Experiments on upstream-migrating erosional narrowing and ... et...Experiments on upstream-migrating erosional narrowing and widening of an incisional channel caused by dam removal

Experiments on upstream-migrating erosional narrowing and

widening of an incisional channel caused by dam removal

Alessandro Cantelli

Department of Environmental Engineering, University of Genova, Italy

Chris Paola

Department of Geology and Geophysics and St. Anthony Falls Hydraulic Laboratory, University of Minnesota, Minneapolis,Minnesota, USA

Gary Parker

Department of Civil Engineering, Institute of Technology, and St. Anthony Falls Hydraulic Laboratory, University ofMinnesota, Minneapolis, Minnesota, USA

Received 10 December 2003; accepted 3 February 2004; published 31 March 2004.

[1] The present paper reports on a laboratory investigation of the erosion of a deltaic frontinduced by the removal of a dam. We built a laboratory model of a dam, and observedboth the sedimentation in the reservoir due to the downstream propagation of a delta frontand the erosion of the delta front during dam removal, including measurement of channelmorphology and flow field. The experiments provide a detailed view of a phenomenonthat has not been described in detail to date: erosional narrowing. After the suddenremoval of a dam, the flow incises into the reservoir deposit, first rapidly and then moreslowly. During the initial period of rapid incision the width of the channel can in somecircumstances undergo rapid and substantial narrowing, all the while incorporatingsediment from its sidewalls. As the rate of incision slows, the channel first stops narrowingand then enters a phase of slow widening. This pattern of narrowing followed by wideningtends to propagate upstream. The minimum channel width attained at a cross section,however, increases with upstream distance from the dam. While the period of erosionalnarrowing is very short, the incision is so intense that large amounts of sediment aredelivered downstream in a short period of time. The process thus has practical implicationsin regard to the strategy of dam removal. Undistorted Froude similitude is used to scalethe results up to field dimensions. INDEX TERMS: 1815 Hydrology: Erosion and sedimentation;

1824 Hydrology: Geomorphology (1625); 1857 Hydrology: Reservoirs (surface); KEYWORDS: erosional

narrowing, erosional widening, Dam Removal, Reservoir, Froude Similitude, delta front propagation

Citation: Cantelli, A., C. Paola, and G. Parker (2004), Experiments on upstream-migrating erosional narrowing and widening of an

incisional channel caused by dam removal, Water Resour. Res., 40, W03304, doi:10.1029/2003WR002940.

1. Introduction

[2] Dams offer a renewable energy source and are usefulfor irrigation, transportation, and flood protection. However,many dams, especially smaller, older structures, have out-lived their usefulness. A number of these dams have alreadybeen removed, and plans exist to remove others in the nearfuture.[3] There are many reasons to remove a dam: many of

these structures may be approaching the end of their designlifespans and may become unsafe; reservoirs behind damseventually fill with sediment, thus reducing the dam’sability to store water and produce electricity; dams caninduce environmental damage (i.e., in fish habitat); andrivers returned to their natural state may have positiveeconomic and social benefits. Removing a dam is the mostdrastic of available options for dealing with old or otherwiseundesirable dams. Removal increases upstream fish pas-

sage, allows the transport of debris and gravel, and encour-ages the reinstatement of natural peak flows and seasonalflooding. However, the massive release of sediment and thedestruction of desirable habitats that have developed afterdam installation are two possible negative consequences.[4] Dams cause the formation of deltaic deposits of sedi-

ment in the reservoirs they impound. Dam removal causeseither sudden or gradual incision into and erosion of thesedeposits. While case histories describing the effects of damremoval on the sediment deposits behind them can be foundin the literature [e.g., Task Committee on Guidelines for theRetirement of Dams and Hydroelectric Facilities, 1997;Morris and Fan, 1997], the processes associated with sedi-ment evacuation remain underinvestigated.

2. Overview of the Problem

[5] The installation of a dam on a river induces sedimen-tation at the upstream end of the impoundment it creates.The long profile and plan view of the patterns of sedimen-tation are summarized in Figures 1a and 1b.

Copyright 2004 by the American Geophysical Union.0043-1397/04/2003WR002940$09.00

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[6] The long profile of reservoir sedimentation is charac-terized by the formation of coarse-grained topset and foresetdeposits and fine-grained bottomset deposits [e.g., Graf,1971; Vanoni, 1975; Leeder, 1999;Kostic et al., 2002; Kosticand Parker, 2003a, 2003b], as shown in Figure 1a. Theforeset defines a front that gradually migrates downstreaminto the reservoir. Coarser, generally noncohesive sediment(sand and/or gravel) is emplaced in the topset by means offluvial deposition. Similar sediment is emplaced in the foresetbymeans of avalanching. Silt and clay are emplacedmainly inthe bottomset by means of either fallout from surface plumesor plunging turbidity currents.[7] The 2-D picture of reservoir sedimentation given in

Figure 1a is, however, an oversimplification, because asdelta fronts prograde into reservoirs they generally widenas well. Lobe switching and channel avulsion allow for

the delta to build out incrementally, with the focus ofdeposition (depocenter) varying laterally over time. Thisprocess is illustrated for the delta of the Eau ClaireRiver at the upstream of Lake Altoona, Wisconsin, inFigures 1b and 1c. The lake is a reservoir created by adam. Figure 1b shows the delta in 1951, and Figure 1cshows it in 1988, by which time it had prograded andexpanded laterally.[8] In the experiments reported here the deltaic deposit

has a well-developed topset and foreset, but negligiblebottomset due to the lack of sufficiently fine material inthe sediment supplied to the model river. Depending onflow conditions, the delta front varied from essentially 2-Dto mildly 3-D, the latter case illustrated in Figure 1d.[9] The removal of a dam causes erosion into the

resulting deposit. Deposition due to dam constructionand erosion due to dam removal are not mirror-imageprocesses. Deposition tends to quickly fill the entirelateral extent of space available by depocenter migration(avulsion, channel migration, lobe switching, overbankdeposition), whereas erosion usually leads to the incisionof one or a few distinct canyons into the deposit, leavingmuch of what remains as a semipermanent terrace that isremoved only very slowly by channel migration.[10] The relative irreversibility of deposition is best

illustrated by means of field examples of sediment flush-ing from reservoirs. In sediment flushing, the watersurface in the reservoir is drawn down as low as possible,causing upstream-migrating erosion to form a canyon andremove a part, but only rarely all, of the deposit. Batucaand Jordaan [2000] and Morris and Fan [1997] providemany field examples of this (e.g., Figure 19.6 of theMorris and Fan). The case of sudden dam removal can beconsidered to be an extreme limiting case of sedimentflushing, in which the flushing is accomplished by theremoval of the dam itself.

Figure 1a. Schematic diagram of the typical long profileof a reservoir delta. Flow is from left to right.

Figure 1b. View of the delta of the Eau Claire River as it entered Lake Altoona, a reservoir inWisconsin, in 1951. Flow was from right to left.

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[11] The experiments reported here were designed tocapture this irreversibility between deposition and erosion.They nevertheless provide only a partial model of realreservoirs. The most important simplification in this regardis the use of noncohesive sediment that is too coarse tosuspend in substantial quantities. As a result, the experi-ments provide a reasonable model of both the emplacementof topset and foreset material by deposition and theirremoval after dam removal, but do not model the moredifficult problem of cohesive bottomset deposits and theirremoval.

3. Conceptualization and Modeling of theProcess of Incision

[12] Pickup [1975] reports field measurements of theincision of a channel, Crawfords Creek, into its ownalluvium. Hey [1979] presents a conceptual model for suchincision. Schumm et al. [1987] report on the results ofexperiments on incision in response to upstream knickpointmigration. Doyle et al. [2003] appear to be the first to applythese ideas to the problem of dam removal. They have usedfield observations from two rivers in Wisconsin, USA toconstruct a conceptual model of channel incision into areservoir deposit. Of relevance here are stages A-E of Doyleet al. [2003]. Stage A is the pre-removal state. In stage B,the water surface is lowering after dam removal, but thereservoir deposit has not yet been mobilized. In stage C anincisional channel forms, and cuts down, apparently withoutchanging bottom width. In stage D, the channel continues toincise, but also widens. In stage E the channel begins toaggrade as it widens.[13] The models of Hey [1979] and Doyle et al. [2003]

assume that a channel widens as it incises, in consonancewith the field observations of Pickup [1975] and Doyle et al.[2003] and the experiments of Schumm et al. [1987]. The

possibility that in the early stage of rapid incision thechannel might narrow as it incises appears not to have beenrecognized.[14] Few numerical models have been developed to

specifically describe the erosion, transport and depositionof sediment after the removal of a dam. Sudden damremoval in particular presents significant problems to thenumerical modeler because (1) the steep streamwise bedslope created by dam removal induces high flow veloc-ities and high sediment transport rates and (2) no methodhas yet been developed to predict the width of thechannel incising into the deposit. These comments not-withstanding the DREAM suite of models [Cui et al.,2004a, 2004b] have been specifically designed for thecase of dam removal.[15] The DREAM models include a conceptualization of

a feature that has not been included in most morphodynamicmodels of channel evolution, i.e., the input of sedimentfrom the sidewalls of the channel as it incises. In order toimplement these models, however, it is necessary to pre-

Figure 1c. View of the delta of the Eau Claire River as it entered Lake Altoona, a reservoir inWisconsin, in 1988. Flow was from right to left.

Figure 1d. Delta front prograding into the reservoir of run1 of the experiments reported here. The reservoir has beendrained in order to allow visibility of the front.

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scribe a sidewall slope Ss and a minimum bottom width Bbm

of the incisional channel. If the bottom width Bb of theincising channel is larger than this minimum value, it isallowed to narrow as it degrades without eroding its side-walls, as shown in Figure 2a. Once the minimum width Bm

is attained, the sidewalls are allowed to erode as the channeldegrades at constant width, as shown in Figure 2b. Theseassumptions are schematized in Figure 2c in terms of thetrajectories of the right and left banks of the bottom channel.The prescription of the minimum width is subjective.[16] The DREAM models represent a significant advance

over previous numerical models of channel incision intoalluvium. The experiments documented here, however, adda new element to the problem, i.e., an incising channel thatcan erode its sidewalls at all stages in the process ofincision, and that first undergoes rapid incisional narrowingfollowed by slow incisional widening. The essential resultof the present work is schematized in Figure 2d in terms ofthe trajectories of the right and left banks of the bottomchannel. As shown in the diagram, the rapid incisionimmediately following sudden dam removal suppressessidewall erosion, and the slow incision that evolves later

enhances sidewall erosion. The conceptual picture ofFigure 2d is justified in the text below.

4. Experiments and Results

4.1. Setup and Procedure

[17] The experiments were performed at St. Anthony FallsLaboratory, University of Minnesota, Minneapolis. A rectan-gular glass-walled flume 14 m long, 0.61 m wide and 0.48 mhighwasmodified tomodel a long reservoir of uniformwidth.The initial slope of the sediment bed was set equal to 1.8%.The dam was located 9 m from the inlet of the flume.[18] The dam consisted of a metal frame in which a series

of horizontal wood slats were stacked. In this way the damcould be removed in partial steps. A view of the dam itself isgiven in Figure 3.[19] We used two different types of sediments. The first

type had a specific gravity of 2.67, a median size D50 of0.80 mm and a geometric standard deviation sg of 1.71. Thesecond type had a more homogenous distribution, with aspecific gravity of 2.65, a value of D50 equal to 0.33 mmand a sg value of 1.47.

Figure 2. (a) Schematization of channel incision and narrowing without bank erosion when bottomwidth Bb is greater than the minimum bottom width Bbm, according to the model of Cui et al. [2004a].(b) Schematization of channel incision at constant bottom width Bbn (i.e., without further narrowing)accompanied by bank erosion, according to the model of Cui et al. [2004a]. (c) Schematization of thetrajectories of the left and right side of the channel bottom as the channel cuts into a deposit, according tothe model of Cui et al. [2004a]. (d) Schematization of the process of incision observed in runs 4, 5, 6, 8,and 9 of the experiments reported here, in terms of the trajectories of the left and right side of the channelbottom. Immediately after dam removal, incision is rapid and the channel narrows; while the sidewallserode, narrowing suppresses this erosion. Eventually, rapid incision with channel narrowing gives way toslow incision with channel widening; the widening enhances sidewall erosion.

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[20] The discharge of inflowing water was monitoredwith an orifice meter. Sediment was fed into the flume fromthe upstream end with a screw-type feeder. The appropriatesediment discharge was calculated for any water dischargeand bed slope such that the system without the dam was inequilibrium, i.e., the bed of channel was neither degradingnor aggrading. The combination of sediment and waterdischarges was chosen so as to result in near-completesedimentation of the reservoir in less than 45 hours.[21] We divided the experiments into two phases. During

phase I, we induced sedimentation in the reservoir due tothe progradation of a delta front. In phase II, we inducederosion of the deltaic deposit due to dam removal. Inphase II, two different methods of dam removal were used:instantaneous and staged removal.[22] The instantaneous removal procedure was imple-

mented as follows: the reservoir was first drained of water,then the dam was completely removed, and finally the flowof water was recommenced. The water discharges for theerosional phase, which are documented in Table 1, werechosen to be equal to or less than those of the depositionalphase. This was to facilitate the formation of a channelincising into the deposit with a width less than the totalwidth of the flume.[23] The staged removal procedure required the disassem-

bling of the dam by the sequential removal of the horizontalslats of Figure 3, thereby allowing the structure itself tocontrol the release of sediment.

4.2. Study of the Sedimentation of a Reservoir due tothe Progradation of the Delta Front

[24] The focus of the experiments reported here is onincision following dam removal, not the process of reservoirsedimentation itself. This notwithstanding, two experimentson sedimentation were performed in order to determine arealistic deposit geometry as the initial condition for theexperiments on dam removal.[25] Two experiments on reservoir sedimentation were

performed under identical conditions, i.e., runs 1 and 2 ofTable 1. The water and sediment discharges were equal to1.5 � 10�3 m3/s and 1.4 � 10�2 kg/s respectively. The timerequired to sediment the reservoir to a point just upstream ofthe dam itself was about 42 hours. In both experiments theaggrading topset had a slope of about 0.4%, as compared tothe initial 1.8% bed slope. The time evolution of the processwas essentially the same in the two experiments, confirmingoverall repeatability.[26] Figure 4 shows the evolution of the deposit of run 2

for times corresponding to 4, 6.5, 13, 21, 33, and 42 hours

after commencement. As it prograded, the delta frontmaintained an approximately 2-D configuration, with notendency toward channelization. This observation notwith-standing, a study of videos taken during the depositionalprocess revealed some tendency for the focus of depositionto concentrate first on one side of the flume and then on theother. Thus some lateral depocenter migration was indeedobserved as the depositional front prograded.[27] Sediment tends to sort in the vertical as it slides

down a delta front. The result is the emplacement of adeposit that has a relatively coarse base (just above anybottomset deposits) and that becomes finer upward. Whilesuch a tendency was indeed observed in the present experi-ments (Figure 1d), it was rather weak, most likely becausethe geometric standard deviation of the sediment was notlarge enough to allow for strong sorting.[28] The initial reservoir deposit for most of the experi-

ments on dam removal (runs 3–10 of Table 1) wasemplaced by hand to the geometrical configuration obtainedat the ends of runs 1 and 2. In light of the relatively weakvertical sorting observed in runs 1 and 2, no attempt wasmade to replicate it in the process of manual emplacement.

4.3. Erosion of the Reservoir Deposit During DamRemoval

[29] The morphodynamics of the bed following damremoval was studied in all the runs of Table 1. Most ofthe results reported here pertain to runs 5, 6 (suddenremoval) and 7 (staged removal). As is shown later, how-ever, the other runs also provided useful information.Change occurred very rapidly during the initial stage oferosion. To capture this, we used a combination of fivecameras to collect data from different vantage points: twocameras were positioned above the flume while three werelocated along one side of the flume.

Table 1. Parameters Characterizing the Experiments

Run Delta Front Removal Qw, m3/s Qs, kg/s D50, mm Erosional Narrowing

1 natural sudden 1.5 � 10�3 1.4 � 10�2 0.80 no2 natural sudden 1.5 � 10�3 1.4 � 10�2 0.80 no3 artificial sudden 1.0 � 10�3 9.6 � 10�3 0.80 no4 artificial sudden 0.5 � 10�3 4.1 � 10�3 0.80 yes (weak)5 artificial sudden 0.3 � 10�3 2 � 10�3 0.80 yes6 artificial sudden 0.3 � 10�3 2 � 10�3 0.80 yes7 artificial staged 0.3 � 10�3 2 � 10�3 0.80 yes (weak)8 artificial sudden 0.3 � 10�3 3.2 � 10�3 0.33 yes9 artificial sudden 0.3 � 10�3 2 � 10�3 0.80 yes10 artificial staged 0.3 � 10�3 2 � 10�3 0.80 yes (weak)

Figure 3. Picture of the dam during the run.


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[30] Ten experiments on dam removal are documented inTable 1. Two of these, runs 1 and 2, used the previouslydescribed natural deltaic deposit as the initial condition. Inthe remaining eight runs the initial deposit was emplacedmanually to the same configuration as that observed for runs1 and 2, and the dam was removed after an initial shallowchannel was screeded into the center of the deposit, asexplained below.[31] As shown in Table 1, the value of the inflow water

discharge was varied from 1.5 � 10�3 m3/s (run 1) to0.3 � 10�3 m3/s (run 8). The inflow sediment discharge,which is also given in the Table 1, was estimated basedon the sediment transport relation of Meyer-Peter andMuller [1948] and a number of trial experiments. Itshould be pointed out, however, that the bed evolutionnear the dam in the early stages of the erosional experi-ments proceeded independently of the feed rate of sedi-ment at the upstream end of the flume. In all theexperiments except run 8 the material with a D50 of0.80 mm was used; in the case of run 8 the material witha D50 of 0.33 mm was used.[32] All the experiments in Table 1 pertain to the case of

instantaneous dam removal except for runs 7 and 10, wherewe implemented a staged removal. Target parameters forstudy during the erosional experiments were: the longitudi-nal bed profile, the water surface, the solid dischargeflowing beyond the position of the (former) dam, and therate of bank erosion.

[33] In the experiments on erosion into a naturally de-posited delta (runs 1 and 2) the process of incision devel-oped randomly in a way that was difficult to documentexperimentally. In order to encourage incision to begin at apredictable location, a shallow channel (<10 mm in depth)was excavated into the center of the deposit before recom-mencing the flow and removing the dam. The width of thisinitial channel was estimated to an order of magnitude usingthe equilibrium relation suggested by Parker [1978a,1978b]. The initial channel in the case of run 6 is shownin Figure 5; the width was 27.5 cm. In the case of run 3, thecomputed width of the initial channel was wider than theflume itself, and in the case of run 4 the computed widthwas only slightly smaller, so that no channel was excavatedin either case.[34] During the erosion process we observed the evolu-

tion of the width of the water surface of the channel incisedinto the deposit at different sections using video cameras.An analysis of these experiments allowed us to ascertain theinfluence of the water discharge on both incision andsidewall erosion.[35] Narrowing of the incisional channel was observed in

five of the eight runs of Table 1 pertaining to sudden damremoval of them (runs 4, 5, 6, 8 and 9). More specifically, inthe early stages of the erosion process the channel width ateach section near the dam rapidly decreased to a minimumvalue, and subsequently slowly increases. This process isillustrated in Figures 6a–6d for run 6. The erosional

Figure 4. Evolution of the deposit of run 2 at times corresponding to 4, 6.5, 13, 21, 33, and 42 hours.The origin of the streamwise axis is at the sediment feed point. The dam is located 9 m downstream of thefeed point. Flow was from top right to bottom left.

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behavior during the two runs with stepped removal wassimilar but not as distinct.[36] The narrowing phenomenon is easily explainable

in terms of the distribution of boundary shear stress. Ineach section, the boundary shear stress has a maximumvalue in the middle zone of the channel and drops to zeroat the edges [e.g., Parker, 1978a, 1978b]. Thus, duringchannel incision, the erosion tended to be concentrated inthe central zone. This differential erosion narrows anddeepens the channel. We term this ‘‘erosional narrowing.’’Erosional narrowing also induced a streamwise conver-gence of the streamlines toward the channel center thatincreased net erosion, resulting in a positive feedback.This convergence is readily evident in Figures 6c and 6d.The narrowing process continued until a rough balancewas reached at which lateral sediment transport from thesidewalls sufficiently slowed channel degradation andstopped channel narrowing. Beyond this time the channelslowly widened.[37] Figure 7 shows the time evolution of the width of the

water surface for run 6: each line corresponds to a differentsection (i.e., to a different distance upstream of the inlet) inthe vicinity of the dam. The successive appearance of awidth minimum at increasing upstream distance illustratesthe upstream migration of a wave of channel narrowing andincision. All these data converge to an asymptotic trend thatshows a progressive erosion of the banks toward an equi-librium section.[38] Figure 8 shows the evolution of the bed profile along

the channel center during the erosion of the reservoirdeposit for run 6. The erosion upstream of the delta frontand the deposition downstream are clearly visible. Thedotted line represents the initial bed profile. At the end ofthe experiment the bed slope is approximately equal to theinitial slope value.[39] Figure 9 shows the evolution of the sediment dis-

charge during run 6. The sediment discharge was evaluatedat the (former) position of the dam from an analysis of thevideotapes. There was an initial pulse of sediment just afterdam removal that later decreased as the system slowly

evolved toward equilibration with the sediment supplyupstream. The time to reach the equilibrium value of thetransport rate was about 0.4 � 0.5 hours. In the experimentshown in Figure 9 the initial high-transport phase lastedsome 400 s. Figure 9 also shows oscillations in sedimentdischarge which are partially associated with bank collapseevents.[40] It is relevant to note that right after dam removal the

sediment discharge reached a value comparable to the liquiddischarge, as seen in Figure 9. This suggests that, at the verybeginning, a hyperconcentrated or debris flow developed inthe neighborhood of the dam, quickly dissipating with timeto more normal fluvial transport.[41] In Figure 10, data from run 5 are used in order to

illustrate the pattern of rapid erosional narrowing fol-lowed by slow erosional widening. Figure 10 pertains toa cross section located 8.2 m downstream of the feedpoint and 0.8 m upstream of the dam; the precise locationis shown in Figure 8. In Figure 10 water surface widthBw is plotted against water surface elevation x, the lattermeasured relative to the initial value. The run proceededin time from up to down on the diagram. In the first4.3 min of the run the water surface elevation decreasedby 4.8 cm and the water surface width decreased from aninitial value of 24.7 cm to a minimum value of 21.6 cm.In the following 16.0 min the water surface elevationfurther decreased by another 0.5 cm, and the channelwidth increased from the minimum value of 21.6 cm mto 24.5 cm. This general pattern, which was observed forall the runs showing erosional narrowing, is summarizedin the previously presented Figure 2d.[42] A comparison of Figures 7, 8, and 10 reveals that

erosional narrowing is associated with an early state ofvery rapid incision, whereas erosional widening is asso-ciated with a later state of much slower incision. Theperiod of erosional narrowing is sufficiently brief thatit might be missed in a field observation. This not-withstanding, the rate or sediment production duringerosional narrowing is very high due to the rapid rateof incision.

Figure 5. Front view looking upstream of the channel screeded upstream of the dam after removal butbefore commencing flow. The image, which is a frame grab from a videotape, pertains to run 6.


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[43] Erosional narrowing was not observed in runs 1, 2and 3. In these three runs flow just after dam removalextended from wall to wall of the flume. While incision wasnot uniform across the entire channel width, the entiredeposit remained under water during the duration of theexperiment. It can be seen from Table 1 that runs 1, 2 and 3had the highest discharges of the 10 runs. Evidently adischarge that is sufficiently high leads to erosion of thereservoir deposit without the clear development of an inci-sional channel. Lowered discharge leads to lower flowdepth. A sufficiently low flow depth across the entire widthof a rapidly eroding surface appears to be unstable, so thatthe flow tends to concentrate and form an incisionalchannel.

4.4. Erosion With Staged Dam Removal

[44] The staged removal procedure required the disassem-bling of the dam by the sequential removal of the horizontalslats shown in Figure 3, thereby allowing the remainingstructure to control the release of sediment. Staged removalwas used in runs 7 and 10; the results for run 7 areillustrated in Figure 11.

[45] In this experiment, three horizontal slats were re-moved. Sediment discharge was constantly monitored todetermine the appropriate moment to remove each slat. Theremoval of each slat caused an initial pulse of sedimentdelivery that decreased during the process in a way similarto that for the total removal procedure. Our procedure,which we think would also be appropriate for field cases,was to wait for the sediment outflow discharge to decreaseby at least an order of magnitude before removing the nextslat.[46] Figure 12 shows the longitudinal profile during

experiment 7. Compared to the sudden removal procedure,the data show that staged removal retarded the rate ofrelease of sediment from the deposit behind the dam. Inthe case of instantaneous removal, a removal performed atvery low flow can prevent an overly rapid delivery ofsediment downstream. In the case of staged removal,however, the issue may not be as critical, since the part ofthe dam remaining at each stage serves to limit the down-stream delivery of sediment.[47] Figures 5, 6, and 11 were obtained as frame grabs

from videotapes taken during the experiments. Several of

Figure 6. (a) Front view of the erosion of the front immediately after dam removal for run 6. The viewis looking upstream. (b) Plan view of the front and the channel screeded into the deposit just before damremoval for run 6. Flow is from left to right. (c) Plan view of the progress of the erosion process for run 6at 43 s after dam removal. Flow is from left to right. (d) Plan view of the progress of the erosion processfor run 6 at 1 min 41 s after dam removal. Flow is from left to right. The decrease in channel width byerosional narrowing is made evident by a comparison of section 1 in Figures 6c and 6d. Subsequentwidening can be seen by comparing section 2 in the same pair of figures. All the images are frame grabsfrom videotape.

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these videotapes have been placed for viewing on thewebsite of the National Center for Earth-surface Dynamics,http://www.nced.umn.edu.

5. Upscaling With Undistorted Froude Similitude

[48] Froude and geometric similitude provide a way toupscale the results of small-scale model experiments onrivers to field scale. The principles of Froude and geometricscaling have been outlined in detail in the literature [e.g.,Graf, 1971; Ettema, 2000; Cazanacli et al., 2002] and arenot repeated here. Rather, undistorted Froude and geometricmodeling are used to provide an interpretation of the resultsat field scaled.[49] Let Qw denote the water discharge, Qs denote the

mass sediment discharge, B denote reservoir width, S denotebed slope, D50 denote median sediment size, x denote

downstream distance from a given point (e.g., sedimentfeed point) and t denote time. In addition, let the geometricscale ratio be 1:l, so that any model length scale l takes aprototype (field) value l l. It is further assumed that themodel sediment has the same specific gravity as theprototype sediment, and effects mediated by dimensionlessnumbers other than the Froude number, e.g., Reynolds andWeber effects, can be neglected. Undistorted upscaling so asto preserve the same Froude number in the prototype as inthe model results in the relations

xð Þp¼ l xð Þm ð1aÞ

Bð Þp¼ l Bð Þm ð1bÞ

Figure 7. Time evolution of the width of the channel water surface at various points upstream of thedam after removal for run 6. Each line corresponds to a different section (i.e., to a different distance fromthe sediment feed point, given in m in the legend). The dam is located 9 m from the inlet section.

Figure 8. Evolution of the bed profile along the channel center during the erosion of the front duringrun 6. The dam was located 9 m downstream of the feed point. Flow is from left to right.


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D50ð Þp¼ l D50ð Þm ð1cÞ

Sð Þp¼ Sð Þm ð1dÞ

tð Þp¼ l1=2 tð Þm ð1eÞ

Qwð Þp¼ l5=2 Qwð Þm ð1f Þ

Qsð Þp¼ l5=2 Qsð Þm ð1gÞ

where x denotes streamwise distance. In the above relations,the subscript ‘‘p’’ denotes prototype and the subscript ‘‘m’’denotes model.[50] Consider, for example, a value of l of 75. The

longitudinal extent of the model reach upstream of the damwas 9 m; this translates to a prototype value of 675 m. Themodel flume width of 0.61 m translates to 45.8 m. The valueof median grain size of the feed sediment of 0.80 mm used inall runs except run 8 translates to 60 mm. The aggradingtopset slope of 0.004 of runs 1 and 2 translates to the same0.004 at prototype scale. The model time duration of 5400 sseen in Figure 7 required for the river profile upstream anddownstream of the dam of run 6 to relax to a spatially constantvalue over a reach with a length of about 6.6 m translates to13 hours over a reachwith a length of 495m. Themodel waterand sediment feed discharges of 0.0015 m3/s and 0.014 kg/sof run 1 translate to prototype values of 73.1 m3/s and0.68 tons/s. Themodel experiments thus provide a reasonablemodel of dam sedimentation and erosion due to dam removalin a steep, gravel-bed mountain stream.

6. Conclusions

[51] A series of experiments in which noncohesive sed-iment was deposited behind a dam and then eroded due toremoval of the dam shows the following effects.

Figure 9. Evolution of the sediment discharge at the (former) location of the dam during run 6.

Figure 10. Water surface width is plotted against watersurface elevation at a cross section located 0.8 m upstreamof the former position of the dam. Water surface width isseen to decrease, reach a minimum, and then increase. Theplot shows a decrease in water surface width of 3.1 cm and adecrease in water surface elevation of 4.8 cm during the first4.3 min of the run; in the next 16.0 min the water surfacewidth increased by 2.9 cm, and the water surface elevationdecreased by 0.5 cm. The data are for run 5.

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[52] 1. One is instantaneous complete removal of a damresults in impulsive erosion of stored sediment, with sedi-ment concentrations reaching mass-flow levels, followed bya gradual approach to the upstream supply value. Theamount of stored sediment remaining at this point dependson the discharge of the eroding water flow.[53] 2. During initial rapid erosion at lower discharges,

an incising channel first decreases in width due to thetendency for erosion to be concentrated in the channelcenter. We term this ‘‘erosional narrowing’’. This narrow-ing accompanied by rapid incision is followed by aperiod of widening at a much lower rate of incision, asschematized in Figure 2d. The sidewalls of the incisionalchannel continue to erode whether or not the channelitself is narrowing or widening, but narrowing suppressessidewall erosion. During the period of incisional narrow-ing, however, the rate of incision is so high that a largequantity of sediment is delivered downstream in a veryshort time.[54] 3. Stepped removal of a dam results in a smoother

and more controllable release of stored sediment and is an

option that should be considered for minimizing down-stream damage associated with dam removal.[55] 4. The experiments presented here not only provide

qualitative insight into the processes of dam sedimentationand erosion following dam removal, but can be upscaledusing undistorted geometric and Froude similarity. Theexperiments best model processes pertaining to a reservoirfilled predominantly with gravel on a steep, gravel-bedmountain streams.[56] The experiments reported here have several limi-

tations. Flume width was constant, so that the depositbehind the reservoir did not become narrower in theupstream direction as in a field reservoir. The sedimentused to fill the reservoir was rather well sorted, so thatthe deposit of the model reservoir was not stratified to theextent that might be expected in a field deposit. Inaddition, no allowance was made for deposits of cohesivesediment. These comments notwithstanding, the experi-ments serve to document early stage erosional narrowing,a phenomenon that seems likely to occur at field scale aswell.

Figure 11. Illustration of the staged removal procedure during run 7. The images are frame grabs fromvideotape. Flow is from top to bottom.

Figure 12. Longitudinal profile during the staged dam removal of run 7. The dam is located 9 mdownstream of the feed point. Flow is from left to right.


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[57] Acknowledgments. The authors are grateful to Giovanni Semi-nara for support and insight throughout this work, and to Bianca Federicifor help with the experiments. This paper is a publication of the NationalCenter for Earth-surface Dynamics (NCED), which is funded by theNational Science Foundation Preparation of this paper was partiallysupported by NCED. Partial support has also come from Fondazione Cassadi Risparmio di Verona, Vicenza, Belluno e Ancona (Progetto RIMOF).

ReferencesBatuca, D. G., and J. M. Jordaan (2000), Silting and Desilting of Reser-voirs, 353 pp., A. A. Balkema, Brookfield, Vt.

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Cui, Y., C. Braudrick, W. C. Dietrich, B. Cluer, and G. Parker (2004b), DamRemoval Express Assessment Models (DREAM). Part 2: Sample runs/sensitivity tests, J. Hydraul. Res., in press.

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Ettema, R. (Ed.) (2000), Hydraulic Modeling Concepts and Practice, ASCEManual 97, 390 pp., Am. Soc. of Civ. Eng., Reston, Va.

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Hey, R. D. (1979), Dynamic process-response model of river channel de-velopment, Earth Surf. Processes, 4, 59–72.

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Leeder, M. (1999), Sedimentology and Sedimentary Basins, 592 pp., Black-well Sci., Malden, Mass.

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Morris, G. L., and J. Fan (1997), Reservoir Sedimentation Handbook,685 pp., McGraw-Hill, New York.

Parker, G. (1978a), Self-formed rivers with stable banks and mobile bed:Part I, the sand-silt river, J. Fluid Mech., 89(1), 109–126.

Parker, G. (1978b), Self-formed rivers with stable banks and mobile bed:Part II, the gravel river, J. Fluid Mech., 89(1), 127–148.

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Task Committee on Guidelines for the Retirement of Dams and Hydro-electric Facilities (1997), Guidelines for the Retirement of Dams andHydroelectric Facilities, Am. Soc. of Civ. Eng., Reston, Va.

Vanoni, V. A. (1975), Sedimentation Engineering, 745 pp., Am. Soc. ofCiv. Eng., Reston, Va.

��A. Cantelli, Department of Environmental Engineering, University of

Genova, Via Montallegro 1, 16121 Genova, Italy. ([email protected])C. Paola, Department of Geology and Geophysics, University of

Minnesota, Minneapolis, MN 55455, USA.G. Parker, St. Anthony Falls Laboratory, University of Minnesota,

Minneapolis, MN 55414, USA.

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Experiments on upstream-migrating erosional narrowing and ... et...Experiments on upstream-migrating erosional narrowing and widening of an incisional channel caused by dam removal