# Understanding the Planform Complexity and Morphodynamic Properties of Brahmaputra River in Bangladesh: Protection and Exploitation of Riparian Areas

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## Abstract

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## 1. Introduction

## 2. Study Area

## 3. Methods

#### 3.1. The Anastomosing River Principle

#### 3.2. Channel Network Delineation

#### 3.3. Anastomosing Function

#### 3.4. Discharge Data

#### 3.5. Entropy

#### 3.5.1. Approximate Entropy

#### 3.5.2. Sample Entropy

#### 3.6. Power Spectral Density

## 4. Results and Discussion

#### 4.1. Extracted AF and Corresponding PSD of the Brahmaputra River’s Planform

#### 4.2. Disorder, Complexity and Fluctuation of the Brahmaputra River’s Planform

#### 4.3. Association between River Discharge and Disorder, Complexity, and Fluctuation

## 5. Potential Implications towards Morphological Contexts

## 6. Conclusions

- The generated and investigated $AF$ is capable of accurately transforming a two-dimensional complex network into a one-dimensional spatial signal.
- The Approximate Entropy ($ApEn$) and Sample Entropy ($SampEn$) can be used to quantify the disorder and complexity of river’s planforms, respectively, which confirms the reproducibility of the physical features of the river.
- Dynamic imprints, such as yearly maximum discharge (${Q}_{max}$), have significant contributions to the river’s planform complexity.
- ${Q}_{max}$ also showed a significant and consistent contribution to the Brahmaputra River’s planform fluctuation.

## 7. Limitations and Recommendations

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Leopold, L.B.; Wolman, M.G. River Channel Patterns: Braided, Meandering, and Straight; US Government Printing Office: Washington, DC, USA, 1957.
- Charlton, R. Fundamentals of Fluvial Geomorphology; Routledge: London, UK; New York, NY, USA, 2007. [Google Scholar]
- Makaske, B. Anastomosing rivers: A review of their classification, origin and sedimentary products. Earth-Sci. Rev.
**2001**, 53, 149–196. [Google Scholar] [CrossRef] - Sarker, S. Investigating Topologic and Geometric Properties of Synthetic and Natural River Networks under Changing Climate; University of Central Florida: Orlando, FL, USA, 2021. [Google Scholar]
- Sarker, S. Understanding the Complexity and Dynamics of Anastomosing River Planform: A Case Study of Brahmaputra River in Bangladesh. Earth Space Sci. Open Arch.
**2021**, 1. [Google Scholar] [CrossRef] - Sarker, S.; Veremyev, A.; Boginski, V.; Singh, A. Critical nodes in river networks. Sci. Rep.
**2019**, 9, 1–11. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Khan, I.; Ahammad, M.; Sarker, S. A study on River Bank Erosion of Jamuna River using GIS and Remote Sensing Technology. Int. J. Eng. Develop. Res.
**2014**, 2, 3365–3371. [Google Scholar] - Gao, Y.; Sarker, S.; Sarker, T.; Leta, O.T. Analyzing the critical locations in response of constructed and planned dams on the Mekong River Basin for environmental integrity. Environ. Res. Commun.
**2022**, 4, 101001. [Google Scholar] [CrossRef] - Bridge, J.S. The interaction between channel geometry, water flow, sediment transport and deposition in braided rivers. Geol. Soc.
**1993**, 75, 13–71. [Google Scholar] [CrossRef] - Ferguson, R. Understanding braiding processes in gravel-bed rivers: Progress and unsolved problems. Geol. Soc.
**1993**, 75, 73–87. [Google Scholar] [CrossRef] - Klaassen, G.J.; Mosselman, E.; Bruehl, H. On the Prediction of Planform Changes in Braided Sand-nd-Ed Rivers; Delft Hydraulics: Delft, The Netherlands, 1993. [Google Scholar]
- Pradhan, C.; Chembolu, V.; Bharti, R.; Dutta, S. Regulated rivers in India: Research progress and future directions. ISH J. Hydraul. Eng.
**2021**, 1–13. [Google Scholar] [CrossRef] - Ashmore, P.E. Laboratory modelling of gravel braided stream morphology. Earth Surf. Process. Land.
**1982**, 7, 201–225. [Google Scholar] [CrossRef] - Ashmore, P.E. How do gravel-bed rivers braid? Can. J. Earth Sci.
**1991**, 28, 326–341. [Google Scholar] [CrossRef] [Green Version] - Ashmore, P. Anabranch confluence kinetics and sedimentation processes in gravel-braided streams. Geol. Soc.
**1993**, 75, 129–146. [Google Scholar] [CrossRef] - Young, W.; Davies, T. Bedload transport processes in a braided gravel-bed river model. Earth Surf. Process. Land.
**1991**, 16, 499–511. [Google Scholar] [CrossRef] - Murray, A.B.; Paola, C. A cellular model of braided rivers. Nature
**1994**, 371, 54–57. [Google Scholar] [CrossRef] - Murray, A.B.; Paola, C. Properties of a cellular braided-stream model. Earth Surf. Process. Land.
**1997**, 22, 1001–1025. [Google Scholar] [CrossRef] - Nykanen, D.K.; Foufoula-Georgiou, E.; Sapozhnikov, V.B. Study of spatial scaling in braided river patterns using synthetic aperture radar imagery. Water Resour. Res.
**1998**, 34, 1795–1807. [Google Scholar] [CrossRef] [Green Version] - Pradhan, C.; Bharti, R.; Dutta, S. Assessment of post-impoundment geomorphic variations along Brahmani River using remote sensing. In Proceedings of the 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Fort Worth, TX, USA, 23–28 July 2017; pp. 5598–5601. [Google Scholar]
- Pradhan, C.; Chembolu, V.; Dutta, S. Impact of river interventions on alluvial channel morphology. ISH J. Hydraul. Eng.
**2019**, 25, 87–93. [Google Scholar] [CrossRef] - Sapozhnikov, V.B.; Foufoula-Georgiou, E. Do the current landscape evolution models show self-organized criticality? Water Resour. Res.
**1996**, 32, 1109–1112. [Google Scholar] [CrossRef] - Sapozhnikov, V.B.; Foufoula-Georgiou, E. Experimental evidence of dynamic scaling and indications of self-organized criticality in braided rivers. Water Resour. Res.
**1997**, 33, 1983–1991. [Google Scholar] [CrossRef] [Green Version] - Walsh, J.; Hicks, D.M. Braided channels: Self-similar or self-affine? Water Resour. Res.
**2002**, 38, 1–6. [Google Scholar] [CrossRef] - Lane, S.N.; Westaway, R.M.; Murray Hicks, D. Estimation of erosion and deposition volumes in a large, gravel-bed, braided river using synoptic remote sensing. Earth Surf. Process. Land.
**2003**, 28, 249–271. [Google Scholar] [CrossRef] - Westaway, R.; Lane, S.; Hicks, D. The development of an automated correction procedure for digital photogrammetry for the study of wide, shallow, gravel-bed rivers. Earth Surf. Process. Land.
**2000**, 25, 209–226. [Google Scholar] [CrossRef] - Westaway, R.M.; Lane, S.N.; Hicks, D.M. Remote sensing of clear-water, shallow, gravel-bed rivers using digital photogrammetry. Photogramm. Eng. Remote Sens.
**2001**, 67, 1271–1282. [Google Scholar] - Westaway, R.M.; Lane, S.; Hicks, D. Remote survey of large-scale braided, gravel-bed rivers using digital photogrammetry and image analysis. Int. J. Remote Sens.
**2003**, 24, 795–815. [Google Scholar] [CrossRef] - Coleman, J.M. Brahmaputra River: Channel processes and sedimentation. Sediment. Geol.
**1969**, 3, 129–239. [Google Scholar] [CrossRef] - Mosselman, E.; Huisink, M.; Koomen, E.; Seijmonsbergen, A. Morphological Changes in a Large Braided Sand-Bed River; John Wiley & Sons: Chichester, UK, 1995. [Google Scholar]
- Thorne, C.R.; Russell, A.P.; Alam, M.K. Planform pattern and channel evolution of the Brahmaputra River, Bangladesh. Geol. Soc.
**1993**, 75, 257–276. [Google Scholar] [CrossRef] - Goswami, D.C. Brahmaputra River, Assam, India: Physiography, basin denudation, and channel aggradation. Water Resour. Res.
**1985**, 21, 959–978. [Google Scholar] [CrossRef] - Sarker, S. Essence of MIKE 21C (FDM Numerical Scheme): Application on the River Morphology of Bangladesh. Open J. Modell. Simul.
**2022**, 10, 88–117. [Google Scholar] [CrossRef] - Chembolu, V.; Dutta, S. An entropy based morphological variability assessment of a large braided river. Earth Surf. Process. Land.
**2018**, 43, 2889–2896. [Google Scholar] [CrossRef] - Dubey, A.K.; Chembolu, V.; Dutta, S. Utilization of satellite altimetry retrieved river roughness properties in hydraulic flow modelling of braided river system. Int. J. River Basin Manag.
**2020**, 20, 1–14. [Google Scholar] [CrossRef] - Karmaker, T.; Medhi, H.; Dutta, S. Study of channel instability in the braided Brahmaputra river using satellite imagery. Curr. Sci.
**2017**, 112, 1533–1543. [Google Scholar] [CrossRef] - Sarker, M.H.; Thorne, C.R.; Aktar, M.N.; Ferdous, M.R. Morpho-dynamics of the Brahmaputra–Jamuna river, Bangladesh. Geomorphology
**2014**, 215, 45–59. [Google Scholar] [CrossRef] - Valdiya, K. Why does river Brahmaputra remain untamed? Curr. Sci.
**1999**, 76, 1301–1305. [Google Scholar] - Dutta, S.; Medhi, H.; Karmaker, T.; Singh, Y.; Prabu, I.; Dutta, U. Probabilistic flood hazard mapping for embankment breaching. ISH J. Hydraul. Eng.
**2010**, 16, 15–25. [Google Scholar] [CrossRef] - Nayak, P.; Panda, B. Brahmaputra and the Socio-Economic Life of People of Assam. The Mahabahu Brahmaputra; Flood and River Management Agency of Assam: Guwahati, India, 2016; pp. 77–85.
- Singh, V.; Sharma, N.; Ojha, C.S.P. The Brahmaputra Basin Water Resources; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2004; Volume 47. [Google Scholar]
- Government of Assam, Water Resources. Brahmaputra River System. Available online: https://waterresources.assam.gov.in/portlet-innerpage/brahmaputra-river-system (accessed on 1 October 2021).
- Marra, W.A.; Kleinhans, M.G.; Addink, E.A. Network concepts to describe channel importance and change in multichannel systems: Test results for the Jamuna River, Bangladesh. Earth Surf. Process. Land.
**2014**, 39, 766–778. [Google Scholar] [CrossRef] - Fischer, S.; Pietroń, J.; Bring, A.; Thorslund, J.; Jarsjö, J. Present to future sediment transport of the Brahmaputra River: Reducing uncertainty in predictions and management. Region. Env. Change
**2017**, 17, 515–526. [Google Scholar] [CrossRef] [Green Version] - Sarker, T. Role of Climatic and Non-Climatic Factors on Land Use and Land Cover Change in the Arctic: A Comparative Analysis of Vorkuta and Salekhard. Ph.D. Thesis, The George Washington University, Washington, DC, USA, 2020. [Google Scholar]
- Ranjbar, S.; Hooshyar, M.; Singh, A.; Wang, D. Quantifying climatic controls on river network branching structure across scales. Water Resour. Res.
**2018**, 54, 7347–7360. [Google Scholar] [CrossRef] - Lashermes, B.; Foufoula-Georgiou, E. Area and width functions of river networks: New results on multifractal properties. Water Resour. Res.
**2007**, 43. [Google Scholar] [CrossRef] [Green Version] - Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] [Green Version] - Delgado-Bonal, A.; Marshak, A. Approximate entropy and sample entropy: A comprehensive tutorial. Entropy
**2019**, 21, 541. [Google Scholar] [CrossRef] [Green Version] - Pincus, S.M. Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA
**1991**, 88, 2297–2301. [Google Scholar] [CrossRef] [Green Version] - Sarker, S.; Sarker, T. Spectral Properties of Water Hammer Wave. Appl. Mech.
**2022**, 3, 799–814. [Google Scholar] [CrossRef] - Pincus, S.; Kalman, R.E. Irregularity, volatility, risk, and financial market time series. Proc. Natl. Acad. Sci. USA
**2004**, 101, 13709–13714. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Richman, J.S.; Moorman, J.R. Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol.
**2000**. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Delgado-Bonal, A.; Marshak, A.; Yang, Y.; Holdaway, D. Analyzing changes in the complexity of climate in the last four decades using MERRA-2 radiation data. Sci. Rep.
**2020**, 10, 1–8. [Google Scholar] [CrossRef] [Green Version] - Ranjbar, S.; Singh, A. Entropy and intermittency of river bed elevation fluctuations. J. Geophys. Res. Earth Surf.
**2020**, 125, e2019JF005499. [Google Scholar] [CrossRef] - Sarker, S. A Story on the Wave Spectral Properties of Water Hammer. engrXiv
**2021**. [Google Scholar] [CrossRef] - Stoica, P.; Moses, R.L. Spectral Analysis of Signals; Pearson and Prentice Hall: Upper Saddle River, NJ, USA, 2005. [Google Scholar]
- Stull, R.B. An Introduction to Boundary Layer Meteorology; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012; Volume 13. [Google Scholar]
- Gardner, W.A.; Robinson, E.A. Statistical Spectral Analysis—A Nonprobabilistic Theory; Prentice-Hall Inc.: Upper Saddle River, NJ, USA, 1989. [Google Scholar]
- Pilgram, B.; Kaplan, D.T. A comparison of estimators for 1f noise. Phys. D Nonlin. Phen.
**1998**, 114, 108–122. [Google Scholar] [CrossRef] - Sarker, S. A Short Review on Computational Hydraulics in the context of Water Resources Engineering. Open J. Modell. Simul.
**2022**, 10, 1–31. [Google Scholar] [CrossRef] - Smith, D.G.; Smith, N.D. Sedimentation in anastomosed river systems; examples from alluvial valleys near Banff, Alberta. J. Sediment. Res.
**1980**, 50, 157–164. [Google Scholar] [CrossRef] - David Knighton, A.; Nanson, G.C. Anastomosis and the continuum of channel pattern. Earth Surf. Process. Land.
**1993**, 18, 613–625. [Google Scholar] [CrossRef] - Sarker, S. Fundamentals of Climatology for Engineers: Lecture Note. Eng
**2022**, 3, 573–595. [Google Scholar] [CrossRef]

**Figure 2.**Brahmaputra River study region. The location of discharge data collection is depicted in red.

**Figure 3.**Delineation of the channel network for seven selected years from 1987 to 2020, based on the dry season of the Brahmaputra River.

**Figure 4.**(

**a**) Extracted mean yearly wet and dry discharge data and (

**b**) Yearly maximum discharge data of the BR from 1987 to 2020.

**Figure 5.**Details of the algorithms to compute Approximate Entropy ($ApEn$) and Sample Entropy ($SampEn$) on $AF$ series.

**Figure 6.**(

**a**) Extracted $AF$ for the BR for the seven selected years and (

**b**) corresponding $PSD$ of $AF$ plotted on a log–log scale.

**Figure 7.**(

**a**) Computed Approximate Entropy ($ApEn$) and Sample Entropy ($SampEn$) on $AF$ series in a bar plot and (

**b**) the corresponding $\beta $ calculated by fitting the slope to the estimated $PSD$ of $AF$ series plotted on a log–log scale.

**Figure 8.**Correlation between Approximate entropy ($ApEn$) and (

**a**) Yearly maximum discharge (${Q}_{max}$), (

**b**) Mean yearly wet discharge (${Q}_{mwet}$) and (

**c**) Mean yearly dry discharge (${Q}_{mdry}$).

**Figure 9.**Correlation between Sample Entropy ($SampEn$) and (

**a**) Yearly maximum discharge (${Q}_{max}$), (

**b**) Mean yearly wet discharge (${Q}_{mwet}$) and (

**c**) Mean yearly dry discharge (${Q}_{mdry}$).

**Figure 10.**Correlation between $\beta $ and (

**a**) Yearly maximum discharge (${Q}_{max}$), (

**b**) Mean yearly wet discharge (${Q}_{mwet}$) and (

**c**) Mean yearly dry discharge (${Q}_{mdry}$).

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**MDPI and ACS Style**

Sarker, S.; Sarker, T.; Leta, O.T.; Raihan, S.U.; Khan, I.; Ahmed, N.
Understanding the Planform Complexity and Morphodynamic Properties of Brahmaputra River in Bangladesh: Protection and Exploitation of Riparian Areas. *Water* **2023**, *15*, 1384.
https://doi.org/10.3390/w15071384

**AMA Style**

Sarker S, Sarker T, Leta OT, Raihan SU, Khan I, Ahmed N.
Understanding the Planform Complexity and Morphodynamic Properties of Brahmaputra River in Bangladesh: Protection and Exploitation of Riparian Areas. *Water*. 2023; 15(7):1384.
https://doi.org/10.3390/w15071384

**Chicago/Turabian Style**

Sarker, Shiblu, Tanni Sarker, Olkeba Tolessa Leta, Sarder Udoy Raihan, Imran Khan, and Nur Ahmed.
2023. "Understanding the Planform Complexity and Morphodynamic Properties of Brahmaputra River in Bangladesh: Protection and Exploitation of Riparian Areas" *Water* 15, no. 7: 1384.
https://doi.org/10.3390/w15071384