Reviewing braiding indices of the river channel in an attempt to establish alternatives

Balai Chandra Das; Aznarul Islam

doi:10.1016/j.mex.2023.102042

. 2023 Feb 2;10:102042. doi: 10.1016/j.mex.2023.102042

Reviewing braiding indices of the river channel in an attempt to establish alternatives

Balai Chandra Das ^a, Aznarul Islam ^b,^⁎

PMCID: PMC9950935 PMID: 36845371

Highlights

•
Existing channel braiding indices considered primarily one-dimensional nature of the channel and bar.
•
Four novel indices were proposed considering the linear and areal dimensions of the channel and bar.
•
Proposed indices focus on the unit-free measures with known limits enabling pragmatic comparison with self and other channels.
•
New methods were tested using field data implying a significant correlation with the existing methods.

Keywords: Braiding index, Bar index, Channel count index, Channel length index, Channel sinuosity

Method name: Braiding indices

Abstract

Complex channel planform especially the dynamics of the multi-thread river is empirically examined using the three major dimensions – bar growth, channel length and channel count. To this end, many indices have been proposed to deal with the complex channel response in the context of sediment-energy synergistic scenarios. The existing methods are primarily concerned with the linear or 1D nature of the channel and bar. The present study introduced the areal or 2-D nature of the channel and bar to capture a more realistic picture because, with same length, area of the bar may differ greatly. Therefore, we proposed four indices on channel braiding taking into consideration the area of the channel and bar. We tested our indices to the 28 reaches of the Damodar River, India that showed a significant correlation (∼80%) with the existing standard method. The major highlights of the methods are outlined as follows.

•
Four novel indices were proposed considering the linear and areal dimensions of the channel and bar.
•
Proposed indices focus on the unit-free measures with known limits enabling pragmatic comparison with self and other channels.
•
New methods were tested using field data implying a significant correlation with the existing methods.

Graphical abstract

Specifications table

Subject area:	Earth and Planetary Sciences

More specific subject area:	Fluvial geomorphology and Hydrology
Name of your method:	Braiding indices
Name and reference of original method:	Brice, J.C. 1964. Channel Patterns and Terraces of the Loup Rivers in Nebraska. Geological Survey Professional Paper 422-D. United States Government Printing Office, Washington. P:1–40. https://pubs.usgs.gov/unnumbered/70043714/report.pdf Friend, P. F., & Sinha, R. 1993. Braiding and meandering parameters. Geological Society, London, Special Publications, 75(1), 105–111. https://doi.org/10.1144/GSL.SP.1993.075.01.05 Germanoski, D., & Schumm, S. A. 1993. Changes in braided river morphology resulting from aggradation and degradation. The Journal of Geology, 101(4), 451–466. https://doi.org/10.1086/648239 Hong L.B., Davies T.R.H. 1979. A study of stream braiding. Geological Society of America Bulletin 90(Part II): 1839–1859. https://doi.org/10.1130/GSAB-P2-90-1839 Howard, A. D., Keetch, M. E., & Vincent, C. L. (1970). Topological and geometrical properties of braided streams. Water Resources Research, 6(6), 1674–1688. https://doi.org/10.1029/WR006i006p01674
Resource availability:	Provided as a supplementary file

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Introduction

Channel planform is the manifestation of the processes operating within a river course depending upon the lithology on which the channel is engraved, land use and land cover of the basin, and the two-way feedback mechanisms between forms and processes [6]. All these have made understanding river channels very complex but increasing interest in quantitatively demonstrating this complex system has dominated the study of channel patterns long before [23]. Although several variables have their triggers, channel pattern is closely related to the quantum and character of the available sediment and the volume and variability of the discharge [18]. Leopold et al. [18] stated that rivers are seldom straight through a reach of ten channel width (10 w). The patterns of the single-thread channel have been quantified as the measure of the degree of sinuosity by different scholars from different angles of view [5,13,14,17,18,22]. On the other hand, patterns of multi-thread channels have also been quantified as the measure of the degree of braiding by different scholars from different viewpoints [5,[9], [10], [11], [12],19,24,25]. Egozi & Ashmore [8] grouped all the above-cited indices into three categories- (1) bar indices which measure bar dimensions and frequency (2) channel count index which deal with the number of channels in the network and (3) channel length indices that measures total channel length in a given river length. The next section of this paper will review most of these indices and variations of these numerical tools illustrating some of the factors that may be involved in causing the variation.

Previous methods and limitations

The present study is based on the critical appraisal of the previous methods and formulation of new indices to fill up the gaps in the classical braiding indices. Thus, we have framed a conceptual workflow to give better ideas of the work (Fig. 1). The following sections are focused on the previous methods and novel approaches for advancing knowledge in channel morphology.

Fig 1 — Conceptual workflow to indicate the limitations of the classical braiding indices and advances made in the new indices proposed in the study.

Previous methods

Brice [5] considered bar length as the basis of his formula and proposed the braiding index (BI) and expressed in Eq. (1).

B I = \frac{2 \sum L_{b}}{L_{r}}

(1)

where $L_{b}$ = lengths of islands and (or) bars in reach and $L_{r}$ = length of reach measured midway between banks.

Although Brice [5] considered the length of all the bars within the reach, the theory in devising the tool he used is that- the ‘braiding index is a measure of the sum of island or bar perimeters in a reach and hence of the increase in bank length that results from braiding’. And as bars are very narrow, their perimeter is approximately twice their length. Not only the length of bars but also the number of bars within a reach is stage-dependent and Brice [5] termed it ‘transient’ braiding. However, the index gives us a measure of the braiding magnitude of a particular reach of a particular river. But that value of the index does not tell us whether the braiding nature of the concerned reach is low or high. This limitation is due to the absence of known limits of the index.

Germanoski and Schumm [10] adopted a modified equation as devised by Brice [5]. They added the number of bars per length of the reach and proposed another equation (Eq. (2)).

B I = \frac{2 \sum L_{b}}{L_{r}} + \frac{\sum N_{b}}{L_{r}}

(2)

where $N_{b}$ = the number of bars.

Egozi & Ashmore [8] stated that the purpose of this modification by Germanoski and Schumm [10] was to reduce the possibility that a reach with one very long bar could have an equivalent, or even greater, braiding intensity than a reach with shorter smaller bars [27]. However, it is important to note that both the length and the number of bars are stage sensitive. Although Rust [25], and Friend and Sinha [9] attempted to overcome the stage sensitivity of the length of braids. Even after the effort of adding the ‘number of bars’ as a determining factor of ‘braiding’, the modified index, having no known limits can be compared. Moreover, the value of the index is not unit-free.

The number of braids ( $N_{L})$ per mean channel wavelength (λ) was defined as BI by Rust [25] where λ ∼1·25 times the distance between successive confluence and bifurcation (Λ′) of braided links. To avoid the stage-sensitivity of Λ′, Rust [25] and Friend and Sinha [9] considered a 'braid length' from upstream divergence to downstream convergence of the thalweg line surrounding each bar. Rust [25] proposed the method mentioned in Eq. (3).

B I = \frac{\sum N_{L}}{λ}

(3)

As λ ∼1·25 Λ′, the formula can be written using Eq. (4).

B I = \frac{\sum N_{L}}{1.25 Λ^{'}}

(4)

And Friend and Sinha [9] formulated their BI using Eq. (5).

B I = \frac{L_{c t o t}}{L_{c m a x}}

(5)

where $L_{c t o t}$ is the sum of the mid-channel lengths of all the segments of primary channels in a reach and $L_{c m a x}$ is the mid-channel length of the widest channel through the reach.

Indices formulated in Eqs. (3), (4), and (5) are unit-free but don't have a known limit of values.

Howard et al. [12] counted mean $N_{L}$ per $L_{r}$ on a cross-section to formulate BI expressed in Eq. (6).

B I = \frac{\sum N_{L}}{L_{r}}

(6)

Regarding Eq. (6), cross-sections should be sufficiently far apart that the cross-sections do not cross the same link (or segment) of the network more than once [8]. However, Eq. (6) has no known limit of values and its unit is the number of links per unit of length.

Hong and Davies [11] devised three indices to quantify braided stream geometry. They proposed equations such as width ratio (Eq. 7), sinuosity index (Eq. 8) and braids in a cross-section.

(i)
Width ratio
$(W_{r}) = \frac{\sum b}{B}$ (7)

Where b= the width of an individual channel occupied by water and B= the total width of the whole bed including braids and bars.
(ii)
Sinuosity index,
$P = \frac{\sum L_{L}}{L_{r}}$ (8)
where $L_{L}$ is the length of an individual channel segment in a reach, and $L_{r}$ is the fall-line length of the reach or reach length.
(iii)
The number of braids or channels in a given cross-section of the stream bed, M.

Indices are unit-free as proposed in Eq. (7) and (8) but have no known limit of values (except Eq. 7). And in the case of two different reaches with different numbers of braids ‘b’ (in Eq. (7)) may have the same value. To have a view of a braiding channel, the assimilation of (i), (ii), and (iii) in a single index may result better.

Mosley [19] used channel length in computing the braiding index (total length of bankfull channels cut into the floodplain surface divided by distance along the main channel), as Hong and Davies [11] computed P. Mosley [20,21] also adopted the channel count index [8], i.e. the average number of channel links per cross-section. In this case, cross-sections were 1–2 channel widths apart. Ashmore [3], and Chew and Ashmore [7] followed the same principle as Howard et al. [12] and Mosley [1,[2], [4], [20]] in quantifying braiding magnitude.

Reviewing existing braiding indices, it appears that approaches adopted to quantifying the magnitude of braiding of a multi-thread channel are- (i) the number of bars per unit length of the reach, (ii) the length of bars per unit length of the reach, (iii) the number of channel links per cross-section, and (iv) the length of channel links per unit length of the reach. In computing BI, none of the above indices considered the area occupied by bars, which is very much significant for the purpose and has been discussed in the following section.

Spatio-temporal dynamics of channel braiding and deficiencies in the existing methods

Channel braiding is dependent on the annual flow regime

Leopold et al. [18] and Brice [5] stated that an island has a vegetal cover and generally remains emerged even at the bank-full stage whereas a bar lacks vegetal cover and generally remain submerged during a peak flow, but maybe emerged during lower stages. Braiding that changes in pattern with river stage is characterized by bars and is termed ‘transient’. Braiding that remains nearly constant in the pattern is characterized by islands and is termed ‘stabilized’ [5]. But Ashmore [3] defines braiding as a “distinct bifurcation of the flow and/or bed-load flux (sediment transport along the channel bed) around inactive portions of the channel bed, and need not necessarily involve exposure of an inactive bar above the water surface”. Wooster [28] suggested further attention to the influence of flow stage amongst several key issues in braided river environments. Rust [25] and Friend and Sinha [9] were aware of the variations of bar/ island length that might be caused by fluctuations of flow and proposed thalwegs from upstream divergence to downstream convergence be used to define a 'braid length'. A rise in stage may submerge low bars or, conversely, reactivate ephemeral channels [12]. Therefore, along with the absolute dynamicity of bars and braids through erosion and accretion in response to the variation in discharge and slope [8,16,19,26], the apparent stage dependent dynamicity of braiding channels seems logical to be admitted [8].

Temporal dynamics in the braiding nature of a channel

Bars in the sand and gravel-bed rivers are sensitive to discharge, slope, sediment regime and sediment size. They are very much dynamic in terms of their size, shape and position. In Figs. 2A and 2C, the number of bars and their lengths remained the same over the passage of years. The length and width of the reach also remained the same. Obviously, the lengths of braids also remained unchanged. Only what happened over time is that, suppose all the bars have been narrowed down causing a reduction in their area (Fig. 2C). As per standard indices (except for Eq. 7), despite this significant change, the BI of past (Fig. 1A) and present (Fig. 1C) will be the same, which seems unjustified in the context of the magnitude of (areal) braiding. To address this issue, we considered the bar area as a parameter in devising the index.

Fig 2 — Numbers and area of bars per unit channel area controlling braiding intensity of a channel. A, B.and C are the three different conditions of the bars and channels. The detailed descriptions are mentioned within the text.

Spatial variation in BI

In Fig. 1, suppose the reach length, number of bars, length of bars, and even areas of bars are the same for two different reaches A and B of the same river or of two different rivers A and B. Actually, what differs is that the width of channel B is twice the width of channel A. However, if the existing bar indices, channel count indices, and channel length indices [8] are applied to detect any variation in the braiding of A and B channels, they will produce no differences at all. That is why to address this spatial variation, the present BI is devised.

Novel approaches and methods

Considering the limitations of the existing braiding indices, especially the inadequacy to detect the spatio-temporal dynamics of bars and the lack of both the linear (1D) areal (2D) consideration of bars, the present study would be a novel attempt to address these issues for a better understanding of the bar dynamics. To devise the revised BI, we considered the following principles and precautions.

(i)
The index values should be unit-free.
(ii)
The index values should have known limits (Knighton [29]). In the present index, the value ranges between 0 and 1.
(iii)
A zero value of the index indicates the absence of braids/ bars while the unity of the value (though impossible in reality) indicates 100% braided.
(iv)
The presence of mid-channel bars or bars surrounded by wetted channels is a prerequisite for calculating BI and no bank-attached bar (point bars) is to be considered for calculating the index.
(v)
If there is a bar, there are braids. Therefore, we considered only the parameters of the bars (numbers and areas) to quantify the braiding magnitude of a channel.
(vi)
The number of bars and their areas are stage sensitive. Therefore, there is a stage dependency and seasonality in the value of the braiding index.
(vii)
The reach length ( $L_{r})$ should be 10 w. If $L_{r}$ ≠ 10 w, in that case, the clue for guessing the average area of bars will differ.

To assess the nature of river channel pattern, at least 10 w (w = channel width) was proposed by Leopold et al. [18] . Egozi & Ashmore [8] proposed that the reach lengths of at least 10 times the average wetted width are needed to measure braid indices with the precision of the order of 20% of the mean. We also followed that principle in deciding channel patterns. Before formulating the revised braiding index, we here explain, why instead of braids length/ numbers and bar length, we considered bar numbers and their areas. Theoretically, if and only if there is a bar there are braids or more than one channel segment within the reach. Moreover, the one-dimensional bar length lies within the two-dimensional bar area. That is why, instead of the numbers and lengths of braids/ channel segments, the numbers of bars and their areas were taken into consideration.

As already explained, definitely the area of bars within a channel reach does control braiding magnitude. We, therefore, calculated the ratio of the area occupied by bars (A_b) to the area occupied by the reach using (A_r) Eq. (9).

B I^{*} = \frac{\sum A_{b}}{A_{r}}

(9)

If there is no mid-channel bar, $B I^{*}$ = 0 and if 50% of the channel is occupied by bars, $B I^{*}$ = 0.5. $B I^{*}$ = 1.0 is impossible as the river will no longer be a flow of water. The main limitation of this equation is that, if there is a single bar of a very large area ( $A_{b}$ ) in a reach, it will produce a greater value of $B I^{*}$ than the reach having multiple bars with lesser $\sum A_{b}$ .

Not only the area of bars is the determinant factor of braiding intensity of a reach. The number of bars (therefore the number of braids) also controls the braiding intensity [[10], [27]]. Therefore, we have counted the number of bars ( $N_{b}$ ) per channel reach length ( $L_{r}$ ). To decide on the reach length ( $L_{r}$ ), avoiding issues related to the channel dimension, we considered channel width (w) as the unit of length and designated the reach measured in ‘w’ unit as $L_{r w}$ which is equal to 10 w. And the bar index is formulated using Eq. (10).

B I_{1} = 1 - \frac{1}{\sum N_{b}}

(10)

Again, theoretically, the value of BI₁ ranges between 0 and →1. If there is no mid-channel bar, $B I_{1}$ = 0. However, if there is one bar within the reach length, as per the equation, it will also produce 0. In that case, to eliminate this fallacy of being a zero value of $B I_{1}$ , a single bar within the reach may be written numerically as 1.1 and this will produce a very negligible value of $B I_{1}$ = 0.09. And if there are 10 bars within the reach, the $B I_{1}$ will produce 10 times the value of 0.09, i.e. 0.90. If $B I_{1}$ →1, the channel is covered with an innumerable number of bars. This index not only gives the number of bars within the reach but also provides clues regarding the average areal dimension of bars in a very intensively braided channel with $B I_{1}$ ≥ 0.95. In that case, the average area of bars within the reach is $\sim (0.5 w \times 0.5 w) o r \sim 0.25 w^{2}$ .

As the number of bars and the area occupied by bars jointly determine the intensity of braiding, the product of Eq. (9) and (10) results in Eq. (11).

B I_{2} = \frac{\sum A_{b}}{A_{r}} \times (1 - \frac{1}{\sum N_{b}})

(11)

As the braiding intensity of a reach of the river channel is manifested through the number and area of bars and the number and length of channel segments, we suggest a modified assimilation of the indices by Brice [5], Germanoski and Schumm [10], Friend & Sinha [9] and $B I^{*}$ devised in this present paper. This modification keeps the value of the index unit-free and within the range of zero and unity as mentioned in Eq. (12).

B I_{3} = (1 - \frac{L_{c m a x}}{L_{c t o t}}) \times (1 - \frac{1}{\sum N_{b}}) \times (\frac{\sum A_{b}}{A_{r}})

(12)

Known limits of the measuring tools are essential (Knighton [29]) for having an insight into the degree of braiding of a river. Known limits of braiding indices can enable one to comprehend the braiding intensity of river reaches of different magnitudes of width. Comparing braiding of channel reaches of the same river or of different rivers also demands known limits of the values of the indices. For instance, although there is a significant difference in braiding between reaches A, B, and C of Fig. 2, Eqs. (1), (2), (3), (4), (5), (6), and (8) may produce the same values of BI for channel reaches A, B, and C of Fig. 2. However, the tool mentioned in Eq. (7) by Hong and Davies [11] may address this issue to an extent. Eqs. (9), (10), (11), and (12) of this present study not only differentiate the intensity of braiding of these reaches but also, having known limits, can comprehend their different braiding intensity.

Method validations

To validate methods (BI*, $B I_{1}$ , $B I_{2}$ and $B I_{3}$ ) introduced in this study, for estimating the degree of braiding, we followed two approaches: firstly we counted the number of bars from 28 reaches of 10 km (approximately equal to 10 w) each of Damodar River, a controlled braided river of India. We also calculated the area of each reach and of bars within each reach (Table S1) using ArcGIS software (v. 10.2). Then we applied tools BI*, $B I_{1}$ , $B I_{2}$ and $B I_{3}$ for estimating braiding intensity and found that indices’ values range between 0 and 1. Five reaches having no bars or braids showed zero value for indices BI*, $B I_{1}$ , $B I_{2}$ and $B I_{3}$ whereas previous indices by, Howard et al. [12], and Friend and Sinha [9] resulted in positive non-zero values indicating the existence of braids. The linear equation y = a+bx and significant correlation values (R² > 0.60) between number of bars and the value of indices indicate the consistency and validity in replication. The linear equation y = a+bx and significant correlation values (R² > 0.80, except $B I_{1}$ ) between the area of bars and the value of indices also indicate the consistency and validity of indices (Fig. 3a, b).

Fig 3 — Relationship between proposed braiding indices and a. Numbers of bars and b. Area occupied by the bars. The proposed indices in the study show a strong correlation with the number and area of the bars under consideration.

Secondly, we calculated the Pearson's correlation coefficient between indices formulated in this study and previous indices ([5,12]; Germanoski and Schumm 1993; and [9]) to estimate the degree of association amongst indices. For this purpose, we used some data from Islam et al. [15] coupled with the data derived from geospatial data extractions. It was found that BI*, $B I_{1}$ , $B I_{2}$ and $B I_{3}$ are strongly correlated (R² = 0.7 to 0.9) with previous indices with a 99% level of significance (Fig. 4).

Fig 4 — Correlation heatmap showing the relationship among the existing and proposed braiding indices. The good correlation among the indices reflects the validity of the present indices for future attempts.

Conclusions

The most exciting novelty is that tools designed in this study for estimating the degree of braiding intensity of a reach of the river channel, have known limits which is very much important in knowing the relative position of a river reach in braiding scale ranging from zero to unity and which is lacking in the earlier tools. Moreover, these indices produce unit-free values. However, our proposed indices have a few limitations. The structural equation of BI₁ index results in zero braiding in the case of only one bar within a reach. In that case, the bar number has to be considered in fraction (say 1.1). The index value of BI₁ and BI₂ will be infinity in case of the absence of any bar within a reach. Thus, these indices will not be worked out for this situation. The methods of detecting channel braiding, to date, are primarily dependent on the stage of the river. Thus, any seasonal fluctuations in water level may lead to altered situations making the comparison difficult. Future attempts may focus on the computation of indices independent of the stage if possible. Moreover, the volumetric (3D) measurement of the bar and channel may be focused.

Ethics statements

If your work involved human subjects: Not applicable

If your work involved animal experiments: Not applicable

If your work involved data collected from social media platforms: Not applicable

CRediT authorship contribution statement

Balai Chandra Das: Conceptualization, Methodology, Investigation, Formal analysis, Writing – original draft. Aznarul Islam: Methodology, Software, Writing – review & editing, Visualization.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. We acknowledge Nuruddin Sardar and Suman Deb Barman for data support.

Footnotes

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.mex.2023.102042.

Appendix. Supplementary materials

mmc1.xlsx^{(30.8KB, xlsx)}

Data availability

Data will be made available on request.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

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Data Availability Statement

Data will be made available on request.

[bib0001] 1.Ashmore P.E., Parker G. Confluence scour in coarse braided stream. Water Resour Res. 1983;19:392–402. [Google Scholar]

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PERMALINK

Reviewing braiding indices of the river channel in an attempt to establish alternatives

Balai Chandra Das

Aznarul Islam

Highlights

Abstract

Graphical abstract

Introduction

Previous methods and limitations