Optimization of significant morphometric parameters and sub-watershed prioritization using PCA and PCA-WSM for soil conservation: a case study in Dharla River watershed, Bangladesh

Abstract

Proper knowledge of watershed geometry and the geomorphic condition is a prerequisite before developing and implementing any watershed management plan. Hence, GIS-based morphometric analysis has gained more importance in delineating natural drainage systems as well as watershed prioritization and management. The present study introduces a hybrid model by integrating geo-informatics and multivariate statistical models to evaluate the most significant erosion-prone morphometric parameters (EPMPs) and sub-watersheds (SWS) in the Dharla River watershed (DRW). Two statistical methods i.e. principal component analysis (PCA) and PCA adopted weighted sum model (PCA-WSM) are combinedly applied to prioritize the SWS. Nine SWS along with the stream network are delineated using shuttle radar topography mission digital elevation model (SRTM-DEM) of the study area to optimize the morphometric parameters (MPs) (i.e. linear, areal, and shape). Twelve primarily selected EPMPs are successfully reduced to the four most significant EPMPs (T, Ff, Re, and Cc) through PCA to optimize the most susceptible SWS for land management practices. PCA identifies SWS-6 as the most vulnerable zone, with the lowest compound factor (CF) value, and the PCA-WSM yields a similar conclusion. The correlative study between these two methods reclassifies the nine SWS into the high, medium, and low priority zones, with SWS-1, SWS-5, SWS-6, and SWS-9 in the high priority zone, SWS-4 in the medium priority zone, and SWS-3 in the low priority zone, while others show their existence in different zones. The high priority reflects a high risk for erosion; hence, required an immediate action plan for soil conservation and protection. The PCA and PCA-WSM show a significant level of consistency (66.67%) in identifying susceptible zone for soil erosion. Therefore, the proposed methods will be more effective for watershed prioritization study in terms of erosion risk assessment.

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Modeling Earth Systems and Environment
https://doi.org/10.1007/s40808-021-01255-9
ORIGINAL ARTICLE
Optimization ofsignificant morphometric parameters
andsub‑watershed prioritization using PCA andPCA‑WSM forsoil
conservation: acase study inDharla River watershed, Bangladesh
Md.MahabuburRahman1 · MohammadNazimZaman1,2· PradipKumarBiswas2
Received: 24 June 2021 / Accepted: 8 August 2021
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
Abstract
Proper knowledge of watershed geometry and the geomorphic condition is a prerequisite before developing and implement-
ing any watershed management plan. Hence, GIS-based morphometric analysis has gained more importance in delineating
natural drainage systems as well as watershed prioritization and management. The present study introduces a hybrid model by
integrating geo-informatics and multivariate statistical models to evaluate the most significant erosion-prone morphometric
parameters (EPMPs) and sub-watersheds (SWS) in the Dharla River watershed (DRW). Two statistical methods i.e. prin-
cipal component analysis (PCA) and PCA adopted weighted sum model (PCA-WSM) are combinedly applied to prioritize
the SWS. Nine SWS along with the stream network are delineated using shuttle radar topography mission digital elevation
model (SRTM-DEM) of the study area to optimize the morphometric parameters (MPs) (i.e. linear, areal, and shape). Twelve
primarily selected EPMPs are successfully reduced to the four most significant EPMPs (T, Ff, Re, and Cc) through PCA to
optimize the most susceptible SWS for land management practices. PCA identifies SWS-6 as the most vulnerable zone, with
the lowest compound factor (CF) value, and the PCA-WSM yields a similar conclusion. The correlative study between these
two methods reclassifies the nine SWS into the high, medium, and low priority zones, with SWS-1, SWS-5, SWS-6, and
SWS-9 in the high priority zone, SWS-4 in the medium priority zone, and SWS-3 in the low priority zone, while others show
their existence in different zones. The high priority reflects a high risk for erosion; hence, required an immediate action plan
for soil conservation and protection. The PCA and PCA-WSM show a significant level of consistency (66.67%) in identify-
ing susceptible zone for soil erosion. Therefore, the proposed methods will be more effective for watershed prioritization
study in terms of erosion risk assessment.
Keywords GIS· Morphometric analysis· Principal component analysis· Weighted sum model· PCA-WSM· Soil erosion
Introduction
Watershed management is concerned with the preservation
of natural resources, such as land and water, and corresponds
to an area of land that flows to a certain place along a river
or watercourses (Tomer 2014). Watershed management
gains more importance in conservation planning due to the
degradation of the watershed resources resulting from vari-
ous natural and manmade activities. World statistic shows
that about 52% of agricultural lands worldwide are affected
by different types of degradation processes, among which
almost 80% are affected by water erosion (Kumawat etal.
2021). Furthermore, global food production systems are
jeopardized as aquifers continue to deplete and demands
on underground water increase day by day, also resulting
in serious climatic issues (i.e. land subsidence, drought,
desertification, etc.) worldwide (Chitsazan etal. 2020;
Dalin 2021). These extensive losses of watershed resources
are deteriorating environmental quality and posing a threat
to global sustainable economic development. Bangladesh,
like other countries around the world, also faces various
water and land degradation calamities (i.e. flood, soil loss,
* Md. Mahabubur Rahman
mahabubur07geology@gmail.com
1 Mineral Processing Center (MPC), Institute ofMining,
Mineralogy, andMetallurgy (IMMM), Bangladesh Council
ofScientific andIndustrial Research (BCSIR), Joypurhat
Sadar, Joypurhat5900, Bangladesh
2 Institute ofMining, Mineralogy, andMetallurgy (IMMM),
Bangladesh Council ofScientific andIndustrial Research
(BCSIR), Joypurhat Sadar, Joypurhat5900, Bangladesh
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Modeling Earth Systems and Environment
1 3
riverbank erosion, drought, etc.) (Rahaman etal. 2016; Kabir
and Hossen 2019). Over the last few decades (1996–2015),
Bangladesh has lost a significant amount of its GDP owing
to various types of land and water degradation, amounting to
several hundreds of billion takas each year (Rahman 2016;
NPDM 2020; Hossain etal. 2021). Hence, considering the
looming picture of serious water and land degradation, we
must train our model on identifying the most susceptible
zones to develop an action plan for soil and water conserva-
tion in the DRW, Bangladesh.
The Dharla is a dynamic Himalayan river system that
changes direction with the immense flow and transports a
huge amount of sediment from the Himalayas and surround-
ing area during floods (Bose and Navera 2017; Rahman etal.
2021). As a result, soil erosion and riverbank shifting is the
common issue in DRW during the rainy season, while severe
water scarcity occurs here during the dry season. Therefore,
the area has been coping with numerous watershed-related
crises, resulting in various socio-economic problems and
severe nutrition deficiency (Rahman 2016; NPDM 2020).
In these circumstances, watershed prioritization is the prime
requirement to address the risk zone in this watershed to
manage the available natural resources. Micro-level hydro-
logic units (sub-watersheds) are, therefore, cautiously cho-
sen to conduct an extensive geo-morphometric study.
The geo-morphometric analysis can be explained through
the measurement of the configuration of the earth’s surface
in the form of linear, aerial, shape, and relief aspects of the
drainage basin (Horton 1945; Nooka Ratnam etal. 2005;
Aher etal. 2014). Morphometric study of a watershed offers
a quantitative evaluation of the natural drainage system and
geometry, which are essential components for watershed
delineation (Strahler 1964). The geo-morphometric analysis
is regarded as the most commonly used practice for prior-
itizing sub-watersheds (Biswas etal. 1999; Nooka Ratnam
etal. 2005; Rama 2014; Aher etal. 2014; Yadav etal. 2014;
Krishnan etal. 2017; Malik etal. 2019; Sutradhar 2020;
Kumar etal. 2021). Apart from these, several researchers
have integrated the morphometric model with a few other
factors, including sediment yield index, land use/land cover
(Khanday and Javed 2016), soil erosion (Pandey etal. 2011;
Nitheshnirmal etal. 2019; Jothimani etal. 2020), runoff
(Pathare and Pathare 2020), flash flood modeling (Prasad
and Pani 2017), and so on, to prioritize watersheds. In ear-
lier studies (Biswas etal. 1999; Kumar etal. 2012; Yadav
etal. 2014; Khanday and Javed 2016; Nitheshnirmal etal.
2019; Sutradhar 2020), prioritization of sub-watershed
has traditionally been done based on compound parameter
values by taking a simple arithmetic mean of preliminary
priority rankings of each morphometric parameter, where
all morphometric parameters were assigned equal impor-
tance. Aside from previous research, Aher etal. (2014)
proposed the weighted sum approach (WSA) of watershed
prioritization in which the compound ranking factors were
derived using the weightage factor of the various morpho-
metric variables. Various scientists have also used PCA
to identify the significant morphometric parameters and
watershed prioritization for soil conservation (Sharma etal.
2015; Meshram and Sharma 2017; Arefin etal. 2020). Based
on the previous researches this study introduces a hybrid
and logical model of watershed prioritization that is PCA-
WSM, where watershed prioritization is done based on the
integrated application of PCA and WSM. The PCA was
employed on the EPMPs (linear, areal, and shape) (Nooka
Ratnam etal. 2005; Aher etal. 2014) to reduce these varia-
bles into significant number of new variables known as prin-
cipal components (PCs) by orthogonal transformation (Syms
2019). This transformation leads to one or more parameters
from each PCs based on the highest loading coefficient,
which were further considered for SWS prioritization using
the PCA and WSM. In light of the above, the objectives of
the present study are made:
(i) Delineation of the drainage network and associated
SWS to calculate the linear, areal, and shape morpho-
metric parameters in the GIS environment.
(ii) Application of PCA to identify most significant
EPMPs and PCA-based SWS prioritization.
(iii) Application of PCA-WSM to prioritize SWS based
on the most significant EPMPs derived from PCA.
(iv) The correlative study between PCA and PCA-WSM
to get the final priority zonation map for soil conser-
vation.
Materials andmethods
Study area
The study area encompasses the Dharla River and its water-
shed area (approximately 369 km2), about 20km from the
left bank and 27km from the right bank of the main channel
excluding the effect of the Brahmaputra, Teesta, and Dudh-
kumar River. It falls within the northern part of Bangladesh
between 89° 22′ 49″E and 26° 0′ 18″N, and 89° 41′50″E
and 25° 48′42″N (Fig.1a). The area is characterized by
three distinct seasons, i.e. a warm, humid summer between
March and June; a wet, rainy monsoon between June and
October; and a cold, dry winter between October and March
with temperatures varying from 25 to 35°C. Evapotran-
spiration in April reaches a maximum when temperatures,
sunshine, and wind are near maximum (Rahman etal. 2021).
The long-term average annual rainfall of the study area is
about 2859.67mm/year and about 86% is received during
the monsoon season.
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Modeling Earth Systems and Environment
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Drainage network andSWS delineation
The SRTM-DEM (Fig.1b) downloaded from the USGS
online database in GeoTIFF format having a spatial reso-
lution of 30m was used to identify and extract the sub-
watersheds boundaries and drainage networks of the study
area to conduct the morphometric study. According to Singh
etal. (2014), DEM-based hydrological evaluation at the
watershed scale is more functional and accurate compared
to other available techniques. The sub-watersheds along with
the stream networks were extracted from SRTM-DEM using
the ArcHydro tool in ArcGIS 10.4.1 following the model as
illustrated in Fig.2 adopted from the “ArcHydro tools-Tuto-
rial” handbook (ESRI 2009). In this model, the input DEM
was represented in a yellow rectangle, which was projected
in the WGS 1984 datum and universal transverse mercator
(UTM) Zone 45 North coordinate system. The light green
rectangle represents the tools that were used for geoprocess-
ing the variables (output/input) presented in light blue fields.
These sets of variables and tools are linked together by con-
nectors to process the input data and the location path of
each variable was specified. The orange fields represent the
final output (SWS map and stream order map) (Fig.2). At
the beginning of the model, this study introduced the fill tool
to process the input DEM as the fill tool automatically fixes
the artifacts and error data concerning sinkholes (Fig.2).
Furthermore, the flow direction tool was employed to extract
the flow direction of each pixel using the method of ‘trian-
gular multi-flow algorithm’ (Seibert and McGlynn 2007)
where preceding output fill-DEM was used as the input
variable (Fig.2). This output raster was later used as an
input variable to generate flow accumulation raster using the
representative tool and the output was stored in a specified
location. This output flow accumulation raster was further
used along with the flow direction raster to define stream
definition, stream link, drainage line processing, and stream
to feature and stream order processing using their respec-
tive tools (Fig.2) according to the guideline of “ArcHydro
tools-Tutorial” handbook (ESRI 2009). Furthermore, the
catchment grid, catchment polygon, and adjacent catchments
data layer were processed from the flow direction raster and
stream link data layer using the respective ArcHydro tools
(Fig.2). The output catchment grid and adjacent catchments
data layers along with the flow accumulation raster were pro-
cessed using the drainage point processing tool in ArcHydro
to extract the watershed drainage points (Fig.2). Which were
further used in batch point extraction to delineate watershed
boundary and sub-watersheds of the study area using the
batch watershed and batch sub-watershed delineation tools
in ArcHydro. In this model, the stream orders were assigned
based on the theory proposed by Strahler (1964).
Morphometric study
Morphometric studies were conducted to analyze the overall
geometry and features of the Dharla River SWS. The fun-
damental parameters, namely, the stream order (u), number
of streams (Nu), stream length (Lu), area (A), perimeter (P),
basin length (Lb), and total relief (Rt) were derived directly
from the drainage map, sub-watershed map, and DEM
respectively in GIS environment. Later these fundamental
parameters were used to compute the linear, areal, shape,
Fig. 1 a Geographical location map of the studied Dharla River watershed (DRW), Bangladesh; b shuttle radar topography mission digital eleva-
tion model (SRTM-DEM) downloaded from the USGS online library and masked according to the study area shape
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Modeling Earth Systems and Environment
1 3
and relief aspects of the studied watershed with standard
formulae proposed by Horton (1932, 1945), Smith (1950),
Miller (1953), Schumm (1956), Melton (1957), Strahler
(1964), and Nooka Ratnam etal. (2005). In this research,
mean stream length (Lsm), stream length ratio (RL), bifurca-
tion ratio (Rb), RHO coefficient (RHO), length of overland
Fig. 2 Comprehensive work flow sheet model of the present research showing watershed delineation, drainage line extraction, and SWS prioriti-
zation methodology
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Modeling Earth Systems and Environment
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flow (Lg) were computed using Eqs. (i), (ii), (iii), (iv), and
(v) respectively (Table1) and clustered into linear param-
eters. Stream frequency (Fs), drainage density (Dd), drain-
age texture (T), drainage texture ratio (Dt) were computed
using Eqs. (vi), (vii), (viii), (ix) respectively (Table1) and
grouped as the areal morphometric parameter. Basin shape
(Bs), form factor (Ff), circularity ratio (Rc), elongation ratio
(Re), compactness constant (Cc) were computed using Eqs.
(x), (xi), (xii), (xiii), (xiv), respectively (Table1) and clus-
tered into shape morphometric parameters. The formula (Eq.
i to xiv)are given in Table1 and the calculatedresults of
the morphometric study are shown in Table2 (linear MPs),
Table3 (linear MPs), and Table4 (areal and shape MPs).
SWS prioritization using PCA
The principal components or component analysis is a
statistical method first introduced by Pearson (1901)
which was letter revised to principal component analysis
suggested by Hotelling (1933). PCA is a widely used data
transformation method for simplifying the complexity of
multidimensional data. It identifies the variance within
a dataset of inter-correlated variables in terms of two or
more new pseudo-variables also known as principal com-
ponents (PCs) (Syms 2019) which were uncorrelated and
orthogonal to each other and arranged according to their
relative significance. This method can be the best pos-
sible approach to simplify the relations among the geo-
morphometric features as well as to find the most signifi-
cant parameters in the sub-watershed scale. Following five
simple steps were considered to run the PCA model in the
present study (also shown in Fig.2):
i. In the first step, the data set derived from the mor-
phometric analysis was standardized to enhance the
performance of PCA. In this study, morphometric
parameters, which are sensitive to soil erosion, were
particularly considered for PCA.
Table 1 Formulae used for computation of morphometric parameters of the Dharla River sub-watersheds (DR-SWS)
Morphologic parameters Formula References Eq. no.
Linear parameters
Stream order (u) Hierarchical rank Strahler (1964)
Stream number (Nu) Total number of stream segments of order ‘u’ (Calculated from drainage
map)
Strahler (1964)
Stream length (Lu) Total length of stream segments of order ‘u’ (Calculated from drainage
map)
Horton (1945)
Mean stream length (Lmu)Lsm = Lu/NuStrahler (1964) i
Stream length ratio (RL)RL = Lu/Lu − 1Horton (1945) ii
Where Lu = total length of stream segments of order ‘u’, Lu − 1 = total stream length of the previous
lower order
Bifurcation ratio (Rb)Rb = Nu/Nu + 1Schumm (1956) iii
Where Nu = total number of stream segments of order ‘u’, Nu + 1 = number of segments of the next
higher order
RHO co-efficient (RHO) RHO = RL/RbHorton (1945) iv
Length of overland flow (Lg) Lg = 1/2DdHorton (1945) v
Areal parameters
Basin area (A) The area covered inside the watershed boundaries (km2) (calculated from SWS map)
Perimeter (P) The perimeter of SWS (km) (calculated from SWS map)
Basin length (Lb) Distance between the outlet and farthest point on the basin boundary
(km)
Nooka Ratnam etal. (2005) v
Stream frequency (Fs)Fs = ∑Nu/AHorton (1945) vi
Drainage density (Dd)Dd = ∑Lu/A (km/km2) Horton (1945) vii
Drainage texture (T)T = Fs × DdSmith (1950) viii
Drainage texture ratio (Dt)Dt = ∑NU/PHorton (1945) ix
Shape parameters
Basin shape (Bs)Bs = Lb2/AHorton (1945) x
Form factor (Ff)Ff = A/Lb2 (Ff < 1) Horton (1932) xi
Circularity ratio (Rc)Rc = 4πA/P2 (Rc ≤ 1) Miller (1953) xii
Elongation ratio (Re)Re = 1.128 × A0.5/Lb (Re ≤ 1) Schumm (1956) xiii
Compactness constant (Cc)Cc = 0.2821 × P/A0.5 (Cc ≥ 1) Strahler (1964) xiv
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Modeling Earth Systems and Environment
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ii. The second step involved the computation of the cor-
relation matrix to identify any possible correlation
between the variables of the data set.
iii. The third step involved the calculation of eigenvalues
to identify the number of PCs. Here eigenvalues > 1
suggest substantial PC loading.
iv. The fourth step was the calculation of the first factor
PCs loading matrix.
v. The fourth and final step was the computation of the
Varimax-rotated matrix (also known as Kaiser-Vari-
max rotation) to depict the most significant EPMPs
in the Dharla River SWS. Here the parameters those
Table 2 SWS wise stream orders and stream lengths of the study area
SWS No. Order wise stream numbers
(Nu)
Total NuStream lengths (Lu) in km Total LuMean stream lengths (Lsm) in km
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
SWD-1 69 15 4 1 – 89 36.1 18.7 5.8 13.4 – 74.0 0.5 1.2 1.5 13.4 –
SWD-2 47 10 2 1 – 60 26.8 15.0 2.6 8.5 – 52.9 0.6 1.5 1.3 8.5 –
SWD-3 99 20 5 1 1 126 48.4 26.8 16.9 2.5 11.1 105.8 0.5 1.3 3.4 2.5 11.1
SWD-4 89 15 3 1 108 47.4 20.3 11.0 12.1 – 90.8 0.5 1.4 3.7 12.1 –
SWD-5 74 20 5 1 1 101 40.7 20.8 12.7 3.9 8.4 86.5 0.5 1.0 2.5 3.9 8.4
SWD-6 72 10 2 – 1 85 37.1 17.0 13.4 – 5.4 72.9 0.5 1.7 6.7 – 5.4
SWD-7 91 17 2 – 1 111 52.0 21.7 14.7 – 12.8 101.2 0.6 1.3 7.3 – 12.8
SWD-8 40 13 3 1 – 57 19.1 13.1 7.5 1.5 – 41.2 0.5 1.0 2.5 1.5 –
SWD-9 52 10 1 – 1 64 32.3 11.2 4.8 – 11.1 59.4 0.6 1.1 4.8 – 11.1
Table 3 SWS wise linear morphometric parameters of the study area
SWS No. Stream length ratio (RL) Mean RLBifurcation ratio (Rb) Mean Rbm RHO co-efficient (RHO) Mean RHO Length of over-
land flow (Lg)
RL1RL2RL3RL4Rb1Rb2Rb3Rb41234
SWD-1 0.52 0.31 2.30 – 1.04 4.6 3.8 4.0 – 4.12 0.11 0.08 0.57 – 0.26 0.75
SWD-2 0.56 0.18 3.23 – 1.32 4.7 5.0 2.0 – 3.90 0.12 0.04 1.62 – 0.59 0.73
SWD-3 0.55 0.63 0.15 4.42 1.44 5.0 4.0 5.0 1.0 3.74 0.11 0.16 0.03 4.42 1.18 0.69
SWD-4 0.43 0.54 1.10 – 0.69 5.9 5.0 3.0 – 4.64 0.07 0.11 0.37 – 0.18 0.65
SWD-5 0.51 0.61 0.31 2.15 0.89 3.7 4.0 5.0 1.0 3.43 0.14 0.15 0.06 2.15 0.62 0.64
SWD-6 0.46 0.79 – 0.40 0.55 7.2 5.0 – 2.0 4.73 0.06 0.16 – 0.20 0.14 0.53
SWD-7 0.42 0.68 – 0.87 0.65 5.4 8.5 – 2.0 5.28 0.08 0.08 – 0.43 0.20 0.54
SWD-8 0.69 0.57 0.20 – 0.48 3.1 4.3 3.0 – 3.47 0.22 0.13 0.07 – 0.14 0.55
SWD-9 0.35 0.43 – 2.29 1.02 5.2 10.0 – 1.0 5.40 0.07 0.04 – 2.29 0.80 0.68
Table 4 SWS wise areal and
shape morphometric parameters
of the Dharla River watershed
(DRW)
A area in km2, P perimeter in km, Lb basin length in km, FS stream frequency, Dd drainage density, T drain-
age texture, Dt drainage texture ratio, Bs basin shape, Ff form factor, Rc circulatory ratio, Re elongation
ratio, Cc compact constant
SWS No. APLbFSDdT DtBsFfRcReCc
SWD-1 46.18 44.40 13.03 1.93 1.60 3.09 2.00 3.68 0.27 0.29 0.59 1.84
SWD-2 27.58 27.62 8.47 2.18 1.92 4.17 2.17 2.60 0.38 0.45 0.70 1.48
SWD-3 54.94 42.59 11.09 2.29 1.93 4.42 2.96 2.24 0.45 0.38 0.75 1.62
SWD-4 52.04 47.39 12.08 2.08 1.75 3.62 2.28 2.80 0.36 0.29 0.67 1.85
SWD-5 44.86 44.18 12.67 2.25 1.93 4.34 2.29 3.58 0.28 0.29 0.60 1.86
SWD-6 35.26 45.08 13.41 2.41 2.07 4.99 1.89 5.10 0.20 0.22 0.50 2.14
SWD-7 53.56 57.43 12.23 2.07 1.89 3.92 1.93 2.79 0.36 0.20 0.68 2.21
SWD-8 20.92 27.29 7.46 2.72 1.97 5.36 2.09 2.66 0.38 0.35 0.69 1.68
SWD-9 33.24 28.90 10.90 1.93 1.79 3.44 2.21 3.57 0.28 0.50 0.60 1.41
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Modeling Earth Systems and Environment
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were showed the highest coefficient value from each
component in the rotated matrix were considered for
further PCA-based and PCA-WSM based watershed
prioritization study.
All these mathematical operations were carried out using
the software interface of IBM SPSS v26.0 following the pro-
cedure described in the IBM-SPSS Statistics guide (George
and Mallery 2019).
To conduct PCA-based SWS prioritization analysis the
primary step was assigning preliminary priority ranking
to the most significant EPMPs derived from the Varimax-
rotated matrix. In this study, the preliminary priority ranks
were assigned based on the relative significance of mor-
phometric parameters to soil erosion potential as stated by
Nooka Ratnam etal. (2005), Aher etal. (2014), Prasad and
Pani (2017), Malik etal. (2019), Pathare and Pathare (2020),
and Kumar etal. (2021). These earlier researches proposed
that the linear and areal parameters (i.e. Rb, Lg, Dd, T, Dt,
and Fs) were directly proportional to runoff and soil erosion
potential and were ranked in such a way that the highest
value of these morphometric parameters was rated as rank
1, and next highest value was assigned rank 2 and so on.
On the other hand, the shape parameters (i.e. Rc, Re, Bs, and
Ff) showed an inverse relation with runoff as well as soil
erosion potential. As a result, the preliminary priority rank
of this group of parameters was assigned in such a way that
parameters with the lowest value received the first rank, and
the rest of the ordering followed suit. Finally, the PCA-based
compound factors (CF) of each SWS were calculated using
Eq.(xv). The SWS that achieved the minimum CF value
was received the highest priority and the maximum value
received the least priority.
SWS prioritization using PCA‑WSM
The PCA-WSM is an integrated model of principal com-
ponent analysis and weighted sum model in which the
most significant EPMPs obtained from PCA were used in
weighted sum analysis to calculate compound factor (CF)
values. In this model, the first step was the calculation of a
cross-correlation matrix using the preliminary assigned rank
value of the EPMPs to compute the final weightage factors
for each parameter. According to the WSM, weightage for
each morphometric parameter was computed by dividing the
sum of the correlation coefficients of each parameter by the
grand total of all correlation coefficients. Finally using these
weighted factors were used to compute the final compound
factor for SWS prioritization. The mathematical expression
(xv)
CF
=
Sum of all the preliminary ranks of most significant EPMPs suggested by PCA
The total number of most significant EPMPs suggested by PCA .
of CF assessment can be expressed by Eq.(xvi) (modified
after Aher etal. 2014; Malik etal. 2019):
Here PPREPMPs denote preliminary priority ranking of all
erosion-prone morphometric parameters (EPMPs) identified
through PCA and WEPMPs denote the weighted factors of
each EPMPs obtained from the cross-correlation analysis.
The final prioritization ranking of the Dharla River SWS was
ascertained based on CF in such a way that the lowest value
of compound factor was given 1st priority rank, next lower
value was given 2nd priority rank, and vice versa.
Furthermore, the SWS were broadly categorized into
three priority zones based on their CF values (derived from
PCA and PCA-WSM) such as high, medium, and low prior-
ity zones. Finally, a correlative study was conducted between
the results of the above two methods that yielded a final
ranking of the SWS by picking the common SWS falling
under each priority zone to evaluate erosion-prone areas for
proper conservation planning and management practices.
Result anddiscussion
Morphometric characterization
The study area comprises nine sub-watersheds, labeled as
SWS-1 to SWS-9 (Fig.3a). The area of the Dharla River
SWS varies from 27.58 km2 (SWS-2) to 54.94 km2 (SWS-3)
(Table2) with a total area of about 369 km2. The morpho-
metric analysis suggests that the DRW is 5th order watershed
and typically characterized by dendritic drainage patterns
(Fig.3b) with a total number of streams (Nu) is about 801,
signifying the potential amount of surface runoff and sedi-
ment yield into the main channels (Malik etal. 2019). The
study also reveals that the SWS-3 and SWS-5 belong to the
5th order stream and the rest of the sub-watersheds (SWS-
1, SWS-2, SWS-4, SWS-6, SWS-7, SWS-8, and SWS-9)
belong to the 4th order stream (Table2). The Lu for all the
nine SWS have calculated in ArcGIS 10.4.1 software using
the calculation geometry tool, and the results display in
Table2 reflect that SWD-6, SWD-7, SWD-8, and SWD-9
fully satisfy Horton’s general statement that is the number
of stream segments has an inverse relationship with stream
order (Horton 1945). While the others do not satisfy Hor-
ton’s statement suggesting that streams may flow through
various geological formations with moderately steep slopes
(xvi)
CF
=
∑(
PPREPMPs ×WEPMPs
).
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Modeling Earth Systems and Environment
1 3
in these SWS areas (Singh and Singh 1997). The stream
length ratio (RL) of different SWS (i.e. SWS-3, SWS-4,
SWS-5, SWS-7, and SWS-9) shows an increasing trend
from lower to higher stream order (Table3) reflecting the
developed geomorphic stage of streams. The computed mean
Rb values range between 3 and 5, except for SWS-7 and
SWS-9 (5.28 and 5.40 respectively) (Table3), suggesting
less intervention of geologic structures to the stream network
(Aher etal. 2014). While the higher value of Rb in SWS-7
and SWS-9 suggests tectonic control on drainage patterns
and excess overland flow (Jothimani etal. 2020). RHO is a
significant parameter to assess the storage capacity as well
as the physiographic growth of streams (Horton 1945). The
mean RHO coefficient varies from 0.14 (SWS-6 and 8) to
1.18 (SWS-3) (Table3). The SWS with lower RHO values
(SW-6, and 8) store less water during floods, and as a result,
more erosion takes place at these SWS during high discharge
(Rama 2014). The Lg values range between 0.53 (SWS-6)
and 0.75 (SWS-1)km/km2 (Table3). Shorter value of Lg in
SWS-6 suggest comparatively quick runoff process and high
erosion potential than the others (Horton 1945).
The areal parameters i.e. Fs, Dd, T, and Dt, have a direct
relationship to the surface runoff processes as well as soil
erosion in the SWS scale (Melton 1957; Aher etal. 2014;
Prasad and Pani 2017; Pathare and Pathare 2020). The stud-
ied SWS shows the Fs and Dd values varying between 1.93
(SWS-1 and 9) and 2.72 (SWS-8) and 1.60 (SWS-1) and
2.07 (SWS-6) (Table4) respectively. The high value of Fs
in SWS-8 suggests excess runoff and more erosional effects
during the flood (Malik etal. 2019). Also, the higher Dd and
T value in SWS-6 (Table4) suggests relatively impermeable
subsoil conditions and intermediate drainage texture that
provokes more erosion due to excess runoff depth than the
lower one (Smith 1950).
The shape parameters i.e. Ff, Rc, Re show an inverse rela-
tion to runoff as well as erosion potentials (Nooka Ratnam
etal. 2005). The Ff values range between 0.20 (SWS-6)
and 0.45 (SWS-3) (Table4) suggesting relatively elongated
watersheds with a flatter peak flow over an extended period
(Horton 1932). The Rc values are varying between 0.20 and
0.50 (Table4) which is less than unity suggesting that the
SWS are almost elongated in shape. The lower value of Rc in
SWS-7 (0.20) and SWS-6 (0.22) suggest high runoff depth
as well as more erosion in these regions. The Dharla River
SWS have Re values less than unity (0.50–0.75; Table4)
suggesting that the SWS are mostly elongated in shape.
The lower value of Re observed in SWS-6 (0.20) suggests
quick surface runoff and is thus prone to more erosion dur-
ing floods (Malik etal. 2019). According to Nooka Ratnam
etal. (2005), Cc value is directly proportional to the ero-
sion risk assessment factors. The Cc values range between
1.41 (SWS-9) and 2.21 (SWS-7) (Table4). Lower Cc value
(< 2) observed in SWS-9 indicate less exposure to erosion
risk factors, while higher values (> 2) observed in SWS-6
and SWS-7 indicate high susceptibility to soil erosion (Aher
etal. 2014). As a result, these SWS must need some conser-
vation measures.
Inter‑correlation ofEPMPs
The inter-correlation matrix among the 12 selected EPMPs
of the nine SWS as shown in Table5 typically reveals the
Fig. 3 a Sub watersheds (SWS) map showing nine SWS by individual color and number from SWS-1 to SWS-9 and b drainage map of the study
area showing 5th order streams
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Modeling Earth Systems and Environment
1 3
degree of relative significances of each constraint among
them. According to Meshram and Sharma (2017) and Arefin
etal. (2020), morphometric parameters shows high signifi-
cance when correlation coefficient value is > 0.90, good cor-
relations when correlation coefficient value is between 0.75
and 0.90, moderate correlation when correlation coefficient
value between 0.60 and 0.75 and value < 0.6 suggest poor
correlation among the morphometric parameters. Table5
shows strong correlations for Fs with T (0.97), Re with Ff,
(0.99), Rc with Cc (− 0.98), and Bs with Re and Ff (− 0.98 and
− 0.96 respectively). The correlation matrix also reveals few
good correlations between Dt with RHO (0.84), Dd with T
(0.89), and Fs with Dd (0.75); moderate correlation among
RHO with Rc and Cc (0.63 and − 0.62 respectively), Dt with
Ff and Re (0.65 and 0.61 respectively), Lg with Dd, T, and Cc
(− 0.65). Most of the parameters in the correlation matrix
show poor correlations among them that create difficulties
in assembling the parameters into significant components
based on their relative importance (Arefin etal. 2020). Con-
sequently, the obtained inter-correlation matrix was consid-
ered for PCA to group the EPMPs into principal components
PCs that describe the information of the given data.
PCA
PCA is a bilinear analysis method that provides a compre-
hensible summary of the original information in a multivari-
ate data table. In the present study, twelve initial eigenvalues
are obtained through PCA, which are presented in Table6.
The eigenvalue, generally known as the Kaiser criterion, is
a frequently used indicator for computing the number of PCs
by selecting the components with eigenvalues > 1. Table6
Table 5 Inter-correlation
matrix among the erosion-prone
morphometric parameters
(linear, areal, and shape) of the
DR-SWS (calculated in IBM
SPSS v.26 software)
Note: linear morphometric parameters: Bf, RHO, Lg; areal morphometric parameters: Fs, Dd, T, Dt; and
shape morphometric parameters: Bs, Ff, Rc, Re, and Cc
BfRHO LgFsDdT DtBsFfRcReCc
Bf1.00
RHO − 0.19 1.00
Lg− 0.22 0.52 1.00
Fs− 0.57 − 0.18 − 0.58 1.00
Dd− 0.20 0.05 − 0.65 0.75 1.00
T− 0.45 − 0.12 − 0.65 0.97 0.89 1.00
Dt− 0.38 0.84 0.41 0.04 0.04 0.03 1.00
Bs0.29 − 0.35 − 0.28 − 0.04 0.15 0.06 − 0.55 1.00
Ff− 0.32 0.40 0.18 0.18 0.03 0.12 0.65 − 0.96 1.00
Rc− 0.09 0.63 0.58 − 0.13 − 0.13 − 0.15 0.41 − 0.35 0.30 1.00
Re− 0.31 0.39 0.22 0.12 − 0.02 0.05 0.61 − 0.98 0.99 0.32 1.00
Cc0.25 − 0.62 − 0.65 0.07 0.18 0.13 − 0.48 0.42 − 0.36 − 0.98 − 0.38 1.00
Table 6 Total variance explained for the DR-SWS
Note: extraction method: principal component analysis (PCA)
Comp no. Initial eigenvalues Extraction sums of squared loadings Rotation sums of squared loadings
Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative %
1 4.92 41.00 41.00 4.92 41.00 41.00 3.36 28.02 28.02
2 3.49 29.08 70.08 3.49 29.08 70.08 3.33 27.75 55.77
3 1.60 13.36 83.44 1.60 13.36 83.44 3.32 27.67 83.44
4 0.92 7.65 91.09
5 0.81 6.74 97.83
6 0.17 1.42 99.25
7 0.07 0.55 99.80
8 0.02 0.20 100
95.6E − 16 4.7E − 15 100
10 − 2.0E − 17 − 1.7E − 16 100
11 − 2.0E − 16 − 1.6E − 15 100
12 − 3.0E − 16 − 2.5E − 15 100
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Modeling Earth Systems and Environment
1 3
reveals that the first three components have eigenvalues > 1
and cumulatively account for 83.44% of the total variance.
Table6 also shows that component-1 has an eigenvalue of
4.92, which explains 41% of the total variance; component-2
has an eigenvalue of 3.49, which accounts for 29.08% of the
total variance; and component-3 has an eigenvalue of 1.60,
which accounts for 13.36% of the total variance. Hence, the
twelve EPMPs can be represented by three PCs while retain-
ing 83.44% of their information.
The PCA generated first-factor loading matrix (Table7)
shows that the component-1 has good correlations with
RHO, Dt, Bs, Ff, Re, and Cc (0.75–0.90), moderate corre-
lation with Lg, and Rc (0.60–0.75); component-2 shows a
strong correlation with Fs and T (> 0.90), good correlation
with Dd (0.82); and component-3 don’t show any signifi-
cant correlation. The above results of the first factor-loading
matrix (Table7) cannot provide any satisfactory result for
identifying significant components. Therefore, the first-fac-
tor loading matrix was rotated using the Varimax algorithm
to obtain a reliable correlation. Table8 depicts the rotated
PC loading matrix, which reveals the highest significant
loading observe in PC1 for Cc (coefficient: − 0.91), in PC2
for Ff and Re (coefficient: 0.97), and in PC3 for T (coeffi-
cient: 0.99). In addition, it is important to keep in mind that
a high value for a PC loading indicates a strong connota-
tion between the component and the specific morphometric
parameter. Hence, the rotated PC loading matrix derived
from PCA reduces twelve EPMPs into four most important
EPMPs (i.e., Cc, T, Ff, and Re), which are further considered
for SWS prioritization. The final priority rankings of nine
SWS and their calculated CF values based on the prelimi-
nary priority ranks of the four most significant EPMPs are
given in Table9. The analysis reveals that SWS-6 receives
the highest rank (1st) with the lowest CF value of 3.00 and
SWS-7 receives the lowest rank (9th) (Fig.4a) with the high-
est CF value of 6.75 (Table9) suggesting SWS-6 as a high-
risk zone for soil erosion and hence requires an effective soil
conservation strategy.
PCA‑WSM forSWS prioritization
The PCA-WSM was employed to the four most significant
EPMPs (i.e., Cc, T, Ff, and Re) obtained from PCA to cal-
culate the compound factor (CF) values for computing the
final priority ranking of each SWS. Table10 shows the
cross-correlation matrix among the most significant EPMPs
and the calculation of their final weightage values. Based
on these weightage values the equation of CF calculation
(Eq.xvi) can be expressed as follows (modified after Aher
etal. 2014):
Here T, Ff, Re, and Cc denote the preliminary rank-
ing of drainage texture, form factor, elongation ratio,
and compactness constant respectively. Table11 shows
the final priorities of nine SWS of the studied region and
their respective CF values calculated using Eq.(xvii).
The study reveals that the SWS-6 with a compound factor
value of 0.99 receive the highest priority rank (1st) fol-
lowed by series of SWS-6 (0.99) > SWS-1 (2.73) > SWS-5
(3.04) > SWS-9 (4.50) > SWS-4 (5.21) > SWS-7
(5.95) > SWS-8 (6.38) > SWS-2 (7.77) > SWS-3 (8.44)
(xvii)
CF
=(T×0.11)+
(
F
f
×0.45
)
+
(
R
e
×0.45
)
−
(
C
c
×0.01
).
Table 7 First factor loading matrix of principal components (PCs)
extracted through PCA
Note: EPMPs denote erosion-prone morphometric parameters; coef-
ficient values < 0.3 are suppressed in this model
EPMPs Components
123
Bf− 0.34 − 0.54
RHO 0.76 0.38
Lg0.67 − 0.58
Fs0.94
Dd0.82
T0.95
Dt0.80
Bs− 0.80 0.51
Ff0.78 0.40 − 0.47
Rc0.73 0.51
Re0.79 0.34 − 0.49
Cc− 0.79 − 0.48
Table 8 Varimax rotated PCs loading matrix extracted through PCA
orthogonal transformation
Note: coefficient value < 0.3 are suppressed in this method; extraction
method: Varimax with Kaiser normalization; rotation converged in
four iterations. The bold values represent the most significant EPMPs
EPMPs Components
123
Bf− 0.31 − 0.52
RHO 0.81
Lg0.69 − 0.57
Fs0.95
Dd0.90
T0.99
Dt0.61 0.55
Bs− 0.96
Ff0.97
Rc0.89
Re0.97
Cc− 0.91
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Modeling Earth Systems and Environment
1 3
Table 9 PCA-based final
prioritization of the DR-SWS
Note: compound factor (CF) = sum of preliminary priority ranks of EPMPs/total number of EPMPs
SWS no. EPMPs Preliminary priority ranks SWS prioritization by PCA
model
T FfReCcT FfReCcCF value Final priority
SWS-1 3.09 0.27 0.59 1.84 9 2 2 5 4.50 4th
SWS-2 4.17 0.38 0.7 1.48 5 8 8 2 5.75 6th
SWS-3 4.42 0.45 0.75 1.62 3 9 9 3 6.00 8th
SWS-4 3.62 0.36 0.67 1.85 7 5 5 6 5.75 7th
SWS-5 4.34 0.28 0.6 1.86 4 3 3 7 4.25 2nd
SWS-6 4.99 0.2 0.5 2.14 2 1 1 8 3.00 1st
SWS-7 3.92 0.36 0.68 2.21 6 6 6 9 6.75 9th
SWS-8 5.36 0.38 0.69 1.68 1 7 7 4 4.75 5th
SWS-9 3.44 0.28 0.6 1.41 8 4 4 1 4.25 3rd
Fig. 4 SWS prioritization ranking map of the study area based on the
compound factor (CF) values derived from a the principal component
analysis (PCA) method and b the PCA adopted weighted sum model
(PCA-WSA). Here, the numerical numbers display on both maps are
SWS numbering
Table 10 Cross-correlation analysis among the most significant
EPMPs obtain through PCA model to calculate their final weight-
age for SWS prioritization using PCA-adopted weighted sum model
(PCA-WSM) (Modified after Aher etal. 2014)
Note: final weightage = sum of coefficients/grand total of the coeffi-
cients; here the grand total of the coefficients = 2.83
T FfReCc
T1− 0.27 − 0.27 0.15
Ff− 0.27 11− 0.45
Re− 0.27 11− 0.45
Cc− 0.15 − 0.45 − 0.45 1
Sum of coefficients 0.32 1.28 1.28 − 0.05
Final weightages 0.11 0.45 0.45 − 0.01
Table 11 Final priority ranking of nine SWS based on the compound
factor obtain from the PCA-WSM
SWS no. SWS prioritization by PCA-WSM
CF value Final priority
SWS-1 2.73 2nd
SWS-2 7.77 8th
SWS-3 8.44 9th
SWS-4 5.21 5th
SWS-5 3.04 3rd
SWS-6 0.99 1st
SWS-7 5.95 6th
SWS-8 6.38 7th
SWS-9 4.50 4th
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Modeling Earth Systems and Environment
1 3
(Fig.4b; Table11). The highest rank represents a high
risk for erosion; hence, required an effective action plan
for soil conservation and protection.
Final prioritization oftheDharla River SWS
The final prioritization of the SWS was computed by the
correlative study between the results obtained from the
PCA and PCA-WSM. Through this study, the SWS are
recategorized into three new priority zone based on the
CF values i.e. CF value of ≤ 4.50 denotes the high prior-
ity zone, CF value from 4.50 to 5.99 denotes the medium
priority zone, and CF value > 5.99 denotes the low priority
zone (Table12). The study also shows that according to
the PCA model the SWS-1, SWS-5, SWS-6, SWS-9 fall in
high priority zone; SWS-2, SWS-4, SWS-8 fall in medium
priority zone; and SWS-3, SWS-7 fall in low priority zone.
However, according to the PCA-WSM the SWS-1, SWS-
5, SWS-6, SWS-9 fall in the high priority zone; SWS-
4, SWS-7 fall in the medium priority zone; and SWS-2,
SWS-3, SWS-8 fall in low priority zone. The final priority
zonation map (Fig.5) depicts that SWS-1, SWS-3, SWS-
4, SWS-5, SWS-6, and SWS-9 come under the common
priority zone while others are not in the common zone
which reflects 66.67% consistency in the results obtained
from both these models. The correlative study (Table12;
Fig.5) suggests that SWS-1, SWS-5, SWS-6, and SWS-9
reflect the high priority zone, SWS-4 in the medium pri-
ority zone, and SWS-3 in the low priority zone, and the
others fall in the mixed priority zones. The high priority
zone, which represents 43.29% of the overall watershed
area (Fig.5), is associated with higher soil erosion, hence
required immediate soil conservation initiatives to protect
the region from further degradation. Sub-watersheds in the
medium priority zone (SWS-4) also need some strategic
management plans, as they have the potential to worsen
into the high priority zone. Furthermore, the SWS-2,
SWS-7, and SWS-8 are grouped as mixed zones of sig-
nificance (Fig.5) as they fall under different priority zone
(between low to medium) in different methods (Table12).
Conclusion
Geo-morphometric analysis of the DR-SWS was performed
by the assessment of linear, areal, and shape morphometric
parameters to demonstrate their relationship with the water-
shed hydrology. Furthermore, this research demonstrates an
integrated model based on the PCA and PCA-WSM for SWS
prioritization to access the susceptible zone affected by soil
erosion. The study reveals that the watershed comprises
nine sub-watersheds (labeling from SWS-1 to SWS-9) with
a total number of streams is about 801. The entire water-
shed is characterized as the 5th order watershed that usually
reflects the dendritic drainage system. Twelve EPMPs (i.e.
Bf, RHO, Lg, Fs, Dd, T, Dt, Bs, Ff, Rc, Re, and Cc), com-
puted from the stream network map and SWS map, were
primarily selected as the input variables for PCA. In this
Table 12 Priority zonation of DR-SWS based on the comparative study of the resultant ranks derived from PCA, and PCA-WSM
Priority SWS prioritization by PCA model SWS prioritization by IPCA&WSM model Common SWS
CF value SWS CF value SWS
High ≤ 4.50 SWS-1, SWS-5, SWS-6, SWS-9 ≤ 4.50 SWS-1, SWS-5, SWS-6, SWS-9 SWS-1, SWS-
5, SWS-6,
SWS-9
Medium 4.5–5.99 SWS-2, SWS-4, SWS-8 4.5–5.99 SWS-4, SWS-7 SWS-4
Low > 5.99 SWS-3, SWS-7 > 5.99 SWS-2, SWS-3, SWS-8 SWS-3
Fig. 5 Final priority zonation map of DR-SWS based on the thresh-
old values of CF derived from the correlative study between PCA and
PCA-WSM
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Modeling Earth Systems and Environment
1 3
study, PCA was conducted through five mathematical steps
i.e. standardization, inter-correlation study, identify PCs by
extracting eigenvalues > 1, first-factor loading matrix, and
rotated matrix calculation. The final output of PCA (rotated
matrix) effectively reduces the twelve EPMPs into four
most significant EPMPs with the highest axial loading for
Cc (coefficient: − 0.91) in PC1, Ff and Re (coefficient: 0.97)
in PC2, and T (coefficient: 0.99) in PC3. The PCA-based
prioritization study demonstrates SWS-6 as the high-risk
zone for soil erosion with the lowest CF values of 3.00 and
SWS-7 as the low-risk zone with the highest CF value of
6.75. Furthermore, the PCA-WSM-based watershed prior-
itization analysis reflects a similar type of results in iden-
tifying high-risk SWS that is also in agreement with the
SWS-6 with the lowest CF value of 0.99. The correlative
study between these two methods reclassified the entire
watershed into three broad groups that define the SWS-1,
SWS-5, SWS-6, and SWS-9 as the high-risk zone, SWS-4
as the medium risk zone, and SWS-3 as the low-risk zone,
while other SWS (SWS-2, SWS-7, and SWS-8) show vari-
ations in their priority rank for different statistical models.
Results obtained from the integrated application of these two
methods (PCA and PCA-WSM) show 66.67% consistency
proves the successful application of this approach to identify
the vulnerable SWS for soil erosion. The SWS belong to the
high-risk zone (about 43.29% of the total watershed) should
be considered for advance and efficient watershed manage-
ment planning. Hence, this research may be regarded as a
valuable resource for river geo-morphologists and hydro-
geologists to develop and implement advanced watershed
management plans for vulnerable zones.
Acknowledgements The authors are thankful to anonymous review-
ers for their valuable suggestions and comments on data processing
and interpretation, which helps to enhance the manuscript’s quality.
We would like to express our gratitude to the USGS for providing the
SRTM DEM available online and also thanks to the Survey of Bang-
ladesh for providing the topographic map. We would also like to thank
the IMMM staff for their tireless efforts in the field and laboratory.
Finally, we would like to express our appreciation to Mst. Arifa Akter
for her pleasant assistance in developing the manuscript.
Funding No funding was received for conducting this study.
Declarations
Conflict of interest The authors have no conflict of interest to declare
that are relevant to the content of this article.
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