EARTH SURFACE PROCESSES AND LANDFORMSEarth Surf. Process. Landforms 34, 547–557 (2009)Copyright © 2009 John Wiley & Sons, Ltd.Published online 16 January 2009 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/esp.1755

John Wiley & Sons, Ltd.Chichester, UKESPEarth Surface Processes and LandformsEARTH SURFACE PROCESSES AND LANDFORMSEarth Surface Processes and LandformsThe Journal of the British Geomorphological Research GroupEarth Surf. Process. Landforms0197-93371096-9837Copyright © 2006 John Wiley & Sons, Ltd.John Wiley & Sons, Ltd.2006Earth ScienceEarth Science99999999ESP1755Research ArticleResearch ArticlesCopyright © 2006 John Wiley & Sons, Ltd.John Wiley & Sons, Ltd.2006

Planform dynamics of braided streamsPlanform dynamics of braided streams

Walter Bertoldi,* Luca Zanoni and Marco TubinoDepartment of Civil and Environmental Engineering, University of Trento, Trento, Italy

Received 20 March 2008; Revised 13 August 2008; Accepted 25 August 2008

* Correspondence to: Walter Bertoldi, University of Trento, Dept. of Civil and Environmental Engineering, Trento, Italy. E-mail: walter.bertoldi@ing.unitn.it

ABSTRACT: The high dynamism and complexity of braided networks poses a series of open questions, significant for riverrestoration and management. The present work is aimed at the characterization of the morphology of braided streams, in order toassess whether the system reaches a steady state under constant flow conditions and, in that case, to determine how it can bedescribed and on which parameters it depends. A series of 14 experimental runs were performed in a laboratory physical modelwith uniform sand, varying the discharge and the longitudinal slope. Planimetric and altimetric configurations were monitored inorder to assess the occurrence of a steady state. A set of parameters was considered, such as the braid-plain width and thenumber and typology of branches and nodes. Results point out that a relationship exists between braiding morphology and twodimensionless parameters, related to total water discharge and stream power. We found that network complexity increases athigher values of water discharge and a larger portion of branches exhibits morphological activity. Results are then compared tothe outputs of a simple one-dimensional model, that allows to easily predict the average network complexity, once the bedtopography is known. Model computations permit also the investigation of the effect of water discharge variations and to comparedifferent width definitions. The at-a-station variability of planimetric parameters shows a peculiar behaviour, both regardingnumber of branches and wetted width. In particular, the analysis of the relationship between width and discharge highlightedrelevant differences in comparison to single thread channel. Copyright © 2009 John Wiley & Sons, Ltd.

KEYWORDS: fluvial morphology; braided rivers; planimetric configuration; laboratory modelling; 1D modelling

Introduction

Braiding is a fascinating fluvial pattern, characterized by com-plex dynamics in which water and sediment flow are dividedin multiple branches, joining and splitting at the nodes andshifting continuously in the floodplain. A high morphologicalcomplexity arises from the coexistence of several spatialstructures, controlled by different spatio-temporal scales. Thesestrongly interact in the development of the braided patternand give rise to strong fluctuations both in time and in space.This dynamic behaviour yields a biological and ecologicalrichness, higher than any other river pattern, determining ahigh functionality of the whole fluvial system (e.g. Tockneret al., 2003; Tockner et al., 2006).

The high dynamism and the instability of braided streams;their planimetric and altimetric evolution acting at similarscales; their strong and intrinsic unsteadiness lead to a strongdifficulty to explain and to predict their evolutionary pro-cesses (e.g. Paola, 2001; Murray, 2007). The issue of predictingbraided stream morphology is largely unresolved and thereis not enough convergence on which the key parametersare controlling the evolution (e.g. Parker, 1976; Murray andPaola, 1997). A better understanding is relevant both in themanagement of existing braided rivers and in the frameworkof river restoration practices, that often rely on artificialwidening of target reaches and on re-opening of old sidechannels (Stanford et al., 1996; Kondolf, 1998; Gilvear, 1999;

Rohde et al., 2005; Habersack and Piégay, 2007; Murray et al.,2007).

Equilibrium in geomorphology is a debated task (Church,1992; Thorn and Welford, 1994) and it mainly depends on theconsidered spatial and temporal scales (Howard, 1988). In thiscase, we refer to a steady state in which the altimetric andplanimetric configuration can be described and predicted asa function of the external parameters, like water discharge,longitudinal valley slope and grain-size. In the present workwe tackle the problem of the occurrence and quantificationof such a state in braided streams, despite their high morpho-logical dynamism.

Few works are devoted to investigate whether the wholesystem reaches a steady state and its relationship with thehydraulic parameters. Theoretical analysis (Parker, 1976;Struiksma and Klaassen, 1988) and statistical analysis ofnatural braided streams (Mosley, 1983) were conducted inorder to study the influence of slope and water discharge onthe complexity of the network. These contributions showed anincreasing trend of the network complexity with the increaseof the longitudinal slope and water discharge. Ashmore(1991a) confirmed these results through physical laboratorymodelling, pointing out the product of discharge and gradientcould be the key parameter for the network complexity. Morerecently, using a physical model, Egozi and Ashmore (2005)highlighted the tendency of the system to reach a statisticallysteady-state configuration and the increasing trend of the

Copyright © 2009 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 34, 547–557 (2009)DOI: 10.1002/esp

548 EARTH SURFACE PROCESSES AND LANDFORMS

braiding intensity at higher values of the channel formingdischarges.

A different approach focussed on the statistical propertiesof braided river morphology, pointing out that multi-channelgeometry is self-affine over a range of spatial scales (Howardet al., 1970; Foufoula-Georgiou and Sapozhnikov, 2001; Rosatti,2002). These findings suggest an element of universality in thebraiding process and the possibility to individuate a spatialscaling, also considering morphological changes (Lane, 2006).Paola (1996) constructed a spatially averaged model of braid-ing, imposing a shear stress distribution based on a form ofReynolds averaging over the braid plain width. The modelsuggested that fluctuations in stress are extremely importantin determining the mean properties. Although the authorclaimed the need for more laboratory and field data, it seemspossible to construct a theory of the overall behaviour (spatiallyaveraged) of the braided rivers.

Although it seems that these river systems can reach asteady state (Howard et al., 1970; Young and Davies, 1990)a deeper insight is still needed to quantitatively describethe planimetric configuration of multi-channel patterns. Inparticular, it is not clear whether the network complexity,represented by the number of branches in a cross-section(defined as braiding index), can be predicted. Robertson-Rintoul and Richards (1993) suggested a relationship betweenthe total sinuosity of a braided reach and the stream power,even if it seems (Ashmore 2001; Chew and Ashmore, 2001) thatpredictions do not compare well with field data. Laboratoryexperiments performed by Warburton (1996) tried to high-light possible correlations between sediment transport, widthand braiding index. Analogously, the extensive fieldworkscarried out by Mosley (1981, 1982, 1983) pointed out a seriesof relationships between braided parameters and how theyare influenced by the external conditions. Data show a strongvariability, both at-a-station and between-station and theresults are not easy to interpret also because a comparisonbetween field measurements on different rivers and withlaboratory investigations is made difficult by the lack of a setof dimensionless parameters.

The present work is aimed at the quantitative descriptionof braided networks morphology, through the planimetric andaltimetric survey of laboratory model streams, with constantdischarge and sediment feeding. We investigate the intrinsicresponse of the system and highlight the controlling parameters,using a dimensionless form, not dependent on the fluvial size.Moreover, we propose a simple one-dimensional (1D) numericalmodel, able to provide information about the braiding indexof a braided stream, when the bed topography is known.Modelling allows also the investigation of the networkconfiguration at different stage conditions. The paper endswith a discussion on different width definitions and on therelationship between width and discharge, that distinctivelycharacterize the braided pattern.

Experimental Set-up and Procedure

The experiments were performed on a large laboratory flume,25 m long and 2·90 m wide, located at the University ofTrento (Figure 1). All the runs were carried out using well-sorted sand with a mean grain size ds equal to 0·63 mm,characterized by a submerged relative density Δ equal to 1·63.The hydraulic circuit comprised a submerged pump, regulatedwith an inverter, that allows discharge values up to 20 litresper second to be set. The sand was supplied by a volumetricsand feeder at the upstream end of the flume through threerotating screws and a diffuser. At the downstream end a chute

conveyed both the liquid and solid flux in a submerged tank,where the sediment transport rate was measured by samplingthe cumulative weight. Bed topography was surveyed by a laserprofiler supported by a carriage mounted on a rail, positionedwith high accuracy on the top of the concrete flume walls.Bed elevation was measured on a regular grid, with longitu-dinal spacing of 0·1 m and transverse spacing of 0·01 m.Bottom topography was surveyed with a time interval varyingbetween 2 to 4 hours depending on the morphologicalactivity and at the end of each run.

A second hand-movable carriage positioned on the samerails supported a high resolution digital reflex camera, bywhich the evolution of channel planform was monitored indetail. The photographic device was located about 4 m abovethe sand bed and it was controlled by a laptop, positioned onthe same carriage. A series of 15 vertical images were neededto survey the planimetric configuration on the whole flumelength.

Three sets of experiments were performed with three differentlongitudinal slope, namely 0·7%, 1·3% and 1·7%. In total 14experimental runs were carried out, varying the water dischargeQ for each slope S (see Table I). Experimental conditions werechosen in order to reproduce values of the Shields stress ϑtypical of natural gravel-bed braided rivers.

According to Ashmore (1991b), in each experimental run thefollowing procedure was adopted. First the bed was flattenedin order to obtain a topographic configuration made up bya single straight channel cut on the flat sand surface andlevelled at the prescribed slope. The geometry of the initial

Figure 1. View of the laboratory flume. Flow is towards the camera.

Table I. Measured dataset

Run S [–] Q [ls–1] TBI ABI Bb [m] Duration [hours]

q07-s07 0·0067 0·7 4·2 1·1 0·93 45q09-s07 0·0068 0·9 5·4 1·3 1·70 84q10-s07 0·0086 1·0 4·6 1·5 1·63 52q12-s07 0·0069 1·2 5·3 1·6 1·80 58q15-s07 0·0072 1·5 6·3 2·3 2·16 59q05-s13 0·0119 0·5 – 1·5 1·59 37q05-s13 0·0122 0·5 – 1·6 1·54 30q06-s13 0·0120 0·6 3·7 1·7 1·98 59q07-s13 0·0120 0·7 4·2 2·0 1·82 30q10-s13 0·0119 1·0 4·5 2·6 2·15 30q15-s13 0·0118 1·5 5·1 3·0 2·46 17q03-s17 0·0154 0·3 1·7 1·0 1·17 23q05-s17 0·0155 0·5 2·1 1·8 1·88 25q07-s17 0·0155 0·7 3·1 2·2 2·13 14

Copyright © 2009 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 34, 547–557 (2009)DOI: 10.1002/esp

PLANFORM DYNAMICS OF BRAIDED STREAMS 549

channel was selected in order to ensure bankfull conditions,with an initial width to depth ratio equal to 10, i.e. lower thanthe threshold value for alternate bars to occur (see Colombiniet al., 1987). The system was freely run to generate a braidednetwork, subject to a constant water and sediment supplythroughout the run. The sand feed rate was adjusted tomaintain mass balance between long-term input and outputand to limit bed elevation changes at the upstream cross-section.

The time evolution of the network planform was surveyedthrough regular photographic surveys. The time lapse betweenacquisitions was set to 1–2 hours, depending on the morpho-logical dynamism. All the channels were identified andmanually marked on each series of vertical images, instantlyprinted to facilitate the procedure. A distinction was madebetween branches transporting sediments (morphologicallyactive) and branches not carrying sediments at that moment(as defined also by Ashmore, 2001). The recognition of channelson pictures is not obvious since it may give rise to subjectivityproblems. This limitation is due to water transparency combinedwith very shallow flows. However, the problem was avoidedthanks to direct and continuous channels observation, whichallows the correspondence between observed channels andthe pictures to be checked. It is worth noting that a correctdefinition of number and type of channels could be a problemalso in field observations due to the complexity of the rivernetwork, particularly at a formative stage.

In order to measure the planimetric parameters, the collectedpictures of the network were scaled and stitched usinggraphical software. Then, all the channels were digitized, asdrawn on the printed images and the lateral border of thenetwork was identified. In Figure 2 a braided reach is sketched,where the wetted (dashed line) and active (solid line) branchesare marked off. On each survey 44 cross-sections wereidentified, every 0·5 m along the flume, where a set of plani-metric parameters was quantified, aimed to the description ofnetwork complexity. In detail we measured:

• total braiding index (TBI), defined as the number of wettedchannels per cross-section;

• active braiding index (ABI), defined as the number ofchannels that transport sediments in a cross-section;

• river corridor width, or belt width, Bb that represents thewidth of the whole area subjected to morphological pro-cesses (Figure 2);

• node density, defined as the number of nodes per unitarea, scaled with the belt width in order to obtain adimensionless parameter:

(1)

where A is the total area of the river network.This planimetric survey allowed also the monitoring of

confluences and bifurcations that were classified accordingto the sediment mobility in their branches. In particular, wedefined active bifurcation a node entirely composed by activechannels, as reported on the sketch in Figure 2.

In Table I the quantified morphological parameterscharacterizing each run are reported.

Experimental Results

Steady-state configuration

The planimetric configuration of the initial straight channelevolves forming a braided network, mainly through the chutecut-off process described by Ashmore (1991b). During thisformative phase the channel widens and alternate bars start toform, inducing bank erosion and creating a sinuous patternwhich, in turn, affects the bars migration. Once the singlechannel reaches a threshold value of sinuosity, flow cuts thebars originating a bifurcation (see Bertoldi and Tubino, 2005).Starting from this first diversion, the system evolves in spaceand time, through a cascade of creation and obliterationof branches. Hence, the number of channels, belt width, aswell as the number of nodes, increase in time. The processof widening and increasing of complexity does not continueindefinitely, but it displays an asymptotic trend and thesystem reaches a steady-state configuration, when the numberof new bifurcations equals on average the number of abandonedbranches. This process is depicted in Figure 3, where TBI andpercentage of active bifurcations are reported for two runs (on

Figure 2. Sketch of a braided reach, definition of the measure parameters and distinction between wetted (dashed line) and active (solid line)branches.

node densitynodes

b=#

,A

B2

Copyright © 2009 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 34, 547–557 (2009)DOI: 10.1002/esp

550 EARTH SURFACE PROCESSES AND LANDFORMS

the plots an exponential fit is also reported). The reached steadystate shows the occurrence of superimposed fluctuations thatrepresent the continuous reworking of the network configura-tion. Therefore, on a smaller spatial (or temporal) scale, as thatof the instantaneous single cross-section, the configurationseems not to be predictable as a function of the controllingparameters.

In order to characterize the network configuration, para-meters were averaged in time, excluding the initial formativephase, which range between 1 and 8 hours according tothe sediment mobility. Moreover, the spatial average wasperformed excluding the first 4 m upstream and the last 2 mdownstream in order to avoid inflow and outflow effectson the morphology. Through this double averaging procedurewe obtained a mean value of the parameters, which isrepresentative for each run and can be related to thehydraulic conditions.

It is worth pointing out that this steady state supposesconstant water and sediment discharges, equivalent to forma-tive flow and represents the necessary condition to quantifybraiding characteristics and therefore to identify and evaluatehow external controlling parameters affect the planimetricconfiguration.

Morphodynamic influence of governing parameters

Experimental observations suggest distinguishing two categ-ories of parameters, that characterize the planimetric config-uration of the braided network. On the one hand, one classcomprises the parameters that describe the network as awhole, as TBI, belt width, node density and link length. Onthe other hand, a second class can be individuated that isrelated to the instantaneous morphological activity in thebranches and therefore to the part of the network subject tosediment transport. This latter category includes ABI, percentage

of active bifurcation, percentage of active branches expressedas the ratio between ABI and TBI. Experimental analysishighlighted that these two classes can be controlled bydifferent external variables.

In order to assess this observation and to make possible acomparison between laboratory data and field measurements,experimental results will be hereinafter plotted as a functionof dimensionless parameters.

For this purpose, a normalization procedure is proposed,where water discharge and stream power index ω (that is theproduct of slope and discharge ω = Q · S) were scaled using

the Einstein scale and a length scale L defined as:

(2)

where g is the acceleration due to gravity. This length scale Lwas introduced by Parker et al. (2007) as a suitable parameterto normalize width and depth of single-thread channels in orderto describe bankfull geometry. In the case of braided rivers itprovides a well defined length scale, since the definition of atransversal scale is not obvious and unique (see section 5).The width, generally used in single-thread rivers, can bedefined in different ways in a braided network, consideringthe sum of the single branches widths (wetted width), thedistance between the external channels, the belt/corridorwidth or the active width where sediment transport occurs. Toavoid this ambiguity, and with the aim not to introduce internalparameters (Q, ds and g are imposed external controls) thelength scale L was used to normalize the variables. So thefinal dimensionless expressions for water discharge andstream power index are:

(3)

Figure 3. Examples of the temporal trend of TBI and percentage of active bifurcations (left run q06-s13 and right run q10-s13).

g dΔ s3

LQg

=2 5

1 5

/

/,

qQ

L g d L g dq S* * *

s s

= = =Δ Δ3 3

, .ωω

Copyright © 2009 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 34, 547–557 (2009)DOI: 10.1002/esp

PLANFORM DYNAMICS OF BRAIDED STREAMS 551

In the following plots (Figures 4, 5 and 6) the averaged valuesof the measured planimetric parameters are reported as afunction of these two variables. These values quantify thesteady-state configuration of a braided network at formativeconditions, as discussed earlier.

Figure 4 reports on the braiding intensity, quantified boththrough TBI and ABI, shown as a function of dimensionlessdischarge and stream power. Figures 4(A) and 4(D) show thatthe adopted normalization is correct, as the experimental pointscollapse on a unique curve. Moreover, from published data,the ranges of dimensionless discharge (200–600) and streampower (2–7) cover approximately the observed values forgravel-bed braided rivers of a wide range of scales atapproximately formative discharge.

As pointed out earlier, total and active braiding indexesare parameters representative of the two different classes,as they describe, respectively, the global complexity of thenetwork and the instantaneously active branches. Theydisplay a different behaviour: we found that the former isa function of the dimensionless discharge q*, whereas thelatter depends on the dimensionless stream power ω*. Thesimilar distinction was pointed out also for all the otherconsidered parameters. Therefore, we found that dischargeand stream power control the two different aspects of theplanimetric configuration of a braided network in formativeconditions. Dimensionless discharge q* is, therefore, theparameter that better describes network configuration asresults by the continuous morphological evolution, keepingmemory of the historical legacy of the subsequentchannel rearrangements. However, the dimensionlessstream power, as a surrogate of the sediment mobility, isthe suitable variable to characterize the instantaneousdynamics of the network, quantifying the proportion of activebranches.

Possible controls on the planimetric configuration

Averaged configurations are described in Figures 4, 5 and 6 andthe planimetric parameters are discussed and compared withthe results of previous experimental and field investigations.

In Figure 4 it is possible to observe the natural trend of thesystem which responds to increasing the number of wettedand active channels for higher values of water discharge. Thisresult is confirmed by previous experimental and field observa-tions (e.g. Mosley, 1983; Ashmore, 1991a), that showed ahigher network complexity at larger values of water dischargeand longitudinal slope. The performed runs characterized bythe longitudinal slope equal to 1·7% are not reported in theplots in Figures 4(A) and 4(B) since only the active channelswere monitored during those runs, because of the highmorphological activity of the system, that hinders therecognition of minor branches.

A similar way to quantify the braiding intensity is thetotal sinuosity Σ; defined by Hong and Davies (1979) as theratio between total channel length and valley length. Totalsinuosity was also estimated through the two formulasproposed by Robertson-Rintoul and Richards (1993), whichforesee Σ; from water discharge, mean longitudinal slope andgrain size. In this case, the formulas heavily underestimatethe measured values, showing also a different increasingtrend if plotted with respect to the dimensionless waterdischarge. This discrepancy is due to the dimensional natureof the proposed formulas, since they were extrapolated froma regression of field data, relating a dimensionless parameter(Σ;) to dimensional variables.

The graph showed in Figure 5(A) represents the dimen-sionless belt width bb* as a function of the dimensionlesswater discharge q*. Note that the belt width bb* was alsoscaled using the length scale L

Figure 4. Quantification of the network steady state configuration: A) total braiding index TBI as a function of the dimensionless water discharge;B) total braiding index TBI as a function of the dimensionless stream power index; C) active braiding index ABI as a function of the dimensionlesswater discharge; D) active braiding index ABI as a function of the dimensionless stream power index.

Copyright © 2009 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 34, 547–557 (2009)DOI: 10.1002/esp

552 EARTH SURFACE PROCESSES AND LANDFORMS

(4)

Values of bb* were found to depend slightly on discharge,with values ranging between 40 and 60 and displaying adecreasing trend for larger values of dimensionless discharge.This implies that the dependency of the belt width on thedischarge can be described by a power law with an exponentlower than 0·4. This is somewhat different from the wellknown empirical relationship between water discharge andchannel width valid for single-thread, gravel-bed channels(Leopold and Wolman, 1957), recently proved also by Parkeret al. (2007), who individuate a power-law dependence withan exponent equal to 0·47. However, these experimentalfindings describe a different process, since the belt width Bb

includes several channels, exposed bars and islands and arenot obvious. The Discussion section will be devoted to adeeper analysis of the different width definition in a braidednetwork.

Planimetric configuration and complexity of a network canbe described also taking into account the number and typologyof nodes, including both confluences and bifurcations. Nodedensity (Equation 1) was found to be related to the waterdischarge, showing higher values at higher formative conditions(Figure 5B). This result is similar to that obtained from theanalysis of the TBI (Figure 4A). Even though the measure ofnumber of channels is more common, the description ofnetwork complexity through the nodes is a fruitful alternativesince nodes are characteristic ecotones within aquatic systemswith both upstream and downstream connections (Arscott et al.,2000). Focussing on the morphological activity, it is possibleto observe that the percentage of bifurcations composed bythree active branches increases at higher values of the dimen-sionless stream power index (Figure 5C). This observationmeans that the percentage of active branches increases, as canbe evaluated also computing the ratio between the ABI andthe TBI (Figure 5D). This ratio ABI = TBI increases at highervalues of dimensionless stream power index, ranging between

bBL

*bb= .

Figure 5. Quantification of the dynamic equilibrium of the network: (A) dimensionless belt width b b* as a function of the dimensionless waterdischarge; (B) node density as a function of the dimensionless water discharge; (C) ratio between total and active braiding indices as a function ofthe dimensionless stream power index; (D) percentage of the active bifurcations as a function of the dimensionless stream power index.

Figure 6. (A) Dimensionless link-length as a function of the dimensionless water discharge; (B) comparison between measured link-length andthe formula proposed by Ashmore (2001).

Copyright © 2009 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 34, 547–557 (2009)DOI: 10.1002/esp

PLANFORM DYNAMICS OF BRAIDED STREAMS 553

0·2 and 0·6. This result agrees with the observations of Egoziand Ashmore (2005) who found values of the ratio ABI = TBIranging in the interval 0·4 and 0·6. This indicator gives aquantification of the network morphological activity, showingthat even in formative conditions, only a percentage of thebranches are subject to sediment transport. This observationconfirms the results and investigations by Stojic et al. (1998)and Luchi et al. (2007), who highlighted the relevance ofprocesses at single channel scale to describe and predictbraided network morphology.

Combining the measured parameters, other representativeindicators for braided streams were computed, for examplethe link-length Λ calculated by dividing the total length of allchannels in the measured reach by the number of nodes (asdefined by Ashmore, 2001). In order to obtain a dimensionlessform, the link-length Λ was scaled using the belt width:

(5)

Note that the link-length was normalized using the belt widthand not the length scale L because longitudinal scales ofmorphological features are usually related to the width (i.e.rivers bars or meanders). In Figure 6(A) the dimensionlesslink-length λ* is plotted as a function of the dimensionlessdischarge. A decreasing trend can be observed, with lowervalues for higher dimensionless water discharge. Thisobservation could be misleading, since the dimensionalrelationship observed by Ashmore (2001) showed that highervalues of water discharge imply a larger link-length. Thedifferent behaviour is due to the scaling effect, since beltwidth increases faster than dimensional link-length Λ. Thecomparison between measured λ* and values computedusing the formula proposed by Ashmore (2001) is reported inFigure 6(B). The agreement is sufficiently good, consideringthat the proposed formula is mainly inferred from field data,over a wide range of discharges.

1D Modelling

We propose the application of a simple 1D numerical modelbased on measured cross-section topography, in order toevaluate mean values of parameters describing the networkconfiguration. In the model each transect is divided intovertical panels between each surveyed point and the simpleassumption of the model is that the free surface is horizontaland the downstream slope is the same across the entiresection. Longitudinal slope is computed as the overall riverslope with an adjustment for sinuosity of individual channels,that was observed to range about 1·1. Water and sedimentdischarges of each panel are then computed assuming locallyuniform flow. The simplifying assumption of an horizontalfree surface level across the whole section is known to beinaccurate, as water levels at a given discharge often differbetween adjacent anabranches in a braided river (e.g. Zolezziet al., 2006). Moreover some channels can be dry eventhough they are at a lower elevation than those conveyingwater. In spite of this simplification, the intent of the model isto estimate a mean value of the number of wet and activebranches. This averaging may cancel out the error inindividual cross-sections due to non-uniform water surfaceelevation and local variation in slope while keeping thedependence on the main external parameters. The samemodel was also used by Bertoldi et al. (2008) to computesediment transport rate in braided networks and resultswere found to be satisfactory, when compared to observedvalues.

Water level in the model is computed by iterative estima-tion until the panel discharges sum to the known totaldischarge. Flow resistance was imposed through a logarithmicfunction of relative roughness only (Engelund and Fredsoe,1982):

(6)

where C is the Chezy dimensionless resistance coefficientand D is the water depth.

Once the free surface level is known, the number of branchesis counted in each cross-section. Two thresholds wereintroduced in the model, in order to define the number ofwetted branches: (i) a channel has to be wider than 80 timesthe mean grain size and (ii) the channel discharge has to begreater than 1% of total discharge. These thresholds areimposed not to consider single wetted points as effectivebranches and were calibrated with the experimental data.Furthermore, the number of active branches is evaluated,computing the number of channels in which the shear stressexceeds, in at least one panel, a threshold value for sedimentmovement, here considered equal to 0·08. This thresholdvalue is higher than the classical critical values for incipientgrain mobility: it was chosen in order to correctly reproducethe observed values of ABI and can be explained consideringthat it has to define the branches in which a clearlydetectable sediment transport occurs.

Results are slightly sensitive to the choice of resistancefunction (alternative functions could be used), but it is alsosensitive to the width of the panels and to the thresholdvalues defined earlier. The purpose here is not to exactlyreproduce the observed instantaneous configurations, but toassess whether this simple model is able to grasp the mainfeatures that characterize the steady-state planimetry of abraided stream.

Model results are plotted in Figure 7, where both TBI andABI are reported in comparison to the experimental values, asa function of both dimensionless discharge and stream power.Figure 7 shows that the model is able to quantify networkcomplexity, in spite of the simple assumptions. Numericalresults obtained from network topography generally confirmthe experimental results, showing that TBI is a function of theflowing discharge, whereas the ABI depends on the streampower. In the plots of Figure 7 the series referring to themodel computation have a larger number of points, sincebed topography was available for each run and therefore thewhole set of experiments can be presented. In this way it isalso possible to enhance the soundness of the experimentalresults, since a greater number of experimental conditions areconsidered and an eventual bias of visual data interpretationcan be filtered.

Furthermore, the numerical model allows the investigationof the role of discharge variations on the same topography andmakes possible a comparison between at-a-station variabilityand formative conditions. Each measured bed topographywas used to simulate different stage configurations, varyingwater discharge from near zero to four times the value thatformed the network. A total of 30 different increasing valueswere modelled. Both TBI and ABI show a distinctive behaviourwith an initial increasing trend, a maximum and a decreasinglimb, until reaching a single-thread configuration at very highvalues of water discharge (see Figure 8). In the plots, braidingindexes are reported in terms of dimensionless variables, asfound in the previous section. The existence of a maximumvalue of braiding indexes is due to the merging of channelsas discharge increases over the bankfull stage. The analysis

λ*b

=ΛB

.

CD

d= +

⎛

⎝⎜⎜

⎞

⎠⎟⎟6 25

2 5· ln

.,

s

Copyright © 2009 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 34, 547–557 (2009)DOI: 10.1002/esp

554 EARTH SURFACE PROCESSES AND LANDFORMS

shows that the rising limb of the curves lay in a confinedregion of both plots, meaning that at-a-station variability canbe represented by the same function measured in formativeconditions.

Observed trends of braiding indexes highlight that the maxi-mum value is generally reached at a discharge larger thanthat corresponding to formative conditions (solid points inFigure 8) and that ABI peaks for higher values of discharge (orstream power). This characteristic behaviour of braided streams(pointed out, even if in a different way also by Van der Nat et al.2002) can be useful in order to evaluate the hydraulic conditionsthat formed the network topography. The peak of both TBIand ABI is, in this way, a sort of mark that differentiatesnetworks formed under different hydraulic conditions.

Discussion on Width Computation in Braided Streams

The proposed 1D numerical model also allows the com-putation of the width, defined both as the sum of the widths

of the single channels in a cross-section (wetted width) and asthe width of the panels where sediment transport occurs(active width). These two definitions and the braided beltwidth defined in an earlier section are compared in thefollowing, pointing out that each width definition can lead toa distinct behaviour and can depend on different parameters.

Through the comparison with experimental data of Ashmore(1988), Bertoldi et al. (2008) demonstrated that this model, inspite of the simplifying hypothesis, is able to correctly reproducethe wetted width of braided streams, if results are averagedon a sufficiently high number of cross-sections.

Figure 9 reports computed values of the three defined widths(belt width bbelt, wetted width bwet and active width bactive) as afunction of the water discharge (Figure 9A) and of the streampower (Figure 9B), in dimensionless form. Similar graphscould be plotted with the dimensional variables. As pointedout in Figure 5(A), belt width can be expressed as a functionof the discharge or of the stream power (Figure 9B). The ana-lysis points out that wetted width, in accordance to regimetheories (e.g. the recent contribution of Parker et al., 2007), ismainly a function of the discharge (points referring to wetted

Figure 7. Comparison between the measured values of the total and active braiding indexes and values computed by the 1D numerical model,as a function of the dimensionless discharge and stream power.

Figure 8. At-a-station variability of TBI and ABI, as computed by the numerical 1D model. Black dots represent the formative conditions.

Copyright © 2009 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 34, 547–557 (2009)DOI: 10.1002/esp

PLANFORM DYNAMICS OF BRAIDED STREAMS 555

width are more aligned on Figure 9A). However, the coefficientof the interpolating power law is 0·51 in the dimensionlessform of Figure 9(A) and correspond to an exponent equal to0·7 using metric parameters. This exponent is definitely largerthan that found for single-thread channels. This analysisquantifies a peculiar and well-known behaviour of braidedrivers, as pointed out by Ashmore and Sauks (2006) andBertoldi et al. (2008). The multi-channel pattern is characterizedby very shallow cross-sections, where the width increases withdischarge much faster than mean depth, due to the activationof new branches.

However, active width was found to be a function of thestream power (Figure 9B), showing a quasi-linear dependence(the exponents of the power law is close to one). This observa-tion confirms the distinction proposed in an earlier sectionbetween the two classes of planimetric parameters andreinforces the definition of the discharge as the index of the‘global’ configuration and of the stream power as the indicatorof the ‘instantaneous’ morphological activity.

Moreover, in Figure 9 the at-a-station variability of wettedand active width is also reported, as computed by thenumerical model (represented by cross-marks on the plots).The analysis highlighted that only small differences can beobserved between at-a-station variability (computed with fixedbed topography) and formative conditions relationship (squareand triangular symbols). The exponents of the power lawinterpolating wetted and active widths computed at-a-stationare 0·57 and 0·96, respectively, that differs only slightly from

the exponents of the steady state in formative conditions(reported in Figure 9). This result is not obvious, since single-thread channels behave differently. In gravel bed rivers forma-tive width depends on a 0·4–0·5 power law of discharge(Parker et al., 2007), whereas at fixed topography the at-a-station variations are generally slighter.

Finally, a comparison between the ratios ABI over TBI andactive width over wetted width is proposed in Figure 10.These two ratios are in a quite strict relationship, showingalmost equivalent values, both considering the experimentaland the computed values of the braiding indexes. This analogycan be relevant in order to estimate in the field one of thetwo parameters, once the other is known. From field data it isnot always obvious to recognize in which branches sedimenttransport occur, but from bed topography surveys it is possibleto infer useful information about the area where morpho-logical changes take place.

Conclusions

We presented the results of an experimental work on gravel-bedbraided streams morphology aimed to investigate the plani-metric configuration at formative conditions. Moreover, resultshave been compared and reinforced by the application of asimple 1D numerical model.

In particular the outcomes can be summarized in thefollowing points:

Figure 9. Braid belt width, wetted width and active width as a function of dimensionless discharge (A) and stream power (B). Cross-marksrepresent the computed at-a-station variability.

Figure 10. Relationship between the ratio ABI/TBI and the active portion of wetted width.

Copyright © 2009 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 34, 547–557 (2009)DOI: 10.1002/esp

556 EARTH SURFACE PROCESSES AND LANDFORMS

(1) Braided streams reach a ‘steady state’ configuration, interms of belt width, number of branches and nodes in across-section.

(2) Two controlling dimensionless parameters were individu-ated, namely dimensionless discharge and dimensionlessstream power, scaled with the grain-size and an intrinsiclength scale. These parameters can be used to validatepresent experimental results with field data.

(3) Morphological parameters can be divided into twogroups: (i) those characterizing the whole network (width,braiding index) that depend on the total discharge and (ii)those related to the instantaneous morphological activity(such as the ABI and the number of active bifurcations)that depend on the stream power.

(4) The proposed 1D numerical model is able to correctlyreproduce the averaged planimetric configuration, allow-ing the investigation of different hydraulic conditions,comparing in this way at-a-station variability and forma-tive conditions behaviour.

(5) Model computations include the evaluation of both wettedand active width, showing that relationship between widthand discharge or stream power can be different, dependingon the chosen definition. Moreover, wetted width can becomputed by a power law function of the discharge withan exponent equal to 0·7, much larger than those gener-ally proposed for single-thread channels.

The quantification of the steady-state planimetric configurationof a braided river provides the scientific, morphologically basedknowledge to better understand the present status and theevolutionary dynamics of these river systems. Results are relevantfor designing river restoration, particularly considering thewidening projects. The quantified values of the planimetricparameters provide the range of the forcing hydraulic para-meters needed to restore and maintain the multi-channel natureof a river system, hindering the failures of the restoration projects.Moreover, according to these results, it is possible to understandif a braided river configuration is statistically stable or not. Theissue of morphological stability is important to assess the ecolo-gical stability of the system and the related habitat evolution.

Acknowledgements—This work has been developed within theframework of the ‘Centro di Eccellenza Universitario per la DifesaIdrogeologica dell’Ambiente Montano – CUDAM’ and of a series ofresearch projects, namely: ‘Morphodynamical processes in river andriparian ecosystems–PRIN 2006’, co-financed by the Italian Ministryof University and Scientific Research (MIUR) and by the University ofTrento; RIMOF, financed by the Fondazione Cassa di Risparmio diVerona, Vicenza, Belluno e Ancona; ‘Monitoraggio della morfologiae della portata del fiume Tagliamento’, co-founded and jointly carriedout by the DICA and the Autorità di Bacino dell’Alto Adriatico.

The authors gratefully acknowledge the fundamental support ofStefano Miori, Thomas Amplatz, Martino Salvaro, Federica Castaman,Anna Costa, Daniele Crescimanno, Luca Adami, Andrea Zin and thestaff of the Hydraulic Laboratory who helped in the execution ofthe experimental runs and in the data analysis. The paper greatlybenefitted from comments and suggestions by Guido Zolezzi andChris Paola.

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