# Machine Learning-Based Assessment of Watershed Morphometry in Makran

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## Abstract

**:**

^{2}) between the output of the method and the actual dataset. The ANN model demonstrated high accuracy with an R

^{2}value of 0.974, MSE of 4.14 × 10

^{−6}, and MAE of 0.0015. The results of the machine learning algorithms were compared to the tectonic characteristics of the area, indicating the potential for utilizing the ANN algorithm in similar investigations. This approach offers a novel way to assess watershed morphometry using ML techniques, which may have advantages over other approaches.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Extracting the Geomorphic Parameters

#### 2.3. Calculating Criterion Weights by FAHP

#### 2.4. Description and Application of the Criterion

#### 2.4.1. Hypsometric Integral (Hi)

#### 2.4.2. Basin Shape (Bs)

#### 2.4.3. Circularity Basin (Cb)

#### 2.4.4. Elongation Ratio (Er)

#### 2.4.5. Ruggedness Number (Rn)

_{max}– H

_{min}

_{max}and H

_{min}are the highest and lowest elevations of the watershed. The Rn close to 473 is allocated the highest weight utilizing the rising fuzzy linear membership. As the Rn value approaches 1, the weight drops until it reaches zero.

#### 2.4.6. River Sinuosity (Rs)

#### 2.4.7. Compactness Coefficient (Cc)

#### 2.4.8. Form Factor (Ff)

#### 2.5. Machine Learning Algorithms

#### 2.5.1. Artificial Neural Networks (ANNs)

- Data processing occurs in the units known as neurons. The neurons (or artificial neurons) present a model of brain neurons.
- The exchange of data is facilitated through communication between neurons.
- There is a weight for communicative ways between neurons.
- Every neuron utilizes a nonlinear function to process its inputs (weighted data), producing a specific output [82].

#### 2.5.2. Support Vector Regression (SVR)

_{i}= [x

_{1,i}, …, x

_{n,i}] ∈ ${\mathrm{R}}^{\mathrm{n}}$ and X

_{i}represents the i

_{th}element in a space with n dimensions, y

_{i}(y

_{i}∈ R) indicates the actual value for X

_{i}, the definition of a nonlinear function is as follows: φ: ${\mathrm{R}}^{\mathrm{n}}$ → R

^{nh}. For mapping the entry data, X

_{i}represents an ${\mathrm{R}}^{\mathrm{nh}}$ space of high dimension known as feature space, which specifies the nonlinear transformation φ. Hence, a linear function $\mathrm{f}$ in a high-dimensional space, and consequently, the entry data, X

_{i}can be related to output y

_{i}. Equation (9) presents the linear function, i.e., SVR.

_{ε}in the R

^{nh}space for finding a function with the ability to fit present training data with a deviation equal to or below ε. Using the mentioned function, the training error is minimized between the data training, and Equation (12) provides the function ε-insensitive [84].

_{i}represents errors more minor than −ε and ξ

_{i}

^{∗}indicates training errors larger than ε.

#### 2.5.3. Multivariate Linear Regression (MLR)

#### 2.6. Integrating the FAHP and ML Algorithms

^{2}) were utilized as performance metrics. These metrics are described in Equation (14a–c) [82].

^{2}value of 0.974, MSE of 4.14 × 10

^{−6}, and MAE of 0.00151.

^{−6}and 1.94 × 10

^{−3}, respectively.

^{−6}and 1.61 × 10

^{−3}, respectively.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Location of Makran subduction zone and border of 423 extracted watersheds. The number labels show the randomly selected watershed used in AI.

**Table 1.**Saaty’s 1–9 scale of relative importance [63].

Intensity of Importance | Interpretation |
---|---|

1 | Equal importance |

3 | Moderate importance |

5 | Essential |

7 | Extreme importance |

9 | Extreme importance |

2, 4, 6, 8 | Intermediate values between adjacent scale values |

Linear and Areal Aspects | Hi | Bs | Cb | Er | Rn | Rs | Cc | Ff | Score |
---|---|---|---|---|---|---|---|---|---|

Hypsometric integral (Hi) | 0.5 | 0.5 | 2 | 0.5 | 0.5 | 2 | 2 | 0.136 | |

Basin shape (Bs) | 2 | 2 | 2 | 2 | 2 | 2 | 0.037 | ||

Circularity basin (Cb) | 0.33 | 0.5 | 2 | 2 | 0.5 | 0.123 | |||

Elongation ratio (Er) | 2 | 2 | 2 | 2 | 0.084 | ||||

Ruggedness number (Rn) | 2 | 3 | 2 | 0.078 | |||||

River sinuosity (Rs) | 0.5 | 0.5 | 0.297 | ||||||

CoefficientCompactness (Cc) | 0.5 | 0.050 | |||||||

Form factor (Ff) | 0.197 | ||||||||

CI | 0.03 |

Methods | MSE | MAE | R^{2} |
---|---|---|---|

ANN | 4.14 × 10^{−6} | 0.00151 | 0.974 |

SVR | 8.12 × 10^{−6} | 0.00194 | 0.947 |

MLR | 5.06 × 10^{−6} | 0.00161 | 0.967 |

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## Share and Cite

**MDPI and ACS Style**

Derakhshani, R.; Zaresefat, M.; Nikpeyman, V.; GhasemiNejad, A.; Shafieibafti, S.; Rashidi, A.; Nemati, M.; Raoof, A.
Machine Learning-Based Assessment of Watershed Morphometry in Makran. *Land* **2023**, *12*, 776.
https://doi.org/10.3390/land12040776

**AMA Style**

Derakhshani R, Zaresefat M, Nikpeyman V, GhasemiNejad A, Shafieibafti S, Rashidi A, Nemati M, Raoof A.
Machine Learning-Based Assessment of Watershed Morphometry in Makran. *Land*. 2023; 12(4):776.
https://doi.org/10.3390/land12040776

**Chicago/Turabian Style**

Derakhshani, Reza, Mojtaba Zaresefat, Vahid Nikpeyman, Amin GhasemiNejad, Shahram Shafieibafti, Ahmad Rashidi, Majid Nemati, and Amir Raoof.
2023. "Machine Learning-Based Assessment of Watershed Morphometry in Makran" *Land* 12, no. 4: 776.
https://doi.org/10.3390/land12040776