014 John Wiley & Sons, Ltd.Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/esp.3596

Modelling palaeosol preservation in aeolian dunesMatt W. Telfer*School of Geography, Earth and Environmental Sciences, Plymouth University, Plymouth, UK

Received 16 January 2014; Revised 24 April 2014; Accepted 28 April 2014

*Correspondence to: Matt W. Telfer, School of Geography, Earth and Environmental Sciences, Plymouth University, Drake Circus, Plymouth, Devon PL4 8AA, UK.E-mail: [email protected]

ABSTRACT: In some of the world’s desert and desert-marginal areas (e.g. Simpson/Strzelecki, Australia) dunefields preserve well-developed palaeosols, whereas in other regions with broadly similar climatic regimes and topography (e.g. southwest Kalahari),the dunes are characterized by very poorly developed internal stratigraphy. It has been postulated that dunes such as those in theKalahari may never have had conditions conducive to soil formation, or that soils once formed but any evidence of palaeosolshas been lost due to reworking. This study develops and applies a one-dimensional numerical model to simulate dune development,soil formation and soil preservation. Variables in the model allowed experimentation on the influence of sediment supply, the timetaken for soil to form, and the additional resistance to erosion offered by the soil.Reduced sediment supply plays a vital role in landscape development during periods of initial pedogenesis. Although re-exhumed

palaeosols influence sediment supply, the effect is minimal. Although under almost all parameterized conditions more than half (andup to 80-90%) of those soils initially formed are lost due to reworking, evidence of their past formation remains in the large majorityof profiles, and the dominant factor in controlling the preservation of palaeosols is the frequency of their formation. The implication isthat where dunes are found without palaeosols, the most likely (albeit not certain) inference is that they have never formed. Counter-intuitively, the limited sediment supply means their additional resistance to erosion becomes almost inconsequential to their preser-vation, at least until the unit approaches complete invulnerability. Short chronostratigraphic hiatuses around palaeosols are normal,and although long gaps can occur, they are extremely infrequent. Where such gaps are observed in field studies, external forcingfactors (e.g. climatic or environmental changes) are implied, as they are highly unlikely to result from stochastic net preservation.Copyright © 2014 John Wiley & Sons, Ltd.

KEYWORDS: linear dunes; palaeosols; stratigraphy; pedogenesis; modelling

Introduction

The internal stratigraphy of many dunes reveals palaeosolspreserved within the sands, in both desert (e.g.Mauz andFelix-Henningsen, 2005) and coastal (e.g. Tamura et al., 2011)locations around the world. Palaeosols are the sedimentologi-cal remains of former pedological profiles. They may exhibitconsiderable complexity in some sedimentary settings, but insand dunes, where pedogenesis is typically very limited, theyare typically recorded in the sedimentary record as briefexcursions in the characteristics of the sediment. Such changescan be physical (e.g. an increased fine-grained component),inorganic geochemical (e.g. carbonate content) and organic geo-chemical (e.g. increased organic carbon), biological (e.g. rootlets)and/or sedimentological (e.g. trace fossils of root casts). These canrange from barely-discernible physical and/or geochemicalchanges in the dune sands to highly-indurated horizons resultingfrom well-developed and well-preserved pedogenesis (e.g. Amitet al., 2011). Such features are not unique to Quaternary sedi-ments, and interbedded aeolian sands and palaeosols have beendescribed from Mesozoic sandstones (e.g. Basilici et al., 2009).Palaeosols within dunes are frequently found in some desert-

marginal regions (e.g. Sahel, much of Australia), where suchdunes may have taken long periods (>103–105 years) to form,and where environmental conditions may have been marginal

between conditions favouring aeolian activity and landscape sta-bility for much of this time. For instance, in Australia, the dunes ofthe Strzelecki (Figure 1) and Tirari deserts (Fitzsimmons et al.,2007), the Murray Basin (Lomax et al., 2011), and the Simpsondesert (Hollands et al., 2006) have all demonstrated frequent oc-currence of palaeosols. Possibly more remarkably however, inother regions with broadly similar climatic regimes, desert dunesshow very little evidence at all of past periods of soil formation.Typical of this are the dunes of the semi-arid south-westernKalahari. Here, despite abundant evidence that the dunes havetaken many millennia to form (e.g. Telfer and Thomas, 2007;Stone and Thomas, 2008), that rates of net dune accumulationhave varied during this time, and that the region currentlysupports extensive vegetation cover today, there is almost noevidence of soil preservation within the linear dunes chara-cteristic of the region (Stone and Thomas, 2008). The dunes arecomprised of almost homogenous well-sorted aeolian sands,with only very subtle changes in physical or chemical composi-tion, and very little evidence of internal stratigraphy of any kind,much less well-developed palaeosols.

The significance of paleosols within dunes (or, indeed,possibly their absence) lies in the potential for dunes to serveas palaeoenvironmental archives. Preserved soils within a duneare important for two principal reasons. Firstly, in drylandenvironments, soil formation is generally taken to imply

Figure 1. Palaeosols preserved in a linear dune in the Strzeleckidesert, Australia, demonstrate increased resistance to erosion by outcrop-ping as small (10�1–1m scale) scarps. Three preserved surfaces are visiblein this photograph, the lowest one being the most degraded.

M. W. TELFER

landscape stability (Fitzsimmons et al., 2009), and is generallyassociated with increased moisture availability and vegetationdevelopment (e.g. Bowler and Magee, 1978; Lomax et al.,2003; Yang et al., 2013). Secondly, where palaeosols can beshown to be laterally extensive, it also reveals that aeolianreworking has not affected units below the soil since its forma-tion (Fitzsimmons et al., 2009). Pedogenesis may be recordedin the sedimentary column by the presence of illuviated clays,especially in the form of grain cutans, and by the presence ofpedogenic precipitates, such as carbonates and gypsum (Dhiret al., 2004; Retallack, 2005; Fitzsimmons et al., 2009; Gockeet al., 2012). Even in dunes in which palaeosols are not pre-served, bounding surfaces of varying degrees of developmenthave frequently been reported (e.g. Holliday and Rawling,2006), and the degree to which these might be used to inferlandscape stability tested (Leighton et al., 2013a).Understanding why some regions demonstrate well-

developed paleosols whereas others do not is not straightfor-ward, primarily due to propensity of dune sands for reworkingduring periods of enhanced aeolian activity. Although there islittle doubt that many dunes, particularly linear (longitudinal)dunes, have formed over tens of thousands of years, this accumu-lation has been very discontinuous, and in many areas is likely tohave been punctuated by periods of net erosion of the dunes(Telfer and Thomas, 2007; Stone and Thomas, 2008). In otherareas, the physical and chemical characteristics of the sedimentshave been postulated to offer increased resistance to reworking,thus accounting for the longevity of these apparently vulnerablelandforms (Hesse, 2011). Spatial variability in palaeosol andbounding surface occurrence between dunes, even at a localscale, may be common (Lomax et al., 2011; Leighton et al.,2013a, 2013b). The question thus arises as to whether a lack ofpalaeosols implies that surface conditions were never conduciveto pedogenesis and thus soils never formed, orwhether the natureof the net dune accumulation simply removed any evidence ofsoil formation by continuous cannibalization of the dune body,as postulated by Munyikwa (2005).Due to the long timescales (>102 years) typically involved in

both dryland palaeosol and dune formation, the topic does notlend itself to field experimentation. Although micromorpho-logical analyses have proved invaluable in understanding theprocesses and environmental implications of palaeosol forma-tion (Fitzsimmons et al., 2009), they can contribute less to theunderstanding of the preservational system of dunes, and thelikelihood of the soils being recorded within a sedimentary

Copyright © 2014 John Wiley & Sons, Ltd.

system that is at times accretionary, and at times erosive. Funda-mentally, this is a question simply not testable by field study, asit inherently relies upon evidence which by definition mightnow be absent. Telfer et al. (2010) developed a one-dimensionalstochastic model of dune accumulation to investigate the effectsof external forcing on net accumulation within linear dunes,and this model is taken as the basis from which to investigatepalaeosol formation and preservation within aeolian dunes.

Aims and objectives

This study aims to explore the nature of, and controls on, thepreservation of palaeosols in dunes, using a one-dimensionalstochastic numerical dune accumulation model. The objectivesare thus to:

1. Extend the accumulation model of Telfer et al. (2010) tosimulate dune units of greater resistance that occur as afunction of surface exposure time, and remain within thesedimentary column after burial.

2. Investigate the sedimentological evidence recorded bysystems in which palaeosols form with varying degrees offrequency and offer varying degrees of resistance to subse-quent removal, under conditions which simulate the contin-ual, albeit essentially stochastic, potential for reworking.

3. Ascertain what, if anything, can be inferred of the environ-mental background of sedimentary records which do, ordo not, preserve palaeosols (e.g. south-eastern Australiaversus Kalahari).

Methods

The original model of Telfer et al. (2010) has been modified toallow representation of soil and palaeosol units within thesedimentary column of the dune, but its essence remainsunchanged. The model iterates a one-dimensional dynamicinteger array, with each value representing the timestep at whichthat element was added, over a given number of timesteps, exe-cuting a number of stochastic tests characterized by simple feed-backs at each step. This simple array represents a profile througha linear dune, which might be thought of either as an augeredcore, or an exposed section through the dune (such as those thathave been utilized for sampling for palaeoenvironmental studiesat roadcuts). At initiation (time, t=1), the pre-existing dune bodyconsists of 50 stacked elements within the array (each with avalue of t=0), representing the column of sediment at the startof the simulation. The model assumes that sand can be input(‘blown in’) at the top of this sedimentary column (the likelihoodof which is determined by the depositional probability, pd), thuslengthening the array by the addition of one ‘unit’ at the top ofthe column (with a value equal to t), or removed by erosion (i.e. ‘blown out’ by aeolian entrainment, at probability pr), whichshortens the array by removing the uppermost unit. Once adepositional or erosional event has occurred, a basic feedbackis incorporated into the model, temporarily increasing the proba-bility of further depositional or entrainment events (pd* and pr*) atthe same timestep, as appropriate. This simulates the feedbackeffects of aeolian processes at work on a dune; for instance, onceerosion begins, it is assumed to be promoted by reptation(Andreotti, 2004), and once deposition begins, it is assumed thesurface begins stabilization and thus limits the scope for furtherdeflation (Wiggs et al., 1995). This positive feedback is in turnmoderated by a negative feedback which iteratively reduces theinfluence of the revised probability, to represent topographiceffects as the dune either extends above its surroundings, and thus

Earth Surf. Process. Landforms, (2014)

MODELLING PALAEOSOL PRESERVATION IN AEOLIAN DUNES

becomes more prone to erosion, or sinks to become a topo-graphic low in the dune crest, thus favouring accretion. Themodel is run iteratively for 2000 timesteps. In contrast to theexperiments of Telfer et al. (2010), all model runs here areparameterized with the probabilities of deposition andreworking constant throughout the model run – that is, theseprobabilities are not forced to simulate varying external influ-ences (such as climate, vegetation or sediment availability atthe dunefield scale).Soils are determined to form purely stochastically, when the

surface has neither eroded nor been buried for a given periodof time (ts). This is achieved by the parallel use of a secondarray, mirroring the main array used to record the timing ofdune accumulation, and recording the presence of a soil unitas a simple binary. Note that for the purposes of this study,the soil is assumed to form only at the surface of the dune

Figure 2. Schematic overview of the model, showing the basic structureemployed in this paper highlighted in grey. The four boxes labelled (A)–(D) reways of modelling the effects of soils and palaeosols on the sedimentary sup


column, whereas in reality, some aspects of pedogenesis, nota-bly carbonate precipitation, would most probably occur atsome depth within the sedimentary body (Gile et al., 1966).This assumption is justified here on the grounds that depth ofcarbonate precipitation is correlated to available precipitation(Retallack, 2005), and thus in the arid and semi-arid regionsin which dunes typically occur, this effect is likely to be mini-mized. Once a soil is formed, it affects the probability of depo-sition and/or aeolian entrainment, to simulate the effects ofchanged sediment supply and/or erosional potential (see laterfor details of the scenarios used here). In addition, a counterrecords the formation of each soil unit, independent of whetheror not it is subsequently removed by erosion; this is valuable, asit offers the scope for quantitatively describing the eventualpreservation potential of each system. Figure 2 summarizesthe model schematically.

of the model as described in Telfer et al. (2010), with the additionspresent the four scenarios described in Table I which represent differentply and erosive susceptibility of the dune.


M. W. TELFER

The degree of pedogenesis is, for the purposes of this study,parameterized in terms of magnitude of influence of a soil.‘Soils’ and ‘palaeosols’ are defined by the geomorphologicaland sedimentological expression of periods of landscape stabil-ity (i.e. when exposed, they have some effect on the erodibilityand/or depositional potential of the surface of the landscape).Thus highly resistant units might be thought of as well-developed relict soils, and those that only slightly increaseresistance to erosion as simple bounding surfaces betweensedimentological units. Throughout this paper, the term ‘soil’is used to describe a unit which is actively forming still, orhas not been buried since its formation; the term ‘palaeosol’is used as soon as this unit is buried for the first time, regardlessof whether or not it is subsequently exhumed. Thus the influ-ence of ‘soils’ might be considered to incorporate not just theeffects of pedogenetic processes on the physical resistance ofthe sediment, but also the increased propensity for moistureretention and the effects of the vegetation which might formpart of the landscape.Four scenarios are considered in initial experimentation with

the model, representing different ways in which the presence ofa soil/palaeosol might affect sediment supply and the suscepti-bility of the surface to deflation. These are summarized inTable I, and can be described more fully as:

(A) Reworking effect only: Once a soil has formed due to thesurface being stable for ts timesteps, it reduces the proba-bility of subsequent reworking of this unit by rs. This repre-sents both the armouring effect of the formation of a soildecreasing its susceptibility to erosion, and the fact thatthe landscape is presumably vegetated at this point, reduc-ing the likelihood of aeolian deflation. Note that in thismost simple scenario, the soil still has this effect if it hasbeen buried and subsequently exhumed, when the effectsof soil induration will still increase resistance to aeolianerosion (and indeed the post-burial pedogenetic processesmay have enhanced this even further) but presumably anyeffect due to vegetation will be negated as the once-present vegetation will have died on burial.

(B) Supply-limited reworking effect: Once a soil has formeddue to the surface being stable for ts timesteps, it reducesthe probability of subsequent reworking and depositionof this unit by rs. This scenario attempts to account forthe fact that although the model is one-dimensional, andrepresents a single point on the crest of a linear dune,unlike the situations described in Telfer et al. (2010). Thusthe model described here is no longer truly independent ofits boundary conditions. That is, when the model simulateslong periods of inactivity, and a soil forms, the period ofinactivity is assumed to have occurred at a local orregional scale, and thus the effects ascribed to it – namelya reduction in potential for erosion or deposition – wouldalso operate on the rest of the dune, which is assumed tosupply the sediment to the modelled sediment column.

Table I. Summary of the experimental conditions of the four initial scenariocolumn which are more resilient to erosion) and palaeosols (the same units aof entrainment and deposition of the sediment column

Model property

Presence of soil or palaeosol at surface affects entrainment probabilitiesPresence of soil or palaeosol at surface affects depositional probabilitiesPresence of soil at surface affects depositional probabilities, palaeosol re-expPresence of soil at surface affects depositional probabilities, palaeosol re-exp


Thus there would be reduced sediment supply from thesurrounding neighbourhood, and the sediment supply ata given point on the dune would also be reduced. Notethat this effect is here assumed to continue even on subse-quent exhumation of the palaeosol, which might be attrib-uted to higher sand transport capacity over a hardenedsurface, which is also still resistant to erosion.

(C) Supply-limiting effect only at initial deposition: Once a soilhas formed due to the surface being stable for ts timesteps,it reduces the probability of subsequent reworking anddeposition of this unit by rs as long as the unit is at thesurface. If it is buried and subsequently exhumed, thepalaeosol is still assumed to have an armouring effect,and thus reduce the probability of reworking at this point(that is, pr is reduced by rs), but there is assumed to be noeffect on the probability of depositional events. The effectof the palaeosol being exposed at points surrounding thesediment column in question, and thus reducing the sedi-ment supply (and hence the probability of depositionalevents), is here assumed to be negligible. Field evidence(Figure 1) suggests that even where palaeosols are exposedin dunes, local-scale topographic variation of the duneoften ensures that they are not exposed homogenously,and thus there is assumed to be a continuous sedimentsupply on exhumation of the palaeosol.

(D) Full supply-limiting effect only at initial deposition, re-duced thereafter: This scenario is very similar to ScenarioC), but in order to take account of a likely reduction in sed-iment supply due to the exposure of the palaeosol fromthe surrounding area, the probability of deposition at thesedimentary column on subsequent exhumation of thepalaeosol is assumed to be somewhat affected (by rs/2).

Each model run is parameterized as follows; each run isallowed to run for 2000 timesteps (tmax = 2000), each run isrepeated 10 000 times (runs = 10 000), probabilities of deposi-tion and reworking at each timestep are assumed equal at0.05 (pd and pr = 0.05), the feedback effect is assumed to dou-ble the probability of aeolian activity (pd* and pr* = 0.1). Thenegative forcing applied to this positive feedback is 0.01 t�1,and thus in the highly unlikely event of 10 consecutive deposi-tion/erosional events during a single timestep, the probability offurther events is reduced to zero. The sedimentary column isinitially 50 units deep, and the run is stopped (and conditionsrecorded at this point) if the dune reaches zero or 100 unitsdeep; the frequency of such events occurring is recorded.Although, due to the stochastic nature of the model, it mustbe expected occasionally, a scenario which tends to build asedimentary column too high, or low, is interpreted as beingunrealistic, as linear dunes in the field show a remarkabletendency to be consistent in heights over distances of metresto hundreds of kilometres (Lancaster, 1995). Mean dune heightcan thus be used as an indicator of the viability of the scenarioto represent reality (i.e. boundary conditions which frequently

s designed to represent the likely effects of soils (units in the depositionalfter burial and subsequent re-exhumation) on the modelled probabilities

Model scenario

A B C D

✓ ✓ ✓ ✓✘ ✓ ✘ ✘

osed has no effect ✘ ✘ ✓ ✘osed has reduced (50%) effect ✘ ✘ ✘ ✓



promote uncontrolled growth, or shrinkage, of the dunecolumn can be considered to poorly represent reality). The timefor soil formation was varied from 10 to 50 timesteps, and theadditional resistance effect of soil/palaeosol units varied from10 to 90% of the original effect (i.e. a slight reduction effect,to a situation in which it was very unlikely that the soil/palaeosol would subsequently be removed).Although the model is essentially dimensionless, the temporal

and spatial parameters are coherently scaled such that t=10years, and each unit in the array represents 0.1m of sedimentaccumulation. Model runs are thus in the order of 104 years,which is known to be approximate to the timescale on whichlinear dunes accumulate over ~1–10m scales (Telfer and Hesse,2013), and individual timesteps represent the decadal-scale forc-ing evident in many dryland environments (Swetnam andBetancourt, 1998; Hereford et al., 2006; Hesse and Simpson,2006). The timescale of soil development is thus 100–500years, which is also coherent with reality (Gocke et al.,2012), although Roskin et al. (2013) have demonstrated soilformation occurring during periods of stability in the order of103 to 104 years. The spatial dimensions of the array equate to0–10m, consistent with the height of many of the world’slinear dunes (Lancaster, 1995), and the thickness of individualpalaeosols is of the order of 10�2m (i.e. 10 cm), the order ofwhich is again consistent with observational data (e.g. Figure 1;Fitzsimmons et al., 2009; Lomax et al., 2011).It must be noted that, by necessity, this model is a simplication

of a complex geomorphological system, and some aspects ofreal-world behaviour may not be sufficiently captured. Forinstance, the ability of psammophilic vegetation to persist despitenet deposition of aeolian sand may mean that the influence of avegetated surface might persist despite burial (Barchyn andHugenholtz, 2012; Jerolmack et al., 2012). It is also not possible

Figure 3. Modelled results for four key parameters for the four scenarios dvarying combinations of soil resistivity and formation times, of which eachin arbitrary units, and it should be noted that the model terminates when dunegrowth and thus non-realistic boundary conditions. Values diverging far froreality. ‘Preserved soils’ are also in arbitrary units and represents the meanrun, and ‘preservation ratio’ is the ratio of soils preserved in the sediment coluformed in the column at any point (including those subsequently eroded). ‘Mcircumstances, the presence of palaeosols affects net dune accumulation.


to completely capture the effects of landscape spatial variabilityon dune behaviour. For instance, patchiness of vegetation willinfluence the transport capacity of the boundary (Okin, 2008),and dune topography is included in this model only in mostrudimentary form (by the inclusion of feedbacks which limit thetendency of the dune column to grow or shrink uncontrollably),whereas real-world dune/boundary-layer interactions are farmore complex. Moreover, the model does not discriminateexplicitly between ‘internal’ sediment supply to the dune sandcolumn, and additional ‘external’ sediment supply. Such changesare parameterizable only in terms of probabilities of deposition,and periods when such probabilities may exceed the subsequenterosional potential (see Telfer et al., 2010).

Results

The results for some of the key properties of the model runs, un-der different combinations of the time needed for soil formation(ts) and soil resistivity (rs) are shown in Figure 3. The results ofScenario A (in which the effects of the presence of soils andpalaeosols are limited to affecting the erosional susceptibilityof the column of sediment) are markedly different to the resultsof the other three scenarios (Figure 3, top row). In circum-stances other than soil formation being very slow (>30timesteps), and the effect of soil formation on the resistivity ofthe sediment column is minimal (<30%), Scenario A tendstowards uncontrolled dune growth. As described in Telferet al. (2010), model boundary conditions in which the sedimentcolumn at a given point strays far from conservatism (i.e.main-tenance of the sediment column at ~50 units) are consideredpoorly representative of reality. This is manifested in the accu-mulation of both new dune units and palaeosols, especially

escribed in Table I. Each panel shows the interpolated results from 25is the mean result of 10 000 model runs. ‘Mean dune height’ is givenheight reaches 100 units, as this is considered to represent uncontrolledm the start value of 50 units are thus considered less representative ofnumber of soils preserved in the sediment column at the end of eachmn at the end of the model run, compared to the total of those that haveean new dune units’ is in arbitrary units, and demonstrates that in some


M. W. TELFER

when soil formation is rapid and highly effective at resistingsubsequent erosion. The soil preservation ratio varies widely,from 10% to 90% (and, obviously, approaches 100% preserva-tion when soil resistivity is 100%, regardless of the time neededfor soil formation). In all scenarios, the soil preservation ratio isshown in most cases to be more dependent on the additionalresistivity the soil offers than to the likelihood of soil formationacross the range of ts and rs values tested here.Scenarios B–D are, it is argued here, conceptually a closer

approximation to realistic boundary conditions, with varyingdegrees of complexity, as they incorporate the effects of re-duced sediment supply to the sediment column duringperiods of landscape stabilization. The most striking aspect ofthe results of Scenario B is the stability of the system (Figure 3,second row). Dune height is conserved across all tested rangesof soil resistivity. The abundance of preserved soils in thesystem is dependent not on how resilient they are, but almostexclusively on how long they take to form; a counter-intuitiveoutcome. The soil preservation ratio is much less sensitive tochanges in rs and ts than in Scenario A, but a weak dependenceon the resistance of the soil is indicated. The most resilient soils(rs = 90%) have approximately twice the soil preservation ratioof the least (rs = 10%). Under Scenario C (Figure 3, third row),the dune system is conservative under most permutations of rsand ts, although there is a weak tendency for dune growth un-der intermediate soil resistivities, and frequent soil formationconditions. Although the probabilities of erosional events areunchanged in this scenario, dune units are slightly more fre-quently preserved, and, as with Scenario B, the primary control

Figure 4. Time-series of the age of preserved soils under all four scenarioScenario A is characterized by a range of forms of time-series. Those whichto model runs having run out of bounds (i.e. dune height reaching 100), andunder Scenarios B–D, the frequency of ages of preserved soils decreases withage–frequency plots are interconnected. Note that frequency (on the y axis)


on the abundance of preserved soils is the time taken for theirinitial formation. Not only are soils slightly more frequentlyfound under Scenario C, compared to Scenario B, but the ratioof soils formed/preserved is also slightly higher, suggestingthat the increase in soils is due to preservation potential ratherthan the frequency of their formation. In all aspects, perhapsunsurprisingly, Scenario D (Figure 3, bottom row) represents amid-point between Scenarios B and C.

The model also allows for interrogation of the timing ofevents. Figures 4–6 show time-series of the frequency of agesof preserved soils/palaeosols within the dune, the frequencyof ages of dune units (cf. Telfer et al., 2010), and the ratio ofthese two variables. Both the dune units and the soil units inmost instances show the characteristic rapid decay with timedemonstrated by Telfer et al. (2010). The only marked excep-tion to this pattern is for many parameter combinations forScenario A, in which there is a sharp decline in frequencytowards more recent events, which is attributable to the modelfrequently running out of bounds (i.e. growing to a height of100 units, at which point the model is stopped). There can belittle doubt that if the model were allowed to continue evenScenario A would show the same rapid decay with time. Thetime-series of both preserved soil units and preserved duneunits are sensitive to both ts and rs in most instances, with thetime taken for soils to form (ts) being the dominant control onthe absolute magnitude of soil abundance, but also revealinga complex interrelationship with the soil resistivity (Figure 4).This interplay is also evident for the time-series of preserveddune unit formation (Figure 5), with ts being the main control

s under a range of different permutations of different rs and ts regimes.decline towards recent ages (i.e. closer to zero on the x-axis) are due

stopping before completion of the 2000 timesteps. Under all conditionsincreasing age, but the roles of rs and ts in affecting the structure of thevaries by more than two-orders of magnitude between panels.


Figure 5. Time-series of the age of all preserved new dune units under all four scenarios under a range of different permutations of different rs and tsregimes. As with Figure 4, Scenario A demonstrates some time-series which decline towards recent ages (i.e. closer to zero on the x-axis), due tomodel run stopping when they have exceeded realistic boundary conditions. Under Scenarios B–D, the age–frequency relationships are all variationson the power-law decay observed by Telfer et al. (2010) as typical for model conditions in which forcing parameters are unvaried during the progres-sion of a model run.


on absolute magnitude once again. Soil resistivity exerts asecondary effect only evident when soil formation is relativelyrapid, in which the time-series decay of highly resistant soilsis subdued compared to those with minimal resistance toerosion. The ratio of soils preserved compared to dune unitspreserved at different times (Figure 6) shows remarkable stabil-ity, and for each scenario, under almost all permutations ofdifferent rs and ts the ratio is relatively stable. It is also relativelyinsensitive to the scenario chosen, although once again,Scenario A reveals the effects of poor parameterization as runswhich have been stopped result in the ratio changing towardsthe end of the time-series. At low values of ts (i.e. frequent soilformation), the relationship is also insensitive to the resistivityof the soil, but if soil formation is infrequent, its resistivitybecomes more important. Under Scenario B, there is a slighttendency for the ratio of soils/total dune units to increasetowards younger ages when soils are very resistant.

Discussion

The first key point to be drawn from the experiments is thegeneral failure of Scenario A to produce a stable dune form.The influence of soils in stabilizing the landscape has oftenbeen considered primarily in terms of resistance to erosion (e.g.Hesse, 2011). The model suggests, however, that when theinfluence of soils and palaeosols is limited solely to vulnera-bility, the dune tends quickly to grow out of control. Only whensoil formation is extremely infrequent, and the effect onincreased resistance very modest, is stability demonstrated


[which may well be the case in the Australian examples ofHesse (2011), where the longevity of dune bodies is well docu-mented]. More crucial to landscape development than thearmouring influence of soils/palaeosols is the concurrent limita-tion on sediment supply, simulated in Scenarios B–D. Under allpermutations of soil resistivity and formation times, dune heightis conserved in these cases (Figure 3), which is considered to bea better representation of reality than Scenario A, which is thusgenerally discounted from further discussion in this section.This is in accordance with recent field observation (Roskinet al., 2013), who concluded that sediment supply representedthe dominant control of dune/palaeosol formation in the Negevduring the Late Quaternary. Even when the dune height isconserved during model runs, the level of reworking of thedune does vary dependent on soil characteristics. Figure 3reveals that under Scenarios B–D, the addition of new duneunits to the dune body is favoured under conditions of slow soilformation and low soil resistivity.

Counterintuitively, the frequency of preserved soils is primar-ily a function of how long soils take to form; their resistivity isalmost immaterial (Figure 3). This must primarily be a functionof the effect of increased resistivity affecting both sedimentsupply and erosion, as the two counter-acting influenceslargely cancel each other out. The much higher soil preser-vation ratio at high rs values under Scenario A supports this asbeing part of the explanation, but even in this instance, thetime for soil formation remains a major control. Some quanti-fication of this effect is possible by considering four end-points (Table II), representing combination of soils that formeither very rapidly and very slowly, and are either highly


Figure 6. Time-series of the ratio between preserved soils (Figure 4) and total new dune units (Figure 5) under all four scenarios.

Table II. Summary of some of the key model parameters under the extremes of the parameters ts and rs, under Scenarios B and C

Rapid development, Easilyerodible (ts = 10, rs = 10)

Rapid development, Highlyresistant (ts = 10, rs = 90)

Slow development, Easilyerodible (ts = 50, rs = 10)

Slow development, Highlyresistant (ts = 50, rs = 90)

Scenario BMean dune height 1 1.005 0.999 0.995Mean new dune units 1 0.377 1.035 0.970Preserved soils 1 0.512 0.023 0.037Total soils 1 0.213 0.022 0.021Soil preservation ratio 1 2.431 0.745 1.284

Scenario CMean dune height 1 1.078 0.991 1.005Mean new dune units 1 0.592 1.020 0.999Preserved soils 1 0.742 0.023 0.064Total soils 1 0.238 0.022 0.022Soil preservation ratio 1 3.103 0.740 2.219

For each scenario, results are normalized to conditions in which soils form readily, and offer minimal additional resistance to erosion (ts = 10, rs = 10).Note that in either scenario, the rate of development of soils has a much greater effect on both preserved and total soils than changes to their resistivity.

M. W. TELFER

resistant to erosion, or offer little additional resistance. Underboth Scenarios B and C (Scenario D is intermediate betweenthese cases, and is not considered in detail), highly resistantsoils do indeed increase the ratio of soil preservation by afactor of two or three, but nonetheless, the net effect is arounda 1.5 order of magnitude reduction in preserved soils.Whether or not exhumed palaeosols are considered to affectsediment supply in the same way as initial soil-formingperiods (Scenarios C and D) has an insignificantly small effectin reducing the dominant effect of ts on soil preservation.The implication is that by far the most likely reason for dunes

in which palaeosols are not preserved is that they were never


formed (cf. Munyikwa, 2005). Although more than half(and typically 80–90%) of the soils formed under almost allconditions were subsequently lost to erosion, it is not sufficientto account for field studies where multiple profiles and coresover several decades of study have yielded no evidence of soils(e.g. the south-western Kalahari). It must be noted at this pointthat the role of bioturbation, which could conceivably entirelydestroy internal stratigraphy within a dune, is not considered inthis model. However, soils offering relatively slight resistance,and thus being most prone to large-scale in situ bioturbation,are those where the dependence on soil initial formation timeis strongest.


igure 7. Under all permutations of the main model parameters, shortiatuses between a soil and the overlying units are most abundant.he relationship between frequency and length of hiatus is approxi-ated in most instances by a power law decay, and long hiatusesre very rare indeed.


The time-series of soil and dune age frequencies (Figures 4and 5) reveal that the preservation of soils is subject to the sametime-dependent effects on preservation as has been observedon the dune body itself by Telfer et al. (2010) and Bailey andThomas (2014). Indeed, Figure 6 reveals this relationship tobe remarkably consistent and stable across a wide range ofconditions. Soils are more likely to come from the recentgeological record, simply because the older ones have beenexposed to the possibility of reworking for longer. However,the time-series also reveal much more subtle influences onboth dune and soil preservation, as the shape of the preserva-tion decay curve is a function of both rs and ts (Figures 4 and 5).When soils form readily (low ts) and are highly resilient (high

rs), the preservation decay curve for both soil and dune units ismuch less pronounced. This is less clear for the soils (Figure 4),as low absolute numbers at high ts values mean the decay isvery noisy. This is most readily explained by an interpretationsimilar to that of Hesse’s (2011) ‘sticky dunes’ or the descriptionof Bagnold’s (1941) roll vortex model by Munyikwa (2005);under these conditions, dunes do begin to approximate astacked record. In terms of mechanisms for dune formation,however, it must be noted that field evidence for roll vorticesat the correct scale remains almost entirely absent; this modelalone cannot be taken as evidence for the transport process. Itmust also be noted that even under these conditions thesedimentary record is far from complete (cf. Munyikwa,2005), as dune height is approximately conserved (Figure 3),and the ratio of soils preserved by the dune body comparedto those which have formed at any time does not exceed~40% under any of the tested conditions for Scenarios B andC. Similarly, especially for Scenario C, systemic dune growthis experienced, but only to a modest degree (~20%). Theremay be, it seems, a ‘Goldilocks’ zone where the net effect ofdeposition, reworking and pedogenesis almost entirely removethe time-dependency of preservation, whilst maintaining low-level reworking and not resulting in uncontrolled dune growth.Applying this knowledge in the field, however, may be prob-lematical, as it requires a priori knowledge of the time takenfor soils to form in the past as well as their time-averaged resis-tance to erosion if exposed. Perhaps more pragmatically, itshould be recognized that in most cases, soils, as with dunesands themselves, are likely to be subject to time-dependentpreservation. Furthermore, the relationship between the preser-vation ratio of soils and their resistance is highly non-linear;only when resistance nears 100% (i.e. soils are unremovable)does the ratio of soil preservation also begin to rapidly ap-proach 100%. In other words, even moderately resistant soilsare very likely to be reworked in due course.There has been recent attention on the field significance of

both lithostratigraphic and chronostratigraphic hiatuses indunes (Leighton et al., 2013a). The model allowed investi-gation of the intervals between the recommencement of accu-mulation above soil horizons (Figure 7). In all cases underScenarios B and C, preserved hiatuses above palaeosols aredominated by short intervals, and the relationship betweenfrequency and length of hiatus is approximated by a power-lawdecay function. In other words, although some very long hiatusesaround bounding surfaces are always to be expected, presumablywhere resilient soils have formed a surface at which erosion ismore likely to stop, they would be expected to be very rareindeed. The field observations of Leighton et al. (2013a,2013b), however, suggested that whilst the degree of develop-ment of bounding surfaces (that is, allostratigraphic order) didnot correlate with the length of the chronostratigraphic hiatus,comparatively long hiatuses were frequent.There are likely to be two reasons for this, the first of which

has significant implications for the interpretation of long


FhTma

chronostratigraphic hiatuses in the field. Crucially, the basicparameters which control deposition and erosion (i.e.pr and pd)in these simulations are unchanging. That is, there is no attemptmade to simulate changing climatic forcing events, unlike Telferet al. (2010) and Bailey and Thomas (2014), and soil formationoccurs during randomly-determined periods of dune inactivity.By contrast, if soils were formed as a result of periods when exter-nal forcing reduced dune activity, and the duration of that forcingexceeded the time necessary for soil formation to occur, then lon-ger hiatuses would be more frequent. There may thus be apalaeoenvironmental significance to long hiatuses in the record,as the model suggests that they are highly unlikely (although pos-sible) under unchanging environmental conditions. It may bepossible to test this by correlation of long hiatuses aroundbounding surfaces with additional proxies, but this is made chal-lenging by the paucity of such proxy records in most dunefields.Another possibility exists, however. The simple one-dimensionalnature of the model may not adequately capture the behaviour oflinear dune geomorphology. In reality, linear dunes exhibit acomplex range of morphologies (Tsoar, 1989); their crests maybe sinuous (with alternating slip-faces), and they may includeblow-outs or even multiple crests. Thus the assumed modelgeometry of a single crest-line with essentially equal probabilitiesof erosion and deposition along its length may not, in reality bemet in some circumstances. Thus observed chronostratigraphichiatuses around bounding surfaces may be attributed simply todifferential deposition on the dune surface. Indeed, such


M. W. TELFER

depositional unconformities have been identified using geophys-ical methods (e.g. Bristow et al., 2007), as well as chrono-stratigraphic surveys (Telfer, 2011).

Conclusions

A model has been successfully developed, based on that ofTelfer et al. (2010), which simulates the development ofsedimentary units with different characteristics (namely varyingresistance to subsequent erosion) within an actively accretingand eroding dune. This has been used to investigate the pre-servation of relic soils and other bounding surfaces within ageomorphologically dynamic dune system. Four differentscenarios, with slightly different model behaviour, were used,and for each a range of permutations of basic model parameterswas investigated to characterize system behaviour. Thesimplest of these (Scenario A), in which soils were assumedonly to influence the probability of subsequent erosion,performed poorly in simulating relatively stable dune behav-iour, emphasizing that an essential aspect of landscape devel-opment in terms of palaeosols is that they represent periods ofreduced sediment supply. When sediment supply was limitedduring the exposure of soils and palaeosols (Scenario B),newly-formed soils only (Scenario C) or a situation intermediateto these conditions (Scenario D), the model produced largelystable dune behaviour. Scenarios B and C differed only rela-tively subtly, emphasizing that it is the role of sediment supplyat the time of soil formation which is critical. Experimental fieldtesting of this observation is challenging, but investigation ofthe spatial distribution of palaeosols within a dunefield and itsrelationship to sediment sources may be fruitful.Perhaps surprisingly, the key control on palaeosol preserva-

tion within dunes was found not to be their resistance toerosion (even where the probability of erosion of a soil unitwas only 10% that of the surrounding sands), but howfrequently they formed. The implication of this for dune systemsin which soils are not preserved is that it is much more likelythat soils and other major bounding surfaces were neverformed in the first place, contrary to some suggestions that itis likely to be attributable to subsequent erosion and poorpreservation. Where bounding surfaces are preserved, thechronological gap between the preserved soil and the firstpreserved unit above can be highly variable, but short hiatusesare very much more likely. When long hiatuses aroundbounding surfaces are observed in the field, they are most likelyattributable to either environmental forcing (e.g. climaticchanges) or spatially-complex dune geomorphological behav-iour (such as progression of slip-faces along an undulose crest).

Acknowledgements—Thanks are due to all the colleagues at theUniversity of Oxford for ideas and discussion during the original devel-opment of the model. Aimee Brackpool (formerly of Plymouth Univer-sity) is thanked for her work exploring the initial potential in developingthe simulation of palaeosol units. Two anonymous reviewers arethanked for their thorough and insightful comments, which have im-proved this manuscript.

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Modelling palaeosol preservation in aeolian dunes