Geometry of meandering and braided gravel-bed threads from the Bayanbulak Grassland, Tianshan, P. R. China

The Bayanbulak Grassland, Tianshan, P. R. China, is located in an intramontane sedimentary basin where meandering and braided gravel-bed rivers coexist under the same climatic and geological settings. We report and compare measurements of the discharge, width, depth, slope and grain size of individual threads from these braided and meandering rivers. Both types of threads share statistically indistinguishable regime relations. Their depths and slopes compare well with the threshold theory, but they are wider than predicted by this theory. These findings are reminiscent of previous observations from similar gravel-bed rivers. Using the scaling laws of the threshold theory, we detrend our data with respect to discharge to produce a homogeneous statistical ensemble of width, depth and slope measurements. The statistical distributions of these dimensionless quantities are similar for braided and meandering threads. This suggests that a braided river is a collection of intertwined threads, which individually resemble those of meandering rivers. Given the environmental conditions in Bayanbulak, we furthermore hypothesize that bedload transport causes the threads to be wider than predicted by the threshold theory.


Introduction
The morphology of alluvial rivers extends between two endmembers: in meandering rivers, the flow of water and sediments is confined in a single thread, whereas in braided rivers the flow is distributed into intertwined threads separated by bars (Fig. 1; Leopold and Wolman, 1957;Fergu-son, 1987;Ashmore, 1991;Schumm, 2005;Kleinhans and van den Berg, 2011).
Linear stability analyses, supported by laboratory experiments, explain how bedload transport generates bars, and favors the formation of meandering or braided patterns (Parker, 1976;Fredsøe, 1978;Fujita and Muramoto, 1985;Devauchelle et al., 2007;Ashmore, 1991;Zolezzi et al., 2012).This mechanism proves more efficient in wide and shallow channels.Field measurements indicate that the bankfull aspect ratio (ratio of width to depth) of braided rivers is usually much larger than that of meandering ones, thus suggesting that the bar instability is indeed responsible for braiding (Parker, 1976;Fredsøe, 1978;Fujita and Muramoto, 1985;Devauchelle et al., 2007;Ashmore, 1991;Zolezzi et al., 2012).What exactly controls the aspect ratio of an alluvial river remains an open question, although sediment discharge and riparian vegetation seem significant in this respect: high sediment load and weak vegetation both favor wider and shallower channels, and often induce braiding (Smith and Smith, 1984;Gran and Paola, 2001;Tal andPaola, 2007, 2010;Brauderick et al., 2009;Dijk et al., 2012;Métivier and Barrier, 2012).
In a fully developed braided channel, emerged bars separate the threads from each other (Fig. 1), and the very definition of bankfull conditions becomes ambiguous.Most authors treat the channel as a whole by defining lumped quantities, such as the total channel width or the average water depth (Métivier and Barrier, 2012).Conversely, few studies focus on the morphology of braided and meandering channels at the level of individual threads (Church and Gilbert, 1975;Mosley, 1983;Ashmore, 2013;Gaurav et al., 2015).In sand-bed rivers, the geometry of braided threads appears to be indistinguishable from that of meandering ones.This observation accords with recent laboratory experiments (Seizilles et al., 2013;Reitz et al., 2014).To our knowledge, this similarity has not been fully investigated in gravel-bed rivers.
Here, we report on measurements in the Bayanbulak Grassland, Tianshan Mountains, P. R. China, where tens of meandering and braided gravel-bed rivers develop in the same environment.After comparison with other data sets from the literature, we compare the morphology of braided and meandering threads in our data set.Finally, we rescale our measurements based on the threshold theory to generate and analyze a single statistical ensemble from rivers highly dispersed in size (Glover and Florey, 1951;Henderson, 1963;Seizilles et al., 2013;Gaurav et al., 2015).

Field site
The Bayanbulak Grassland is an intramontane sedimentary basin standing at an elevation of about 2500 m in the Tianshan Mountains (Fig. 2).Two main wetlands, the Qong Yulduz basin (known as the Swan Lake in Chinese), and the Kizik Yulduz basin, are distributed around the main Kaidu River.They are immediately surrounded by sloping meadows (slope S ∼ 0.01), themselves enclosed with the Tianshan Mountains which provide water to the Kaidu River (Zhang et al., 2002).The hydrology of the basins is controlled by snowmelt and summer orographic precipitations (Zhang et al., 2002;Yang and Cui, 2005).Snow accumulates from November to March, and starts melting in April, inducing the water discharge to rise in all rivers (Zhang et al., 2007).Orographic precipitation takes over in summer (be-  tween 260 and 290 mm), and the discharge continues to rise until August (Fig. 3).
The morphology of the Bayanbulak rivers varies between highly meandering (sinuosity above 1.3 to 1.5) and braided, and the same river often switches from one to the other along its course (Figs. 4 and 5).The rivers span about 4 orders of magnitude in discharge, and about 2 in width (Fig. 6).Although a variety of grass species grow in the basin, their influence on the channel morphology is probably moderate (Zhang et al., 2002;Andrews, 1984;Métivier and Barrier, 2012).Finally, most rivers flow over gravel, whose size distribution does not vary significantly over the basin (Fig. 6).All these features combine to make the Bayanbulak Grassland an ideal field site to investigate the morphology of gravel-bed rivers.

Method
We carried out two field campaigns in July 2012 and July 2013, during the high-flow season to compare the geom-  (Church and Rood, 1983;Parker et al., 2007;King et al., 2004;Ashmore, 2013).
etry of braided and meandering threads (Fig. 3).We treated the threads of braided rivers individually, based on the wetted area at the time of measurement (Fig. 1).We measured the cross section geometry, the discharge, the grain-size distribution and the slope of the threads from as many rivers, spanning as broad a range in discharge, as possible.We chose the sections at random, according to their accessibility, our purpose being to collect a statistically significant data set.
To measure the cross section and the water discharge of large rivers, we used a 2 Mhz acoustic Doppler current profiler (ADCP, Teledyne-RDI StreamPro).The instrument was mounted on a raft and cross sections were performed from which we extracted both the geometry and the discharge of the threads.
In shallower rivers, we used wading rods and rulers to measure the thread geometry.The mean surface velocity was measured using floats.The average velocity was obtained from the surface velocity using a correction factor of 0.6 (Sanders, 1998;Gaurav et al., 2015).The discharge was obtained by the product of the average velocity with the wetted area.
Repeated ADCP profiles across the same section show that discharge, width and depth measurements are all reproducible within less than 15 %.Manual measurements yield an uncertainty of about 2 % for width, 12 % for depth and 25 % for velocity.The resulting uncertainty on discharge is less than 40 % for both methods.
We used a Topcon theodolite with a laser rangefinder to measure the long profile of the threads, and estimate their slope.The length of topographic profiles varies from 100 m for small braided threads to more than 3 km for one meandering thread.Uncertainties on the location of the theodolite and atmospheric inhomogeneities curtail the precision of long-distance profiles.For our measurements, we expect the uncertainty on angles to reach 90 .The corresponding absolute uncertainty on the slope of a river is about 5 × 10 −4 .
We measured the grain-size distribution from surface counts.Depending on the size of exposed surfaces, the number of counts ranged from 200 to 500 (Wolman, 1954;Bunte and Abt, 2001).We extracted the median grain size d 50 and the size of the 90th percentile d 90 from these distributions.
Finally, the sinuosity of the threads was measured using the topographic profiles when available.When these were not available, we used Google images and calculated the sinuosity from 1 km long stretches centered on the measurement site.The Bayanbulak rivers we surveyed exhibit two very distinct planforms.Single-thread rivers are, on average, highly meandering with a sinuosity of 1.5 ± 0.2 (Schumm, 2005).The braided rivers we surveyed have a total braiding index ranging from 3.3 to almost 11.2.As our objective is to compare these two endmembers, we ignored rivers with intermediate wandering morphology (Church, 1983).Overall, our data set is composed of 92 measurements of width, depth, average velocity, discharge, slope and grain size, among which 53 correspond to braided-river threads (Table 1), and 39 to meandering-river threads (Table 2).

Regime equations
Figure 6 compares our measurements to four other sources.Three of them, the compendiums of Parker et al. (2007), Church and Rood (1983) and King et al. (2004) include measurements from single-thread rivers.The fourth one corresponds to measurements on individual threads of the braided Sunwapta River (Ashmore, 2013).These sources are hereafter referred to as the GBR data set.
The Bayanbulak threads are widely dispersed in size (0.6 ≤ W ≤ 35 m) and discharge (0.002 ≤ Q ≤ 51 m 3 s −1 ).On average, they are smaller than the GBR threads.The median grain size of the Bayanbulak threads d 50 0.013 m is finer (the standard deviation of the d 50 is σ d 50 ∼ 0.008 m).Our data set therefore extend the GBR ones towards smaller threads with finer sediments.
We now consider the empirical regime equations of individual threads (Fig. 7).To facilitate the comparison between the GBR data set and our own, we use dimensionless quantities, namely W/d 50 , H /d 50 , S and Q * = Q/ g d 5 50 , where g is the acceleration of gravity.Not surprisingly, the geometry of a thread is strongly correlated with its water discharge: its width and depth increase with discharge, while its slope decreases.At first sight, these trends are similar for meandering and braided threads.They also compare well to the GBR data set, although the Bayanbulak threads are slightly wider than the GBR ones on average.The measurement uncertainty, although significant, is less than the variability of our data, except for slopes smaller than about 5 × 10 −3 .Despite considerable scatter, both our measurements and the GBR data sets gather around straight lines in the log-log plots of Fig. 7, suggesting power-law regime equations: where α w , α h , α s , β w , β h and β s are dimensionless parameters.To evaluate them, we use reduced major axis regression (RMA) instead of least square regression because the variability of our data is comparable along both axes (Sokal and Rohlf, 1995;Scherrer, 1984).The resulting fitted coefficients are reported in Table 3.The scatter in the slope measurement is too large to provide significant estimates of the slope coefficients α s and β s .At the 95 % confidence level, the regime relationships of meandering and braided threads cannot be distinguished.Similarly, the depth of the Bayanbulak threads cannot be distinguished from those of the GBR threads.Conversely, the Bayanbulak threads are significantly wider than the GBR threads with respect to their median grain size.So far we have made the width, depth and discharge dimensionless using d 50 as the characteristic grain size of the sediment.This choice, however, is arbitrary (Parker et al., 2007;Parker, 2008).Large grains are arguably more likely to control the geometry of the threads than smaller ones, and a larger quantile might be a better approximation of the characteristic grain size.For comparison, we rescaled our measurements using d 90 instead of d 50 , and repeated the above analysis.Our conclusions are not altered significantly by this choice of characteristic grain size (Table 3).

Detrending
So far, we have found that the empirical regime equations of meandering and braided threads are statistically similar.To proceed further with this comparison, we would like to convert our measurements into a single statistical ensemble.We thus need to detrend our data set with respect to water discharge, based on analytical regime equations.Following Gaurav et al. (2015), we propose to use the threshold theory to do so.
This formulation is similar to the one proposed by Parker et al. (2007), but for two points.First, Eqs.(2) to (4) represent a threshold channel, whereas Parker et al. (2007) extend the theory to active channels.Second, the formulation of Glover and Florey (1951) uses a constant friction coefficient in the momentum balance, whereas Parker et al. (2007) use a more elaborate friction law.Here we use the simplest formulation, as the variability of our data overshadows these differences (Métivier and Barrier, 2012).The dashed lines on Fig. 7 represent Eqs. ( 2) to (4).On average, the Bayanbulak threads are wider, shallower and steeper than the corresponding threshold thread.However, the theory predicts reasonably their dependence with respect to discharge, thus supporting its use to detrend our data.Accordingly, we define a set of rescaled quantities as follows: Here the coefficients C W , C H , C S correspond to the prefactors in square brackets of Eqs. ( 2) to (4).We used the typical values reported above for the coefficients that do not vary in our data set.
Figure 8 shows the relationship between the rescaled thread geometry and its dimensionless discharge, using d 50 to approximate the characteristic grain size d s .The new quantities W * , H * and S * appear far less dependent on the water discharge than their original counterpart, although a residual trend remains for all of them.Using ordinary least squares, we fit power laws to our rescaled data to evaluate this residual trend.We find W * ∝ Q −0.19±0.03* and H * ∝ Q −0.10±0.05* for the Bayanbulak threads, and for the GBR threads.The width of the Bayanbulak threads shows the strongest correlation, yet even this correlation is mild.Finally, slopes are more strongly correlated with discharge than width and depth both for the GBR threads (S * ∝ Q 0.21±0.05* ) and the Bayanbulak threads (S * ∝ Q 0.39±0.11* ).However, most of the difference between the Bayanbulak and GBR threads is due to slopes well below the measurement precision.In all cases, the scatter is large, and all correlations fall within the standard deviation of the data set.

Thread geometry
We now analyze our rescaled measurements as a homogeneous statistical ensemble (Fig. 8).The means of the rescaled distributions of width, depth and slope all fall about 1 order of magnitude away from one, and their dispersion around this mean is also about 1 order of magnitude (Table 4).This observation supports the use of the threshold theory to scale the morphology of the Bayanbulak rivers.According to the rescaling Eqs. ( 6) to ( 8) the aspect ratio of a river W/H should be naturally detrended (Fig. 9).Indeed, the correlation coefficient of aspect ratio and discharge is less than 0.01 for all data sets.As expected, the aspect ratio of braided and meandering threads cannot be distinguished at the 95 % level of confidence.Finally, the difference between the width of the Bayanbulak threads and that of the GBR threads also appears in the distribution of aspect ratios: the Bayanbulak aspect ratios are larger than the GBR ones.

Conclusion
Our measurements on gravel-bed rivers in the Bayanbulak Grassland reveal that braided threads are geometrically similar to meandering ones.Their size can be virtually detrended with respect to water discharge using the threshold theory.As a result, their aspect ratio is naturally detrended.These findings accord with recent observations in sand-bed rivers of the Kosi Megafan (Gaurav et al., 2015).They also accord with recent results from rivers of the Ganges-Brahmaputra plain (Gaurav, 2016).
The striking similarity between braided and meandering threads in gravel-bed and sand-bed rivers supports the view that fully developed braided rivers are essentially a collection of threads interacting with each other, rather than a single wide channel segmented by sediment bars.If confirmed, this would suggest that a braid results from the collective behavior of individual threads, the property and dynamics of which would be close to that of meandering threads (Sinha and Friend, 1994;Ashmore, 2013;Reitz et al., 2014).
Our observations, like those of Gaurav et al. (2015) or the GBR data set, are highly dispersed around their average value, which points at the influence of hidden parameters on their morphology.Among those, the intensity of sediment transport is likely to play a prominent role, at least in the case of the Bayanbulak rivers where both vegetation and grainsize distributions are relatively uniform over the grassland.
More specifically, field observations suggest that a heavier sediment load tends to increase the aspect ratio of a thread, other things being equal (Smith and Smith, 1984;Tal and Paola, 2010;Métivier and Barrier, 2012).This proposition remains speculative though, and needs to be thoroughly tested against dedicated field measurements, which we believe should include both braided and meandering threads.Finally, if the sediment discharge is indeed the most prominent parameter after water discharge, its influence on the geometry of a channel should also manifest itself in laboratory experiments.

Figure 4 .
Figure 4. (a) Meandering and (b) braided rivers in the Bayanbulak Grassland.Left panels: field picture; right panels: satellite image (Google Earth).The corresponding locations also appear in Fig. 2.

Figure 5 .
Figure 5. Satellite and panoramic view of a metamorphosis from braided to meandering (Bayanbulak Grassland, 84.578 • E, 42.721 • N, Google Earth).Marker on the satellite image indicates the viewpoint of the panoramic image.Its location also appears in Fig. 2.

Figure 7 .
Figure 7. Dimensionless width, depth and slope of individual gravel-bed threads as a function of dimensionless water discharge.Dashed lines represent the threshold theory.

FFigure 9 .
Figure 9. Aspect ratio of braided and meandering threads from Bayanbulak and the GBR data sets, as a function of rescaled water discharge (Q * ).

Table 1 .
Data gathered for braided-river threads.Latitude (lat) and longitude (long) are in degrees centesimal; measurement stands for measurement type (Fl: float, ADCP: acoustic Doppler current profiler); Q: discharge, Sec: wetted area, V : average velocity, W : width, H : depth, d 50 : median grain size, d 90 : size of the 90th percentile, S: slope.All physical quantities are given in the International System of Units.

Table 2 .
Data gathered for meandering-river threads.Latitude (lat) and longitude (long) are in degrees centesimal; measurement stands for measurement type (Fl: float, ADCP: acoustic doppler current profiler); Q: discharge, Sec: wetted area, V : average velocity, W : width, H : depth, d 50 : median grain size, d 90 : size of the 90th percentile, S: slope.All physical quantities are given in the International System of Units.

Table 3 .
Linear regressions on the log 10 of width and depth as functions of discharge and for two characteristic grain sizes.The confidence level is 95 %.RMA: reduced major axis regression σ β stands for confidence interval on the slope of the regression β.Width: log 10 (W/d s ) = β w log 10 Q * + α w

Table 4 .
Mean and standard deviations of the logarithms of detrended widths, depths and slopes.The aspect ratios is naturally detrended and does not depend on grain size.