# 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

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**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