autocyclic behaviour of fan deltas: an analogue experimental...

Autocyclic behaviour of fan deltas: an analogue experimentalstudy

MAURITS VAN DIJK*, GEORGE POSTMA* and MAARTEN G. KLEINHANS�*Department of Earth Sciences, Faculty of Geosciences, Utrecht University, PO Box 80.021, 3508 TAUtrecht, The Netherlands (E-mail: [email protected])�Department of Physical Geography, Faculty of Geosciences, Utrecht University, Utrecht, TheNetherlands

Associate Editor – Steve Rice

ABSTRACT

Fan deltas are excellent recorders of fan-building processes because of their high

sedimentation rate, particularly in tectonically active settings. Although

previous research focuses mainly on allogenic controls, there is clear evidence

for autogenically produced storage and release of sediment by flume and

numerical modelling that demands further definition of characteristics and

significance of autogenically forced facies and stratigraphy. Analogue

experiments were performed on fan deltas with constant extrinsic variables

(discharge, sediment supply, sea-level and basin relief) to demonstrate that

fan-delta evolution consists of prominent cyclic alternations of channellized

flow and sheet flow. The channellized flow is initiated by slope-induced

scouring and subsequent headward erosion to form a channel that connected

with the valley, while the removed sediment is deposited in a rapidly

prograding delta lobe. The resulting decrease in channel gradient causes a

reduction in flow strength, mouth-bar formation, flow bifurcation and

progressive backfilling of the channel. In the final stage of channel filling,

sheet flow coexists for a while with channellized flow (semi-confined flow),

although in cycle 1 this phase of semi-confined flow was absent. Subsequent

autocyclic incisions are very similar in morphology and gradient. However, they

erode deeper into the delta plain and, as a result, take more time to backfill. The

duration of the semi-confined flow increases with each subsequent cycle.

During the period of sheet flow, the delta plain aggrades up to the ‘critical’

gradient required for the initiation of autocyclic incision. This critical gradient

is dependent on the sediment transport capacity, defined by the input

conditions. These autogenic cycles of erosion and aggradation confirm earlier

findings that storage and release of sediment and associated slope variation play

an important role in fan-delta evolution. The erosional surfaces produced by the

autocyclic incisions are well-preserved by the backfilling process in the deposits

of the fan deltas. These erosional surfaces can easily be misinterpreted as

climate, sea-level or tectonically produced bounding surfaces.

Keywords Analogue experiment, autocyclic behaviour, channellized flow,fan delta, sedimentary cycles, sheet flow, slope variation.

INTRODUCTION

Fan deltas are coastal prisms of sediment derivedfrom an alluvial-fan feeder system. These deltas

are deposited partly or fully subaqueously at theinterface between the active fan and a standingbody of water and are common along tectonicallyactive basin margins (Nemec & Steel, 1988a). Fan

Sedimentology (2009) 56, 1569–1589 doi: 10.1111/j.1365-3091.2008.01047.x

� 2009 The Authors. Journal compilation � 2009 International Association of Sedimentologists 1569

deltas can preserve sensitive records of variabletectonic, climate and base-level conditions(Collinson, 1988; Nemec & Steel, 1988b; Whipple& Trayler, 1996). Variations in climate conditionsare inferred to have a large impact on the gradientof the fan and on stratigraphic architecture due tochanges in water and/or sediment yield (e.g. Bull,1977; Hooke & Rohrer, 1979; DeCelles et al., 1987,1991; Blair & McPherson, 1994; Milana & Ruzycki,1999; Milana & Tietze, 2002; Saito & Oguchi,2005). The effects of tectonics and base-levelchanges on alluvial fans and fan deltas have alsobeen described extensively (Steel et al., 1977;Gloppen & Steel, 1981; Garcıa-Mondejar, 1990;Gawthorpe & Collela, 1990; Fernandez et al., 1993;Nemec & Postma, 1993; Li et al., 1999; Soria et al.,2001; Harvey, 2002; Viseras et al., 2003; Garcia-Garcia et al., 2006; Pope et al., 2008).

Flume and numerical modelling of alluvial andfan delta-type systems reveal that autogenic con-trol plays an important role in fan-delta evolution(e.g. Schumm et al., 1987; Whipple et al., 1998;Kim et al., 2006; Kim & Muto, 2007; Kim & Paola,2007; Nicholas & Quine, 2007). However, auto-genic behaviour is usually observed during allo-genic variations, which makes it difficult to studyits characteristics and significance. Schummet al. (1987) modelled alluvial fans using acatchment as a sediment source which wasprogressively eroded by precipitation. The waterand sediment were led to a basin where the fanswere deposited. Those authors concluded that thefrequency of fan-head entrenchment observed inanalogue experiments had no relation to thechanges which were measured in the unsteadysediment supply. Hence, Schumm et al. attrib-uted the trenching to autocyclic behaviour. Acloser investigation of the measurements reportedby Schumm et al. (1987, fig. 9.22) shows that, ingeneral, the frequency of entrenchment decreaseswith decreasing ratio of sediment to water dis-charge (Qs/Qw). However, during the experimentthe frequency of entrenchment increased occa-sionally with decreasing Qs/Qw, contradicting thegeneral trend within the same data set. The use ofa catchment as a sediment source and the result-ing unsteady supply make interpretation of thesemeasurements difficult and conclusions regard-ing autocyclic processes ambiguous. Whippleet al. (1998) investigated quasi-steady surfaceaggradation of an alluvial fan in a flume underconditions of base-level rise and constant waterand sediment supply. These authors observedautogenic flow variation on the fan that varied inspace and time between a state of sheet flow and a

state of distinctly channellized braiding. Duringbraiding, zones of flow concentration formed,entrenched and backfilled. Building further onthe experiments of Whipple et al. (1998), Clarkeet al. (2008) performed a set of experiments oninternal processes of alluvial fans. A specificaspect of these models was the removal ofsediment at a certain radius, limiting fan growthto simulate truncation by, for instance, axial riversystems. Short-term fluctuations between sheetand channellized flow were observed throughoutthese runs. Fan-head entrenchment dominatedduring the last third of these experiments whichlasted from 5 to 13 h. Studying relative sea-levelforced shoreline migration in an analogue flumeexperiment, Kim et al. (2006) found that signifi-cant, high-frequency autogenic slope fluctuationspersisted even when the effect of channel switch-ing was eliminated by lateral averaging of theshoreline migration rate and after accounting forthe sea-level variations. The autogenic signal inthe laterally averaged shoreline migration rateimplied a fluvial process that caused variation inthe sediment yield to the shoreline. These authorsalso observed sheet-like flow alternating withphases of strongly channellized flow, suggestingthat the fluvial system alternated between statesof storing sediment and then releasing it byincision. The one-dimensional numerical modelthat Kim et al. (2006) derived from the analogueexperiments treated the autogenic variations as acyclic change between two extreme slopes.Hence, two potential fluvial profiles were de-fined, representing maximum possible aggrada-tion or maximum possible incision. Nicholas &Quine (2007) found autogenic channellized inci-sions using constant sediment and water input ina three-dimensional numerical model of evolvingalluvial fans. Muto et al. (2007) combine previ-ously published experimental and numericalmodelling results to show the non-equilibriumbehaviour of fluvial systems during steady forc-ing. This analysis allows the detection and iden-tification of autogenic responses and allogenicevents in the stratigraphic record. Muto et al.show convincingly that at least part of theassumptions on which sequence stratigraphicmodels have been built in the late 1980s and1990s is in need of modification to include theimpact of autogenic behaviour during allogenicvariations (see also Muto & Steel, 1997, 2000).

All of the above experimental studies demon-strate that autogenic incisions in the alluvial-fanapex may occur during allogenic variations; butcan they occur when allogenic conditions are

1570 M. Van Dijk et al.

� 2009 The Authors. Journal compilation � 2009 International Association of Sedimentologists, Sedimentology, 56, 1569–1589

constant? To date, experimental studies on auto-genic behaviour have never been conductedentirely without change in external forcing.Hence, the present work aimed to study thebehaviour of fan-delta systems under steadyconditions, in the absence of variations in tecton-ics, sea-level, sediment supply and water dis-charge, so that the resulting behaviour must thenbe of autogenic origin. This study contrasts withthe work focussing on autostratigraphy, per-formed by, for example, Muto & Steel (2000),who studied delta evolution by ‘steady’ forcingduring constant base-level rise and fall.

By repeating the same controlled experimentfor different steady discharge values, insight willbe gained into autogenic behaviour in relation towater discharge. As shown by Schumm et al.(1987), Bryant et al. (1995), Whipple et al. (1998)and Milana & Tietze (2002), different dischargeconditions lead to different sediment transportcapacities that have effects on the dynamics of thefan-delta plain. Therefore, it is expected thatthese differences in discharge will also affect theautogenic behaviour. Finally, the stratigraphicarchitecture of the model is evaluated to deter-mine whether autogenic features can be preservedin real-world fan-delta deposits.

EXPERIMENTAL DESIGN

Flume set-up and materials

The experiments were conducted in the EurotankFlume Facility at Utrecht University. Threeexperiments, were carried out, R1, R2 and R3,each using different water discharge, but all otherinput conditions extrinsic to the system wereheld constant (i.e. sea-level, discharge and sedi-ment supply). The input conditions and othervariables are provided in Table 1.

The set-up of experiment R1 (the experimentthat lasted longer than the other two and whichwas also measured in more detail) consisted of ahorizontal shelf (5Æ4 · 3Æ0 m) and duct(1Æ5 · 0Æ05 m), the latter acting as a feeder chan-nel (Fig. 1). The shelf was submerged under 1 cmof water, while a drain located in the basinensured a constant water level. The bed of boththe shelf and the channel consisted of fine sand toprovide a realistically rough and also erodableinitial surface. The sand bed in the duct couldaggrade freely to produce a sloped surface con-nected with the evolving fan delta. The horizontalshelf ensured progradation into a constant waterdepth throughout the experiment. Feeder channeldimensions allowed the flow to leave the feederchannel and enter the shelf in a steady, centredjet, located in the centre of the upstream edge ofthe shelf. The sediment was delivered at aconstant rate from a hopper with a rotating helixand mixed with the water supply before enteringthe feeder channel. Deviations of the delivery bythe feeder were measured to be less than 1% over15 min. All sediment was stored in the flume.

For the smaller set-ups (R2 and R3), the size ofthe shelf was limited to 2Æ7 by 2Æ7 m, in order to fittwo set-ups side by side for simultaneous exper-iments. A ditch between the two prevented theexperiments from influencing each other. Bothset-ups had their own separate feeder channel,located in the centre of the upstream edge of theirshelf. Apart from the smaller shelf size, all othercomponents of the set-up were identical. Sedi-ment input in all three experiments was identical(1Æ0 l h)1); water discharges were 600 l h)1 (R1),550 l h)1 (R2) and 350 l h)1 (R3).

To enhance visualization of the morphologicalchanges on the fan deltas, grey and white sandwere supplied intermittently. The grey sand wasalso used as substrate in both the shelf and thefeeder channel. Both sand types consisted ofquartz, with a bulk density of 2650 kg m)3, andthe grain-size distributions of the two sands werevery similar (Fig. 2). The critical Shields para-meters of the two sand types, calculated using themodel of Vollmer & Kleinhans (2007) accountingfor shallow flow depth, were 0Æ0668 and 0Æ0622for the grey and white sands, respectively. It isassumed here that the small difference betweenthe two sand types has a negligible effect on theexperiments. The grain-size of the sediment usedin the experiments was chosen such that sedi-ment transport would occur as bed load underthe range of discharges used, in analogy withmodern alluvial fans and fan deltas that are

Table 1. Input conditions and dimensions of theexperimental set-up.

RunLaboratory name

R1A008

R2A004.1

R3A004.2

Sediment supply,Qs (m3 h)1)

0Æ001 0Æ001 0Æ001

Water supply, Qw

(m3 h)1)0Æ60 0Æ55 0Æ35

Ratio Qs/Qw 0Æ00167 0Æ00182 0Æ00286Set-up size (m) 5Æ4 · 3Æ0 2Æ7 · 2Æ7 2Æ7 · 2Æ7Total run time (h) 186 44 44

Autocyclic behaviour of fan deltas 1571


dominated by bed load transport. The transportcapacity h of the channellized flow was estimatedby means of Eq. 1:

h ¼ s0

ðqs � qwÞgD50ð1Þ

with:

s0 ¼ qwgu

C 0

� �2

ð2Þ

and:

C 0 ¼ 1810 log12d

2 � 5D50

� �ð3Þ

where d is the depth (m), u is the velocity(m sec)1), g is the gravitational constant[9Æ81 m sec)2], C ¢ is the Chezy constant (msec)0Æ5), qs is the sediment density (kg m)3), qw

is the density of water (kg m)3) and s¢ is thebottom shear stress (N m)2). Calculated values forh averaged 0Æ20 and were never higher than 0Æ28.These values easily exceed the critical Shieldsparameters for the sediment used and are justabove the criterion for suspended sediment trans-port derived by Soulsby (1997), indicating thattransport as bed load will be the rule rather thanthe exception. The smaller flow depths of thenon-channellized flows yield higher Chezy values

and smaller values of h, ruling out suspendedtransport outside the channels.

Measurements

The surface topography was quantified usingphotogrammetry based on stereoscopy (for exam-ple, Chandler et al., 2001; Brasington & Smart,2003). In the Eurotank flume, an automatedmovable platform is attached to the ceiling. Itcontains a set of cameras, which takes foursimultaneous photographs of the surface fromdifferent angles. The images are processed usingsoftware package sandphox� (Geodelta, Delft, theNetherlands), into a Digital Elevation Model(DEM) of the sand surface. The vertical resolutionof the DEMs is 250 lm and the horizontal resolu-tion is better than 100 lm. To avoid reflections ofthe running water in the images, the experimentwas stopped before each photogrammetry scanand the water was slowly drained to avoid com-paction of the bed. The experiments R2 and R3were halted every 4 h, while experiment R1 wasstopped at uneven intervals depending on theprogress of the experiment. The intervals rangedfrom two photogrammetry scans every hour dur-ing periods of high (autogenic) activity to a singlescan every 8 h during periods of less activity.

Fig. 1. Schematic view of the set-upof experiment R1. Experiments R2and R3 were carried out in smallerbut otherwise identical set-ups.



In addition, time-lapse photography using dig-ital video cameras recorded the entire experi-ment. During experiment R1, the camera wasmounted directly above the fan delta for a planview of the experiment. The images were re-corded on a digital recorder, the camera takingthree images every 10 min. The flow depth withinconfined flows was measured directly with aruler, especially when the flow within the chan-nels was not bankfull. When flow was bankfull,the flow depth was derived from the DEMs.

RESULTS

The experimental fan deltas accumulated throughcycles of alternating sheet and channellized flow.The fan-delta evolution of experiment R1, pre-ceded by sheet flow building up the initial fandelta, involved five channellization events. Theinitiation and backfilling of the first of thechannellization events is shown in detail inFig. 3A to H. Figure 3I to L shows later eventsas the delta grows in size. The detailed develop-ment of a single cycle is demonstrated by a set ofshaded relief maps (Fig. 4A to G) and topograph-ical profiles (Fig. 5) from the first autogenic cycleof experiment R1. The duration of sheet flow andchannellized flow for R1 is given in Fig. 6 and forexperiments R2 and R3 in Fig. 7. Both Figs 6 and7 also show curves for the aggradation on theapex, slope measurements and delta growth ratesfor given positions on the delta.

Fan-delta morphodynamics during anautogenic cycle

At the initiation of the experiment, the waterentered the basin as a jet to produce an initiallobate-shaped, submerged delta at the outlet of

the feeder channel. Within an hour, a distinctdelta plain formed that was covered entirely by asingle sheet flow. After 9 h, deposition shiftedfrom the centreline to the flanks of the delta andits morphology changed from lobate to semi-circular (Fig. 3A), while the initial jet transformedinto an expanding sheet flow, which produced asmooth delta plain topography (Fig. 4A).

Six hours later, the morphology of the fan deltahad changed and white sediment radial ‘spokes’appeared on the fan-delta surface (Fig. 3B and C),demonstrating that the sheet flow was onlycapable of sediment transport to the shoreline indistinct flow paths, leaving small segments of thedelta plain inactive. Apparently, the area of thedelta plain had grown too large to maintain sheetflow, which responded by breaking up intosmaller sheet-flow segments separated by inactiveparts. These ‘fractionated’ shallow sheet flowsranged in width from 5 to 50 cm. With increasingsize of the delta, the fractionated flows near thedelta shoreline began to concentrate, finallydeveloping small-scale channels. Flow depths inthe incipient channels increased to a maximum of5 mm, while flow width decreased to severalcentimetres. As a result the small-scale channelsbecame more pronounced and also started to formdistinct ‘delta lobes’ at the shoreline (Fig. 4B).The lobes measured only a few centimetres indiameter. Usually, a single fractionated flow fedseveral of these small-scale nearshore channels.

At this point in time, the delta plain can besubdivided into three zones: (i) continuous sheetflow on the fan apex; (ii) fractionated sheet flowjust downstream of the apex; and (iii) small-scalechannellized flow near the shoreline (Fig. 4B).The small-scale channels shifted regularly acrossthe delta plain in conjunction with the fraction-ated sheet flows, causing the delta lobes to shiftlaterally, thereby retaining the overall semi-circular shape. The shifting occurred by bothlateral channel migration and channel avulsions,all well-known processes previously described insimilar physical experiments (Schumm et al.,1987; Bryant et al., 1995; Whipple et al., 1998;Ashworth et al., 2004, 2007).

After nearly 38 h, progressive aggradation at theapex increased the gradient of the delta plain upto the point when a scour hole was initiated alongthe centreline of the fan delta (Figs 3D and 4C).The scour hole developed quickly into a knickpoint that moved upstream (Fig. 3E) connectingthe scour with the feeder channel (Figs 3F and4D). Upon connection, the flow became fullyconfined to a depth of just below 1 cm, leaving a

Fig. 2. Cumulative grain-size distributions of the greyand white sands used in the experiments.



large part of the delta plain dry and inactive. Theenhanced transport capacity of the channellizedflow further widened and deepened the entrench-

ment, depositing the eroded sediment in a rapidlyprograding delta lobe, followed by the develop-ment of a distinct mouth bar (Figs 3F and 4D).

A B C

D E F

G H I

J K L

Fig. 3. Video images of the plan view development of the alluvial-fan delta of experiment R1. Blue areas representthe standing body of water, the black lines show the shoreline of the delta and the red lines mark the boundary of theincised channel. Run time is indicated in the lower left of each picture. The curvature of the boarding at the bottom ofall the pictures is caused by the bird’s eye view lens used to capture the entire set-up with one camera. The inside ofthe feeder channel at the bottom of the diagrams is 5 cm wide. In Fig. 3K the width and length and the location of theprofiles along the centreline and flanks of the delta are specified. Note that the inflow in these images is from thebottom upwards, whereas in Figs 1, 4, 5, 8, 9 and 11 flow enters from the left-hand side.



A B

C D

E

12 h 00 35 h 36

36 h 16 38 h 27

41 h 00

42 h 00 64 h 00

F G

Fig. 4. Shaded relief maps of thedevelopment of the first autogeniccycle of experiment R1. Run time isshown in the lower right corner. Thelocation of the cross-sections ofFig. 5 is indicated in Fig. 4A, andalso the maps correspond to thelabelled lines in Fig. 5. The scale ofthe plots is indicated in the upperright corner; the position of panel(E) is given by the inset in panel (D).



The bar caused the flow to bifurcate around it,leading to lateral migration of the flow away fromthe centreline of the fan delta (Figs 3G and 4E).Progressive deposition around the bar increasedthe angle of bifurcation, shifting sediment depo-sition and resultant delta progradation sideways.

The bifurcation of the flow around the barproduced two scour holes, just upstream of thebar at the inner bends of the bifurcating flows(Fig. 4E) instigating erosion of the channel wallsand flow widening. This effect must have decel-erated the flow sufficiently for aggradation to start

Fig. 5. Topographic development of an autogenic cut and fill cycle. The sequence of cross-sectional linescorresponds to the shaded relief maps in Fig. 4. The labels marked in the figure correspond to one of the panels orto a transition between two of the panels in Fig. 4. The location of the transects is indicated in Fig. 4A.

A

B

C

Fig. 6. The development of the fandelta during experiment R1. Thelight grey areas represent periods offully confined channellized flow,in the dark grey areas channellizedflow coexisted with sheet flow; areaswithout grey shade represent sheetflow only. (A) Plot of the elevationand aggradation rate of the apex, thedepth of the incised channel duringphases of channellized-flow domi-nation and the average surface-channel depth during sheet flow. Thecurve showing the elevation of thedelta apex also designates whichsand type was supplied: the blackpart of the curve indicates dark greysand, the light grey part of the curvecorresponds to the white sand;(B) plot of the development of thegradient of a profile along thecentreline of the fan delta and acrossthe flanks (perpendicular to thecentreline); (C) plot of the growthrates of the delta along the centreline(black) and the flanks (grey).



along the full length of the channel, as seen fromthe cross-sections E of Fig. 5 (labelled ‘start ofchannel fill-up’). Flow widening and aggradationled to headward migration of the intersectionpoint (at the bifurcation). The flow graduallystarted to exceed the confining channel walls andincreasingly spilled over the margin in the courseof the backfilling process (Fig. 4F); this progres-sively decreased the amount of water in thechannel which is assumed to explain the in-creased aggradation, clearly visible in line F–G ofFig. 5. After 3 h, the incised channel completelybackfilled from migration of the mid-channel bar,with the bar crest (visible on Fig. 5) shiftingupstream towards the apex. When the entirechannel had been filled, fractionated sheet flowand aggradation of the apex were restored(Figs 3H to K and 4G, line G in Fig. 5). Sheetflow persisted until the gradient had increasedsufficiently to initiate another cycle of incision,progradation and backfilling (Fig. 3I, J and L).

A summary of the development of the delta isgiven in Fig. 6. The elevation of the apex at thepoint of scour initiation is shown in Fig. 6A andthe change in gradient from the apex to theshoreline along the centreline of the fan delta isshown in Fig. 6B. Both diagrams show a cleartrend towards a maximum followed by a consid-erable reduction when incision occurs. Followingthe backfilling process, both elevation and gradi-ent grow towards new maxima. During the periodof incision, the length of the delta along thecentreline increases significantly (Fig. 6C), whilethe delta width remained more or less constant.

Slope variation

From a morphodynamical perspective, it is inter-esting to determine the variation of the slope as itvaries around the average slope during deltaevolution (see Kim et al., 2006). The gradientsalong the centreline clearly show a slope building

A

B

C

A

B

C

Fig. 7. The development of the fandeltas from experiments R2 and R3.Labelling and legend as in Fig. 6,except that data on channel depthare excluded.



up to a critical value, followed by a significantdecrease in slope due to erosion and lengtheningof the profile during channellized flow for eachcycle (Figs 5, 6B and 7B). The variability of theslope (calculated as the standard deviation fromthe mean slope) is also different. The slopevariability can be found in Figs 6B and 7B asthe range between the maximum and minimumslope values, and differs between the locationsalong the flanks and the centreline and betweenexperiments. Along the flanks (see Fig. 3K forlocations of the profiles), the variability was 4Æ4%,7Æ5% and 4Æ2% for experiments R1, R2 and R3,respectively, much smaller than the variabilityparallel to the jet flow, which was 8Æ8%, 13Æ6%and 9Æ9% for experiments R1, R2 and R3, respec-tively. The higher slope variability in the jet-flowdirection reflects the greater variation in sedimenttransport due to the autogenic processes andcorrelates with the incision events. By contrast,the slope building on the flanks is active duringthe semi-confined flow stage and the sheet-flowstage, thus showing dominance of sheet-flowprocesses related with flow fractionation andrandom rill formation.

Kim et al. (2006) report that the autogenic slopevariation decreases with (normalized) down-stream system size. In the present case, Figs 6and 7 both show that the maximum slope remainsconstant and that the minimum slope duringincisions increases slightly, confirming the re-sults by Kim et al. (2006). Unfortunately, theminimum slope is difficult to measure. The rate ofslope change during active channellized flowscauses very high measurement error. Therefore,the measured minimum slopes most likely are notthe actual minima; the true minima probablyoccur just before or after the measurements. Forthe maximum slope measurements, this problemdoes not exist, as the rate of slope changebecomes increasingly smaller when aggradationapproaches its maximum magnitude. It is impor-tant to note that, although the minimum slopevalues of subsequent incisions increase duringthe experiments, the subsequent incisions man-age to erode deeper into the delta plain.

Development of subsequent autogenic cyclesduring delta growth

Does the increasing size of the fan delta affect theautogenic behaviour of the alluvial-fan feedersystem? Intuitively, it would be expected thatthe frequency of the autogenic behaviour woulddecline as the fan delta grows. The progressively

larger aerial size of the delta plain needs increas-ingly more sediment to regain the gradient neces-sary for incision to commence. Hence, withsediment input being constant, it would beexpected that that the time in between subsequentincisions would increase exponentially with deltagrowth and the related growth in sediment accu-mulation space (space available for backfilling).The term ‘accumulation space’ has been broughtforward by Blum & Tornqvist (2000) followingearlier studies by Kocurek & Havholm (1993) andKocurek (1998) to avoid the confusion whichwould result from the use of ‘accommodation’ in aterrestrial context. Those authors defined accu-mulation space as ‘‘the volume of space that canbe filled within present process regimes, and isgoverned fundamentally by the relationship be-tween stream power and sediment load, and howthis changes in response to geomorphic baselevel’’. Figure 6 shows that the time in betweenthe incisions does not increase exponentially.Basically, the incisions occurred at regular inter-vals of roughly 40 h (except for the fourth cycle,which started earlier than expected). So whatcontrols the cycle time? If it is not the size of thedelta, the answer, as will be discussed below,must lie in the constant, upstream conditions.

With constant boundary conditions, similar gra-dients are expected throughout the evolution ofthe fan (e.g. Whipple et al., 1998). Figure 8A to Eleft column shows topographic profiles along thecentreline for each cycle (various colour tones)measured just before and after incision andduring the activity of the channellized flows. Toshow the similarity in style of each cycle, theprofiles for each cycle have been shifted verticallyuntil they overlie each other (Fig. 8 right-handcolumn). The patterns in gradients are strikinglysimilar in each cycle and confirm the idea thatupstream conditions play a major role in theautocyclic fan-delta evolution. The cause ofsubsequent channellization is clearly over-steep-ening of the delta plain apex. The incision andheadward erosion start just at the down-slope endof the water jet on the convex-up surface, thusalways about the same distance from the valleyoutlet. Figure 8A shows the topographic profilesalong the centreline just prior to incision. Theblue arrows indicate where the first mark ofincision (scour hole) was observed on the plan-view camera images. Scouring started roughly110 cm downstream from the feeder channel inall five cases. The topographic profiles of exper-iments R2 and R3 are not included, but the firstincision of experiment R2 started 70 cm from the



feeder channel and the second one started 75 cmfrom the feeder channel. Experiment R3 showedonly one incision, which was initiated at adistance of 70 cm from the feeder channel. Theconstant input of water and sediment not onlyleads to the same ‘critical gradient’ responsiblefor the initiation of the channellized flow, but

also to the location of incision. The gradients andconcave-up shape of the channel are strikinglysimilar, as well as the position of the mid-channelbar and the slope downstream of the bar. More-over, the backfilling of the channels shows thesame development in morphology and gradient.Hence, the increasing size of the delta had no

A

B

D

C

E

Fig. 8. Comparison of the individ-ual incisions of experiment R1.On the left-hand side the originalprofiles are shown, on the right-hand side the profiles are shiftedvertically to overlay them over eachother in order to compare themorphology of the profiles. Thelocalities where scouring started inexperiment R1 are indicated byarrows in Fig. 8A.



impact on the delta plain slope which is governedprimarily by water discharge and sediment yield.

Especially later on in the delta evolution, thegradients near the shoreline tended to becomeless steep (Fig. 8). After the delta had grownbeyond a radius of 150 cm, the profile becameslightly concave-up near the shoreline. This pointremained stationary during the experiment. Theconcavity might be related to fractionation of thesheet flow and progressive rill formation, leadingto enhanced concentration of the flow in the rills(small channels that adopt their concave profilein a way similar to the incision events on theapex). Although the present experiments are notdirectly scalable to natural systems, it wasnoticed that concave-up profiles away from theapex of fans are very common in natural alluvialfans and fan deltas. Moreover, the incised chan-nel length (the distance from the outlet of thefeeder channel to the intersection point) grewvery little compared with the delta radius,although its slight lengthening appears to coin-cide with a reduction in its width (compareFig. 3F, I, J and L). The slight growth in channellength with each cycle can be attributed to theprogressive narrowing of the channel in eachsubsequent cycle due to progressive deepening ofthe subsequent incisions, enhancing the effect ofthe jet ‘pushing’ the intersection point morebasinward. The jets in experiments R2 and R3are considerably smaller in length, reflected bythe fact that the scourings in R2 and R3 wereinitiated significantly further upstream and con-firming the control of the length of the jet.

The increasing size of the delta does play a role,however, in the backfilling process. From incisioncycle 2 onwards (after approximately 80 h runtime), the increased duration of channellized flowwas accompanied by the occurrence of a newstage in delta evolution. The channellized flowgraded from fully confined (light grey in Fig. 6) tosemi-confined, coexisting with sheet flow (darkgrey in Fig. 6). This result contrasts with the firstincision, when the transition from channellizedflow to sheet flow was quite abrupt. After theoccurrence of the semi-confined flow stage, back-filling of the incised channels took progressivelylonger. The first incision lasted 4 h, whereas theincision of cycle 4 took 18 h to fill (see Fig. 6). Asthe sediment supply is constant, it must be areflection of the progressively larger accumula-tion space characterizing subsequent cycles. Thevolume of the five incisions in experiment R1does indeed increase (see Fig. 9), although thevolume change is smaller than expected from the

growth of the delta radius. The decreasing chan-nel width and the increasing minimum slopeprobably are the limiting factors on the growth ofaccumulation space.

Varying water discharge and sediment supply

The delta growth rate associated with the inci-sions decreases sharply with decreasing waterdischarge. Experiment R1 on several occasionsshowed growth rates of more than 50 mm h)1

(Fig. 6), the growth rate of experiment R2 is nomore than 20 mm h)1 and of R3 only 10 mm h)1

(Fig. 7). These growth rates vary in a non-linearway with imposed water discharge, as noted by,for example, Postma et al., 2008. Yet, what are theconsequences for the frequency of the autocyclic-ity? It can be argued that erosion and backfillingcycles will shorten in duration with increasingdischarge, due to higher sediment transport rates.

Using the numerical acronym 6 model of Parkeret al. (1998) (available at http://cee.uiuc.edu/people/parkerg), depositional slopes were calcu-lated for both sheet and channellized flow on thedeltas (Appendix) and the characteristic convex-up shape for delta plain development duringsheet-flow conditions and the concave-up tostraight shape for channellized segments of thedelta were reproduced for the three differentexperiments R1, R2 and R3 (Fig. 10A). The eleva-tion plots in Fig. 10 have been normalized to thehighest apex elevation obtained for sheet flow. Thenormalized gradients predicted by the numericalmodel show much similarity with those obtainedin the flume, and confirm that for any discharge thegradients for channellized flow are much lowerthan for sheet flow (Fig. 10A). To extrapolate theseresults to a wider range of conditions and naturalsystems, the impact of discharge variations forfans constructed of gravel-sized sediment was

Fig. 9. Volume of the five subsequently incised chan-nels, normalized by the first incision.



assessed, as performed theoretically by Parkeret al. (1998). The same data which Parker et al.(1998) listed for their Sand and Gravel Fans andused to calculate the normalized gradients fordischarge values were used in this study. Toillustrate the effect of small deviations in dis-charge on the depositional profile, slopes werealso calculated for discharges that are 25% lowerand higher, respectively (Fig. 10B and C). Theresults show that the impact of variations in waterdischarge on the slopes produced by sheet-flowconditions is much greater than for channellized-flow conditions (shaded areas), and also that theimpact is largest for the Gravel Fan. The numericalresults show that the greatest difference in gradi-ents (and thus accumulation) between sheet flowand channellized flow occurs at low discharge,when sediment transport rates are minimal. Insuch conditions, accumulation space requiresmore time to be refilled, which increases cycleduration.

However, although relationships between auto-genic cycles and delta growth rates and dischargecan be inferred, the present experimental resultsdo not show them explicitly. The erroneous cyclein experiment R2 produced an anomalous inci-sion after roughly 13 h (Fig. 7), as shown by thedecrease in gradient of the apex (Fig. 7A), yet theincision generated hardly any degradation. Theother phase of incision generated during experi-ment R2 and also the incisions in the experimentsR1 and R3 did show significant degradation priorto backfilling of the incision (Fig. 6A and 7A).The cause of the aberrant incision remainsunclear.

DISCUSSION

The present experiments show similarity of pro-cess with gravelly alluvial fans built by sheet-flowand sheet-flood processes. Hogg (1982) separates

A B C

Fig. 10. Numerical modelling results using the model ‘acronym 6’ from Parker et al. (1998): (A) uses the inputvariables also used in experiments R1, R2 and R3; (B) and (C) show data from Parker et al. (1998) for comparison. Seethe Appendix for further details.

Table 2. Variables used in the acronym 6 numerical modelling runs.

Variable Physical model Gravel fan Sand fan Notes

L (m) 2 10 000 10 000 Basin radiush ()) 180� 120� 120� Fan angleD (mm) 0Æ25 20 0Æ3 Grain-sizep ()) 0Æ33 0 0 Exponent in resistance relationar ()) 10 10 15 Coefficient in resistance equationn ()) 1Æ5 1Æ5 2Æ5 Exponent in transport equationaso ()) 11Æ25 8 11Æ25 Coefficient in transport relationasa ()) 1 3 1Æ5 Channel morphology coefficientsc* ()) 0Æ03 0Æ03 0 Dimensionless critical shear stresssa* ()) 1Æ8 0Æ042 1Æ8 Dimensionless channel forming shear stressQw (m3 sec)1) 1Æ67 · 10)4 (R1) 250 25 Water discharge

1Æ53 · 10)4 (R2) 200 200Æ97 · 10)4 (R3) 150 15

Qso (m3 sec)1) 0Æ278 · 10)6 0Æ1 0Æ04 Sediment dischargeI ()) 1 0Æ02 0Æ05 Intermittency



sheet flows from sheet floods based on the lessermagnitude and more frequent occurrence of sheetflows. Factors contributing to the formation ofsheet flow include sufficient intensity of precip-itation, lack of channellized drainage and lowground permeability (Hogg, 1982). These charac-teristics also emerge from the descriptions ofmodern, sheet-flood dominated fans in DeadValley described by Blair (1999, 2000). The fandeposits consist mostly of flood-generated depos-its, comparing well with the models describedhere, if they are considered to be in a continuousstate of flooding (see also Paola, 2000).

In flume models not all geometric features,kinematics and dynamics governing natural sys-tems are captured. Hooke & Rohrer (1979) suggestthat observations of processes on laboratory fansand their characteristics can still provide a basisfor understanding similar characteristics on natu-ral fans (see also Hooke, 1967; Paola, 2000).Peakall et al. (1996) refer to such experiments as‘analogue experiments’. Whipple et al. (1998)question the extrapolation of fan-head trenchingeffects to the scale of natural systems. Reducedflow Reynolds numbers and exaggerated geo-metric scaling relationships may exaggerate theincision depth and suddenness of initiation of theentrenchment process. However, slopes in thepresent experiments are quite similar comparedwith gravelly alluvial fans. Blair (1999, 2000)reported slopes ranging from 0Æ044 to 0Æ087 (2Æ5� to5�) which compare well with values generated inthe present experiments and those of others(Whipple et al., 1998; Clarke et al., 2008). How-ever, as the streams constructing these deposi-tional slopes are much shallower than those onnatural fan deltas, the authors agree with Whipplethat, from a hydraulic viewpoint, the experimen-tal processes cannot be extrapolated to the naturalsystems directly as the time and spatial scalessimply prohibit doing so. Sediment transport ratescompare nicely with transport rates in naturalsystems if transport is time averaged over suffi-ciently long time periods (hundreds to thousandsof years) to mimic sediment transport occurringmainly during catastrophic events (e.g. Sheetset al., 2002). Hence, although the hydraulic pro-cesses are not scaled, the sedimentary processesresponsible for creating or filling of accumulationspace are (e.g. Postma et al. 2008). These are theprocesses that ultimately define depositionalarchitecture in depositional systems and that arealso captured by analogue flume models.

One important conclusion to draw from thelarge experiment R1 is that the autocyclic

fan-delta behaviour is a product of the steadyinput conditions, although more long-term exper-iments with steady input conditions are neededto demonstrate how the magnitude and frequencyof the cut and fill events are related to differencesin discharge. The incisions in R1 are the result ofinternal feedback mechanisms at regular timeintervals. The findings complement the auto-stratigraphy mechanism derived by Muto et al.(2007) which maintains that, for stationary sea-level, systems will remain aggradational andshow monotonous progradation basinward at anever-decreasing rate over longer temporal scales.The only other factor influencing this prograda-tion rate in the autostratigraphy concepts is theshelf-platform topography (Muto et al., 2007).The findings of the present study show howsedimentary systems behave when external forc-ing is steady, and, although overall aggradationoccurs, sediment is released occasionally leadingto pulsating rather than monotonous prograda-tion. How these findings (mainly based on theextensive data base of experiment R1) relate toearlier experiments described in the literatureand to natural fan-delta systems is discussed indetail below.

Slope variation and related sediment release

What are the consequences of the observedautocyclicity for sediment release and delta pro-gradation rate? Firstly, the slope varies both onthe flanks and along the centreline between amaximum value and a minimum value, confirm-ing the conceptual model presented by Holbrooket al. (2006) where two potential (fluvial) profilesare defined, representing maximum possibleaggradation and maximum possible incision.These authors proposed that the two potentialprofiles are determined by the variability of theupstream controls. The slope variability observedhere shows that the conceptual model can beexpanded for constant upstream input, whichactually inhibits the dynamic storage and releaseeffect found by Kim et al. (2006). The shorelineprogradation in the present case is governedcompletely by these dynamics as the smoothhorizontal shelf prevents any effects due tobottom relief changes. The standard variationsof the gradient in these experiments (13Æ6% thehighest of experiment R2) are within the range ofthose given by Kim et al. (2006) for the Missis-sippi, Po and Niger river deltas (up to 40%, Kimet al., 2006; fig. 13). The dynamic equilibriumslope averaged over time for several cycles is



constant (Figs 6C and 7C) and can be seen as amean slope that is related to sediment mobility(Schumm et al., 1987; Whipple et al., 1998).

Secondly, the slope and the delta progradationrate along the centreline are much larger than thevariation at the flanks of the fan (cf. Figs 6C and7C). Kim et al. (2006) and Kim & Muto (2007)averaged supply variation over the entire mod-elled width, which may well be justified for theirrectangular model set-up that produced an almoststraight (two-dimensional) prograding shoreline.However, the present experiments show that theassumption does not appear to be valid forsystems that produce a semi-circular fan delta,which illustrates important autogenically con-trolled lateral variation in shoreline progradation.While the variation along the centreline is relatedclearly to the channellization events, the slopevariations along the flanks of the fan are not; theirvariation is more likely controlled by changes inelevation near the apex, which will inducechanges in flow fractionation and rill formation.The lateral shift in these rills must also beautogenically controlled, but that process oper-ates on a spatial and temporal scale very differentfrom the self-channellization that occurs alongthe centreline. As a consequence of these differ-ent autogenic processes, the faster progradationrate along the centreline steepens the flanks (seealso Hooke & Rohrer, 1979), and it is to beexpected that the steepening will produce a majorshift in deposition from the centreline to a flankposition; this occurs during the semi-confinedflow stage. The final shape of the delta followingthe backfilling process is close to semi-circular.Hence, all available accumulation space is filledat the end of the autogenic cycle.

An important implication is that the autogenicentrenchments always occur more or less alongthe centreline of the fan-delta plain, the locationbeing controlled mainly by the inertia of the jet,as has also been discussed by Weaver (1984),Schumm et al. (1987) and DeCelles et al. (1991).The latter justifies the use of deterministic meth-ods for modelling autocyclical processes in fan-delta simulations (cf. Hooke & Rohrer, 1979), butonly if sediment transport is averaged over asufficiently long time and spatial scales.

Critical slope for autogenic entrenchment

The present experiments show that the criticalslope for entrenchment is the maximum slopeattained during sheet flow. Interestingly, theexperiments performed by Weaver (1984), in spite

of the highly variable yield at the apex of the fan,also describe a critical slope, because ‘gradientsexceeding 0Æ049 are characterized by erosion’.Weaver (1984) concludes that in these experi-ments the locations of entrenchment are con-trolled by local slope instead of average surfaceslope. The present experiments do similarly showa relationship between the initiation of incisionand a local maximum slope which was constantfor each cycle reflecting the constant sedimentsupply and discharge conditions. Whipple et al.(1998) also report fan-head entrenchments inexperiments with rising base level, where dis-charge and sediment supply were held constant.The results of Whipple et al. show a critical slopefor channel incision, although it is unknown towhat extent the channel incisions were triggeredby the changing base level itself. Base-level fallwill trigger or enhance headward erosion reduc-ing the relief and increasing the channel length bylocal progradation, while base-level rise reducesthe channel length and potentially increasessediment storage and steepens the relief (Milana,1998; Van Heijst & Postma, 2001; Milana & Tietze,2002; Van den Berg van Saparoea & Postma,2008).

As the critical slope necessary for initiatingautogenic fan incision depends on the upstreamconditions, a relationship between the criticalslope and sediment/water ratio is expected.A plot of maximum experimental slopes versusQs/Qw from this and other experimental studies(Whipple et al., 1998; Clarke et al., 2008) is givenby the blue symbols in Fig. 11. From Whippleet al. (1998) only the data from the bed loaddominated run were selected and the maximumgradient was estimated by taking the averagegradient and adding twice the standard deviation.The maximum slopes for the same experimentalQs/Qw values were calculated using acronym 6

(Parker et al., 1998) and are shown as red symbolsin Fig. 11. The solutions (indicated by solid linesin Fig. 11) are also extended by doubling andquadrupling the water discharge and by dividingthe water discharge by two and four. It is notedthat the slopes measured in the other experiments(Whipple et al., 1998; Clarke et al., 2008) arehigher than the present experimental slopes,which can partly be attributed to the fact thatthe fan models differed in spreading angle. In theset-up used here, the fan cone angle is 180�, whilein the others it is only 90�, spreading the supplyand water discharge over a much larger area. Bothexperimental and numerical data show a positiverelationship between slope and Qs/Qw, but the



slope trends predicted by the Parker et al. (1998)model are much steeper than those of the exper-iments. It is also noted that the data by Clarkeet al. (2008) include three experiments with thesame ratio of Qs/Qw, but with different maximumslopes. All experiments, no doubt suffer fromnon-scalable hydraulic defects caused by the verylimited flow depth, grain-size distributions andbed roughness, causing important non-linearityin transport rate (see Postma et al. 2008), whichare not reproduced in the Parker et al. (1998)model. Moreover, the flow width may not beparameterized correctly (Nicholas & Quine,2007). At present, there is no firm basis to justifyextrapolation to natural spatial and temporalscales of either the experimental critical slopesas related to Qs/Qw or those obtained by theParker et al. (1998) model.

Application of experimental results to naturalsystems

Before discussing how experimental results applyto natural systems, it is important to evaluate thevarious boundary conditions controlling fan-delta

evolution. Both upstream and downstreamboundary conditions appear to play an importantrole in the morphodynamics of the fan deltas.

The upstream boundary conditions of the fandelta include water and sediment input, type ofsediment transport and width of the feeder chan-nel outlet. The narrow outlet (5 cm width) usedin the present experiments leads to narrow anddeep incisions that are stable and do not migratelaterally. The only lateral process is flow widen-ing. By contrast, the experiments of Clarke et al.(2008) and Whipple et al. (1998) were carried outwith a much wider feeder channel outlet (15 cm).As a result, both sediment and water discharge atthe outlet are affected by bar formation. Themigration of the bars leads to pulsating ratherthan steady sediment transport and also to vari-ations in flow direction on the fan apex. Theautogenic incisions associated with wide feederchannels are less pronounced and avulsionsshow much more variation in direction awayfrom the centreline. As a consequence, lateralchannel migration plays a much bigger role infans with a wide feeder channel compared withthose with a narrower feeder. The experimentscarried out by Clarke et al. (2008) show dominantchannels up to 30� from the centreline. Theseboundary conditions (e.g. width of the feederchannel, water and sediment input) can bereconstructed by mapping the individual incisedchannels if the fan-delta setting is still intact (e.g.Nemec & Postma, 1993; Blair, 1999, 2000). Withsome notion of the dimensions of a fan body, thelateral extent of large fan-head channels andwidth–depth ratios can be used to estimateupstream input conditions and processes.

The downstream boundary condition for thefan delta is the shoreline. The importance of thepresence of a shoreline for the development ofautogenic incisions becomes clear when thepresent results are compared with those of Clarkeet al. (2008). In the set-up used here, the fan deltacould prograde freely in all directions and pro-gradation was only limited by internal feedbackmechanisms. The set-up used by Clarke et al.(2008) limited fan growth to a radius of 2Æ8 m.Sediment surpassing that maximum radius wasremoved, thereby imitating the effect of toetrimming by, for instance, axial rivers. Clarkeet al. (2008) observed very similar autocyclicbehaviour as described here until the point thatthe fan was trimmed. At that point in time,channel backfilling ceased as the incised channelcame to grade with the new and now fixed baselevel. The feedback mechanism leading to flow

Fig. 11. A compilation of data on maximum gradientsin experiments and of numerical investigations inrelation to water discharge. The blue and red lines withsmall symbols represent results with the numerical fanmodel by Parker et al. (1998). The symbols on thoselines correspond to the numerical products using thesame input conditions as the experiments. The linesshow the variation in slope caused by different waterdischarges. The measured gradients from the experi-ments are shown by the solitary symbols. The dashedblue line is a regression line through the experimentaldata. See text for detailed explanation.



deceleration and subsequent backfilling seen inthese experiments was eliminated by limiting thefan growth through sediment removal. In sum-mary, autogenic cycles depend on a number ofboundary conditions including the width of thefeeder channel and the possibility for continuousgrowth of the fan radius. These boundary condi-tions apply to both experimental and naturalsystems.

Extrapolation to natural systems andpreservation potential

The autogenically triggered fan processes andresulting depositional profiles changed little dur-ing the R1 experiment. Only the duration andmagnitude of the fan entrenchment increasedwith the size of the growing fan delta and they arelikely to increase as the size of the catchmentincreases. The stratigraphic architecture of thesuccessive autocyclic erosional events of experi-ment R1 is shown in Fig. 12. In the five cycles ofaggradation and incision, on average 60% of theaggraded deposits were preserved (see alsoFig. 5). In other words, the incised channel depthon average equalled 40% of the previouslyaggraded deposits. The exact number here de-pends on the experimental input conditions.However, at least some of the material depositedin between two subsequent incisions must bepreserved, because on a fixed spot on the surfacean incision cannot erode to the same depth as theprevious one due to the progradation associatedwith the previous incision event.

To illustrate the significant impact that auto-genic incisions would have on fan deltas in thefield, the depth of incision was normalized withthe average channel depth on the fan surface.This value offers an indication of the impact of

autogenic incisions on natural alluvial fans. Inexperiment R3 the entrenchments reached depthsof more than 2 cm (Fig. 6). The average depth ofthe small-scale channels covering the surface ofthe fan increased from 3 mm during the first cycleto 7 mm at the end of the experiment (Fig. 6).Throughout experiment R1, the incision wasmore than twice the average channel depth, witha maximum of three times the average channeldepth during cycle 4. On the mid-fan and outerfan regions of natural fans comparable with theseexperimental fans, surface-channel depths aver-age just under 0Æ5 m but occasionally reachdepths of 2 m (Blair, 2000). The ratio betweensurface-channel depth and depth of entrench-ment suggests that on natural fans autogenicincisions could easily reach a depth of 5 to10 m, similar to the values presented above.Assuming that in nature also 60% of the backfillis preserved (as justified above), backfill succes-sions may be expected to range from severalmetres up to a few tens of metres on the apex offan deltas with radii of a few kilometres or more.

The aggradational part of the autogenic cyclescould then be estimated at 10 to 20 m on such fandeltas. Even as an extreme upper limit, at leastmetre-scale successions will be produced by theautocyclic behaviour and be recognizable in thefield. Metre-scale incisions are also reported fromalluvial fans subjected to climate change. Asshown above, the downstream boundary condi-tion affects autogenic fan-delta behaviour in adifferent way than alluvial fans, and it is obviousthat allogenic fan-delta behaviour will also differfrom that of alluvial fans.

However, it is very likely that upstream-con-trolled incisions will have a comparable impacton alluvial fans and fan deltas, and thus acomparison between them is justified. Climate

Fig. 12. Cross-section along thecentreline of experiment R1, show-ing its stratigraphic architectureresulting from five autocyclicallygenerated erosion surfaces. Theprofiles measured just before initia-tion of incision that might be pre-served in nature as terraces areshown as well. Timing of initiationis indicated in the legend.



change is the most cited cause for upstream-controlled incision on alluvial fans. Harvey(1978) found a 2 m deep incised channel on aSpanish alluvial fan, with a radius of approxi-mately 1 km. Ritter et al. (1995) showed that an11 m deep incision was controlled largely byclimatic variations on a fan roughly 10 km long.Weissmann et al. (2002) report a 10 m deepincised valley on the Kings River alluvial fan,which measured 30 km in radius.

In summary, autocyclic incisions produce largeenough changes in accumulation space to berecognizable in stratigraphic successions of allu-vial fans and fan deltas if produced under condi-tions of fan aggradation, i.e. during periods of fangrowth and limited base-level change. However,if preserved, their infill (Fig. 5) will be difficult todistinguish from onlap and offlap patterns pro-duced by climate change (Milana, 1998; Milana &Ruzycki, 1999; Milana & Tietze, 2002).

Scott & Erskine (1994) report on 12 alluvial fanswhich show an evolution pattern that is remark-ably similar to the autocyclic evolution observedin experiment R1. The fans and catchment areasinvolved have similar sizes and gradients andwere all located in a zone which received verysimilar rainfall intensities. Hence, the fans weresubject to similar but significant flood discharges.Of the 12 fans, seven were entrenched and fivewere untrenched before the storm event. The fansreacted in a different way to the storm event.Effects ranged from no change at all to trenchincision or backfilling. Scott & Erskine (1994)propose that each fan showed a different stageof a similar autogenic cycle. The cycle consists of:(i) aggradation of the fan; (ii) the initiation of afan-head trench due to the exceedance of athreshold slope; (iii) coalescence of scour poolsto a continuous trench; and (iv) backfilling of thetrench due to its widening and slope reduction.

Facies characteristics of autogenically pro-duced channels and their fill (see Fig. 5) mustinclude successions characterized by coarsechannel lags (pavement and minimum gradient)at the base, covered by thick successions oflongitudinal bars and subordinate stream-channeldeposits which are capped by combinations ofsheet-flow and shallow channellized-flow depos-its. Studies from the late Palaeocene BeartoothConglomerate reveal tens of metres-thick con-glomerate cycles in alluvial fans that can beattributed to autogenic behaviour (DeCelles et al.,1991). The entrenchments show typical staircaseerosion surfaces (terraces) with bar flank accre-tions. The backfill consists of onlapping stream

flow facies with gravelly longitudinal-bar andside-bar deposits and rare deposits of hyper-concentrated flows (DeCelles et al., 1991). Thechannel-fill successions do not need to haveconspicuous grain-size trends in contrast withthe coarsening and fining upward alluvial suc-cessions as described by Steel et al. (1977) andGloppen & Steel (1981) from the Devonian Horne-len Basin (Norway).

By definition, the erosional bounding surfacesof autogenic cycles are restricted to the fan, andcannot be traced regionally. Hence, highly syn-chronous entrenchments in adjacent fans ratherpoint to a tectonic (cf. Gloppen & Steel, 1981) orclimate origin (cf. Nemec & Postma, 1993; Popeet al., 2008), while non-synchronous evolutionmight allude to autogenic origin.

CONCLUSIONS

1 Autocyclic behaviour of fan-delta systems isobserved from flume experiments to consist ofalternations of sheet flow and channellized flowalong the central line of deposition of the fan andmore rapid events related to crevassing (rapidmigration) of rills along its flanks. The flankssteepen progressively, increasing the availableaccumulation space.

2 The cyclical alternations of sheet flow andchannellized flow consist of distinct stages.(i) Channellization commences when the fan apexreaches a critical slope value. Incipient scouringand headward erosion forms a channel that con-nects with the feeder channel. The now confinedwater flow deepens the channel and deposits theremoved sediment in a rapidly prograding deltalobe. (ii) Progressive reduction in the channelgradient makes the flow decelerate, leading todeposition of a mouth bar; this causes wideningof the flow upstream of the bar and the beginningof backfilling of the channel. (iii) Progressivebackfilling causes the water to leave its channelconfinement at some point in time resulting in thecoexistence of both channellized and sheet flowsfilling the available accumulation space at theflanks. (iv) When the channel is filled completely,sheet flow resumes again over the entire fan untilthe critical slope is attained and the channelli-zation process begins once again. This criticalslope for entrenchment to start is constant for agiven discharge and sediment supply.

3 The slope of alluvial-fan feeder systemscyclically varies around a mean value and thelatter is defined by the imposed constant water



and sediment discharge. The autogenic cyclesproduce variations around the equilibrium slopeof the fan leading to autogenically forced dynamicstorage and release of sediment, corroborating thefindings of Kim et al. (2006).

4 At least 60% of the total thickness of theautocyclic incisions and their channel fills werepreserved in these experiments that were rununder constant boundary conditions. This obser-vation makes it very likely that similar autogeni-cally forced successions are recorded in naturalfan-delta stratigraphy. In studies that focus onone single fan-delta system, such incisions couldeasily be confused with successions of similarsize that are produced by allogenic forcing.However, if compared with contemporaneousand adjacent systems, they are likely to be re-vealed by characteristic, non-synchronous timingof the incision events. Moreover, the depths of theautocyclic incisions were two to three timesdeeper than the average channel depth on thedelta plain; this provides an application of theexperimental results to the field scale and inter-pretation of fan-delta surface dynamics.

5 Autogenic fan morphodynamics, particularlythe tendency to entrench either cyclically orpermanently, depends on both the width–depthratio of the upstream feeder channel and thepresence of downstream boundary conditionssuch as toe trimming or limits to the lateralgrowth of the fan.

ACKNOWLEDGEMENTS

We wish to thank Piet-Jan Verplak, Henk van derMeer and Thony van der Gon-Netcher for helpingwith the set-up and preparation of the experi-ments. The suggestions of E.R. Kraal, P.L. de Boer,P. Ashworth, W. Kim and two anonymousreviewers are gratefully acknowledged andsignificantly improved the original manuscript.

REFERENCES

Ashworth, P.J., Best, J.L. and Jones, M. (2004) Relationship

between sediment supply and avulsion frequency in brai-

ded rivers. Geology, 32, 21–24.

Ashworth, P.J., Best, J.L. and Jones, M.A. (2007) The rela-

tionship between channel avulsion, flow occupancy and

aggradation in braided rivers: insights from an experimental

model. Sedimentology, 54, 497–513.

Blair, T.C. (1999) Sedimentary processes and facies of the

waterlaid Anvil Spring Canyon alluvial fan, Death Valley,

California. Sedimentology, 46, 913–940.

Blair, T.C. (2000) Sedimentology and progressive tectonic

unconformities of the sheetflood-dominated Hell’s Gate

alluvial fan, Death Valley, California. Sed. Geol., 132, 233–

262.

Blair, T.C. and McPherson, J.G. (1994) Alluvial fans and their

natural distinction from rivers based on morphology,

hydraulic processes, sedimentary processes, and facies

assemblages. J. Sed. Res. Sect. A Sed. Petrol. Process., 64,450–489.

Blum, M.D. and Tornqvist, T.E. (2000) Fluvial responses to

climate and sea-level change: a review and look forward.

Sedimentology, 47, 2–48.

Brasington, J. and Smart, R.M.A. (2003) Close range digital

photogrammetric analysis of experimental drainage basin

evolution. Earth Surf. Proc. Land., 28, 231–247.

Bryant, M., Falk, P. and Paola, C. (1995) Experimental-study

of avulsion frequency and rate of deposition. Geology, 23,365–368.

Bull, W.B. (1977) The alluvial-fan environment. Prog. Phys.Geogr., 1, 222–270.

Chandler, J.H., Shiono, K., Rameshwaren, P. and Lane, S.N.(2001) Measuring flume surfaces for hydraulics research

using a Kodak DCS460. Photogrammetric Record, 17, 39–61.

Clarke, L.E., Quine, T.A. and Nicholas, A.P. (2008) An eval-

uation of the role of physical models in exploring form-

process feedbacks in alluvial fans. In: Sediment Dynamicsin Changing Environments (Eds J. Schmidt, T. Cochrane, C.

Phillips, S. Elliott, T. Davies and L. Basher), pp. 175–183.

IAHS publication 325, Proceedings of a Symposium held in

Christchurch, New Zealand.

Collinson, J.D. (1988) Foreword to: ‘‘Fan deltas; sedimentology

and tectonic settings’’. In: Fan Deltas; Sedimentology and

Tectonic Settings (Eds W. Nemec and R.J. Steel), pp.

v. Blackie and Son, Glasgow.

DeCelles, P.G., Tolson, R.B., Graham, S.A., Smith, G.A.,Ingersoll, R.V., White, J., Schmidt, C.J., Rice, R., Moxon, I.,Lemke, L., Handschy, J.W., Follo, M.F., Edwards, D.P.,Cavazza, W., Caldwell, M. and Bargar, E. (1987) Laramide

thrust-generated alluvial-fan sedimentation, Sphinx Con-

glomerate, southwestern Montana. AAPG Bull., 71, 135–155.

DeCelles, P.G., Gray, M.B., Ridgway, K.D., Cole, R.B., Pivnik,D.A., Pequera, N. and Srivastava, P. (1991) Controls on

synorogenic alluvial-fan architecture, Beartooth Conglo-

merate (Paleocene), Wyoming and Montana. Sedimentology,

38, 567–590.

Fernandez, J., Bluck, B.J. and Viseras, C. (1993) The effects of

fluctuating base-level on the structure of alluvial-fan asso-

ciated fan-delta deposits – an example from the Tertiary-

of-the-Betic-Cordillera, Spain. Sedimentology, 40, 879–893.

Garcia-Garcia, F., Fernandez, J., Viseras, U. and Soria, J.M.(2006) Architecture and sedimentary facies evolution in a

delta stack controlled by fault growth (Betic Cordillera,

southern Spain, late Tortonian). Sed. Geol., 185, 79–92.

Garcıa-Mondejar, J. (1990) Sequence analysis of amarine

Gilbert-type delta, LaMiel Albian Lunada Formation of

northern Spain. In: Coarse-Grained Deltas (Eds A. Collela

and D.B. Prior), Int. Assoc. Sedimentol. Spec. Publ., 10,255–269. Blackwell International, Oxford.

Gawthorpe, R.L. and Collela, A. (1990) Tectonic controls on

coarse-grained delta depositional systems in rift basins. In:

Coarse-Grained Deltas (Eds A. Collela and D.B. Prior), Int.

Assoc. Sedimentol. Spec. Publ., 10, 113–127. Blackwell

International, Oxford.

Gloppen, T.G. and Steel, R.J. (1981) The deposits, internal

structure and geometry in six alluvial-fan delta bodies



(Devonian-Norway) – a study in the significance of bedding

sequences in conglomorates. In: Recent and Ancient Non-

marine Depositional Environments: Models for Exploration

(Eds F.G. Ethridge and R. Flores), Spec. Publ. Soc. Econ.Palaeontol. Mineral., 31, 49–69.

Harvey, A.M. (1978) Dissected alluvial fans in southeast

Spain. Catena, 5, 177–211.

Harvey, A.M. (2002) The role of base-level change in the dis-

section of alluvial fans: case studies from southeast Spain

and Nevada. Geomorphology, 45, 67–87.

Hogg, S.E. (1982) Sheetfloods, sheetwash, sheetflow, or ...?

Earth-Sci. Rev., 18, 59–76.

Holbrook, J., Scott, R.W. and Oboh-Ikuenobe, F.E. (2006)

Base-level buffers and buttresses: a model for upstream

versus downstream control on fluvial geometry and archi-

tecture within sequences. J. Sed. Res., 76, 162–174.

Hooke, R.L. (1967) Processes on arid-region alluvial fans.

J. Geol., 75, 438–460.

Hooke, R.L. and Rohrer, W.L. (1979) Geometry of alluvial

fans; effect of discharge and sediment size. Earth Surf. Proc.,

4, 147–166.

Kim, W. and Muto, T. (2007) Autogenic response of alluvial-

bedrock transition to base-level variation: experiment and

theory. J. Geophys. Res. Earth Surf., 112, F03S14, doi:

10.1029/2006JF000561.

Kim, W. and Paola, C. (2007) Long-period cyclic sedimenta-

tion with constant tectonic forcing in an experimental relay

ramp. Geology, 35, 331–334.

Kim, W., Paola, C., Swenson, J.B. and Voller, V.R. (2006)

Shoreline response to autogenic processes of sediment

storage and release in the fluvial system. J. Geophys. Res.

Earth Surf., 111, F04013, doi:10.1029/2006JF000470.

Kocurek, G. (1998) Aeolian system response to external forc-

ing factors – a sequence stratigraphic view of the Saharan

region. In: Quaternary Deserts and Climatic Change (Eds

A.S. Alsharhan, K. Glennie, G.L. Whittle and C.G.S.C.

Kendall), pp. 327–337. Balkema Press, Rotterdam.

Kocurek, G. and Havholm, K.G. (1993) Eolian sequence

stratigraphy: a conceptual framework. In: Silliciclastic

Sequence Stratigraphy: Recent Developments and Appli-

cations (Eds P. Weimer and H.W. Posamentier), AAPGMem., 58, 393–410.

Li, Y.L., Yang, J.C., Tan, L.H. and Duan, F.J. (1999) Impact of

tectonics on alluvial landforms in the Hexi Corridor,

Northwest China. Geomorphology, 28, 299–308.

Milana, J.P. (1998) Sequence stratigraphy in alluvial settings: a

flume-based model with applications to outcrop and seis-

mic data. AAPG Bull., 82, 1736–1753.

Milana, J.P. and Ruzycki, L. (1999) Alluvial-fan slope as a

function of sediment transport efficiency. J. Sed. Res., 69,553–562.

Milana, J.P. and Tietze, K.W. (2002) Three-dimensional ana-

logue modelling of an alluvial basin margin affected by

hydrological cycles: processes and resulting depositional

sequences. Basin Res., 14, 237–264.

Muto, T. and Steel, R.J. (1997) Principles of regression and

transgression: the nature of the interplay between

accommodation and sediment supply. J. Sed. Res., 67,994–1000.

Muto, T. and Steel, R.J. (2000) The accommodation concept in

sequence stratigraphy: some dimensional problems and

possible redefinition. Sed. Geol., 130, 1–10.

Muto, T., Steel, R.J. and Swenson, J.B. (2007) Autostrati-

graphy: a framework norm for genetic stratigraphy. J. Sed.

Res., 77, 2–12.

Nemec, W. and Postma, G. (1993) Quarternary alluvial fans in

southwestern Crete: sedimentation processes and geomor-

phic evolution. In: Alluvial Sedimentation (Eds M. Marzo

and C. Puigdefabregas), Int. Assoc. Sedimentol. Spec. Publ.,17, 235–276.

Nemec, W. and Steel, R.J. (1988a) Preface to: ‘‘Fan deltas;

sedimentology and tectonic setting’’. In: Fan Deltas; Sedi-

mentology and Tectonic Setting (Eds W. Nemec and

R.J. Steel), pp. vii–ix. Blackie and Son, Glasgow.

Nemec, W. and Steel, R.J. (1988b) What is a fan delta and how

do we recognize it? In: Fan Deltas; Sedimentology andTectonic Settings (Eds W. Nemec and R.J. Steel), pp. 3–13.

Blackie and Son, Glasgow.

Nicholas, A.P. and Quine, T.A. (2007) Modeling alluvial

landform change in the absence of external environmental

forcing. Geology, 35, 527–530.

Paola, C. (2000) Quantitative models of sedimentary basin

filling. Sedimentology, 47, 121–178.

Parker, G., Paola, C., Whipple, K.X. and Mohrig, D. (1998)

Alluvial fans formed by channelized fluvial and sheet flow.

I. Theory. J. Hydraul. Eng., 124, 985–995.

Peakall, J., Ashworth, P.J. and Best, J.L. (1996) Physical

modelling in fluvial geomorphology: principles, applica-

tions and unresolved issues. In: The Scientific Nature of

Geomorphology (Eds B.L. Rhoads and C.E. Thorn), pp. 221–

253. John Wiley & Sons Ltd., Chichester.

Pope, R., Wilkinson, K., Skourtsos, E., Triantaphyllou, M. and

Ferrier, G. (2008) Clarifying stages of alluvial fan evolution

along the Sfakian piedmont, southern Crete: New evidence

from analysis of post-incisive soils and OSL dating. Geo-morphology, 94, 206–225.

Postma, G., Kleinhans, M.G., Meijer, P.Th. and Eggenhuisen,J.T. (2008) Sediment transport in analogue flume models

compared with real-world sedimentary systems: a new look

at scaling evolution of sedimentary systems in a flume.

Sedimentology, 55, 1541–1557.

Ritter, J.B., Miller, J.R., Enzel, Y. and Wells, S.G. (1995)

Reconciling the roles of tectonism and climate in quaternary

alluvial-fan evolution. Geology, 23, 245–248.

Saito, K. and Oguchi, T. (2005) Slope of alluvial fans in humid

regions of Japan, Taiwan and the Philippines. Geomor-phology, 70, 147–162.

Schumm, S.A., Mosley, P.M. and Weaver, P.H. (1987) Exper-

imental Fluvial Geomorphology. John Wiley & Sons, New

York, 413 pp.

Scott, P.F. and Erskine, W.D. (1994) Geomorphic effects of a

large flood on fluvial fans. Earth Surf. Proc. Land., 19, 95–

108.

Sheets, B.A., Hickson, T.A. and Paola, C. (2002) Assembling

the stratigraphic record: depositional patterns and time-

scales in an experimental alluvial basin. Basin Res., 14,287–301.

Soria, J.M., Alfaro, P., Fernandez, J. and Viseras, C. (2001)

Quantitative subsidence-uplift analysis of the Bajo Segura

Basin (eastern Betic Cordillera, Spain): tectonic control on

the stratigraphic architecture. Sed. Geol., 140, 271–289.

Soulsby, R. (1997) Dynamics of Marine Sands. Thomas Tel-

ford, London, 215 pp.

Steel, R.J., Maehle, S., Nilsen, H., Roee, S.L. and Spinnangr, A.(1977) Coarsening-upward cycles in the alluvium of Horne-

len Basin (Devonian) Norway; sedimentary response to tec-

tonic events. Geol. Soc. Am. Bull., 88, 1124–1134.

Van den Berg van Saparoea, A.P. and Postma, G. (2008)

Control of climate change on the yield of river systems. In:

Recent Advances in Models of Siliciclastic Shallow-marine



Stratigraphy (Eds G. Hampson, R.J. Steel, P.M. Burgess and

R.W. Dalrymple), SEPM Spec. Publ. (in press).

Van Heijst, M. and Postma, G. (2001) Fluvial response to sea-

level changes: a quantitative analogue, experimental ap-

proach. Basin Res., 13, 269–292.

Viseras, C., Calvache, M.L., Soria, J.M. and Fernandez, J.(2003) Differential features of alluvial fans controlled by

tectonic or eustatic accommodation space. Examples from

the Betic Cordillera, Spain. Geomorphology, 50, 181–202.

Vollmer, S. and Kleinhans, M.G. (2007) Predicting incipient

motion, including the effect of turbulent pressure fluctua-

tions in the bed. Water Resour. Res., 43, W05410, doi:

10.1029/2006WR004919.

Weissmann, G.S., Mount, J.F. and Fogg, G.E. (2002) Glacially

driven cycles in accumulation space and sequence strati-

graphy of a stream-dominated alluvial fan, San Joaquin

Valley, California, U.S.A. J. Sed. Res., 72, 240–251.

Weaver, P.H. (1984) Experimental Study of Alluvial Fans.

Colorado State University, Fort Collins, CO.

Whipple, K.X. and Trayler, C.R. (1996) Tectonic control of fan

size: the importance of spatially variable subsidence rates.

Basin Res., 8, 351–366.

Whipple, K.X., Parker, G., Paola, C. and Mohrig, D. (1998)

Channel dynamics, sediment transport, and the slope of

alluvial fans: experimental study. J. Geol., 106, 677–693.

Manuscript received 28 March 2008; revision accepted2 December 2008

APPENDIX

The numerical modelling runs were performedusing the model developed by Parker et al.(1998), acronym 6, available on http://vtchl.uiuc.edu/people/parkerg. The plots showing the Sandfan and Gravel fan were produced using theidentical variables as reported by Parker et al.(1998, their table 1). The deviating examples were

produced by varying the reported water dis-charges by 25% (Table 1). For the sand fan(Qw = 20 m3 sec)1) three runs were performedusing a Qw of 15 , 20 and 25 m3 sec)1, and for theGravel fan (Qw = 200 m3 sec)1) the deviationsmeasured 150 , 200 and 250 m3 sec)1. The plotsof Fig. 10 were calculated using the values ofR1, with a Qw of 0Æ97 · 10)4 m3 sec)1 (R3) and1Æ67 · 10)4 m3 sec)1 (R1), Qs was 0Æ278 ·10)6 m3 sec)1 and the same in all runs. All othermodel inputs are identical (see Parker et al., 1998;Table 1), except for fan angle, which was set to180�, fan length to 2 m and the grain-size to0Æ25 mm to better match the flume experimentsfor the present study (Table 1). Intermittency, avariable included in the model to incorporate theeffect of fan activity, was set to 1. In contrast tomost natural fans which are active only part-time,these flume experiments were active all thetime. Some ‘auxiliary’ input was also modifiedto better represent the bed load transport inthe flume experiments: the coefficient of adjust-ment in sediment transport relation to channelmorphology (asa) was set to 1, as the flumeexperiments lacked braiding or meandering.The dimensionless exponent in the sedimenttransport equation (n) was set to 1Æ5 reflectingthe lack of suspended transport. The dimension-less exponent in the resistance equation (p)was set to 0Æ33 instead of 0 to account for theincreased roughness of the present flumeexperiments compared with the numericalmodel.



autocyclic behaviour of fan deltas: an analogue experimental...

Documents