# Prioritization of watershed through morphometric parameters: a PCA-based approach

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## Abstract

Remote sensing (RS) and Geographic Information Systems (GIS) techniques have become very important these days as they aid planners and decision makers to make effective and correct decisions and designs. Principal Component Analysis (PCA) involves a mathematical procedure that transforms a number of (possibly) correlated variables into a (smaller) number of uncorrelated variables. It reduces the dimensionality of the data set and identifies a new meaningful underlying variable. Morphometric analysis and prioritization of the sub-watersheds of Shakkar River Catchment, Narsinghpur district in Madhya Pradesh State, India, is carried out using RS and GIS techniques as discussed in Gajbhiye et al. (Appl Water Sci 4(1):51–61, 2013b). In this study we apply PCA technique in Shakkar River Catchment for redundancy of morphometric parameters and find the more effective parameters for prioritization of the watershed and discuss the comparison between Gajbhiye et al. (Appl Water Sci 4(1):51–61, 2013b) and the present prioritization scheme.

## Keywords

Watershed GIS Remote sensing Morphometric analysis Prioritization Principal component analysis## Introduction

India supports 16 % of world population on 2.42 % of global land area. An estimated 175 million hectares (M ha) of land constituting about 66 % of total geographical area suffers from deleterious effect of soil erosion and land degradation. Active erosion caused by water and wind alone accounts for 150 M ha of land, which accounts for soil loss of about 5300 million tons of top soil. In addition, 25 M ha is degraded due to ravine and gullies, shifting cultivation, salinity/alkalinity, water logging, etc. (Gajbhiye 2015).

The watershed management planning highlights the management techniques to control erosion in the catchment/watershed area (Gajbhiye et al. 2015a, b). Land and water resources are limited and their wide utilization is imperative, especially for countries like India, where the population pressure is continuously increasing (Sharma et al. 2014a, b). The growing pressures on land for food, fiber and fodder in addition to industrial expansion and consequent need for infrastructure facilities due to even increasing population have given rise to competing and conflicting demands on finite land and water resources (Biswas et al. 1999). The watershed is an ideal unit for planning and management of land and water resources (Gajbhiye et al. 2013a, b). Therefore, realistic assessment of the hydrological behavior of a watershed is important to develop an effective management plan (Sharma et al. 2014a, b). The watershed management concept recognizes the inter-relationships among the linkages between soil, slope, uplands, low lands, land use and geomorphology. Soil and water conservation is the key issue in watershed management while demarcating watersheds. However, while taking into consideration watershed soil-conservation work, it is not possible to take the whole area at once. Thus, the whole basin area is divided into several smaller units, as sub-watersheds or micro-watersheds, by considering its drainage system. Quantitative morphometric analysis of watershed can provide information about the hydrological nature of the rocks exposed within the watershed (Singh et al. 2014). Morphometric analysis is a significant tool for prioritization of sub-watersheds even without considering the soil map (Biswas et al. 1999). Morphometric analysis requires measurement of the linear features, gradient of channel network and contributing ground slopes of the drainage basin (Nautiyal 1994).

Many works have already been reported on morphometric analysis using Geographical Information Systems (GIS) and soil erosion (Shrimali et al. 2001); Sharma et al. 2015). Srinivasa et al. (2004) and Gajbhiye (2015) have used GIS techniques in morphometric analysis of sub-watersheds of Pawagada area, Tumkur district, Karnataka. Chopra et al. (2005) carried out morphometric analysis of Bhagra-Phungotri and Haramaja sub-watersheds of Gurdaspur district, Panjab. Khan et al. 2001 used RS and GIS techniques for watershed prioritization in the Guhiya basin, India. Nookaratnam et al. 2005 carried out a study on check dam positioning by prioritization of micro-watersheds using the sediment yield index (SYI) model and morphometric analysis using GIS. Gajbhiye et al. 2014b carried out a study on prioritization of watershed through SYI using RS and GIS approaches. Morphometric analysis and prioritization of eight sub-watersheds of Uttala river watershed, which is a tributary of Son River, was carried out by Sharma et al. (2010). Gajbhiye et al. 2013a, b Prioritizing erosion-prone area through morphometric analysis: an RS and GIS perspective. Many researchers (Gajbhiye et al. 2014a, b, c; Sharma et al. 2013a, b; Singh et al. 2013) have already reported on hypsometric analysis using Geographical Information System (GIS). Geographical Information System has been used for the calculation and delineation of the morphometric characteristics of the basin (Singh et al. 2013).

Factor analysis technique is very useful in the analysis of data corresponding to large number of variables; analysis via this technique produces easily interpretable results, and this method has been used successfully in hydrochemistry for many years; surface water, ground water quality assessment and environmental research employing multi-component techniques are well described in the literature (Praus 2005). The application of different multivariate statistical techniques, such as cluster analysis (CA), principal component analysis (PCA) and factor analysis (FA) help identify important components or factors accounting for most of the variances in a system (Ouyang et al. 2006; Shrestha and Kazama 2007). They are designed to reduce the number of variables to a small number of indices while attempting to preserve the relationships present in the original data. In recent years, many studies have been done using PCA in the interpretation of water quality parameters (Gajbhiye et al 2010, 2015b), geomorphometric parameters (Sharma et al. 2009), etc.

The geomorphologic studies are helpful in regionalising the hydrologic models. Since most of the basins are either ungauged or sufficient data are not available for them, the study on geomorphologic characteristics of such basins becomes much more important. The linking of geomorphologic parameters with the hydrological characteristics of the basin provides a simple way to understand the hydrological behaviour of different basins. The need for accurate information on watershed runoff and sediment yield has grown rapidly during the past decades because of the acceleration of watershed management programs for conservation, development, and beneficial use of all natural resources, including soil and water (Gajbhiye and Mishra 2012; Mishra et al. 2013; Gajbhiye et al. 2014a). In this study, morphometric analysis and prioritization of sub-watersheds are carried out for Shakkar River Catchment in Narsinghpur district of Madhya Pradesh, India.

### Our contribution

As outlined above, unfortunately, we found that not all the existing techniques have provided the optimum effective parameters for prioritization of a watershed. Therefore, our main contribution in this paper is to find the more effective parameters for prioritization of watershed and also show the comparison between previous prioritization by taking all the parameters in Gajbhiye et al. (2013b). Other researchers, as discussed above, also adopted the same approach by taking all the geomorphic parameters and then prioritizing the watersheds.

### Organization

The rest of this paper is organized as follows: Study area is introduced in “Study area”. Materials and methods is discussed in “Materials and methods”. Result and discussion are explained in “Results and discussion”. Finally, “Conclusions and findings” concludes and discusses the paper.

## Study area

^{2}area. The climate of the basin is generally dry except for the southwest monsoon season. The southwest monsoon starts from the middle of June and lasts till the end of September. October and middle of November constitute the post-monsoon or retreating monsoon season. The normal annual rainfall is 1192.1 mm. The normal maximum temperature during the month of May is 42.5 °C and minimum during the month of January is 8.2 °C. Soils are mainly clayey to loamy in texture with calcareous concretions invariably present. They are sticky and in summer, due to shrinkage, develop deep cracks. They generally predominate in montmorillonite and beidellite type of clays. In rest of alluvial areas, mixed clays, black to brown to reddish brown, derived from sandstones and traps are observed which is sandy clay in nature with calcareous concretions. Near the banks of the rivers and at the confluence, light yellow to yellowish brown soils are noticed which were deposited during the recent past . These soils are clayey to silt in nature (Gajbhiye et al. 2013b).

## Materials and methods

Formula for computation of morphometric parameters

Morphometric parameters | Formula | References |
---|---|---|

Stream order ( | Hierarchical rank | Strahler (1964) |

Stream length ( | Length of the stream | Horton (1945) |

Mean stream length ( | where, | Strahler (1964) |

Bifurcation ratio ( | where, | Schumn (1956) |

Mean bifurcation ratio ( | | Strahler (1964) |

Basin length ( | where, | Nookaratnam et.al. (2005) |

Drainage density ( | where, | Horton (1945) |

Stream frequency ( | where, | Horton (1945) |

Texture ratio ( | where, | Horton (1945) |

Form factor ( | where, | Horton (1945) |

Circulatory ratio ( | where, | Miller (1953) |

Elongation ratio ( | where, | Schumn (1956) |

Compactness constant ( | where, | Horton (1945) |

*R*

_{bm}), drainage density (

*D*

_{d}), mean stream length (

*L*

_{sm}), compactness coefficient (

*C*

_{c}), stream frequency (

*F*

_{s}), texture ratio (

*T*), length of overland flow (

*L*

_{o}), form factor (

*R*

_{f}), circulatory ratio (

*R*

_{c}) and elongation ratio (

*R*

_{e}) are also termed as erosion risk assessment parameters and have been used for prioritizing sub-watersheds. The linear parameters such as drainage texture, drainage density (

*D*

_{d}), stream frequency (

*F*

_{s}), bifurcation ratio (

*R*

_{b}), length of overland flow (

*L*

_{o}) have a direct relationship with erodibility; higher the value, more is the erodibility (Singh et al. 2013; Nookaratnam et al. 2005). Hence for prioritization of sub-watersheds, the highest value of linear parameters was rated as rank 1, second highest value was rated as rank 2 and so on, and the least value was rated last in rank. Shape parameters such as elongation ratio, compactness coefficient, circulatory ratio, basin shape and form factor have an inverse relationship with erodibility (Nookaratnam et al. 2005; Javeed et al. 2009); lower the value, more is the erodibility. Thus the lowest value of shape parameters was rated as rank 1, next lower value was rated as rank 2 and so on and the highest value was rated last in rank. Hence, the ranking of the sub-watersheds has been determined by assigning the highest priority/rank based on highest value in case of linear parameters and lowest value in case of shape parameters. After the ranking has been done based on every single parameter, the ranking values for all the linear and shape parameters of each sub-watershed were added up for each of the eight sub-watersheds to arrive at compound value (

*C*

_{p}). Based on average value of these parameters, the sub-watershed having the least rating value was assigned the highest priority; the next higher value was assigned second priority and so on.

Basic parameters of the Shakkar River catchment

SW No. | SW name | Basin area (km | Perimeter (km) | Basin length (km) |
---|---|---|---|---|

1 | S1 | 9.23 | 17.03 | 3.41 |

2 | S2 | 37.87 | 41.11 | 9.00 |

3 | S3 | 114.00 | 71.70 | 18.01 |

4 | S4 | 538.22 | 171.78 | 43.00 |

5 | S5 | 158.35 | 75.06 | 23.61 |

6 | S6 | 581.45 | 150.45 | 36.89 |

7 | S7 | 383.43 | 164.68 | 46.90 |

8 | S8 | 397.96 | 131.84 | 25.27 |

### Another approach using the Principal Component Analysis

The geomorphic parameters are usually many times correlated. The correlation indicates that some of the information contained in one variable is also contained in some of the other remaining variables. The method of components analysis involves the rotation of coordinate axes to a new frame of reference in the total variable space—an orthogonal or uncorrelated transformation wherein each of the *n* original variables is describable in terms of the new principal components. An important characteristic of the new components is that they account, in turn, for a maximum amount of variance of the variables. Principal component analysis is applied for all geomorphic parameters to calculate the correlation matrix and also to derive principal components and find out the most effective parameter. The first factor-loading matrix and the rotated factor-loading matrix are used in this analysis. The same process of the ranking of parameter is followed as discussed earlier (Javeed et al. 2009).

## Results and discussion

The information about basic morphometric parameters such as area (*A*), perimeter (*P*), length (*L*), and number of streams (*N*) was obtained from sub-watershed delineated layer, and basin length (*L* _{b}) was calculated from stream length, while the bifurcation ratio (*R* _{b}) was calculated from the number of streams. Other morphometric parameters were calculated using the equations as described in Table 1.

### Stream order (*u*)

Linear aspect of the Shakkar River catchment

Sub-watershed | Stream order | Mean bifurcation ratio ( | |||||||
---|---|---|---|---|---|---|---|---|---|

I | II | III | IV | V | VI | VII | VIII | ||

Sub-watershed-1 | |||||||||

No. of streams | 58 | 13 | 2 | 0 | 0 | 0 | 2 | 1 | 3.49 |

Stream length (km) | 20.98 | 6.26 | 2.34 | 0 | 0 | 0 | 0.098 | 4.23 | |

Sub-watershed-2 | |||||||||

No. of streams | 209 | 49 | 14 | 2 | 0 | 2 | 1 | 0 | 3.55 |

Stream length (km) | 66 | 30 | 16 | 6 | 0 | 0.097 | 10 | 0 | |

Sub-watershed-3 | |||||||||

No. of streams | 590 | 125 | 29 | 7 | 2 | 1 | 0 | 0 | 3.73 |

Stream length (km) | 163 | 83 | 38 | 12 | 24 | 4.37 | 0 | 0 | |

Sub-watershed-4 | |||||||||

No. of streams | 2992 | 646 | 138 | 28 | 5 | 3 | 1 | 0 | 4.30 |

Stream length (km) | 867 | 411 | 185 | 72 | 58.12 | 0.18 | 75.66 | 0 | |

Sub-watershed-5 | |||||||||

No. of streams | 913 | 211 | 52 | 8 | 2 | 1 | 0 | 0 | 4.17 |

Stream length (km) | 246 | 121 | 52 | 40 | 20 | 7.36 | 0 | 0 | |

Sub-watershed-6 | |||||||||

No. of streams | 3237 | 715 | 164 | 45 | 11 | 1 | 0 | 0 | 5.52 |

Stream length (km) | 961 | 433 | 237 | 108 | 50 | 48.83 | 0 | 0 | |

Sub-watershed-7 | |||||||||

No. of streams | 2165 | 463 | 117 | 25 | 3 | 1 | 0 | 0 | 4.93 |

Stream length (km) | 633 | 286 | 127 | 71 | 29 | 42.68 | 0 | 0 | |

Sub-watershed-8 | |||||||||

No. of streams | 2340 | 544 | 125 | 29 | 5 | 1 | 0 | 0 | 4.75 |

Stream length (km) | 662 | 279 | 154 | 87 | 30 | 40.37 | 0 | 0 |

### Stream number

It is the number of stream segment of various orders and it is inversely proportional to the stream order. It is observed from Table 3 that the maximum frequency is in case of first-order streams. It is also noticed that there is a decrease in stream frequency as the stream order increases. Sub-watershed-6 has maximum number of streams of 1st order (*N* _{ u } = 3237), 2nd order (*N* _{ u } = 715), 3rd order (*N* _{ u } = 164), 4th order (*N* _{ u } = 45), 5th order (*N* _{ u } = 11), 6th order (*N* _{ u } = 1), among all other comparisons.

### Total stream length (*L* _{ u })

The stream lengths of the various segments are measured with the help of GIS software. All the sub-watersheds show that the total length of stream segments is maximum in first-order streams and decreases as the stream order increases (Table 3). Sub-watershed-4 has the longest stream length (*L* _{ u } = 1268.96 km), while sub-watershed-1 has the minimum value of *L* _{ u } = 33.91 km.

### Bifurcation ratio (*R* _{b})

Horton (1945) considered bifurcation ratio as an index of relief and dissection. Strahler (1957) demonstrated that *R* _{b} shows only small variations for different regions in different environments except where powerful geological control dominates. Lower *R* _{b} values are the characteristics of structurally less disturbed watershed without any distortion in drainage pattern (Nag 1998). The sub-watershed-6 has maximum (*R* _{b} = 5.52) while sub-watershed-1 has minimum (*R* _{b} = 3.49). *R* _{b} characteristically ranges between 3.0 and 5.0 for watershed where the influence of geological structure on the drainage network is negligible (Verstappen 1983). The values of *R* _{b} for eight sub-watersheds are presented in Table 3.

### Drainage density (*D* _{d})

*D*

_{d}is the characteristic of regions underlain by highly permeable materials with vegetative cover and low relief. Whereas, high values of

*D*

_{d}indicate regions of weak and impermeable subsurface material, sparse vegetation and mountainous relief (Nautiyal 1994). Drainage density in the study area varies between 2.84 and 3.67 indicating low drainage density (Table 4).

Aerial aspect of the Shakkar River catchment

Sub-watershed | Drainage density ( | Stream frequency ( | Circulatory ratio ( | Form factor ( | Elongation ratio ( | Texture ratio ( | Length of overland flow ( | Compactness constant ( | Ruggedness number ( |
---|---|---|---|---|---|---|---|---|---|

1 | 3.673 | 8.232 | 0.403 | 0.794 | 1.006 | 4.464 | 0.136 | 0.126 | 0.147 |

2 | 3.383 | 7.315 | 0.283 | 0.468 | 0.772 | 6.739 | 0.148 | 0.048 | 0.203 |

3 | 2.845 | 6.614 | 0.281 | 0.351 | 0.669 | 10.516 | 0.176 | 0.021 | 1.682 |

4 | 3.101 | 7.085 | 0.231 | 0.291 | 0.609 | 22.197 | 0.161 | 0.007 | 1.896 |

5 | 3.071 | 7.496 | 0.356 | 0.284 | 0.602 | 15.815 | 0.163 | 0.015 | 1.659 |

6 | 3.161 | 7.177 | 0.325 | 0.427 | 0.738 | 27.738 | 0.158 | 0.006 | 1.865 |

7 | 3.100 | 7.235 | 0.179 | 0.174 | 0.471 | 16.845 | 0.161 | 0.009 | 2.483 |

8 | 3.147 | 7.649 | 0.290 | 0.623 | 0.891 | 23.088 | 0.159 | 0.008 | 1.825 |

### Stream frequency/drainage frequency (*F* _{s})

Stream frequency is the total number of stream segments of all orders per unit area (Horton 1932). The stream frequency relates to permeability, infiltration capability and relief of watershed. A low value 6.61 is observed in sub-watershed-3, while a high value 8.23 is observed in sub-watershed-1. Stream frequency values indicate positive correlation with the drainage density of all the sub-watersheds suggesting increase in stream population with respect to increase in drainage density.

### Form factor (*R* _{f})

It is the ratio of basin area *A*, to the square of maximum length of the basin *L* _{b}. It is a dimensionless property and is used as a quantitative expression of the shape of basin form. The sub-watershed-1 has maximum value (*R* _{f} = 0.79) while sub-watershed-7 has minimum value of (*R* _{f} = 0.17). The smaller the value of form factor is, the more elongated the basin will be. The basin with a high form factor has high peak flows of shorter duration, whereas the basin with a low form factor has lower peak flows of longer duration. Therefore, sub-watershed-7 will have lower peak flows of longer duration. However, sub-watershed-1 will have high peak flows of shorter duration.

### Circulatory ratio (*R* _{c})

Miller (1953) introduced the circulatory ratio to quantify the basin shape. It is the ratio of the watershed area and the area of circle of watershed perimeter (*P*). Circulatory ratio (*R* _{c}) is influenced by the length and frequency of streams, geological structures, land use/land cover, climate, relief and slope of the basin. Values of circulatory ratio of all sub-watersheds are presented in Table 4. The sub-watershed-7 has minimum value (*R* _{c} = 0.17), while sub-watershed-1 has maximum value (*R* _{c} = 0.40). According to the Miller range, sub-watersheds are elongated in shape, with low discharge of runoff and high permeability subsoil condition.

### Elongation ratio (*R* _{e})

The elongation ratio is an indication of the shape of the watershed. According to Schumn (1956), elongation ratio is defined as the ratio of the diameter of a circle having the same area as the basin and the maximum basin length. The values of elongation ratio generally vary from 0.6 to 1.0 over a wide variety of climatic and geologic types. Values close to 1.0 are typical of regions of very low relief, whereas values in the range 0.6–0.8 are generally associated with high relief and steep ground slope (Strahler 1964). It is a very significant index in the analysis of basin shape, which helps to give an idea about the hydrological character of a drainage basin. A circular basin is more efficient in the discharge of runoff than an elongated basin. The value of elongation ratio of eight sub-watersheds is presented in Table 4. The lowest values of 0.47 (sub-watershed-7) and 0.97 (sub-watershed-1) indicate high relief and steep slopes, while remaining sub-watershed indicates a plain land with low relief and low slope.

### Length of overland flow (*L* _{o})

The overland flow and surface runoff are quite different; the overland flow refers to that flow of precipitated water, which moves over the land surface leading to the stream channels, while the channel flow reaching the outlet of watershed is referred as surface runoff. The overland flow is dominant in smaller watershed instead of larger watersheds. The length and depth of overland flow are small and found in laminar condition (Horton 1945). Sub-watershed-3 has maximum (*L* _{o} = 0.17 km) and sub-watershed-1 has minimum (*L* _{o} = 0.13 km) length of overland flow among 8 sub-watersheds (Table 4).

### Relief ratio (*R* _{h})

Relief aspect of the Shakkar River catchment

Sub-watershed | Relative relief ( | Relief ratio ( | Average slope (Sa) | HI |
---|---|---|---|---|

1 | 0.012 | 0.002 | 6.036 | 0.498 |

2 | 0.007 | 0.001 | 4.099 | 0.471 |

3 | 0.030 | 0.008 | 10.085 | 0.501 |

4 | 0.014 | 0.003 | 9.803 | 0.497 |

5 | 0.023 | 0.007 | 11.67 | 0.488 |

6 | 0.016 | 0.004 | 9.329 | 0.491 |

7 | 0.017 | 0.005 | 14.818 | 0.483 |

8 | 0.023 | 0.004 | 13.071 | 0.508 |

### Average slope (*S* _{a})

Average slope of the watershed, *S* _{a} has direct influence on the erodibility of the watershed. It has been proved by researchers that the more the percentage of slopes is, more is the erosion, if other factors remain unchanged. The values of Average slope vary from 9.27 to 88.50 (Table 5).

### Relative relief (*R* _{r})

Relative relief (*R* _{r}) is the ratio of the maximum watershed relief to the perimeter of the watershed. The value of the relative relief for eight sub-watersheds is shown in Table 5. Sub-watershed-2 has minimum *R* _{r} (0.007), while sub-watershed-3 had the maximum value (0.030).

### Ruggedness number (*R* _{N})

The value of *R* _{N} for eight sub-watersheds is shown in Table 5. The sub-watershed-7 has maximum ruggedness number (*R* _{N} = 2.48), while sub-watershed-1 has minimum value (*R* _{N} = 0.14). The sub-watershed has overall high roughness, which indicates the structural complexity of the terrain in association with relief and drainage density. It also implies that the area is susceptible to more erosion.

### Texture ratio (*T*)

Texture ratio is an important factor in drainage morphometric analysis, which depends on the underlying lithology, infiltration capacity and relief aspect of the terrain. The value of the texture ratio is shown in Table 5. The sub-watershed-6 has maximum (*T* = 27.73), while sub-watershed-1 has minimum (*T* = 4.46).

### Compactness constant (*C* _{c})

The value of the compactness constant is shown in Table 5. The sub-watershed-1 has maximum (*C* _{c} = 0.12), while sub-watershed-6 has minimum (*C* _{c} = 0.006).

### Hypsometric integral (HI)

*y*, is the ratio of height of a given contour, h, to total basin relief,

*H*. Relative area,

*x*, is the ratio of horizontal cross-sectional area,

*a*, to the entire watershed area,

*A*. The percentage hypsometric curve is a plot of the continuous function relating relative height,

*y*, to relative area,

*x*. As shown in the lower right part of the diagram, the shape of the hypsometric curve varies in early geologic stages of development of the watershed, but once a steady state (mature stage) is attained, tends to vary little thereafter, despite lowering relief. Several dimensionless attributes of the hypsometric curve are measurable and these can be used for comparison. One such is hypsometric integral,

*H*

_{si}, or the relative area lying below the curve, i.e. the ratio of area under the hypsometric curve to the area of the entire square. It is expressed in percentage and can be estimated from the hypsometric curves of the watersheds by measuring the area under the curve with the help of different methods, but the Pike and Wilson (1971) method (or elevation-relief ratio method) is a less cumbersome and faster method and it is used in the study for estimating hypsometric integral. The relationship is expressed as:

*E*is the elevation-relief ratio equivalent to the hypsometric integral

*H*

_{si}; Elev

_{mean}is the weighted mean elevation of the watershed estimated from the identifiable contours of the delineated sub-watersheds; Elev

_{min}and Elev

_{max}are the minimum and maximum elevations within the sub-watersheds. After obtaining the hypsometric integrals of the selected watersheds and comparing with the model hypsometric curves (Fig. 5, bottom right), the stages of development of the watersheds under study are determined with the following criteria:

- (a)
The watersheds will be in inequilibrium (youthful) stage if

*H*_{si}≥ 0.60, - (b)
The watersheds are considered to attain the equilibrium stage if

*H*_{si}ranges between 0.35 and 0.60, and - (c)
The watersheds are in monadnock phase if

*H*_{si}≤ 0.35.

### Intercorrelation among the geomorphic parameters

*R*

_{h}) and relative relief (

*R*

_{r}); between ruggedness number (

*R*

_{N}) and average slope (

*S*

_{a}); between drainage density (

*D*

_{d}) and length of overland flow (

*L*

_{o}); and between form factor (

*R*

_{f}) and elongation ratio (

*R*

_{e}). Also, good correlations (correlation coefficient more than 0.75) exist between

*R*

_{h}and

*D*

_{d},

*L*

_{o}; between

*R*

_{r}and

*D*

_{d},

*L*

_{o}; between

*R*

_{N}and bifurcation ratio (

*R*

_{b}),

*D*

_{d}, texture ratio (

*T*),

*L*

_{o}, and compactness coefficient (

*C*

_{c}); between

*D*

_{d}and stream frequency (

*F*

_{s}),

*C*

_{c}; and between

*F*

_{s}and

*L*

_{o}. Some more moderately correlated parameters (correlation coefficient more than 0.6) are

*R*

_{N}with circulatory ratio (

*R*

_{c}),

*R*

_{f}and

*R*

_{e};

*D*

_{d}with

*R*

_{f},

*R*

_{e}and

*S*

_{a};

*F*

_{s}with

*R*

_{f},

*R*

_{e},

*C*

_{c}, and hypsometric integral (HI);

*R*

_{c}with

*R*

_{f},

*R*

_{e},

*C*

_{c}, and HI; and

*R*

_{f}with

*L*

_{o}and

*C*

_{c}. It is very difficult at this stage to group the parameters into components and attach physical significance. Hence, in the next step, the principal component analysis has been applied to the correlation matrix.

Intercorrelation matrix of the geomorphological parameter of Shakkar watershed

| | | | | | | | | | | | | HI | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| 1.00 | 0.92 | 0.55 | 0.13 | −0.75 | −0.41 | −0.02 | −0.24 | −0.23 | 0.22 | 0.80 | −0.43 | 0.62 | 0.05 |

| 0.92 | 1.00 | 0.60 | 0.15 | −0.80 | −0.51 | −0.08 | −0.51 | −0.50 | 0.17 | 0.83 | −0.48 | 0.62 | −0.02 |

| 0.55 | 0.60 | 1.00 | 0.74 | −0.78 | −0.52 | −0.61 | −0.69 | −0.71 | 0.75 | 0.75 | −0.84 | 0.91 | 0.13 |

| 0.13 | 0.15 | 0.74 | 1.00 | −0.35 | −0.18 | −0.33 | −0.33 | −0.33 | 0.90 | 0.29 | −0.66 | 0.62 | −0.04 |

| −0.75 | −0.80 | −0.78 | −0.35 | 1.00 | 0.84 | 0.52 | 0.73 | 0.69 | −0.47 | −1.00 | 0.85 | −0.63 | −0.48 |

| −0.41 | −0.51 | −0.52 | −0.18 | 0.84 | 1.00 | 0.60 | 0.72 | 0.67 | −0.28 | −0.85 | 0.70 | −0.22 | −0.69 |

| −0.02 | −0.08 | −0.61 | −0.33 | 0.52 | 0.60 | 1.00 | 0.69 | 0.71 | −0.31 | −0.48 | 0.63 | −0.49 | −0.62 |

| −0.24 | −0.51 | −0.69 | −0.33 | 0.73 | 0.72 | 0.69 | 1.00 | 0.99 | −0.33 | −0.70 | 0.74 | −0.51 | −0.36 |

| −0.22 | −0.50 | −0.70 | −0.32 | 0.69 | 0.67 | 0.71 | 0.99 | 1.00 | −0.30 | −0.66 | 0.69 | −0.55 | −0.30 |

| 0.21 | 0.16 | 0.75 | 0.90 | −0.47 | −0.27 | −0.30 | −0.33 | −0.30 | 1.00 | 0.41 | −0.77 | 0.57 | 0.10 |

| 0.79 | 0.83 | 0.74 | 0.28 | −0.99 | −0.84 | −0.48 | −0.70 | −0.66 | 0.41 | 1.00 | −0.80 | 0.60 | 0.46 |

| −0.43 | −0.45 | −0.83 | −0.65 | 0.85 | 0.69 | 0.62 | 0.74 | 0.69 | −0.77 | −0.80 | 1.00 | −0.65 | −0.54 |

| 0.61 | 0.62 | 0.90 | 0.61 | −0.63 | −0.22 | −0.48 | −0.51 | −0.55 | 0.57 | 0.60 | −0.65 | 1.00 | −0.05 |

HI | 0.04 | −0.01 | 0.13 | −0.03 | −0.48 | −0.68 | −0.61 | −0.36 | −0.30 | 0.10 | 0.46 | −0.54 | −0.05 | 1.00 |

Here, grouping of the parameters into components at this stage is very difficult. Hence, in the next step, the principal component analysis has been applied. The correlation matrix is subjected to the principal component analysis.

#### Principal component analysis

The principal component analysis method was used to obtain the first factor-loading matrix, and thereafter, the rotated loading matrix using orthogonal transformation. The results are shown in the following sections.

##### First factor-loading matrix

*R*

_{N},

*D*

_{d},

*L*

_{o}, and

*C*

_{c}and correlated satisfactorily (more than 0.75) with

*R*

_{f},

*R*

_{e},

*F*

_{s}, and

*S*

_{a}, and moderately (loading more than 0.60) with

*R*

_{r},

*R*

_{c}and

*T*. The second component is moderately correlated with HI and the third component moderately with

*R*

_{h}for Shakkar watershed. It is observed from these results that

*R*

_{b}does not show any correlation with any of the components. Some parameters are highly correlated with some components, some moderately, and some parameters do not correlate with any component. Thus, at this stage, it is difficult to identify a physically significant component. It is necessary to rotate the first factor-loading matrix to get a better correlation.

Total variance explained of Shakkar watershed

Component | Initial eigen values | Extraction sums of squared loadings | Rotation sums of squared loadings | ||||||
---|---|---|---|---|---|---|---|---|---|

Total | % of variance | Cumulative % | Total | % of variance | Cumulative % | Total | % of variance | Cumulative % | |

1 | 8.17 | 58.33 | 58.33 | 8.17 | 58.33 | 58.33 | 4.46 | 31.84 | 31.84 |

2 | 2.10 | 14.99 | 73.31 | 2.10 | 14.99 | 73.31 | 3.98 | 28.42 | 60.26 |

3 | 1.97 | 14.05 | 87.36 | 1.97 | 14.05 | 87.36 | 3.79 | 27.10 | 87.36 |

4 | 0.99 | 7.05 | 94.41 | ||||||

5 | 0.52 | 3.69 | 98.10 | ||||||

6 | 0.18 | 1.27 | 99.36 | ||||||

7 | 0.09 | 0.64 | 100.00 | ||||||

8 | 0.00 | 0.00 | 100.00 | ||||||

9 | 0.00 | 0.00 | 100.00 | ||||||

10 | 0.00 | 0.00 | 100.00 | ||||||

11 | 0.00 | 0.00 | 100.00 | ||||||

12 | 0.00 | 0.00 | 100.00 | ||||||

13 | 0.00 | 0.00 | 100.00 | ||||||

14 | 0.00 | 0.00 | 100.00 |

Unrotated matrix

Component | |||
---|---|---|---|

1 | 2 | 3 | |

Component matrix | |||

| 0.618 | 0.237 | 0.711 |

| 0.703 | 0.156 | 0.676 |

| 0.917 | 0.336 | −0.130 |

| 0.557 | 0.584 | −0.507 |

| −0.950 | 0.112 | −0.248 |

| −0.782 | 0.505 | −0.068 |

| −0.669 | 0.366 | 0.461 |

| −0.830 | 0.271 | 0.136 |

| −0.807 | 0.233 | 0.142 |

| 0.613 | 0.507 | −0.451 |

| 0.922 | −0.132 | 0.329 |

| −0.923 | −0.014 | 0.237 |

| −0.015 | 0.535 | 0.019 |

HI | −0.108 | −0.157 | −0.043 |

##### Rotation of first factor-loading matrix

*F*

_{s},

*R*

_{c}

*R*

_{f}, and HI; and moderately with

*C*

_{c}and

*R*

_{e}which may be termed as stage-form component. The second component is strongly correlated with

*R*

_{h},

*R*

_{r}; and good with

*D*

_{d}and

*L*

_{o}and it can be termed as relief-density component. The third component is strongly correlated with

*R*

_{b}and

*T*and good with

*R*

_{N}and moderately correlated with

*S*

_{a}and may be termed as organization-processes component for Shakkar watershed. As seen (Table 9), the most important parameter is

*F*

_{s}(stream frequency) followed by

*R*

_{r}(relative relief),

*R*

_{b}(bifurcation ratio), so finally these parameters have been taken for the prioritization.

Rotated matrix

Component | |||
---|---|---|---|

1 | 2 | 3 | |

Rotated component matrix | |||

| −0.010 | 0.964 | 0.117 |

| −0.132 | 0.970 | 0.127 |

| −0.366 | 0.476 | 0.781 |

| −0.069 | 0.012 | 0.951 |

| 0.604 | −0.721 | −0.304 |

| 0.836 | −0.412 | −0.046 |

| 0.816 | 0.053 | −0.355 |

| 0.754 | −0.317 | −0.334 |

| 0.714 | −0.305 | −0.350 |

| −0.144 | 0.075 | 0.900 |

| −0.578 | 0.767 | 0.233 |

| 0.634 | −0.338 | −0.626 |

| −0.115 | 0.535 | 0.719 |

HI | −0.808 | −0.057 | −0.143 |

### Comparison of two approaches for prioritization of sub-watersheds

Priorities of sub-watersheds and their ranks

Sub-watershed | | | | | | | | | | | | | | HI | Compound parameter ( | Final priority |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 8 | 1 | 1 | 1 | 8 | 8 | 8 | 8 | 8 | 8 | 7 | 7 | 7 | 3 | 5.93 | 7 |

2 | 7 | 2 | 4 | 5 | 6 | 6 | 7 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 6.43 | 8 |

3 | 6 | 8 | 8 | 6 | 4 | 4 | 6 | 1 | 6 | 5 | 1 | 1 | 4 | 2 | 4.43 | 6 |

4 | 1 | 5 | 7 | 7 | 3 | 3 | 3 | 3 | 2 | 2 | 6 | 6 | 5 | 4 | 4.07 | 5 |

5 | 5 | 7 | 3 | 2 | 2 | 2 | 5 | 2 | 5 | 6 | 3 | 2 | 3 | 6 | 3.79 | 3 |

6 | 1 | 3 | 6 | 3 | 5 | 5 | 1 | 6 | 1 | 3 | 5 | 5 | 6 | 5 | 3.93 | 4 |

7 | 2 | 6 | 5 | 8 | 1 | 1 | 4 | 4 | 4 | 1 | 4 | 3 | 1 | 7 | 3.64 | 2 |

8 | 3 | 4 | 2 | 4 | 7 | 7 | 2 | 5 | 3 | 4 | 2 | 4 | 2 | 1 | 3.57 | 1 |

Priorities of sub-watersheds and their ranks

Sub-watershed | | | | Compound parameter ( | Final priority |
---|---|---|---|---|---|

1 | 8 | 1 | 7 | 5.33 | 7 |

2 | 7 | 4 | 8 | 6.33 | 8 |

3 | 6 | 8 | 1 | 5.00 | 6 |

4 | 1 | 7 | 6 | 4.67 | 5 |

5 | 5 | 3 | 2 | 3.33 | 3 |

6 | 1 | 6 | 5 | 4.00 | 4 |

7 | 2 | 5 | 3 | 3.33 | 2 |

8 | 3 | 2 | 4 | 3.00 | 1 |

## Conclusions and findings

The quantitative morphometric analysis was carried out in eight sub-watersheds of Shakkar River catchment using GIS technique for determining the linear aspects such as Stream order, Bifurcation ratio, Stream length and aerial aspects such as drainage density (*D* _{d}), stream frequency (*F* _{s}), form factor (*R* _{f}), circulatory ratio (*R* _{c}), and elongation ratio (*R* _{e}). The prioritization based on different morphometric parameters is time consuming. However, PCA-based approach allows for more effective parameters for prioritizing watersheds. The morphometric analysis of different sub-watersheds shows their relative characteristics with respect to hydrologic response of the watershed. Results of morphometric analysis show that sub-watershed 7 and 5 are possibly having high erosion. Hence, suitable soil erosion control measures are required in these watersheds to preserve the land from further erosion. The present study demonstrates the utility of RS, GIS and PCA techniques in prioritizing sub-watersheds based on morphometric analysis.

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