Experimental analysis of braided channel pattern response to increased discharge

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2008jf001099, 2009 Experimental analysis of braided channel pattern response to increased discharge Roey Egozi 1,2 and Peter Ashmore 1 Received 1 July 2008; revised 3 December 2008; accepted 9 February 2009; published 25 April [1] Physical models of gravel braided rivers were used to investigate the adjustment of braiding intensity to step changes in channel-forming discharge and the mechanisms by which channel pattern adjustment and maintenance occurs. A braided channel developed at low discharge was subjected to two step increases in discharge between which the channel was given time to develop stable average braiding intensity in response to each steady discharge. Active (with visible bed material movement) and total channel networks were mapped throughout the experiment. Total braiding intensity exceeded active braiding intensity and both adjusted to a stable, average value at each discharge, indicating that channel pattern adjustment to total discharge involves both the active and the total network. Only portions of the total braided channel network developed at a given time, and it formed progressively by migration and avulsion of the (less extensive) active network. At equilibrium, the ratio of active to total braiding intensity stabilized at about 0.4. This stable value may increase with relative mobility of the bed material (stream power relative to grain size). The stable value was achieved via gradual increase of total braiding intensity while active braiding intensity adjusted very quickly to the increased flow. These adjustments are controlled by partial avulsion of the main active channel associated with changes in its sinuosity, and allocation of flow and bed load to secondary anabranches. Braided channel pattern dynamics is closely tied to, and explained by, the local dynamics and symmetry/asymmetry of bifurcations and avulsions. Citation: Egozi, R., and P. Ashmore (2009), Experimental analysis of braided channel pattern response to increased discharge, J. Geophys. Res., 114,, doi: /2008jf Introduction [2] Braided rivers are characterized by a network of unstable anabranches separated by ephemeral bars. One fundamental measure of braided channel pattern characteristics is braiding intensity, which defines the multiplicity of channels in a braided river at a given time and discharge or the complexity of the anabranch network. Previous studies of braided river planform have developed a number of different measurements and indices for braiding intensity [e.g., Brice, 1964; Howard et al., 1970; Rust, 1978; Mosley, 1981; Germanoski and Schumm, 1993] that have been assessed in detail by Egozi and Ashmore [2008]. [3] Braiding intensity measurements usually include all anabranches apparent at any one time in, for example, an aerial photograph of the river. A braiding index based on all these visible channels is referred to here as total braiding intensity (BI T ) [see also Egozi and Ashmore, 2008]. BI T is defined as the number of wetted channels counted and averaged over a number of cross sections (rather than all 1 Department of Geography, Social Science Centre, University of Western Ontario, London, Ontario, Canada. 2 Currently at Soil Erosion Research Station, Ministry of Agriculture and Rural Development, Ruppin Institute, Emek-Hefer, Israel. Copyright 2009 by the American Geophysical Union /09/2008JF channels, both wet and dry), and consequently is sensitive to the flow level at which the measurement is made. Alternatively, braiding intensity may be conceived as referring to the network of channels that is transporting bed material load, i.e., that portion of the network that is actively involved in the channel morphodynamics at a given time and flow level [Ashmore, 1991a, 2001]. This is referred to as active braiding intensity (BI A ) and computed in a similar way to BI T. [4] Observations in physical models of braided channels [Ashmore, 1991a, 2001; Bertoldi et al., 2006] suggest that at any given time, only a subset of the total channels are actually transporting bed material and actively forming the braided pattern and river morphology, i.e., BI A is always less than BI T and the remaining channels convey water and wash load, but no bed load. The implication is that the braided channel network observed at a given time forms progressively over time by shifting of a few active channels rather than by simultaneous development of all channels. [5] Total and active braiding intensity both correlate positively with discharge and stream power [Howard et al., 1970; Mosley, 1981; Ashmore, 1991a; Robertson-Rintoul and Richards, 1993] on the basis of both observations of natural rivers and on physical model experiments. Ashmore [1991a] found that BI A in physical models reached an upper limit beyond which further increases in stream power had no further effect on BI A. 1of15

2 [6] Fractal analysis of different braided morphologies has shown that within a given river, channel pattern characteristics are self similar over a limited range of scales [Sapozhnikov and Foufoula-Georgiou, 1996, 1997; Walsh and Hicks, 2002]. In addition, braiding intensity remains fairly stable because with increasing discharge inundation of islands occurs at a rate compensating for the wetting of new channels [Walsh and Hicks, 2002]. Furthermore, Sapozhnikov and Foufoula-Georgiou [1997] suggested that there is also internal dynamic scaling so that the same processes operate over a range of scales within the system from which it is inferred that small-scale processes are controlled by largerscale processes within the system. This provides some general conceptual physics that sets a context for the development of braiding, but it does not provide insight into actual mechanisms responsible for this behavior nor the nature of the overall controls of braiding intensity and the active channel network. [7] We hypothesize that 1) braiding intensity (both total and active) is a regime or equilibrium property of a river which is adjusted to the imposed flow regime with both BI T and BI A having upper limits imposed by the available discharge or energy. 2) Total braiding intensity develops progressively as a consequence of the instability of the (less extensive) active channel network. Neither of these two fundamental aspects of braided river morphology and processes have been confirmed by systematic experimentation and linked into an overall picture of braided pattern development and bar-scale unit processes [e.g., Ashmore, 1991b, 1993; Ferguson, 1993]. Here we report the results of physical model experiments used to investigate these ideas by (1) simultaneously measuring BI T and BI A at different channel-forming discharge to establish whether there is a consistent relationship between them and with total discharge and stream power; (2) observing the temporal adjustment and development of BI T and BI A to step increase in channel-forming discharge to assess whether an equilibrium value is reached and how quickly this occurs; and (3) mapping the channel pattern development over time to describe the processes by which the active and total channel system develops over time to produce the observed braided channel network morphology. [8] After explaining the experimental procedure the paper discusses the overall response of braid indices to step increases in discharge and shows the differing adjustment times for BI T and BI A and the trend toward a stable value of both indices and of the ratio of the two. The paper then describes the morphodynamic processes involved in the adjustment and the development of BI T by progressive migration and avulsion of the active channel(s). The discussion shows the similarity with other recent analyses of braided river planform properties in relation to discharge and stream power, and the likely link to bifurcation dynamics and asymmetry. The paper ends with concluding remarks, which emphasize the importance of the main active channel in dominating the dynamics of the braided channel pattern. 2. Experimental Methods 2.1. Physical Modeling [9] Physical models, while not necessarily exact scale models of a particular river or reach, have been used extensively in the study of braided river morphodynamics [e.g., Schumm and Khan, 1972; Hong and Davies, 1979; Ashmore, 1982, 1991a; Ashmore and Parker, 1983; Federici and Paola, 2003; Bertoldi and Tubino, 2005]. This study uses a physical model and controlled set of experiments to test the ideas raised in the previous section. In a physical model both BI A and BI T can be observed simultaneously under the same conditions of grain size distribution, stream power and sediment supply and at a discharge known to have formed the observed channel pattern, with minimal historical effect on the morphology. This eliminates some of the uncertainties associated with field-based investigations of braided channel patterns. Also, the use of physical models provides a high temporal resolution of channel pattern change on an accelerated time scale relative to natural streams. [10] The physical model experiments were conducted in a flume 3 m wide, 18 m long, and 0.3 m deep and filled with a 0.15 m thick layer of sediment (Figure 1). The whole flume can be tilted to adjust the slope between values of 0.5 and 2.5 percent. Water is pumped into the flume at a rate of 1 3ls 1. The sediment was a mixture of grain sizes between 0.1 and 8 mm with D 50 of 1.2 mm and D 90 of 3.6 mm (Table 1). Sand leaving the end of the flume was recirculated, along with some water, from the tail tank and fed back into the flume (recirculation time from tail tank to sediment feed is about 25 s) via a vibrating (to aid feeding of wet sand) mesh tray that drained the remaining water so that only sand was fed back to the flume. In this way the sediment feed rate varies naturally and over the long-term matched the sediment transport rate in the model (for more details see Egozi and Ashmore [2008]). [11] There were three consecutive experiments each with a different constant channel-forming discharge but identical slopes of (Table 1). Therefore, total stream power differs between the experiments because of differences in discharge alone. The experiments were run in sequence of progressively increasing discharge: 1.4 ls 1 (experiment 7); 2.1 ls 1 (experiment 8), and 2.8 ls 1 (experiment 14). Prior to the first experiment, the sediment in the flume bed was mixed and leveled, and a straight channel with a trapezoidal cross section was cut with top width of 0.5 m and depth of m deep along the center of the flume. The dimensions of this channel were calculated to just accommodate the planned discharge without going overbank. The bed was not reflattened between the successive experiments so that the channels in experiments 8 and 14 developed from the river topography at the end of the previous experiment to simulate the adjustment to increased channel-forming discharge in an established braided pattern. The three experiments, each at a different constant discharge, were run for approximately equal time (70 hours; Table 1). The duration of the experiments was designed to provide time sufficient for adjustment of the braiding intensity to the prevailing discharge (phase 1) and for subsequent variation in channel pattern to establish a long-term average braiding intensity at that discharge (phase 2) and so observe the interaction between total and active braided networks Data Collection [12] The experimental data were collected in a 12 m long section of the flume beginning 5 m downstream of the 2of15

3 Figure 1. (a) Side view of the University of Western Ontario experimental flume. Note that the figure is not to scale. (b) flume bed during experiment (looking upstream) (c) A braided morphology (North Saskatchewan River, Jasper National Park, Alberta, Canada; courtesy of T. Gardner) similar to model channel pattern. The main active channel (MACh) widths are 0.3 and 10 m, respectively. entrance so as to minimize any entrance and sediment feed effects on the channel pattern (Figure 1). This 12 m length is more than 10 times the average wetted width of the braided channels (Table 1), which provides sufficient length to average out local variations and sampling effects on braided pattern and braiding intensity measurements [Egozi and Ashmore, 2008]. Data on channel pattern development were collected along the study reach over the 70 hours of run time by direct observation and interpretation of vertical photographs. [13] Near-vertical overhead images of the planform were captured throughout the experiments by two wide-angle Table 1. Experiments Parameters a Mean BI A Mean AWW BI T n BI (m) Q (ls 1 ) S F (%) W (W/m) T (hours) D 50 (mm) D 84 (mm) D 90 (mm) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 84 =D 16 Experiment a BI A and BI T values are averages calculated for the duration of phase 2 of each experiment; n BI is the total number of cross-sectionpmeasurements ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of braiding intensity. AWW denotes average wetted width, calculated as the ratio between total wetted area and reach length. The ratio D 84 =D 16 is the standard deviation that shows the degree of sediment mixture homogeneity. 3of15

4 Table 2. Hydraulic Parameters of the MACh a Experiment S B (%) d (m) w/d U (ms 1 ) q We Fr Re Re p a Hydraulic parameters of different experiments (the values are estimated for the main active channel (MACh), nonactive channels show lower values). S B denotes channel bed slope; d denotes average water depth which is determined by water levels extracted from the images and overlaying them on topographic crosses sections; w/d denotes width-depth ratio; U denotes average velocity calculated on the basis of Parker and Peterson s [1980] formula for Chezy C parameter for gravel bed channels; q denotes Shields shear stress defined as the ratio between bed shear stress (t 0 = ds B gr w ) and expression of resistance, (r s r w )gd 50, where r s is particle density (2630 kgm 3 ), r w is water density (1000 kgm 3 ), g is acceleration due to gravity (9.8 ms 2 ), and D 50 is the median grain size in the bed; We is the Weber Number defined as r w U 2 d/s, where s is water surface tension (0.063; given in Nm 1 p ffiffiffiffiffi ); Fr is the Froude Number defined as U/ gd ; Re is the flow Reynolds Number defined as Ud/v, where n is the water kinematic viscosity ( at 20 C); Re p is the particle Reynolds Number p ffiffiffiffiffiffiffiffiffidefined as U* D 90 /v, where U* denotes shear velocity defined as t 0 =r, D90 is particle size coarser than 90% of bed sediment size. digital cameras (Olympus 5060) mounted 3 m above the flume (Figure 1). Each camera covered the full width of the flume and a length of approximately 5.4 m, with 0.5 m overlap between the two cameras. The cameras were controlled remotely by computer using the program PTC camera controller (Pine tree computing, 2003, available at asp) and captured images at 15 min intervals. The images were then ortho rectified to eliminate image distortion, using ERDAS Imagine Orthobase Pro V8.5.1 (for more details see Egozi and Ashmore [2008]). The ortho images were used for mapping channel pattern development throughout each experiment. [14] Braiding indices were measured by direct observation every hour, at which time the total number of channels per cross section (BI T ), and the number of active channels (i.e., channels transporting bed sediment) per cross section (BI A ) were recorded. Thirteen cross sections were established 1 m apart along the study reach and a laser level line was used to mark each section during sampling. The observations were done twice, once from each side of the flume, to assure accuracy of observations of active braiding intensity across the 3m wide flume. A channel was defined as a path of flowing water with definable boundaries (Figures 1b and 1c). An active channel was defined as a channel in which movement of bed material was observed at successive cross sections during the time of observation (less than 1 min). Typically the channel network consisted of one main channel and a number of smaller secondary anabranches, with a range of dimensions carrying flow but not necessarily bed load (Figures 1b and 1c). The main active channel (MACh) is readily identified because it is substantially wider with larger discharge and velocity (Figure 1b) than any of the secondary anabranches (Table 2). The water in the flume was completely clear so that bed particle movement was easy to determine and was checked with tracer particles [e.g., Pyrce and Ashmore, 2003]. Fluorescent painted particles of the finest size found in the bed material mixture were seeded in anabranches which were identified as nonactive. These anabranches were then illuminated with a UV lamp to confirm that no movement occurred. We prefer this direct observation to the indirect (but spatially continuous) threshold depth (dye intensity) method of Gran and Paola [2001] which is based on uniform grain size and threshold depth and needs extensive calibration. The direct method also provides results comparable with those of Ashmore [1991a] and Bertoldi et al. [2006]. 3. Results 3.1. Relationship Between Braiding Intensity and Channel-Forming Discharge [15] When grouped for each experiment, the hourly BI T and BI A data show distinct differences in channel pattern between the three runs, with both indices showing higher means and greater variation and range with increasing total discharge (Figure 2 and Table 1). The modal values of BI T (or BI A ) are 2(1), 2 3(1), and 3 5(2) in experiments 7 (Q chf = 1.4 ls 1 ), 8 (2.1 ls 1 ) and 14 (2.8 ls 1 ), respectively. Maximum BI T values are more than twice the maximum BI A values. Only occasionally, at individual cross sections, was BI A equal to BI T and this occurred only when BI T was 3 or less. These results from the systematic experiments confirm, over a range of channel-forming discharges, the previous preliminary observations [e.g., Stojic et al., 1998; Ashmore, 2001] that the braided channel network is only partially active at any given time and location Time Development of Braiding Intensity [16] In each experiment, BI T increased progressively from the beginning of the experiment (phase 1) until reaching a stable value (phase 2) but with substantial temporal variability even in phase 2 (Figure 3). The initial increase in BI T in experiment 7 is because of the formation of the braided pattern from an initial straight channel. In experiments 8 and 14, this increase in braiding intensity is a response to the Figure 2. Statistics of variation in total and active braiding intensity developed in each of three experiments (experiments 7, 8, and 14) with different constant discharges. 4of15

5 Figure 3. Temporal variations of mean BI T and BI A during each constant discharge experiment and in response to step increases in discharge between experiments. The vertical dashed line separates phases 1 and 2 (see text) of each experiment and the horizontal dashed lines are the overall mean values of phase 2 for each experiment. step increase in discharge and consequent channel pattern adjustment. In experiments 7 and 8, there is a fairly clear divide, marked by a BI T maximum, between the phase 1 of increasing BI T and the subsequent stable phase 2. A t test on the means indicates that mean BI T of the first phase of the experiment is significantly different from mean BI T of the second phase in each experiment (p < for experiments 7 and 8; p < 0.05 for experiment 14). The trends in experiment 14 are not as clear as they are in experiments 7 and 8 perhaps because the braided channel pattern in experiment 14 was affected by the main active channel being against the wall of the flume periodically for a significant amount of time during the experiment. [17] At the beginning of phase 1, in experiments 8 and 14, BI T values are lower than those measured at the end of experiments 7 and 8, respectively. This is because the higher discharge drowns the channel network formed at the lower discharge, so submerging bars and merging channels, until a more extensive channel network develops to accommodate the higher discharge. [18] The time to reach the stable value varied among experiments and was shorter at higher discharges. It took approximately 40, 36 and 20 hours to reach a stable mean BI T in experiments 7, 8 and 14, respectively (Figure 3). The longer time for development in experiment 7 is partly because of the necessity to develop a braided pattern from the initial straight channel and also because bed load transport rates are very low, as indicated by BI A averaging less than 1 so that bed load movement was discontinuous along the flume (Figure 3). This discontinuous transport almost disappeared in experiment 8 and did disappear in experiment 14. [19] Active braiding intensity developed very quickly and stabilized within a few hours of the beginning of each experiment (Figure 3). This is a clear contrast with the development of BI T. The consequence is that for most of the duration of each experiment BI A was effectively constant. BI A values measured in our experiment fall within the range of values measured by Ashmore [1991a] (Figure 4), however, we could not reach the upper limit of BI A due limitations in the discharge range of the flume. [20] The gradual development of the braided network (BI T ) demonstrates that new channels continue to be added and abandoned over a significant period of time. However, for a given discharge, a stable average value of BI T is established in equilibrium with the prevailing discharge. The fact that BI A remains essentially constant during this process indicates that BI T develops by sequential, rather than simultaneous, formation of new channels. Once the equilibrium BI T is established, the stable phase is characterized by periodic reoccupation and/or rearrangement (filling, cutting and migrating) of channels but no increase in number (see also Animations S1 S3). 1 The length of the development phase for BI T reflects the geomorphic work 1 Auxiliary materials are available in the HTML. doi: / 2008JF of15

6 that has to be done to create the initial braided network (experiment 7) or to add sufficient number, and total crosssection area, of channels to accommodate the increased discharge of the river (experiments 8 and 14). BI A increases require only sufficient flow within an existing channel to mobilize the bed material and this can be accomplished very quickly after the beginning of the experiment (experiment 7) or following a step increase in discharge. Consequently, adjustment of BI A is rapid because, unlike BI T, it involves very little adjustment of river morphology. However, in the second phase of each run, BI A varied more widely than BI T as the extent of the active network varied within the established channel system and focusing of the flow into the channels made it possible to maintain bed material movement in more than one channel at a time (Figure 3). Figure 4. The unit stream power index values versus mean BI A (modified after P. E. Ashmore (Process and form in gravel braided streams: Laboratory modeling and field observations, unpublished Ph.D. thesis, University of Alberta, Edmonton, Alberta, Canada, 1985, Figure 7-1). w = QS F W 1, where Q is channel forming discharge (m 3 s 1 ), S F denotes flume slope, and W denotes channel width (m) Relation Between BI A and BI T [21] The observed trends in BI T and BI A translate into a consistent pattern of time variation in the BI A /BI T ratio. A time plot of variation in BI A /BI T during each experiment (Figure 5) shows that there is a consistent trend in which BI A /BI T gradually approaches an asymptote of 0.4, regardless of the initial ratio and the overall braiding intensity. This stable ratio of about 0.4 is reached by a gradual increase in BI T to its stable value, while BI A remains constant. This consistent behavior of BI A /BI T and the tendency toward a stable ratio as the channel pattern develops has not been previously reported and may be fundamental to the dynamics of braided stream networks. Variation in the ratio during the first phase was mainly due to changes in BI T, while in the second phase it correlates Figure 5. BI A /BI T temporal variation in experiments 7, 8, and 14. The vertical dashed lines separate the two phases of each experiment. The horizontal dashed lines mark BI A /BI T values of of15

7 more closely with fluctuation in BI A which became more variable once the total channel network was established. [22] Although the overall (time and reach average) ratio of BI A to BI T is constant in the fully developed braided pattern, locally, at individual cross sections, BI A /BI T can range between zero and one. Zero values (no active channels) occurred occasionally because of excessive local widening, local armouring or when BI T was high (>6), when no channels had sufficient flow to move bed material. Redirection of flow by active channel segments upstream produced the concentration of flow needed to reactivate the channels in these areas Morphological Changes During Braiding Adjustments [23] It is apparent from the analysis of the temporal trends in BI T and BI A that the braided network develops progressively over time to a stable BI A /BI T ratio. The geomorphological processes associated with the temporal trends described above are identified with detailed mapping of the braided channel pattern. The analysis focuses on experiment 8 because experiment 7 started from an initial straight channel rather than from an existing braid plain morphology, and braiding intensity (BI) values of experiment 14 were affected by the flume walls for some periods of time, as mentioned above. [24] Development of the channel pattern in the first 36 hours of experiment 8, following the step increase in discharge, is shown in Figure 6. The series of maps shows the active and inactive channel networks at 2 3 hour intervals as the braided pattern developed. Overall, the braided channel pattern configuration progressively adjusted to accommodate the increased flow (from Q = 1.4 ls 1 to Q = 2.1 ls 1 ) by adding new anabranches through shifting of the main active channel by partial avulsion and cutoffs. Partial avulsion refers to the process of switching of the primary flow into a secondary channel (e.g., at an asymmetric bifurcation [Slingerland and Smith, 2004]) while the original main channel retains flow and may also continue to transport bed material (e.g., Figures 6d 6f). At the same time, flow was progressively concentrated into the main channel from partially channelized marginal areas developed while flow exceeded the initial channel capacity (Figures 6c and 6n). The unconcentrated flow over the sand surface along the margins of the braid plain ceased at about T36 (Figure 6n), coinciding with maximum BI T of 4.5. In addition, the sinuosity of the main channel increased from 1.03 to about 1.2 (Figures 6f and 6j) as flow was concentrated into it, and then decreased again to 1.05 (Figure 6n) during phases of cutoff development. Thus pointing out the significance of another mechanism, changes in sinuosity, through which the main channel adjusts and controls the braid plain development. These morphological changes are best seen when pairs of consecutives maps are superimposed (Figure 7), as well as in the Animations S1 S3. [25] At the second stage of experiment 8 (T > 36.5 hours) the braided river was fully developed and conveyed all the flow within the channel network. During this phase the braided channel pattern configuration continued to change although BI A and BI T remained approximately constant on average (Figure 8). The changes in the braided channel pattern continued to occur by partial avulsion (Figures 8e, 8f, 8i, and 8j), which temporarily added active secondary channel segments branching from the main channel, and cycles of increasing/decreasing sinuosity of the main channel (Figures 8e 8j). However, the resulting changes in channel pattern were less pronounced than in phase one and the path of the main channel remained approximately at the same location for long periods (Figures 8i 8k). In addition, the sinuosity of the main channel was limited, ranging between 1.04 and 1.09 (Figures 8j and 8b, respectively). Total braiding intensity fluctuated slightly as flow was alternately collected into, and dispersed from, the main active channel and as larger secondary channels developed, subdivided or became inactive. [26] Details of channel pattern development processes, and fluctuations in network complexity, during the second phase are shown in Figure 9. The network continually changed configuration by local switching of the main channel and formation or abandonment of secondary channels related to migration of the main active channel (Figures 9a and 9b). Formation of a second, large active channel (9b, T = 63.5) drew water from the smaller chute channels which reduced BI T, but increased BI A, for several hours (see also Figures 3 and 8h 8k). This second active channel was later divided by mid channel bar formation which also diverted a portion of the flow into new and previously abandoned chute cutoff channels, so increasing total braiding intensity and shortening the length of the active portion of the second active channel (Figure 9c). These new channels increased flow to the main active channel which underwent a phase of migration, bar development and partial avulsion via new cutoff channels in the downstream area of the flume (Figure 9c number 7) which maintained (and slightly increased) BI T while BI A decreased again. By these processes BI A,BI T and the ratio of the two fluctuated around the long-term average network state. [27] The mapping of channel pattern development shows that adjustment of the braided river to a channel-forming discharge is gradual. In the first stage, some of the flow could not be accommodated by the channel system inherited from the previous experiment that had lower discharge, and therefore spread across the unchanneled margins of the river. A dominant main channel was established and flow began to concentrate into this anabranch via small eroding channels that were subsequently abandoned. Lateral migration of the main channel, along with increases in its sinuosity, expanded the braid plain width and increased BI T by adding more channels until it reached equilibrium with the channel-forming discharge. The main active channel migrated across the river, occupying almost the entire channel area over time, and there were few components of the entire network not associated with, and developed by, the dynamics of the main active channel and associated Figure 6. Development of the braided channel system in experiment 8 following step increase in channel-forming discharge, (a) stable channel pattern at the end of experiment 7, (b) (n) channel development during adjustment period (phase 1). Note that BI A and BI T values refer to the whole research area of the flume (3 12 m) but each map represents an area of 3 10 m. 7of15

8 Figure 6 8of15

9 Figure 7. Superimposed maps of the braided network at consecutive times showing the geomorphological processes observed during the adjustment stage of experiment 8. Here 1 shows the concentration of the flow in the main active channel, 2 shows the increased sinuosity of the main active channel, 3 shows the new chute cutoff channel, 4 shows the obliteration of pseudoanabranches, 5 shows the channel switching, 6 shows the abandonment of secondary channels, 7 shows the lateral migration of the main active channel, and 8 shows the bank erosion. avulsions, cutoffs or bifurcations (Figure 10) (and see animation accompanying the paper). In the second phase, the entire flow was accommodated within the channel system. Partial avulsion continued but was characterized by smaller changes because the sinuosity of the main channel was limited and creation of new channels was more restricted than in the first stage. The channel system continued to be reconfigured, driven by the main active channel, but without any increase in BI T because diversion of flow from one channel was balanced by loss of flow from another in the network that had sufficient channels and total cross-section area to accommodate the entire discharge of the river. 4. Discussion [28] The results of the experiments confirm previous observations [Stojic et al., 1998; Ashmore, 2001] that, on average, BI A is much smaller than BI T, and demonstrate that this is so over a range of channel-forming discharges. Only 9of15

10 Figure 8. Active and inactive anabranches in a braided channel pattern during the second phase of experiment 8 (continuation from Figure 6). Note that BI A and BI T values refer to the whole research area of the flume (3 12 m) but each map represents an area of 3 10 m. parts of the braided channel are active at any one time and in that sense the morphology and braiding processes are not as complex as they may appear from looking at the entire channel network. For much of the time only one channel was continuously active along the length of the flume. Consequently, the channel morphology (braided pattern) apparent at any given time is developed progressively over a period of time, not simultaneously. The results also 10 of 15

11 Figure 9. Superimposed maps of the braided network at consecutive times showing the geomorphological processes observed during the stable stage of experiment 8. Here 1 is the local channel switching, 2 is the diverting water from secondary channels to other or new secondary channels, 3 is a second active channel, 4 is the abandoning cutoff channels, 5 is the midchannel bar deposition, 6 is the reconnecting of two active channels, and 7 is a sequence of bifurcations and confluences. demonstrate experimentally that both active and total braiding intensity (averaged in time and along the reach) are regime characteristics of the river for a particular channelforming discharge or stream power. [29] This study clearly shows, by mapping channel network morphology over time, that the main channel is the core of the braided channel pattern. Similar observations can be made from maps of natural braided river networks (e.g., Santa Clara River [Krumbein and Orme, 1972], River 11 of 15

12 Figure 10. (a) Sequence of migration of the main active channel during phase 1 of experiment 8; (b) time sequence of the configuration of the total braided network, during phase 1 of experiment 8; and (c) channel network configuration at each time period. Feshie [Rodgers et al., 2004]). Field observations [e.g., Krumbein and Orme, 1972; Mosley, 1983], as well as our experiments, indicate that the main active channel conveys the largest portion of the total discharge (between 50 and 95 percent). Therefore flow continuously converges and diverges into and out of the main active channel from, and to, secondary anabranches, while also transporting the bulk of the bed material load. Over time, the main channel is primarily responsible for developing the entire network through migration, partial avulsion and adjustments in its sinuosity. This behavior, in which multiple channel rivers have only one or two active branches, is also true of anastamosing and other anabranching forms [Kleinhans et al., 2008]. The significance of this main channel has been alluded to in past studies of channel pattern changes of River Feshie using air photos [Werritty and Ferguson, 1980] but not documented in detail. The process of partial avulsion (as described in this paper [see also Slingerland and Smith, 2004, Figure 1a, p.260]), has been observed in the field [e.g., Church, 1972; Reinfelds and Nanson, 1993] and 12 of 15

13 Figure 11. BI A /BI T versus dimensionless stream power [Bertoldi et al., 2009] comparing data from experiments with different grain sizeq and ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi stream power. Dimensionless stream power is (QS F )/L ðgdd 3 50 Þ, L is Q 2/5 /g 1/5 [Parker et al., 2007], g is acceleration due to gravity, D is submerged relative density of sediment (1.63), D 50 is median grain diameter of the bed material. described in detail by Leedy et al. [1993]. On the basis of our observations, partial avulsion is limited to the main active channel and to its connected anabranches (Figures 6 and 8). This finding fits with recent advances in understanding the morphodynamics of bifurcations [Bolla Pittaluga et al., 2003; Federici and Paola, 2003; Bertoldi and Tubino, 2005; Tubino and Bertoldi, 2005; Kleinhans et al., 2008] which provide a basis for understanding braided river network dynamics in a more deterministic framework [see Leedy et al., 1993]. [30] In general, bifurcation studies indicate theoretically [e.g., Bolla Pittaluga et al., 2003], experimentally [e.g., Federici and Paola, 2003; Bertoldi et al., 2006] and numerically [Kleinhans et al., 2008] that, beginning from a symmetrical form, bifurcations evolve toward an asymmetrical configuration (for definitions see Federici and Paola [2003]), in which, while both branches of the bifurcation may have flow, only one transports bed material. In addition, Miori et al. [2006] and Kleinhans et al. [2008] show that the development of the channel network can be tied to local, short-term processes at bifurcations, such as the difference between bed elevations at the mouth of the downstream branches, the curvature of upstream channels and local variation in cross-section geometry. The idea that local channel processes are the basis for larger-scale network development is consistent with our observations, particularly in relation to partial avulsion at bifurcations of the main active channel. Local conditions at bifurcations are also affected by upstream supply of sediment [e.g., Bertoldi et al., 2006; Frings and Kleinhans, 2008; Kleinhans et al., 2008] and migration of bars in the upstream channel [Miori et al., 2006; Kleinhans et al., 2008], making prediction of the development of any particular bifurcation very difficult. Sediment supply upstream of the bifurcation in a braided river is often affected by an upstream confluence of two or more merging anabranches. Confluences are characterized with high local bed shear stresses and therefore funnel large amounts of bed material [Ashmore, 1993; Ashmore and Gardner, 2008] keeping the main channel active at most times. This implies that both bifurcations and confluences interact in channel pattern dynamics and development of partial avulsion. [31] The gradual initial increase in BI T, following an increase in channel-forming discharge, agrees with recent braided river experiments [Bertoldi et al., 2006, 2009] showing that the total number of bifurcations gradually increased and then became stable at a given value of total stream power or discharge. Apparently, the total flow is partitioned into additional channels until the network complexity reaches a dynamic equilibrium. The cumulative changes at specific bifurcations at any given time translate to what we have described as partial avulsion. The active braiding intensity is then limited by the mechanics of bifurcations and the division of flow among several channels limiting the number of competent channels and, again, stabilizes at a given discharge. [32] The ratio of active to total braiding intensity, and its asymptotic trend toward a stable value that is typically (Figure 5), is very similar to the observations of Bertoldi et al. [2006, 2009]. They observed a progressive decrease over time in the number of fully active bifurcations (with both branches transporting bed material), and increase in the number of partially (one branch has flow but no bed load) or inactive nodes (flow but no bed load in both branches and in the upstream channel), as the braided pattern developed. The trends then stabilized into an approximately constant proportion of active, partially active and inactive nodes. This is analagous to our observations of gradual stabilization of the BI A /BI T ratio as BI T gradually increased as a result of migration and partial avulsion of the main active channel, creating new anabranches and nodes that were transiently active. [33] Bertoldi et al. [2006, 2009] converted their proportions of types of node activity into BI A /BI T ratios and found values between 0.3 and 0.6 (Figure 11). This is a wider range than we have observed but is in general agreement with our results. The difference in the range of values between the two studies may be explained by differences in bed sediment mobility and sediment supply regimes. Bertoldi et al. [2006, 2009] used a finer, and better-sorted sand (D 50 = 0.63 mm) than was used in our experiments and ran experiments with different sediment feeding rates. Consequently, bed material mobility is higher in Bertoldi et al. s [2006, 2009] experiments at comparable stream power. When plotted together using a dimensionless stream power index [Bertoldi et al., 2009; Parker et al., 2007] the current data plot with the trend in the Bertoldi et al. results (Figure 11) which suggests that there may a universal function describing the trend in BI A /BI T ratio over a range of dimensionless stream power. The upper BI A limit of two [Ashmore, 1991a] may be a scale limit [Ashmore, 2001] that fits to braided rivers with BI A /BI T of between 0.3 and 0.5. The ratio of BI A /BI T in experiments 7, 8 and 14 may represent braided gravel bed streams with relatively low excess stream power that may fit field case studies that observed an overall more stable braided channel pattern [e.g., Fahnestock and Bradley, 1973; Nicholas and Sambrook Smith, 1998]. On the other hand, braided rivers with more mobile bed material may have higher BI A /BI T 13 of 15

14 values. In these cases of higher bed material mobility, there is a greater probability of maintaining some bifurcations that are fully active (both branches transport bed material) [Bertoldi et al., 2006] and BI A may reach a value of two or higher. Bertoldi et al. [2009] report BI A up to 3 in some cases. In that case the braided channel pattern may be more dynamic as also observed in field studies [e.g., Fahnestock and Bradley, 1973; Maizels, 1979; Goff and Ashmore, 1994]. The general finding that the ratio BI A /BI T tends to develop over time to a stable value for given conditions of formative discharge, valley slope and grain size distribution, seems to be true for most braided rivers and is significant to our understanding of how braided rivers work. [34] The fact that BI A is less than two in these physical models of gravel braided rivers, implies that the overall morphodynamics of braiding may not be substantially different from that of single-thread channels [see also Kleinhans et al., 2008]. A recent study [Tal and Paola, 2007] used physical models to show how vegetation altered a braided morphology into a single dominant channel. In light of the results of this study, which shows that a braided pattern is basically controlled by one active channel, it is possible that vegetation enhances the stability of a natural existing dominant channel configuration rather than controlling and organizing the flow and channel pattern [Tal and Paola, 2007] and closing off the secondary channels. [35] The concept of one dominant channel in a braided pattern seems to be valid, also, when examining the reverse case for which a decreased discharge is applied. Observations in the field at Alpine gravel bed braided streams at the end of a snowmelt season when the total flow is low shows that the braided channel converges into a few single thread channels [Luchi et al., 2007, Figure 3] and chute channels are obliterated. However, decrease in the discharge due to severe alterations of the flow regime [e.g., Surian, 1999; Surian and Rinaldi, 2003; Hicks et al., 2004] may cause incising of the MACh relative to the braided network, and perhaps, up to the extreme case where BI A /BI T equals unity. This process can be accelerated with the invasion of vegetation which increases the bank stability [e.g., Tal et al., 2004]. [36] These gravel braided rivers might be conceived of as very unstable single channels. In that case single-channel theory, concepts and methods [e.g., Struiksma et al., 1985; Tubino and Seminara, 1990] could be applied usefully to braided channels [Ashmore, 2001; Luchi et al., 2007]. The extent to which this is so in all braided rivers, and the same processes are at work, is a significant question that requires field observations along with further experimentation and use of models (physical and numerical) over a wider range of scales. 5. Conclusions [37] The study examines experimentally, using smallscale physical models, the regime response of braided channel pattern (total and active braiding intensity indices) to step increases in channel-forming discharge. The study identifies and describes the processes of adjustment that affect the variation of braided channel pattern (i.e., changes in braiding intensity) at a reach scale and the functioning of the braided river channel network. From the experimental results we conclude that (1) active braiding intensity (BI A ) is always less than total braiding intensity (BI T ), only limited parts of the network were active at any given time during channel-forming discharge; (2) the total channel network forms progressively over time by migration and relocation of the active channels and, in these experiments, the average number of active channels in the reach did not exceed two; (3) pattern development is closely tied to, and limited by, partial avulsion, migration and changes in sinuosity of a single main active channel, which forms most of the total braided network; (4) BI A and BI T are both regime properties of the river which adjust to stable values for a given channel-forming discharge; (5) BI A adjusts quickly to a step change in channel-forming discharge because it reflects mobilization of the bed and banks by increased flow in a limited extent of the existing channel network; (6) BI T responds gradually and slowly to a step change in channel-forming discharge because BI T reflects the history of channel development and migration of the main active channel, and the addition of new channels needed to convey the imposed discharge, which also sets the upper limit for BI T ; and (7) BI A /BI T ratio gradually approaches a stable value (0.4) over time and can be related to the dynamics of channel bifurcations which tend to evolve to an asymmetric state in which both branches convey water but only one branch conveys bed load. [38] Acknowledgments. This research was funded by an NSERC grant awarded to P. Ashmore and supported by a Canada Foundation for Innovation grant used in constructing the flume. R. Egozi was partially supported by an Ontario Graduate Scholarship. We thank Tobi Gardner for help with flume setup and experiments. The authors appreciate Murray Hicks, Maarten Kleinhans, and an anonymous reviewer for comprehensive commentary which improved this manuscript and Rob Ferguson (assistant editor) for additional guidance. We are grateful to Patricia Connor for her diligent and professional work on the diagrams. References Ashmore, P. E. (1982), Laboratory modelling of gravel braided stream morphology, Earth Surf. Processes Landforms, 7, Ashmore, P. E. (1991a), Channel morphology and bed load pulses in braided gravel-bed streams, Geogr. Ann. Ser. A, 73(1), 37 52, doi: / Ashmore, P. E. (1991b), How do gravel bed rivers braid?, Can. J. Earth Sci., 28, Ashmore, P. E. (1993), Anabranch confluence kinetics and sedimentation processes in gravel braided streams, in Braided Rivers, edited by J. L. Best and C. S. Bristow, pp , Geol. Soc., London. Ashmore, P. E. (2001), Braiding phenomena: Statics and kinemetics, in Gravel Bed Rivers V, edited by P. M. Mosley, pp , N. Z. Hydrol. Soc., Christchurch, New Zealand. Ashmore, P. E., and T. Gardner (2008), Unconfined confluences in braided rivers, in River Confluences, Tributaries and the Fluvial Network, edited by S. Rice, A. Roy, and B. L. Rhoads, pp , Wiley, Chichester, U. K. Ashmore, P. E., and G. Parker (1983), Confluence scour in coarse braided streams, Water Resour. Res., 19, , doi: /wr019i002p Bertoldi, W., and M. Tubino (2005), Bed and bank evolution of bifurcating channels, Water Resour. Res., 41, W07001, doi: /2004wr Bertoldi, W., S. Miori, M. Salvaro, L. Zanoni, and M. Tubino (2006), Morphological description of river bifurcations in gravel bed braided networks, paper presented at International Conference on Fluvial Hydraulics, Lisboa, Portugal, 6 8 Sept. Bertoldi, W., L. Zanoni, and M. Tubino (2009), Planform dynamics of braided streams, Earth Surf. Processes Landforms, 34, Bolla Pittaluga, B. M., R. Repetto, and M. Tubino (2003), Channel bifurcation in braided rivers: Equilibrium configurations and stability, Water Resour. Res., 39(3), 1046, doi: /2001wr Brice, J. C. (1964), Channel patterns and terraces of the Loup Rivers in Nebraska, U.S. Geol. Surv. Prof. Pap., 422-D, of 15

15 Church, M. (1972), Baffin Island Sandurs: A Study of Arctic Fluvial Processes, Bulletin 216, 208 pp., Dep. of Energy, Mines and Resour., Ottawa, Ont. Egozi, R., and P. E. Ashmore (2008), Defining and measuring braiding intensity, Earth Surf. Processes Landforms, 33(14), , doi: /esp Fahnestock, R. K., and W. C. Bradley (1973), Knik and Matanuska Rivers, Alaska: A contrast in braiding, in Fluvial Geomorphology, edited by M. Morisawa, pp , State Univ. of N.Y., Binghamton, N.Y. Federici, B., and C. Paola (2003), Dynamics of channel bifurcations in noncohesive sediments, Water Resour. Res., 39(6), 1162, doi: / 2002WR Ferguson, R. I. (1993), Understanding braiding processes in gravel-bed rivers: Progress and unsolved problems, in Braided Rivers, edited by J. L. Best and C. S. Bristow, pp , Geol. Soc., London. Frings, R. M., and M. G. Kleinhans (2008), Complex variations in sediment transport at three large river bifurcations during discharge waves in the River Rhine, Sedimentology, 55, , doi: /j x. Germanoski, D., and S. A. Schumm (1993), Changes in braided river morphology resulting from aggradation and degradation, J. Geol., 101, Goff, J. R., and P. E. Ashmore (1994), Gravel transport and morphological change in braided Sunwapta River, Alberta, Canada, Earth Surf. Processes Landforms, 19, , doi: /esp Gran, K., and C. Paola (2001), Riparian vegetation controls on braided stream dynamics, Water Resour. Res., 37(12), , doi: / 2000WR Hicks, M. D., T. Coulthard, and J. Walsh (2004), Effects of changing flow regime, sediment supply, and Riparian vegetation on the morphology of the braided Waitaki River, New Zealand, Eos Trans. AGU, 85(47), Fall Meet. Suppl., Abstract H42B-01. Hong, L. B., and T. R. H. Davies (1979), A study of stream braiding, Geol. Soc. Am. Bull., 90, Howard, A. D., M. E. Keetch, and C. L. Vincent (1970), Topological and geometrical properties of braided streams, Water Resour. Res., 6(6), , doi: /wr006i006p Kleinhans, M., H. R. A. Jagers, E. Mosselman, and C. J. Sloff (2008), Bifurcation dynamics and avulsion duration in meandering rivers by one-dimensional and three-dimensional models, Water Resour. Res., 44, W08454, doi: /2007wr Krumbein, W. C., and A. R. Orme (1972), Field mapping and computer simulation of braided stream network, Geol. Soc. Am. Bull., 83, , doi: / (1972)83[3369:fmacso]2.0.co;2. Leedy, J. O., P. J. Ashworth, and J. L. Best (1993), Mechanisms of anabranch avulsion within gravel-bed braided rivers: Observations from a scaled physical model, in Braided Rivers, edited by J. L. Best and C. S. Bristow, pp , Geol. Soc., London. Luchi, R., W. Bertoldi, G. Zolezzi, and M. And Tubino (2007), Monitoring and predicting channel change in a free evolving, small Alpine river: Ridanna Creek (north east Italy), Earth Surf. Processes Landforms, 32, , doi: /esp Maizels, J. K. (1979), Proglacial aggradation and changes in braided channel patterns during a period of glacier advance: An Alpine example, Geogr. Ann. Ser. A, 61, , doi: / Miori, S., R. Repetto, and M. Tubino (2006), A one-dimensional model of bifurcations in gravel bed channels with erodible banks, Water Resour. Res., 42, W11413, doi: /2006wr Mosley, P. M. (1981), Semi-determinate hydraulic geometry of river channels, South Island, New Zealand, Earth Surf. Processes Landforms, 6, , doi: /esp Mosley, P. M. (1983), Response of braided rivers to changing discharge, N. Z. J. Hydrol., 22(1), Nicholas, A. P., and G. H. Sambrook Smith (1998), Relationships between flow hydraulics, sediment supply, bedload transport and channel stability in the proglacial Virkisa River, Iceland, Geogr. Ann. Ser. A, 80, , doi: /j x. Parker, G., and A. W. Peterson (1980), Bar resistance of gravel bed streams, J. Hydraul. Div., 106, Parker, G., P. R. Wilcock, C. Paola, W. E. Dietrich, and J. Pitlick (2007), Physical basis for quasi-universal relations describing bankfull hydraulic geometry of single-thread gravel bed rivers, J. Geophys. Res., 112, F04005, doi: /2006jf Pyrce, R., and P. Ashmore (2003), Path length distributions in meandering gravel-bed streams: Results from physical models, Earth Surf. Processes Landforms, 28, , doi: /esp.498. Reinfelds, I., and G. Nanson (1993), Formation of braided river floodplains, Waimakariri River, New Zealand, Sedimentology, 40, , doi: /j tb01382.x. Robertson-Rintoul, M. S. E., and K. S. Richards (1993), Braided channel pattern and paleohydrology using an index of total sinuosity, in Braided Rivers, edited by J. L. Best and C. S. Bristow, pp , Geol. Soc., London. Rodgers, P., C. Soulsby, J. Petry, I. Malcolm, C. Gibbins, and S. Dunn (2004), Groundwater-surface-water interactions in braided river: A tracerbased assessment, Hydrol. Processes, 18, , doi: / hyp Rust, B. R. (1978), A classification of alluvial channel systems, in Fluial Sedimentology, Can. Soc. Pet. Geol. Mem., vol. 5, edited by A. D. Miall, pp , Can. Soc. of Pet. Geol., Calgary, Alberta, Canada. Sapozhnikov, V., and E. Foufoula-Georgiou (1996), Self affinity in braided rivers, Water Resour. Res., 32(5), , doi: /96wr Sapozhnikov, V., and E. Foufoula-Georgiou (1997), Experimental evidence of dynamic scaling and indications of self organized criticality in braided rivers, Water Resour. Res., 33, , doi: /97wr Schumm, S. A., and H. R. Khan (1972), Experimental study of channel patterns, Geol. Soc. Am. Bull., 83, , doi: / (1972)83[1755:esocp]2.0.co;2. Slingerland, R., and N. D. Smith (2004), River avulsion and their deposits, Annu. Rev. Earth Planet. Sci., 32, , doi: /annurev. earth Stojic, M., J. Chandler, P. Ashmore, and J. Luce (1998), The assessment of sediment transport rates by automated digital photogrammetry, Photogramm. Eng. Remote Sens., 64(5), Struiksma, N., K. W. Olesen, C. Flokstra, and H. J. De Vriend (1985), Bed deformation in curved alluvial channels, J. Hydraul. Res., 23(1), Surian, N. (1999), Channel changes due to river regulation: The case of the Piave River, Italy, Earth Surf. Processes Landforms, 24, , doi: /(sici) (199911)24:12<1135::aid-esp40>3.0. CO;2-F. Surian, N., and M. Rinaldi (2003), Morphological response to river engineering and management in alluvial channels in Italy, Geomorphology, 50, , doi: /s x(02) Tal, M., and C. Paola (2007), Dynamic single-thread channels mainted by the interaction of flow and vegetation, Geology, 35(4), , doi: /g23260a.1. Tal, M., K. Gran, B. Murray, C. Paola, and M. Hicks (2004), Riparian vegetation as primary control on channel characteristics in multi thread rivers, in Riparian Vegetation and Fluvial Geomorphology, Water Sci. Appl. Ser., vol. 8, edited by S. J. Bennett and A. Simon, pp , AGU, Washington, D. C. Tubino, M., and W. Bertoldi (2005), Bifurcations in gravel-bed streams, in Gravel-Bed Rivers VI, edited by H. Habersack, H. Piegay, and M. Rinaldi, pp , Elsevier, Amsterdam. Tubino, M., and G. Seminara (1990), Free-forced interactions in developing meanders and suppression of free bars, J. Fluid Mech., 214, , doi: /s Walsh, J., and M. D. Hicks (2002), Braided channels: Self similar or self affine?, Water Resour. Res., 38(6), 1082, doi: /2001wr Werritty, A., and R. I. Ferguson (1980), Pattern changes in a Scottish braided river over 1, 30 and 200 years, in Timescales in Geomorphology, edited by R. A. Cullingford, D. A. Davidson, and J. Lewin, pp , John Wiley, Chichester, U. K. P. Ashmore, Department of Geography, Social Science Centre, University of Western Ontario, 1151 Richmond Street, London, ON N6A 5C2, Canada. R. Egozi, Soil Erosion Research Station, Ministry of Agriculture and Rural Development, Ruppin Institute, Emek-Hefer 40250, Israel. (regozi@ moag.gov.il) 15 of 15