Study area
The study area stretches from Rangpo (27°10′31.26″ N, 88°31′44.43″E, Elevation 300 m) to Ranipool (27°17′28.74″ N, 88°35′31.11″E, Elevation 847 m) in the East district of Sikkim, a stretch of 27 km along the route of NH 10 highway. It is the main route which connects Sikkim with the rest of India. In 2008–09, the broadening of NH 10 had commenced to promote defence and economic growth in Sikkim. The highway has been broadened from its present width of 7–12 m. This broadening of the highway will cause an increase in traffic volume. The project stretches from Sevok in West Bengal to North Sikkim. However, the road corridor chosen for the study is relatively much smaller than the actual stretch of the highway because of its relatively homogenous geography. A drainage area of 147 km2 was delineated to include all the micro-catchments providing runoff to the highway/rivers (Machado et al. 2017; Siqueira et al. 2017). Furthermore, the project impact area of 7.4 km2 was demarcated by merging 50 m buffers around the rivers and the highway. The rationale of considering the project impact area was based on the accessibility of the river water/road runoff by the wildlife and humans living near the river/highway (Antunes et al. 2001; Geneletti 2004). The study area has steep elevations, which is predominated by subtropical vegetation, interspersed with small human habitations, traditional farming areas, and towns like Rangpo, Singtam, and Ranipool. The highway closely follows river Teesta and Rani Khola (Fig. 1). It is also worth noting that Sikkim has high biodiversity and it is home to a large number of endemic species (Arrawatia and Tambe 2011). Moreover, it has a unique culture which gives high value to its natural resources. Therefore, unabated water pollution can severely affect the ecological and cultural sanctity of this area.
Data collection
Based on the changes in Annual Average Daily Traffic (AADT) and landuse & landcover (LULC), three time frames were considered for the study, viz. the year 2004 as pre-project scenario, 2014 as project implementation scenario, and 2039 as post-project scenario (Fig. 3). The changes considered from ‘pre-project’ to ‘project implementation’ scenarios included changes in AADT and LULC. While only change in AADT was considered for ‘post-project year’ scenario. AADT for ‘post-project year’ scenario was calculated based on annual growth rates for traffic, provided by Border Roads Organization. LULC in ‘pre-project’ and ‘project implementation’ scenarios was estimated using satellite images, whereas such an estimation was not possible for ‘post-project’ scenario. Five water pollutants were considered for the study (Table 1) mainly based on the ability of the empirical model to predict their concentration in the road runoff, and second, on the availability of a complete data set of historical water quality of the rivers near the highway. Keeping in view of the ecological and cultural sensitivity of the local water bodies, drinking water quality standards of US Public Health Service (USPH 1962) were considered, except pH, where Bureau of Indian Standards (BIS 2012) standard was considered for the present study. Various inputs for SWQIA model were prepared, as mentioned in Table 2.
Table 1 Description of water quality parameters
Table 2 Data types, source, and processing method for SWQIA model
AHP model
A structured questionnaire on pairwise comparison of water pollutants and project alternatives was administered to a panel of experts, based on a numerical scale having values ranging from 1 to 9 as suggested by Saaty (2000) (Table 3). The expert choice software was used for the preparation of comparison matrix and calculation of the weight of the pollutants. Two project alternatives were considered for the AHP model, viz. ‘with project’ and ‘without project’, for comparison of the impacts. The ‘with project’ alternative assumed that the highway had been broadened and traffic volume had increased, while ‘without project’ alternative assumed no change in the highway width and the traffic volume remains unchanged. In AHP, the elements of the comparison matrix, \(a_{ij} > 0\), express the expert’s evaluation of the preference of the ith criterion in relation with the jth. It is worth noting that \(a_{ij} = 1\) whenever \(i = j\) and \(a_{ij} = 1/a_{ji}\) for \(i \ne j\). The total number of pairwise comparisons by expert is \(n\left( {n - 1} \right)/2\), where ‘n’ is the total number of criteria under consideration. The eigenvector, w, matching the maximum eigenvalue, \(\lambda_{\rm max}\), of the comparison matrix is the preferred solution of the AHP model, that is
Table 3 Importance scale used in AHP
$${\mathbf{Aw}} = \lambda_{\rm max} {\mathbf{w}}.$$
(1)
or
$$\left( {\begin{array}{*{20}c} {a_{11} } & \cdots & {a_{1n} } \\ \vdots & \ddots & \vdots \\ {a_{n1} } & \cdots & {a_{nn} } \\ \end{array} } \right)\left( {\begin{array}{*{20}c} {w_{1} } \\ \vdots \\ {w_{n} } \\ \end{array} } \right) = \lambda_{ \rm {max} } \left( {\begin{array}{*{20}c} {w_{1} } \\ \vdots \\ {w_{n} } \\ \end{array} } \right),$$
(2)
where A is the comparison matrix. The elements of w must fulfill the condition, \(\mathop \sum \limits_{i = 1}^{n} w_{i} = 1\), and under ideal condition, \(\lambda_{ \rm {max} } = n\). The reliability of the AHP model is assessed by consistency ratio, \({\text{CR}} = {\text{CI}}/{\text{RI}}\), where Consistency Index, \({\text{CI}} = (\lambda_{ \rm {max} } - n)/(n - 1)\), and Random Consistency Index, RI, that is obtained by a large number of simulation runs. It varies upon the order of the comparison matrix (Saaty 2000; Taha 2010). An inconsistency value not more than 0.1 is acceptable for an AHP model.
Modelling of seasonal peak storm runoff
Rainfall occurs almost the entire year in Sikkim (IMD 2014). However, there is a substantial drop in rainfall in the non-monsoon months, which is from November to March. While April–October gets a relatively high proportion of annual average rainfall (Rahman et al. 2012). Thereby, the non-monsoon months were considered as antecedent dry period and the highest daily rainfall was considered as maximum intensity rainfall. The drainage area and micro-catchments feeding the road runoff/rivers in the study area were demarcated using Digital Elevation Model (DEM) (Machado et al. 2017; Siqueira et al. 2017) (Fig. 2). HEC-GeoHMS, a geospatial hydrological extension of ArcGIS, was used to prepare Soil Conservation Service-Curve Number (SCS-CN) maps for ‘pre-project and project implementation’ scenarios (Merwade 2012; Flemming and Doan 2013). For this, satellite images from LISS III were converted to LULC rasters using maximum likelihood method under image classification extension of ArcGIS (Fig. 3a, b). LULC rasters were reclassified into water, agriculture, forest, and medium residential areas. Furthermore, soil texture map of the drainage area was prepared from secondary sources (CISMHE 2008b) (Fig. 4). It was further reclassified into Hydrologic Soil Groups (HSG), based on the soil texture types (USDA 2007). CN maps were used to prepare Maximum recharge capacity maps (S Maps) based on the relation:
$$S = \frac{25400}{\text{CN}} - 254.$$
(3)
Runoff from each micro-catchment was estimated using the relation:
$$Q = \left\{ {\begin{array}{ll} 0 & \quad {{\text{if}}~P < 0.2 \times S} \\ {\frac{{\left( {P - 0.2 \times S} \right)^{2} }}{{P + 0.8 \times S}}} & \quad {{\text{if}}~P \ge 0.2 \times S} \\ \end{array} } \right.,$$
(4)
where Q is the runoff and P is the maximum intensity rainfall (Vojtek and Vojteková 2016).
Multiple linear regression model for traffic-induced water pollution
The empirical model developed by Kayhanian et al. (2003) was used in calculating the traffic-induced water pollutants concentration in the highway runoff (Eq. 5). It is reliable in predicting road runoff concentration of conventional water pollutants like COD, pH, TSS, and TDS, while it is unable to predict turbidity and dissolved oxygen:
$$C_{i}^{\text{H}} = { \exp }\left( {b_{i} + \mathop \sum \limits_{j = 1}^{6} a_{j} x_{j} } \right),$$
(5)
where \(C_{i}^{\text{H}}\) is the concentration in the highway H and \(b_{i}\) is the y-intercept of the ith water pollutant, \(a_{j}\) is the proportionality coefficient, and \(x_{j}\) is value of the jth predictor variable. The predictor variables include Event Rainfall as \(x_{1}\), Maximum Intensity Rainfall as \(x_{2}\), Antecedent Dry Period as \(x_{3}\), Cumulative Seasonal Rainfall as \(x_{4}\), watershed area as \(x_{5}\), and AADT as \(x_{6}\). \(a_{j}\) is the coefficient of \(x_{j}\). However, for the year 2039, except for AADT, the values of all other predictor variables were not available. As a result, the most reliable estimate of water pollutants given by Kayhanian et al. (2003) for AADT > 30,000 was considered for the year 2039.
Estimation of water pollutant concentration in the project impact area using mass balance model
The concentration of water pollutants due to traffic-induced pollution at various locations of the rivers within the project impact area was estimated using the mass balance model (Barthwal 2012; Davie 2008):
$$C_{i}^{\text{R}} = \frac{{Q_{\text{D}} C_{i}^{\text{H}} + \mathop \sum \nolimits_{j = 1}^{n} Q_{j} C_{ij} }}{{Q_{\text{D}} + \mathop \sum \nolimits_{j = 1}^{n} Q_{j} }},$$
(6)
where \(C_{i}^{\text{R}}\) is the downstream concentration of the ith water pollutant in the river, \(Q_{j}\) and \(C_{ij}\) are the upstream discharge rate in l/s and concentration of the ith water pollutant in mg/l for the jth stream or river. The runoff from the micro-catchment area, \(Q_{D}\), was calculated using SCS-CN method (Eqs. 3 and 4). The concentration of the water pollutant in the highway runoff, \(C_{i}^{\text{H}}\), was calculated using empirical model (Eq. 5). The concentration of water pollutant \(C_{i}^{\text{R}}\) at Rangpo was taken as the model output and it was compared with the observed data using model validation criteria. (Paliwal and Srivastava 2014). A correlation matrix of water pollutants estimated by the mass balance model was used to assess their nature of association.
Preparation of water quality status index maps
The project impact area map was overlaid upon the micro-watershed map and 100 random points were created within the project impact area. These points were populated with concentration of water pollutants of various years derived from mass balance model as attributes. The attributes of these points were based on their position with respect to the micro-watershed feeding their runoff to the rivers. These points were considered as known points for spatial interpolation of pollutant concentrations over the project impact area.
Empirical Bayesian Kriging (EBK) is a robust and straightforward spatial interpolation technique. Unlike other types of kriging, EBK considers uncertainty in spatial parameters. The algorithm behind EBK generates several semivariogram models to minimize the prediction error generated from the uncertainty of model parameters. Each semivariogram gets a weight, based on Bayes’ rule, which predicts how likely the observed data can be generated from a semivariogram (Banerjee et al. 2016; Cui et al. 1995; Krivoruchko 2012; Pilz and Spöck 2008). Hence, EBK was used for spatial interpolation of the water pollutants. Cross-validation criteria were used to assess the quality of spatial model made from the spatial interpolation. Mean Standardized Error and Standardized Root Mean Square Error were used as cross-validation criteria for the interpolation of the year 2014 (Chang 2017; Lloyd 2009). Pollutant maps prepared from spatial interpolation were converted to Single Factor Pollution Index (SFPI) maps using Eq. 6:
$$P_{ijk} = \frac{{C_{ijk} }}{{S_{j} }}$$
(7)
where \(P_{ijk}\) is the SFPI value and \(C_{ijk}\) is the measured concentration at the ith location for the jth water pollutant of the kth year. \(S_{j}\) is the standard value of the jth water pollutant. The SFPI maps were further reclassified based on Table 4.
\(P_{ijk} < 1\) is an indication of low pollution level, while \(P_{ijk} > 1\) indicate moderate-to-high pollution level depending on how low or how high the SFPI value is from one (Li et al. 2009; Yan et al. 2015). The reclassified SFPI maps were used to prepare WQSI maps for various years using the relation:
$${\text{WQSI}}_{ijk} = \frac{{\mathop \sum \nolimits_{j = 1}^{n} W_{j} P_{ijk} }}{{\left[ {\mathop \sum \nolimits_{j = 1}^{n} W_{j} P_{ijk} } \right]_{ \rm {max} } }},$$
(8)
where \(W_{j}\) is the weight of the water pollutant calculated from AHP model and \(P_{ijk}\) is calculated from Eq. 7. \(\left[ {\mathop \sum \limits_{j = 1}^{n} W_{j} P_{ijk} } \right]_{ \rm {max} }\) is the maximum value in the set of \(W_{j} P_{ijk}\). The WQSI varies from 0 to 1. A WQSI value close to zero indicates no impact, while a value close to 1 implies high adverse impact. The WQSI was further reclassified using natural break classification (Table 5) (Mushtaq et al. 2015).
Table 5 Impact category of WQSI Spatially explicit sensitivity analysis
SA of project alternatives was done with respect to change in water pollutant weight for the AHP model. ‘One-At-a-Time’ is a relatively simple SA method, which mainly involves changing one input variable at a time to see its effect on the model output. Its major limitation is that it does not capture the effect of simultaneous variation of input variables on the model output (Murphy et al. 2004). OAT-based SESA was performed on WQSI of the year 2014 as a case study, by changing the water pollutant weight. The water pollutant weight was changed for a range of ± 20% with a step size of ± 2% for each water pollutant considering a uniform probability distribution within a range of 0–1. The WQSI run maps were generated using Eq. 9:
$${\text{WQSI}}_{t\alpha } = \frac{{W_{t} P_{it} + \mathop \sum \nolimits_{j \ne t}^{n} \left( {1 - W_{t} } \right)\frac{{W_{j} }}{{\mathop \sum \nolimits_{j \ne t}^{n} W_{j} }}P_{ij} }}{{\left[ {W_{t} P_{it} + \mathop \sum \nolimits_{j \ne t}^{n} \left( {1 - W_{t} } \right)\frac{{W_{j} }}{{\mathop \sum \nolimits_{j \ne t}^{n} W_{j} }}P_{ij} } \right]_{ \rm {max} } }},$$
(9)
Subject to the condition:
$$\mathop \sum \limits_{j = 1}^{n} W_{j} = 1$$
(10)
where \({\text{WQSI}}_{t\alpha }\) is dependent on the tth water pollutant and step size, \(\alpha\). \(W_{t}\) is the changed weight, and \(\left( {1 - W_{t} } \right)\frac{{W_{j} }}{{\mathop \sum \nolimits_{j \ne t}^{n} W_{j} }}\) is the adjusted weight for the jth water pollutant. Other variables hold the same meaning, as given in Eqs. 6, 7, and 8 (Chen et al. 2011; Xu and Zhang 2013). To evaluate the change in the WQSI value per pixel per step size, a change function was used:
$${\text{CR}}_{{{\text{it}}\alpha }} = \frac{{{\text{WQSI}}_{{{\text{it}}\alpha }} - {\text{WQSI}}_{{{\text{it}}0}} }}{{{\text{WQSI}}_{{{\text{it}}0}} }} \times 100,$$
(11)
where \(CR_{it\alpha }\) is the change rate of WQSI at the ith location for the tth WQI at the αth step size. Mean Absolute Change Rate (MACR), a summary sensitivity index, was used to assess the overall sensitivity of the entire study area with change in water pollutant weight:
$${\text{MACR}}_{t\alpha } = \frac{1}{N}\mathop \sum \limits_{i = 1}^{N} \left| {\frac{{{\text{WQSI}}_{{{\text{it}}\alpha }} - {\text{WQSI}}_{{{\text{it}}0}} }}{{{\text{WQSI}}_{{{\text{it}}0}} }}} \right| \times 100 = \frac{{{\text{CR}}_{{{\text{it}}\alpha }} }}{N},$$
(12)
where \(MACR_{t\alpha }\) is the mean absolute value of change rate of WQSI value due to change in the weight of water pollutant and N is the total number of pixels. Equation 11 was also used to assess the temporal change in WQSI over various project scenarios. \(MACR_{i\alpha } \ge \alpha\) indicate that the SWQIA model is sensitive to the ith water pollutant weight at the αth step size, while \(MACR_{i\alpha } < \alpha\) implies an insensitivity. In other words, if a change of say ± 10% of a model input brings a ≥ 10% change in model output, the MACR curve slope will be ≥ 45°. In such cases, the model will be considered as sensitive to the model input (Longley et al. 2010). The overall methodology is illustrated in Fig. 5.