Morphology of meandering and braided gravel-bed streams from the Bayanbulak Grassland , Tianshan , China

F. Métivier, O. Devauchelle, H. Chauvet, E. Lajeunesse, P. Meunier, K. Blanckaert, Z. Zhang, Y. Fan, Y. Liu, Z. Dong, and B. Ye Institut de physique du globe de Paris – Sorbonne Paris Cité, Université Paris Diderot, CNRS, UMR7154, 1 Rue Jussieu, 75238 Paris CEDEX 05, France Département de Géologie, UMR8538, CNRS, Ecole Normale Supérieure, 24 Rue Lhomond, 75005 Paris, France Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Beijing, China The States Key laboratory of Cryospheric Science, Cold and Arid Region Environmental and Engineering and Research Institute, Chinese Academy of Sciences, 260 Donggang West Road, Lanzhou, China Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi, China Key Laboratory of Water Environment and Resource, Tianjin Normal University, 393 Binshui West Road, Tianjin 300387, China


Introduction
The morphology of alluvial rivers extends between two end members: in meandering rivers, the flow of water and sediments is confined in a single channel, whereas in braided rivers the flow is distributed into intertwined threads separated by bars (Schumm, 2005).Linear stability analyses, supported by laboratory experiments, explain how bedload transport generates bars, which in turn can grow into a fully developped braided parttern (Parker, 1976;Fredsøe, 1978;Zolezzi et al., 2012).This mechanism proves more efficient in wide and shallow channels.Field measurements indicate that the bankfull aspect ratio of braided rivers is usually much larger that that of meandering ones, thus suggesting that the bar instability is indeed responsible for Figures

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Full braiding (Parker, 1976;Fredsøe, 1978;Zolezzi et al., 2012).What exactly controls the aspect ratio of an alluvial river remains an open question, although sediment discharge and riparian vegetation are significant in this respect: high sediment load and weak vegetation favour wider and shallower channels, and often induce braiding (Smith and Smith, 1984;Gran and Paola, 2001;Tal andPaola, 2007, 2010;Metivier and Barrier, 2012).
In a fully developed braided river, emerged bars separate the threads from each other, and the very definition of bankfull conditions becomes ambiguous.Most authors treat the river as a whole by defining lumped quantities, such as the total river width or the average water depth (Metivier and Barrier, 2012).Conversely, a few studies consider the morphology of individual threads, and compare it to isolated channels (Church and Gilbert, 1975;Mosley, 1983;Gaurav et al., 2015).In sandy braided rivers, the morphology of individual threads appears to be indistinguishable from that of isolated streams from the same environment.This observation accords with recent laboratory experiments (Seizilles et al., 2013;Reitz et al., 2014).To our knowledge, this similarity has not been investigated in gravel-bed braided rivers.
Here, we report on measurements in the Bayanbulak Grassland, Tianshan Mountains, China, where tens of meandering and braided gravel-bed rivers develop in the same environment.After comparison with other datasets from the literature, we compare the morphology of braided and meandering threads in our dataset.Finally, we rescale our measurements based on the threshold theory to generate a single statistical ensemble from streams 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. 1).Two main wetlands, the Qong Yulduz basin (known as the Swan Lake in Chinese) and the Kizik Yulduz basin, are Figures

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Full distributed around the main Kaidu River.They are immediately surrounded by gently 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 streams (Zhang et al., 2007).Orographic precipitation takes over in summer (between 260 and 290 mm), and the discharge continues to rise until August (Fig. 5).
The morphology of the Bayanbulak streams varies between highly meandering and braided, and the same river often switches from one to the other (Figs. 2 and 3).The streams span about four orders of magnitude in discharge, and about two in width (Fig. 4).Various species of grass dominate the vegetation over the entire basins, and their influence on the morphology of the streams is certainly only mild (Zhang et al., 2002;Hey and Thorne, 1986).Finally, most streams flow over gravel, which size distribution does not vary significantly over the basins (Fig. 4).All these features combine to make the Bayanbulak grassland an ideal field site to investigate the morphology of gravel-bed rivers.

Method
To compare the morphology of braided and meandering threads, we carried out two field campaigns in July 2012 and July 2013, during the high-flow season (Fig. 5).We treated the threads of braided rivers as individual channels, based on the wetted area at the time of measurement.We measured the cross-section geometry, the discharge, the grain-size distribution and the slope of as many streams, spanning as broad a range in discharge, as possible.
To measure the cross section and the water discharge of large streams, we used and estimated the vertically-averaged velocity from it (Sanders, 1998;Gaurav et al., 2015).Repeated ADCP profiles across the same section show that discharge, width and depth measurements are all reproducible within less than 15 %.Manual measurements yields 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 streams, and estimate their slope.Uncertainties on the location of the total station and atmospheric inhomogeneities curtail the precision of long-distance profiles.For our measurements, we expect the uncertainty on angle to reach 90 .The corresponding absolute uncertainty on the slope of a river is about 5 × 10 −4 .
Finally, we measured the grain-size distribution from surface counts (Bunte and Abt, 2001), and extracted the median grain size d 50 and the size of the 90th percentile d 90 from these distribution.
Overall, our dataset is composed of 92 measurements of width, depth, average velocity, discharge, slope and grain size, among which 53 correspond to braided-river threads (Table 3), and 39 to meandering threads (Table 4).et al. (2007); Church and Rood (1983) and King et al. (2004), hereafter referred to as GBR.All streams from the GBR dataset are isolated (non braided) threads.
Similarly, their average grain-size d 50 0.013 m is finer (the standard deviation of the d 50 is σ d 50 ∼ 0.008 m).Our dataset therefore extend the GBR one towards smaller channels.
We now consider the empirical regime equations of individual threads (Fig. 6).To facilitate the comparison between the GBR streams and our own, we use dimensionless Figures

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Full quantities, namely W/d 50 , H/d 50 , S and Q * = Q/ gd 5 50 , where g is the acceleration of gravity.Not surprisingly, the morphology 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 isolated and braided threads.They also compare well to the GBR data set, although the Bayanbulak streams 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 (Sect.4).
Despite considerable scatter, our measurements gather around straight lines in the log-log plots of Fig. 6, 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 axis (Sokal and Rohlf, 1995;Scherrer, 1984).The resulting fitted coefficients are reported in Table 1.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 streams cannot be distinguished from those of the GBR ones.Conversely, the Bayanbulak streams are significantly wider than the GBR ones.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 morphology of the river 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 a characteristic grain size (Table 1).Introduction

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Full

Detrending
So far, we have found that the empirical regime equations of isolated 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 dataset 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.
The threshold theory assumes that a river transports its sediment load slowly enough for is bed to be near the threshold of motion (Glover and Florey, 1951;Henderson, 1963;Yalin and Ferreira da Silva, 2001;Seizilles, 2013).Momentum and mass balances then yields power-law regime equations, the original formulation of which reads (Glover and Florey, 1951 where

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This formulation is similar to the one proposed by Parker et al. (2007), but for two points.First, Eqs. ( 2)-( 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 (Metivier and Barrier, 2012).
The dashed line on Fig. 6 represents Eqs. ( 2)-( 4).On average, the Bayanbulak streams are wider, shallower and steeper than the corresponding threshold channel.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)-( 4).We used the typical values reported above for the coefficients that do not vary in our dataset.Introduction

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Full Figure 7 shows the relationship between the rescaled stream morphology 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 ).However, most of the difference between Bayanbulak and GBR streams 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 dataset.

Thread morphology
We now analyze our rescaled measurements as a homogeneous statistical ensemble (Fig. 7).The means of the rescaled width, depth and slope all fall about one order of magnitude away from one, and their dispersion around this mean is also about one order of magnitude (Table 2).This observation support the use of the threshold theory to scale the morphology of the Bayanbulak streams.
The dispersion of the rescaled slope is more significant than that of width and depth.
We believe that, in addition to the technical difficulties associated to the measurement of slope in the field (Sect.3), the dispersion of the grain size explains this scatter.Indeed, gravels are broadly distributed in size, and unevenly distributed over the river bed (Guerit et al., 2014).Since the rescaling for slope involves the grain size d s to the power of 5/4, whereas this exponent is only 1/4 for width and depth (Eqs.6 to 8), we believe the grain-size dispersion impacts more strongly the rescaled slope than the rescaled width and depth.Figures

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Full The means for braided threads and meandering threads differ by less than a factor of two, much smaller than the standard deviation.Fitting lognormal distributions to our data, we find that the meandering and braided channels from Bayanbulak cannot be distinguished from each other, at the 95 % level of confidence.The depth and slope of the Balyanbulak streams are also not significantly different from the GBR ones.Only the width of the Bayanbulak streams is significantly larger than that of the GBR streams.We therefore conclude that, within the natural variability of our observation, meandering and braided streams are morphologically similar.Again, the use of d 90 instead of d 50 as a characteristic grain size does not alter this conclusion.
According to the rescaling Eqs. ( 6)-( 8) the aspect ratio of a stream W/H should be naturally detrended (Fig. 8).Indeed, the correlation coefficient of aspect ratio and discharge is less than 0.1 for all datasets (Table 2).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 streams and that of the GBR streams also appears in the distribution of aspect ratio: the Bayanbulak streams are significantly wider than the GBR ones.

Conclusion
Our measurements on gravel-bed streams in the Bayanbulak grassland reveal that braided threads are morphologically 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 streams (Gaurav et al., 2015).
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 the collective behavior of individual threads, the property and dynamics of which would be close to that of isolated channels.
Our observations, like those of Gaurav et al. (2015) and the GBR dataset, are much 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.More specifically, field observations suggest that a heavier sediment load tends to increase the aspect ratio of a stream, other things being equal (Smith and Smith, 1984;Tal and Paola, 2010;Metivier and Barrier, 2012).This proposition 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 morphology of a channel should also manifest itself in laboratory experiments.Introduction

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Full  Full  2. 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.The difference for the GBR dataset comes from the size of the sample that is different for the two grain sizes.Full  Full  Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | a 2Mhz acoustic Doppler current profiler (ADCP, Teledyne-RDI StreamPro).In shallower streams, we used wading rods, rulers and floats to measure the surface velocity, Discussion Paper | Discussion Paper | Discussion Paper |

Figure 4
Figure 4 compares our measurements to three sources: the compendiums of Parker et al. (2007);Church and Rood (1983) andKing et al. (2004), hereafter referred to as GBR.All streams from the GBR dataset are isolated (non braided) threads.

Table 1 .
Linear regressions on the log 10 of width and depth as functions of discharge and for two characteristic grain sizes.Confidence level is 95 %.RMA: Reduced major axis regression σ β stands for confidence interval on the slope of the regression β.

Table 3 .
Data gathered for braided threads.Latitude (lat) and longitude (lon) are in degrees centesimal; Measurement stands for measurement type (Fl: float, ADCP: Acoustic doppler curent 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 SI units.