# The Implementation of a Hybrid Model for Hilly Sub-Watershed Prioritization Using Morphometric Variables: Case Study in India

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study and Data Collection

^{2}with altitude ranging from 798 m to 2911 m above mean sea level. The area has a mean annual rainfall of 931.3 mm; a significant portion of rainfall in the area comes from the South-West monsoon which commences around mid-June and runs to September. The maximum daily mean temperature is experienced from May to June and the lowest daily mean temperature is experienced from December to January. The geological structure of BW consists of mica, schist, quarzitic sandstone, granitic-gneiss, and some calcareous dolomite rocks. The soil in these watersheds is mainly formed from coarse-textured quartzite although shale and silty-phyllites contribute to the process of pedogenesis in some areas of watershed at middle elevation. The lower surfaces of the watershed are mostly composed of colluvial deposits with fined-grained mica sand; however, the upper surfaces are mainly composed of boulders of metamorphic rocks and well-rounded pebbles. The soil texture varies from gravelly loamy sand to silt loam.

#### 2.2. Morphometric Analysis and Assign Preliminary Priority Rank to the SWs

#### 2.3. Principal Component Analysis and Weighted-Sum Approach

#### 2.3.1. Principal Component Analysis

^{T}CA = D

^{T}P = I). Thus, the rotated components are given as:

#### 2.3.2. Weighted-Sum Approach

_{SMP}× W

_{SMP}

_{MP}= preliminary priority rank of significant morphometric parameter identified using PCA; and W

_{SMP}= weight of significant morphometric parameter obtained using cross-correlation analysis, and computed as:

## 3. Application Results and Analysis

_{u}, $\overline{{L}_{u}}$, L

_{b}and R

_{b}), areal (D

_{d}, F

_{s}, R

_{t}and L

_{om}), and shape (F

_{f}, R

_{c}, C

_{c}and R

_{e}) morphometric parameters of nine SW of BW was computed in the ArcGIS environment and their quantitative values are given in Table 4 and Table 5, respectively. After morphometric analysis, the PPR were assigned (based on direct and inverse relationship concept) to nine SW as given in Table 6. After PPR, the PCA was applied for reducing the dimensionality of data (i.e., linear, areal, and shape morphometric variables) by identifying the significant morphometric variables based on correlations and FL matrix for reducing. After PCA, the weighted-sum analysis was performed on significant morphometric variables for CF valve computation, and finally assigned priority rank and category to the nine SWs based on CF value.

^{2}(SW-7) to 1.759 km/km

^{2}(SW-2). The low value of drainage density for SW-7 indicates highly permeable sub-surface under vegetative cover with low relief, whereas a higher value of drainage density for SW-2 indicates a well-developed efficient drainage network with impermeable sub-surface materials with less vegetative cover and high relief. The value of stream frequency of sub-watersheds varies from 0.421 km

^{−2}(SW-2) to 0.617 km

^{−2}(SW-6). A low value of stream frequency indicates low runoff and a higher value indicates more runoff. The value of texture ratio varies from 0.176 km

^{−1}(SW-2) to 0.854 km

^{−1}(SW-7). Accordingly, all SW fall in the very coarse category of drainage texture. The value of mean length of overland flow of 9 SW varies from 0.284 km to 0.719 km in the watershed. Table 5 reveals that the form factor varies from 0.164 to 0.524 indicating elongated shape with lower peak flow for longer duration. The value of circularity ratio for sub-watersheds varies from 0.311 to 0.534 indicating that SW-4, SW-7, and SW-9 have circular shape, while SW-1, SW-2, SW-3, SW-5, SW-6, and SW-8 have elongated shape. The compactness coefficient ranges from 1.358 to 1.778. A high value (>1) of compactness coefficient indicates more compact SWs. The elongation ratio ranges from 0.457 to 0.817, which indicates that all the SWs are of high relief and steep ground slope. Preliminary priority ranking of SWs based on linear, areal and shape parameters of SWs is given in Table 6.

#### 3.1. Principal Component Analysis of Morphometric Variables

#### 3.2. Weighted-Sum Analysis of Significant Morphometric Variables

#### 3.3. Prioritization of SW Using PCWSA

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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Linear Variables | Formula | References |
---|---|---|

Basin area (A) | Plan area of watershed (km^{2}) | |

Basin perimeter (P) | Perimeter of watershed (km) | |

Stream order (u) | Hierarchical rank | [31] |

Stream length (L_{u}) | Length of stream (km) | [31] |

Mean stream length ($\overline{{L}_{u}}$) | $\overline{{L}_{u}}=\frac{{L}_{u}}{{N}_{u}}$ where $\overline{{L}_{u}}$ is the mean stream length (km), ${L}_{u}$ is the total length of stream of order u, ${N}_{u}$ is the total number of streams of order u | [32] |

Basin length (${L}_{b}$) | ${L}_{b}=1.312\times {A}^{0.568}$, (km) | [33] |

Bifurcation ratio (R_{b}) | ${R}_{b}=\frac{{N}_{u}}{{N}_{u+1}}$ where ${N}_{u+1}$ is the number of stream segments of ($u+1$)th order | [33] |

Areal Variables | Formula | References |
---|---|---|

Drainage density (D_{d}) | ${D}_{d}=\frac{{\displaystyle \sum}{L}_{u}}{A}$, (km/km^{2})where $\sum}{L}_{u$ is the total length of stream of all orders (km) | [34] |

Stream frequency (F_{s}) | ${F}_{s}=\frac{{\displaystyle \sum}{N}_{u}}{A}$, (1/km^{2}) | [34] |

Texture ratio (R_{t}) | ${R}_{t}=\frac{{\displaystyle \sum}{N}_{u}}{P}$, (1/km) | [31] |

Mean length of overland flow | ${L}_{om}=\frac{1}{2{D}_{d}}$ where ${L}_{om}$ is the mean length of overland flow (km) | [31] |

Shape Variables | Formula | References |
---|---|---|

Form factor (F_{f}) | ${F}_{f}=\frac{A}{{L}_{b}^{2}}$, $({F}_{f}<1)$ | [34] |

Circularity ratio (R_{c}) | ${R}_{c}=\frac{12.57A}{{P}^{2}}$, $({R}_{c}\le 1)$ | [35] |

Compactness coefficient (C_{c}) | ${C}_{c}=\frac{0.2821P}{{A}^{0.5}}$, $({C}_{c}\ge 1)$ | [32] |

Elongation ratio (R_{e}) | ${R}_{e}=\frac{1.128{A}^{0.5}}{{L}_{b}}$, $({R}_{e}\le 1)$ | [33] |

Sub-Watershed (SW) Name | Characteristic Variables | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

A (km ^{2}) | P (km) | Streams Order (u) | N_{u} | L_{u}(km) | $\overline{{\mathit{L}}_{\mathit{u}}}$ (km) | ${\mathit{L}}_{\mathit{b}}$ (km) | |||||

1 | 2 | 3 | 4 | 5 | |||||||

SW-1 | 34.849 | 32.844 | 14 | 3 | 0 | 0 | 1 | 18 | 31.593 | 1.755 | 11.422 |

SW-2 | 7.111 | 16.946 | 2 | 0 | 0 | 0 | 1 | 03 | 12.527 | 4.176 | 6.576 |

SW-3 | 22.552 | 24.341 | 9 | 2 | 1 | 0 | 0 | 12 | 17.654 | 1.471 | 7.601 |

SW-4 | 28.089 | 25.942 | 13 | 3 | 0 | 0 | 1 | 17 | 23.024 | 1.354 | 8.223 |

SW-5 | 29.710 | 31.826 | 9 | 2 | 1 | 0 | 1 | 13 | 21.156 | 1.627 | 11.604 |

SW-6 | 51.857 | 39.913 | 24 | 6 | 1 | 1 | 0 | 32 | 37.660 | 1.177 | 13.809 |

SW-7 | 59.623 | 37.456 | 23 | 6 | 2 | 1 | 0 | 32 | 41.441 | 1.295 | 10.664 |

SW-8 | 23.367 | 28.875 | 9 | 2 | 1 | 0 | 0 | 12 | 20.980 | 1.748 | 11.582 |

SW-9 | 37.654 | 30.361 | 12 | 2 | 1 | 0 | 0 | 15 | 28.798 | 1.919 | 8.944 |

Sub-Watershed | Sub-Watershed Wise Morphometric Variables | ||||||||
---|---|---|---|---|---|---|---|---|---|

Linear | Areal | Shape | |||||||

${\mathit{R}}_{\mathit{b}}$ | ${\mathit{D}}_{\mathit{d}}$ (km/km ^{2}) | ${\mathit{F}}_{\mathit{s}}$ (km ^{−2}) | ${\mathit{R}}_{\mathit{t}}$ (km ^{−1}) | ${\mathit{L}}_{\mathit{o}\mathit{m}}$ (km) | ${\mathit{F}}_{\mathit{f}}$ | ${\mathit{R}}_{\mathit{c}}$ | ${\mathit{C}}_{\mathit{c}}$ | ${\mathit{R}}_{\mathit{e}}$ | |

SW-1 | 3.476 | 0.906 | 0.516 | 0.548 | 0.551 | 0.267 | 0.406 | 1.557 | 0.583 |

SW-2 | 2.000 | 1.759 | 0.421 | 0.176 | 0.284 | 0.164 | 0.311 | 1.778 | 0.457 |

SW-3 | 2.621 | 0.782 | 0.532 | 0.493 | 0.638 | 0.390 | 0.478 | 1.435 | 0.704 |

SW-4 | 3.391 | 0.819 | 0.605 | 0.655 | 0.610 | 0.415 | 0.524 | 1.370 | 0.727 |

SW-5 | 1.619 | 0.712 | 0.437 | 0.408 | 0.702 | 0.220 | 0.368 | 1.635 | 0.530 |

SW-6 | 2.289 | 0.726 | 0.617 | 0.801 | 0.688 | 0.271 | 0.409 | 1.551 | 0.588 |

SW-7 | 2.552 | 0.695 | 0.536 | 0.854 | 0.719 | 0.524 | 0.534 | 1.358 | 0.817 |

SW-8 | 2.621 | 0.897 | 0.513 | 0.4155 | 0.556 | 0.174 | 0.352 | 1.672 | 0.470 |

SW-9 | 2.884 | 0.764 | 0.398 | 0.494 | 0.653 | 0.471 | 0.513 | 1.385 | 0.774 |

Sub-Watershed | Linear | Areal | Shape | ||||||
---|---|---|---|---|---|---|---|---|---|

${\mathit{R}}_{\mathit{b}}$ | ${\mathit{D}}_{\mathit{d}}$ | ${\mathit{F}}_{\mathit{s}}$ | ${\mathit{R}}_{\mathit{t}}$ | ${\mathit{L}}_{\mathit{o}\mathit{m}}$ | ${\mathit{F}}_{\mathit{f}}$ | ${\mathit{R}}_{\mathit{c}}$ | ${\mathit{C}}_{\mathit{c}}$ | ${\mathit{R}}_{\mathit{e}}$ | |

SW-1 | 1 | 2 | 5 | 4 | 8 | 4 | 4 | 6 | 4 |

SW-2 | 8 | 1 | 8 | 9 | 9 | 1 | 1 | 9 | 1 |

SW-3 | 4.5 | 5 | 4 | 6 | 5 | 6 | 6 | 6 | 6 |

SW-4 | 2 | 4 | 2 | 3 | 6 | 7 | 8 | 4 | 7 |

SW-5 | 9 | 8 | 7 | 8 | 2 | 3 | 3 | 7 | 3 |

SW-6 | 7 | 7 | 1 | 2 | 3 | 5 | 5 | 5 | 5 |

SW-7 | 6 | 9 | 3 | 1 | 1 | 9 | 9 | 1 | 9 |

SW-8 | 4.5 | 3 | 6 | 7 | 7 | 2 | 2 | 8 | 2 |

SW-9 | 3 | 6 | 9 | 5 | 4 | 8 | 7 | 3 | 8 |

**Table 7.**Correlation matrix between linear, areal, and shape morphometric variables of nine sub-watersheds of BW.

Morphometric Variables | ${\mathit{R}}_{\mathit{b}}$ | ${\mathit{D}}_{\mathit{d}}$ | ${\mathit{F}}_{\mathit{s}}$ | ${\mathit{R}}_{\mathit{t}}$ | ${\mathit{L}}_{\mathit{o}\mathit{m}}$ | ${\mathit{F}}_{\mathit{f}}$ | ${\mathit{R}}_{\mathit{c}}$ | ${\mathit{C}}_{\mathit{c}}$ | ${\mathit{R}}_{\mathit{e}}$ |
---|---|---|---|---|---|---|---|---|---|

${R}_{b}$ | 1.000 | −0.229 | 0.377 | 0.331 | 0.057 | 0.421 | 0.531 | −0.546 | 0.441 |

${D}_{d}$ | −0.229 | 1.000 | −0.399 | −0.710 *** | −0.972 * | −0.527 | −0.607 *** | 0.675 *** | −0.559 |

${F}_{s}$ | 0.377 | −0.399 | 1.000 | 0.721 *** | 0.350 | 0.174 | 0.315 | −0.352 | 0.208 |

${R}_{t}$ | 0.331 | −0.710 *** | 0.72 *** | 1.000 | 0.738 *** | 0.633 *** | 0.677 *** | −0.709 *** | 0.653 *** |

${L}_{om}$ | 0.057 | −0.972 * | 0.350 | 0.738 | 1.000 | 0.569 | 0.615 *** | −0.672 *** | 0.597 |

${F}_{f}$ | 0.421 | −0.527 | 0.174 | 0.633 | 0.569 | 1.000 | 0.975 * | −0.958 * | 0.997 * |

${R}_{c}$ | 0.531 | −0.607 *** | 0.315 | 0.677 | 0.615 *** | 0.975 * | 1.000 | −0.994 * | 0.983 * |

${C}_{c}$ | −0.546 | 0.675 *** | −0.352 | −0.709 | −0.672 *** | −0.958 * | −0.994 * | 1.000 | −0.972 * |

${R}_{e}$ | 0.441 | −0.559 | 0.208 | 0.653 | 0.597 | 0.997* | 0.983 * | −0.972 * | 1.000 |

Morphometric Variables | Initial Eigen Value | Extraction Sums of Squared Loadings | Rotation Sums of Squared Loadings | ||||||
---|---|---|---|---|---|---|---|---|---|

Total | % of Variance | Cumulative % | Total | % of Variance | Cumulative % | Total | % of Variance | Cumulative % | |

${R}_{b}$ | 5.947 | 66.079 | 66.079 | 5.947 | 66.079 | 66.079 | 4.063 | 45.140 | 45.140 |

${D}_{d}$ | 1.347 | 14.970 | 81.049 | 1.347 | 14.970 | 81.049 | 2.696 | 29.958 | 75.099 |

${F}_{s}$ | 1.113 | 12.365 | 93.414 | 1.113 | 12.365 | 93.414 | 1.648 | 18.315 | 93.414 |

${R}_{t}$ | 0.466 | 5.182 | 98.596 | ||||||

${L}_{om}$ | 0.118 | 1.316 | 99.912 | ||||||

${F}_{f}$ | 0.004 | 0.049 | 99.961 | ||||||

${R}_{c}$ | 0.003 | 0.035 | 99.997 | ||||||

${C}_{c}$ | 0.000 | 0.003 | 100.000 | ||||||

${R}_{e}$ | 0.000 | 0.000 | 100.000 |

Morphometric Variables | Principal Component | ||
---|---|---|---|

1 | 2 | 3 | |

${R}_{b}$ | 0.507 | 0.326 | 0.674 *** |

${D}_{d}$ | −0.787 ** | 0.446 | 0.247 |

${F}_{s}$ | 0.481 | −0.551 | 0.623 *** |

${R}_{t}$ | 0.841 ** | −0.388 | 0.155 |

${L}_{om}$ | 0.785 ** | −0.453 | −0.388 |

${F}_{f}$ | 0.903 * | 0.372 | −0.140 |

${R}_{c}$ | 0.951 * | 0.287 | −0.018 |

${C}_{c}$ | −0.972 * | −0.216 | 0.015 |

${R}_{e}$ | 0.922 * | 0.341 | −0.123 |

Morphometric Variables | Principal component | ||
---|---|---|---|

1 | 2 | 3 | |

${R}_{b}$ | 0.556 | −0.251 | 0.667 *** |

${D}_{d}$ | −0.336 | −0.858 ** | −0.173 |

${F}_{s}$ | −0.019 | 0.377 | 0.883 ** |

${R}_{t}$ | 0.390 | 0.668 *** | 0.532 |

${L}_{om}$ | 0.338 | 0.925 * | 0.049 |

${F}_{f}$ | 0.939 * | 0.297 | 0.055 |

${R}_{c}$ | 0.915 * | 0.329 | 0.205 |

${C}_{c}$ | −0.886 ** | −0.389 | −0.236 |

${R}_{e}$ | 0.933 * | 0.322 | 0.085 |

**Table 11.**Cross-correlation matrix of ${F}_{s}$, ${L}_{om}$ and ${F}_{f}$ variables of nine sub-watersheds of BW.

Morphometric Variables | ${\mathit{F}}_{\mathit{s}}$ | ${\mathit{L}}_{\mathit{o}\mathit{m}}$ | ${\mathit{F}}_{\mathit{f}}$ |
---|---|---|---|

${F}_{s}$ | 1.000 | 0.283 | −0.367 |

${L}_{om}$ | 0.283 | 1.000 | −0.600 |

${F}_{f}$ | −0.367 | −0.600 | 1.000 |

Sum of correlation | 0.917 | 0.683 | 0.033 |

Grand total | 1.633 | 1.633 | 1.633 |

Weight | 0.561 | 0.418 | 0.020 |

Sub-Watershed | Compound Factor | Priority Rank |
---|---|---|

SW-1 | 6.235 | 6 |

SW-2 | 8.276 | 9 |

SW-3 | 4.459 | 4 |

SW-4 | 3.776 | 3 |

SW-5 | 4.827 | 5 |

SW-6 | 1.918 | 1 |

SW-7 | 2.286 | 2 |

SW-8 | 6.337 | 7 |

SW-9 | 6.888 | 8 |

Sr. No. | Priority Level | Priority Category | Sub-Watershed | Percentage of Area |
---|---|---|---|---|

1 | 1.918 to ≤3.161 | Very high | SW-6, SW-7 | 37.81 |

2 | 3.161 to ≤4.403 | High | SW-4 | 9.53 |

3 | 4.403 to ≤5.646 | Medium | SW-3, SW-5 | 17.73 |

4 | 5.646 to ≤6.888 | Low | SW-1, SW-8, SW-9 | 32.52 |

5 | >6.888 | Very low | SW-2 | 2.41 |

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**MDPI and ACS Style**

Malik, A.; Kumar, A.; Kushwaha, D.P.; Kisi, O.; Salih, S.Q.; Al-Ansari, N.; Yaseen, Z.M. The Implementation of a Hybrid Model for Hilly Sub-Watershed Prioritization Using Morphometric Variables: Case Study in India. *Water* **2019**, *11*, 1138.
https://doi.org/10.3390/w11061138

**AMA Style**

Malik A, Kumar A, Kushwaha DP, Kisi O, Salih SQ, Al-Ansari N, Yaseen ZM. The Implementation of a Hybrid Model for Hilly Sub-Watershed Prioritization Using Morphometric Variables: Case Study in India. *Water*. 2019; 11(6):1138.
https://doi.org/10.3390/w11061138

**Chicago/Turabian Style**

Malik, Anurag, Anil Kumar, Daniel Prakash Kushwaha, Ozgur Kisi, Sinan Q. Salih, Nadhir Al-Ansari, and Zaher Mundher Yaseen. 2019. "The Implementation of a Hybrid Model for Hilly Sub-Watershed Prioritization Using Morphometric Variables: Case Study in India" *Water* 11, no. 6: 1138.
https://doi.org/10.3390/w11061138