Water Resources Management

, Volume 32, Issue 15, pp 4833–4852 | Cite as

Modelling Impacts of Climate Change on a River Basin: Analysis of Uncertainty Using REA & Possibilistic Approach

  • Jew Das
  • Alin Treesa
  • N. V. UmamaheshEmail author


In the context of climate change, the uncertainty associated with Global Climate Models (GCM) and scenarios needs to be assessed for effective management practices and decision-making. The present study focuses on modelling the GCM and scenario uncertainty using Reliability Ensemble Averaging (REA) and possibility theory in projecting streamflows over Wainganga river basin. A macro scale, semi-distributed, grid-based hydrological model is used to project the streamflows from 2020 to 2094. The observed meteorological data are collected from the India Meteorological Department (IMD) and the streamflow data is obtained from Central Water Commission (CWC) Hyderabad. In REA, meteorological data are weighted based on the performance and convergence criteria (GCM uncertainty). Whereas in possibility theory, based on the projection of different GCMs and scenarios during recent past (2006–2015) possibility values are assigned. Based on the possibility values most probable experiment and weighted mean possible CDF for the future periods are obtained. The result shows that there is no significant difference in the outcomes is observed between REA and possibility theory. The uncertainty associated with GCM is more significant than the scenario uncertainty. An increasing trend in the low and medium flows is predicted in annual and monsoon period. However, flows during the non-monsoon season are projected to increase significantly. Moreover, it is observed that streamflow generation not only depends on the change in precipitation but also depends on the previous state of physical characteristics of the region.


Climate change Possibility theory REA Streamflow Uncertainty Wainganga 

1 Introduction

Having varying degree of regional impacts, climate change and global warming is a reality (Das and Umamahesh 2016). However, impact estimation at finer spatial scales is burdened with substantial amount of uncertainty resulting from several sources (Mujumdar and Ghosh 2008). In addition, due to the availability of several climate models and scenarios, there is always existence of uncertainty in climate change impact analysis (Najafi and Hessami Kermani 2017). According to Intergovernmental Panel on Climate Change (IPCC 2014) the definition of uncertainty represents the lack of complete information, knowledge on what is known and knowable. Due to the uncertainty that is involved in global and regional climate modelling, the outputs cannot be used directly for proposing different adaptation strategies and decisions (Pielke and Wilby 2012). Addressing the climate change consequences without ascertaining the uncertainty will mislead the decision makers in the context of water management (Bennett et al. 2012). Huth (2004) characterized the different level of uncertainty such as (i) scenario uncertainty, (ii) GCM (Global Climate Model) uncertainty, (iii) uncertainty due to downscaling methods, and (iv) intramodel uncertainty, due to different realizations of a single GCM. More often, uncertainties arising from downscaling techniques and scenarios are considered as major sources of uncertainty (Chen et al. 2011; Teng et al. 2012). Moreover, Wilby et al. (2014) illustrated the cascade of uncertainty due to the choice of scenarios, GCM and realization of climate variability in precipitation change under Coupled Model Inter-comparison Project 5 (CMIP5). They stated that the uncertainty associated with scenarios would lead to even larger uncertainties in the regional climate change impact. Therefore, to achieve effective outcomes and modelling performance, it is essential to incorporate the uncertainties which are stemming from aforementioned sources (Lespinas et al. 2014). In order to tackle the uncertainty related to GCM and scenarios in climate change impact analysis, multiple climate models and scenarios are investigated to project a range of possible changes in the hydrologic variables.

Before assessing the uncertainty, it is necessary to understand the primary cause of different uncertainties associated with different sources. The uncertainty associated with the GCM projections derives from the vagueness in future greenhouse emissions, and the response of the GCM to the atmospheric forcing that is associated with parameterization, model structure, and spatial resolution of the GCM (Teng et al. 2012). In addition, the decisions opted by various climate models are different that increases the model complexity and ultimately the model simulations (Clark et al. 2016). However, the scenario uncertainty stems from the unpredictability and incomplete knowledge about the future climate that arises from inadequate information and understanding of the biophysical process (New and Hulme 2000). Hence, it should be noted that scenarios are proposed to be exploratory rather than predictive (Brown et al. 2015). Despite of similar performance during the training period, different downscaling techniques differ in future projections when forced with GCM outputs and that will give rise to the uncertainty due to the multiple downscaling techniques as stated by Ghosh and Katkar (2012). Uncertainty due to the initial conditions is associated with the different realizations from a single GCM, and can also be termed as intramodel uncertainty (Mujumdar and Ghosh 2008).

Kundzewicz et al. (2016) stated that uncertainties are introduced through transfer functions, such as from scenario emissions to the climate change and then to the consequences on water resources mostly on extreme events as well as adaptation strategy. Later, Kundzewicz et al. (2018) advocated that intramodel uncertainty can be lower than intermodel uncertainty and uncertainties in the future projections clearly depend on the concerned time horizon. For example, GCM uncertainty may play an important role than the scenario uncertainty while projecting for the near future (e.g., the 2020s) as near future climate is strongly conditioned by past emissions. However, scenario uncertainty may be significant while projecting for the far future (e.g., the 2090s). Moreover, they also stated that structure and parameterization of the hydrological models would also introduce uncertainty to the impact analysis on water resources in the context of climate change. Vetter et al. (2017) considered five GCMs, four scenarios, and nine hydrological models to evaluate the source of uncertainty in projected hydrological changes. They showed that largest and lowest share of uncertainties stems from the GCMs and hydrological models respectively. In addition, Krysanova et al. (2016) advocated that climate models and scenarios are generally two major sources of uncertainty in climate change assessment.

The uncertainty information is being utilised by practitioners as an important element and they try to model the planning and discussion making process by integrating the uncertainty information (Höllermann and Evers 2017). Therefore, uncertainty analysis in the context of climate change impact study and hydrological modelling has become indispensable and the research community has been progressing rapidly to address the vagueness using different techniques. Example includes Ghosh and Mujumdar (2009) & Das and Umamahesh (2017) who analysed intermodel or GCM uncertainty using imprecise probability and Reliability Ensemble Averaging (REA) respectively; Mujumdar and Ghosh (2008) used possibilistic approach to analyse scenario uncertainty; uncertainty resulting from multiple downscaling methods was examined by Ghosh and Katkar (2012) and Khan et al. (2006). Therefore, REA, imprecise probability, possibilistic modelling, and probabilistic approach are commonly used as uncertainty modelling. REA measures the model uncertainty in the form of model performance and model convergence. It assigns weight to each model based on their ability to capture the observed climate and convergence of the simulated changes across models to minimize the model uncertainty. Imprecise probability is used to model the partial ignorance because of non-availability of the outputs from some GCMs under a few scenarios. It is expressed in the form of outer envelopes (upper and lower bounds), which is resulted from the interval regression. Based on the theory of fuzzy sets and ability of the GCM scenarios to capture the recent past climate, possibilistic approach assigns the possibility value for different GCMs and scenarios. Whereas, the Bayesian approach is generally used in probabilistic modelling of uncertainty with a prior distribution about the uncertain parameter.

Based on the authors’ knowledge a limited number of past investigations have been dedicated to compare the projections based on different uncertainty analysis approach. The approaches that are adopted by the climatic scientists to minimize the uncertainties may lead to new source of uncertainties (Pidgeon and Fischhoff 2011). In this sense, the motive of the present study is to investigate the future projection of monthly streamflow based on different uncertainty approach. In the present study, a semi-distributed, macro scale, and grid-based three-layer Variable Infiltration Capacity (VIC-3 L) hydrologic model is used to obtain the future projections of streamflow. The VIC model has been used in different aspects of water resources dealing with climate change impact across the globe (Wang et al. 2018; Hengade et al. 2018; Das and Umamahesh 2018). As discussed earlier, the uncertainty associated with the hydrological model is not significant as compared to the GCM and scenario uncertainties. Hence, the uncertainty related to the hydrologic model is neglected in the present analysis. Two uncertainty techniques, viz. REA, and possibilistic approach are used to assess the GCM and scenario uncertainties. Outputs from the six-high resolution GCMs with two Representative Concentration Pathways (RCPs) scenarios are obtained from the Coordinated Regional Climate Downscaling Experiment (CORDEX) for South Asia from the Indian Institute of Tropical Meteorology (IITM), Pune. The rest of the paper is organized as follows. Section 2 is dedicated to discuss the study area with data used. The proposed methodology is elaborated under Section 3. Result and discussions are deliberated in section 4, and section 5 focuses on the summary and critical findings of the study.

2 Study Area and Data Used

Wainganga means ‘Arrow of Water,’ is one of the major tributaries of the second largest river basin in India, i.e. Godavari River. The Wainganga sub-basin (Fig. 1) covers the area between latitudes 19o 30’ N and 22o 40’ N and longitudes 78o 0′E and 81o 0′ E and blankets about 16.45% of the total area of Godavari River basin. The annual precipitation varies between 900 mm to 1600 mm with most of the precipitation during south-west monsoon (June to October). The minimum winter temperature fluctuates from 7 °C to 13 °C and maximum summer temperature varies from 39 °C to 47 °C. The area is predominantly covered by fine and medium texture soil with clay and clayey loam as the principal soil types. The land use pattern mostly occupied with cropland and forestland. There is no significant difference in the land use pattern during 1985–2005.
Fig. 1

Location map of the Wainganga Basin

Different meteorological variables are acquired from different sources, such as precipitation, maximum and minimum temperatures are obtained from the high-resolution (0.5o × 0.5o) India Meteorological Department (IMD) dataset during 1971–2005. Whereas, wind velocity is downloaded from Princeton University dataset (Sheffield et al. 2006) during the same period. The streamflow data at the outlet of the Wainganga basin, i.e. Asthi is obtained from Central Water Commission (CWC), Hyderabad from 1971 to 2005.

GCM projects the future climate at a coarser scale; on the other hand, for proper management and adaptation strategy it is required to evaluate the climate signal at finer scales. Finer spatial resolution incorporates the spatial variability such as dynamic land use land cover, variability in soil and orography, which improve the robustness of future climate change projection. Hence, the atmospheric variables at coarser resolution from the GCMs are dynamically downscaled to the finer resolution under CORDEX and can be directly used for vulnerability, impacts and adaptation studies under climate change (Gutowski et al. 2016). Therefore, to evaluate the effect of climate change on streamflows, future simulated six high-resolution GCM datasets (Table 1) for Representative Concentration Pathway (RCP) 4.5 and 8.5 are obtained from the CORDEX for South Asia from the Indian Institute of Tropical Meteorology, Pune (IITM) website All the outputs from the GCMs are dynamically downscaled through CORDEX and brought to 0.5o × 0.5o (~50 km × 50 km).
Table 1

High resolution GCMs used in the present study (reproduced from Das and Umamahesh (2017))


Driving GCM


Commonwealth Australia



Scientific and


Centre National de Recherches Météorologiques

Industrial Research


National Center for Atmospheric Research



Geophysical Fluid Dynamics Laboratory



Max Planck Institute for Meteorology (MPI-M)

Australia- CCAM


Norwegian Climate Centre

3 Methodology

The proposed methodology is presented in the form of flow chart in Fig. 2. Initially, REA is applied to the GCM outputs (rainfall, maximum temperature, minimum temperature, and wind speed) to evaluate GCM uncertainty through assigning weights for different GCMs based on the performance and convergence criteria. Then, the weighted ensemble meteorological variables are forced to the hydrological model to obtain the future projection of the streamflow. In the second approach, individual GCM’s outputs under different scenarios are given to the hydrological model, and a range of projected streamflow is obtained. Next, GCM and scenarios are assigned weights based on the streamflow projection during the recent past (i.e., 2006–2015) using the possibility theory. Finally, a weighted ensemble of streamflow projection is obtained. Possibility theory is adopted to assess the GCM as well as scenario uncertainties. At last, both the streamflow projections achieved from REA and possibilistic approach are analysed.
Fig. 2

Flow chart of the proposed methodology

3.1 Reliability Ensemble Averaging (REA)

As a most credible tool, GCMs are designed to project the atmospheric variables based on the future climate change scenarios that incorporate the dynamic behaviour of greenhouse gases. As discussed earlier (Section 1), that with the availability of more number of GCMs there is always possibility of uncertainty in climate change impact analysis. Therefore, it is essential to understand the strength and weakness of the GCMs (Sengupta and Rajeevan 2013) through evaluating the capability of GCMs to capture the present climate (Sperber et al. 2013). Due to the fact that the outputs from the GCMs are qualitative in nature; hence is given low level of confidence and high level of uncertainty (Visser et al. 2000).

To quantify the uncertainty in the outputs from the GCMs, a quantitative method called as Reliability Ensemble Averaging (REA) is used to assign weights to different GCMs based on their bias as compared to the observed data and convergence of the simulated changes across GCMs (Mujumdar and Ghosh 2008). Higher weight is assigned to more reliable models (Xu et al. 2010), which enables to minimize the uncertainty associated with the multi-model analysis. REA was initially developed by Giorgi and Mearns (2002), which was non-probabilistic. Later, a probabilistic approach of this method was proposed by Giorgi and Mearns (2003). REA involves two reliability criteria such as “model performance,” i.e., the ability of the model to capture the original series and “model convergence,” i.e., convergence of the model simulation for a given forcing scenario. Model performance is evaluated based on errors obtained from the deviation of Cumulative Distribution Functions (CDFs) between GCM simulated and original series; whereas model convergence is calculated with respect to weighted mean CDF obtained from multiple GCM future simulations. Moreover, the convergence criterion measures the agreement of a model’s future projection with respect to the other models. The reader is referred to Chandra et al. (2015) for details on REA. In REA, initial weights (Eq. 2) are obtained based on the ability of the GCMs to simulate the historical observations in term of root mean square error (RMSE) (Eq. 1), which defines the performance criteria.
$$ RMSE={\left[\frac{1}{N}\sum \limits_{i=1}^N{\left({Observed}_i-{GCM}_i\right)}^2\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$
$$ {w}_{\mathrm{int}}=\frac{\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${RMSE}_i$}\right.\right)}{\left(\sum \limits_{i=1}^n\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${RMSE}_i$}\right.\right)} $$

The convergence criterion is measured based on the weighted mean CDF that is calculated by multiplying the initial weights with the future CDF value for the particular GCM. Next, the deviation from the CDF from the weighted mean CDF is individually checked and measured in terms of RMSE. This process is repeated until the obtained final weights for the different RCMs remain same as the previous iteration.

3.2 Non-parametric Quantile Mapping

Previous studies suggest to perform post-processing of high resolution outputs to minimize the errors in the model outputs that arise due to the imperfect conceptualization, discretization, and spatial averaging within the grid cells (Themeßl et al. 2011; Teutschbein and Seibert 2012). Moreover, Teutschbein and Seibert (2013) argued that outputs from the high-resolution models show significant deviations as a result of systematic and random model errors. The bias associated with the precipitation, especially in the extreme events as a result of inadequate special resolution (Rauscher et al. 2010), causes difficulties in hydrological modelling (Argüeso et al. 2013).

The weighted ensemble of atmospheric variables is obtained for different grid points and scenarios after performing the REA analysis. A better agreement is observed between the observed and weighted ensemble for variables, such as maximum temperature, minimum temperature, and wind speed. However, the precipitation (mostly the extreme) is highly underestimated. Hence, in the present study non-parametric quantile mapping (Gudmundsson et al. 2012) is used to correct the weighted precipitation series for the entire grid points using the Eq.3 and the correction is also applied to the future time period for all the grid points and scenarios. The non-parametric bias correction transformation has the better efficiency to reduce the systematic bias associated with precipitation. It does not require the prior distribution information about the data and can be applied to the precipitation series through the entire range of distributions (Gudmundsson et al. 2012).
$$ {P}_{obs}={F}_{obs}^{-1}\left({F}_{wet}\left({P}_{wet}\right)\right) $$
where Pobs and Pwet are observed and weighted precipitation, Fwet is the CDF of Pwet and \( {F}_{obs}^{-1} \) is the inverse CDF corresponding to Pobs.

3.3 VIC-3 L: An Overview

The VIC model (Liang et al. 1994, 1996) is a macro-scale hydrological model, which simulates water and energy storages and fluxes. It is a grid-based semi-distributed hydrological model, which quantifies the dominant hydro-meteorological process that takes place at the land surface atmospheric interface. It incorporates spatially distributed parameters describing topography, soils, land use, and vegetation classes. VIC can accept any combination of daily or sub-daily meteorological variables. At minimum, VIC requires daily precipitation, minimum temperature, maximum temperature, and wind speed to generate the streamflow. The VIC-3 L is the modification of the VIC-2 L, which has one extra thin surface layer for better representation of the bare soil evaporation process. Initially, the VIC generates runoff at each grid point, solving the water and energy balance equations, covering the study area accounting the heterogeneity in the land use and soil type. Then, it routs the generated runoff to the outlet of each grid point and finally to the outlet of the basin based on the stream network using the routing model (Chawla and Mujumdar 2015) developed by Lohmann et al. (1998).

In the present study, VIC-3 L is used to assess the climate change impact on streamflows by forcing it with the climate model simulated future climatic variables. The calibration and validation of the hydrological model is presented in Treesa et al. (2017) using the historical data. The reader is referred to Treesa et al. (2017) for details on hydrological modelling using VIC-3 L.

3.4 Possibility Theory

As discussed in the introduction section, intermodel and scenario uncertainties in the downscaling approach are due to the incomplete knowledge about the underlying geophysical process and uncertain future scenarios. Hence, it necessitates the use of multiple GCMs and scenarios for the risk-based impact studies of future hydrologic situations. Moreover, the fundamental assumption in modelling the scenario uncertainty is that all scenarios are equally likely (Wilby and Harris 2006). Therefore, for effective planning and management, it is relevant to evaluate the usefulness of GCMs and examine which scenarios represent the present situation best under climate forcings. A possibility distribution is developed to model the GCM and scenario uncertainty assigning possibility value based on the performance in modelling signals of recent past that is sensitive to the climate forcing.

Possibility theory (Zadeh 1999) is used to perform uncertainty analysis that arises due to incomplete and partially inconsistent knowledge. For example, let us consider a dataset of known variables of which a probability distribution can be obtained. Hence, the probability of being greater or smaller than a particular variable can be inferred. However, when the complete information about the dataset is not available, it is not possible to apply the probabilistic approach to find out the probability. In that case, possibility value (∏)can be assigned to the dataset. If Y is a variable in the universe Ω and is not possible to estimate precisely, then the possibility value that Y can take can be expressed mathematically and defined as:
$$ {\prod}_Y(y):\Omega \to \left[0,1\right] $$
Where y is degree of possibility that Y can take. The possibility value y = 0 suggests that Y = y is not possible and y = 1 suggests Y = y is possible without any restriction. The restriction suggests the absence of any value other than y, which Y can take with high possibility. In general, the equal possibility of the GCMs and scenarios is assumed that denotes∏Y(y) = 1, ∀ y ∈ Ω. According to Drakopoulos (1995), possibility system is a triple \( \left(\Omega, \mathfrak{B},\prod \right) \)where Ω is the set of all possible outcomes, \( \mathfrak{B} \) is sigma algebra on Ω and ∏is a real-valued function defined for each \( A\in \mathfrak{B} \) such that
$$ \prod \left(\phi \right)=0 $$
$$ \prod \left(\Omega \right)=1 $$
$$ \Pi \left({\cup}_i{A}_i\right)={\sup}_i\left(\prod \left({A}_i\right)\right) $$

The “sup” operator denotes maximum. According to the normalization property of the possibility theory, there must be one \( \tilde{y} \) such that \( {\prod}_Y\left(\tilde{y}\right)=1 \) (Spott 1999). Mujumdar and Ghosh (2008) stated that unlike the probability, the possibility does not depend on the frequency of events and possibility is mainly ordinal.

3.5 Uncertainty Analysis Using the Possibilistic Approach

In the present study, GCM and scenario uncertainty is modelled using the possibility theory. Precise assessment of streamflow projection under different climate forcing is not possible due to the unpredictability and incomplete knowledge about the future climate that arises from inadequate information and understanding about the biophysical process. While ignoring the above-said uncertainty and assuming that all the GCMs and scenarios are equally possible, will lead to difficulties for water resources planner for effective planning and management. The procedures to evaluate the uncertainty using possibility approach are as follows:
  1. 1.

    The baseline period of the present study (1978–2002) is assumed that there is no significant evidence of the climate change forcings.

  2. 2.

    Based on the availability of meteorological data and streamflow data for the recent past (i.e., 2006–2015), where it is believed that there is growing evidence of climate forcing, possibility distribution is applied to assess the uncertainty both in GCM and scenario.

  3. 3.

    Next, the performance of the generated streamflow using different GCMs and scenarios are evaluated as compared to the observed flows. The performance is computed based on the model and observed CDF values using Weibull’s plotting position. The motive of the performance computation is only to measure the deviation of the simulated streamflow from that of the observed flows. The performance index (C) is computed using the Eq. 8. The C value is only computed for the recent past, i.e. 2006–2015.

$$ C=1-\frac{\sum \limits_x{\left({Q}_{obs(x)}-{Q}_{sim(x)}\right)}^2}{\sum \limits_x{\left({Q}_{obs(x)}-{\overline{Q}}_{obs}\right)}^2} $$
where, Qobs(x) and Qsim(x)are the observed and simulated streamflows for the corresponding CDF value of x, and the mean observed flow is denoted as \( {\overline{Q}}_{obs} \).
  1. 4.

    To satisfy the normalization property of the possibility theory, the obtained C values from the all the GCMs and scenarios are divided by the maximum value of C, and the normalization value corresponding to particular GCM and scenario is considered as the possibility value for that particular GCM and scenario.


4 Result and Discussions

4.1 Streamflow Projection After GCM Uncertainty Using REA

GCMs are weighted based on the performance and convergence criteria for each meteorological variable using REA. The weighted ensemble of each variable is considered and given as input to the hydrological model. The weighted ensemble of meteorological variables for one grid point (19.75, 79.75) for the baseline period is presented in Fig. 3. It can be noted from the figure that the temperature and wind velocity profiles are well represented by the weighted ensemble of the GCM. However, the precipitation profile does not capture the observed precipitation profile. The reason for failure to capture the extreme precipitation events can be attributed to the inadequate spatial resolution (Rauscher et al. 2010), and it can be improved by improving the certain features like generation and evolution of tropical storms (Oouchi et al. 2006), monsoon circulation (Gao et al. 2006), orographic precipitation (Iorio et al. 2004).
Fig. 3

Comparison of different meteorological variables between historical and weighted ensemble from GCMs

Hence, it is necessary to correct the bias associated with the rainfall series prior to the hydrological modelling as discussed in section 3.2. The comparison of uncorrected and corrected results is shown in Fig. 4 for the (19.75, 79.75) grid point in the form of quantile plot. From the result, it can be noted that the precipitation series over the grid point has been improved significantly after the bias correction and the statistical correction is also applied to the future scenario of precipitation series for the respective grid points before using it for climate change assessment. Next, the weighted ensemble meteorological variables are forced to the calibrated VIC-3 L hydrological model to obtain the future streamflow projection. The CDFs of the annual, monsoon and non-monsoon plots are presented using Weibull plotting position in the Fig. 5. The Weibull plotting position is suitable as it yields unbiased estimates of exceedance probabilities, regardless of the distribution of the observations (Kroll et al. 2015). It can be noted from the figures that there is no significant change in the flows as compared to the baseline period during annual and monsoon season, where the flows approach the CDF value of 1 (i.e., high flows) under both the scenarios and different time slices. However, the medium and low flows are likely to increase significantly. Das and Nanduri (2018) analysed the climate change impact on monsoon flows using different machine learning techniques and also found an increase in the low and medium flows in the future climate change scenarios. In case of the non-monsoon period, all the flows (high, medium, and low) are projected to increase as compared to the baseline period. The variations are more in the high flows than the medium and low flows under both the scenarios.
Fig. 4

Q-Q plot presenting (a) uncorrected and (b) corrected using quantile mapping for the precipitation dataset (19.75, 79.25)

Fig. 5

CDFs of future projected flows (left panel for RCP4.5 and right panel for RCP8.5): (a)-(b) for annual flows; (c)-(d) for monsoon flows; (e)-(f) for non-monsoon flows under different time slices

Wang et al. (2013) examined the sensitivity of runoff with precipitation and temperature under climate change forcings and showed that the runoff is more sensitive to the precipitation than temperature with nonlinear relation with impact due to climate change. Moreover, Alam et al. (2016) analysed the variability of streamflow over Brahmaputra river basin varying the temperature from 1o to 6o C and percentage change in precipitation from −10 to 40%. They observed that with increasing percentage of precipitation the mean percentage of annual discharge is likely to increase despite increase in temperature. In this sense, the change in the precipitation is computed for and analysed with respect to the change in streamflow. Different quantiles of the annual, monsoon and non-monsoon precipitation for the observed and future periods are computed. For instance, different quantiles of the precipitation during 2020 to 2044 under RCP4.5 scenario are presented in Table 2. It can be noted from the table that the higher quantiles for annual and monsoon season during the baseline period are more than that during 2020–2044. Hence, the streamflow corresponding to the high quantiles is likely to decrease. Despite decrease in monsoon precipitation during 2020–2044 with respect to the baseline period, the monsoon flows are projected to increase. This can be attributed to the process involved in VIC hydrological model. According to the assumption in VIC, the surface runoff will generate from the soil layer when the amount of precipitation exceeds the storage capacity of the soil. Orth and Seneviratne (2013) examined the propagation of soil moisture memory to streamflow and stated that soil moisture-streamflow coupling is strongly related and subsequently resulted in higher streamflow memory. In the present study, January is taken as the starting month to run the model. With the significant increase in the non-monsoon rainfall, the storage capacity of soil may be fulfilled prior to the monsoon season. Seneviratne et al. (2010) stated that precipitation over very wet or saturated soil, for which anomaly in the precipitation will result in anomaly of runoff than soil moisture. Hence, precipitation received during the monsoon season will generate surface runoff with minimal losses. Therefore, streamflow not only depends on the change in precipitation but also depends on the previous state of physical characteristics of the region. Note that the groundwater contribution to the streamflow is not studied in the present analysis.
Table 2

Annual, monsoon, and non-monsoon precipitation (in mm) for different quantiles under baseline period and during 2020–2044


Baseline period











































4.2 GCM and Scenario Uncertainty Based on the Possibilistic Approach

In the present study, it is assumed that the climate forcing has no significant effect during the baseline period. For proper planning and management, it is necessary to evaluate the efficiency of GCM and scenario to model the future projection under climate forcing. Therefore, possibility theory is applied to assign possible weights to GCM and scenarios based on their ability to model the recent past (2006–2015) that is under the climate change forcings. It is worth mentioning that for the precipitation series during 2006–2015 the bias-correction is also carried out for all the GCMs under different scenarios. Using the properties of the possibility distribution, possibility of the GCMs and scenarios are computed. For example, there are three GCMs (G1, G2, and G3) and two scenarios (S1, S2) are available for future projection. Then, based on the possibility theory the possibility of the GCM (G1) is given by:
$$ \prod (G1)=\prod \left(\left(G1,S1\right)\cup \prod \left(G1,S2\right)\right)=\sup \left(\prod \left(G1,S1\right),\prod \left(G1,S2\right)\right)\kern0.5em $$
Likewise, the possibility of scenario of S1 can be obtained by:
$$ \prod (S1)=\prod \left(\left(G1,S1\right)\cup \prod \left(G2,S1\right)\cup \prod \left(G3,S1\right)\right)=\sup \left(\prod \left(G1,S1\right),\prod \left(G2,S1\right),\prod \left(G3,S1\right)\right) $$
To compute the possibility distribution, the performance index (C) is computed for different GCMs and scenarios during the recent past. Then, according to the normalization property of the possibility distribution the C values are divided by maximum C value. The normalized C value of a particular GCM and scenario is known as possibility distribution of that particular GCM and scenario. The C values and the possibility distribution are presented in Table 3. From the obtained possibility values, it is difficult to interpret which uncertainty (GCM or scenario) is predominant. However, the difference in possibility value under RCP8.5 is more than RCP4.5. It can be noted from GCMs with both scenarios that higher C score is obtained for RCP8.5 than RCP4.5, which suggests that climate forcing over the study area follows the pathway of high emission scenario than a stabilized scenario. It is worth mentioning that the possibility distribution is computed based on the recent past, where climate forcing signal is present. However, the forcing signals during this initial period are not very prominent. In other words, the present climate forcing (e.g., greenhouse concentrations) over the study area will continue to affect the climate over next few decades irrespective of future scenarios (Mujumdar and Ghosh 2008). Hence, the differences in the possibility values between the two scenarios are not significantly different. However, with the passage of time and prominent climate change forcing the importance of the possibility approach will increase.
Table 3

C and possibility values for different GCMs and scenarios (bold letter refers to the most possible experiment)



C Value

Possibility Value





































From the analysis of possibility distribution for different GCMs and scenarios, it is observed that MPI-ESM-LR model with the RCP8.5 scenario has highest possibility value. Hence, streamflow projection obtained from MPI-ESM-LR model with RCP8.5 forcing is considered as a most probable experiment (MPE). The CDF plots during annual, monsoon and non-monsoon period are plotted using Weibull plotting position and presented in Fig. 6. Note that possibility value with one does not suggest that the particular GCM captures the climate during the recent past perfectly. However, it implies that the nonexistence of any other better GCMs or scenarios to assess the impact of climate change on streamflow over the study area. It is observed from the figure that the obtained result is quite similar to the outcomes achieved during REA processed streamflows. However, there are differences in CDFs for different time slices. Whereas, the CDFs those are obtained for MPE is not varying significantly for different time slices. MPE suggests that the outputs from a single model and the outputs from that model do not guarantee that the performance of the model will remain same in future. Hence, it is necessary to evaluate the weighted mean possible CDF based on the assigned possibility value for different GCMs and scenarios.
Fig. 6

CDFs of future projected flows under MPE: (a) for annual flows; (b) for monsoon flows; (c) for non-monsoon flows during different time slices

The weighted mean possible CDF (Eq. 11) is computed based on the possibility value assigned to different GCMs and scenarios.
$$ {CDF}_{weighted\ mean}=\frac{\sum \limits_G\sum \limits_S\prod \left(G,S\right)\times {CDF}_{GS}}{\sum \limits_G\sum \limits_S\prod \left(G,S\right)} $$
Where, ∏(G, S) and CDFGSare the possibility and CDF related to the Gth GCM and Sth scenario respectively. The weighted mean possible CDF is presented in Fig. 7. It can be noted from the figure that the variability in the CDFs for annual, monsoon and non-monsoon periods are likely to follow the findings, those are obtained during REA. Hence, considering the outcomes from the two uncertainty methods, it is observed that the low and medium flows are likely to increase during annual and monsoon period as compared to the baseline period. In case of high flows, no significant difference is observed. However, flows during the non-monsoon season are projected to increase significantly. The primary cause of the increase in flow is due to the increase in precipitation. Only GCM uncertainty is modelled using REA, whereas both GCM and scenario uncertainties are modelled using possibility theory. However, the findings from both the methods do not appear to be significantly different from each other. In this sense, it can be stated that GCM uncertainty is more significant than the scenario uncertainty. While quantifying the different uncertainty sources, Mani and Tsai (2017) also advocated that GCMs are the major source of uncertainty during runoff projection as compared to the downscaling techniques and emission scenarios. In addition, the uncertainty linked with the GCM dominates the uncertainty associated with the choice of hydrological models (Md Haque et al. 2015).
Fig. 7

Weighted mean possible CDFs of future projected flows under MPE: (a) for annual flows; (b) for monsoon flows; (c) for non-monsoon flows during different time slices

The limitation of the present study is that the investigation is carried out using one hydrologic model and it should be noted that findings may vary with different hydrological models. The calibrated parameters of the hydrological models are kept constant for the future because there is no significant change in the land use pattern observed during 1985–2005. However, with the passage of time land use pattern may vary, which will induce additional uncertainty to the hydrological model. In a recent study, Chawla and Mujumdar (2017) stated that future land use change would contribute towards the uncertainty along with the GCM uncertainty. Although there are more than 40 GCMs available, the CORDEX downscaled only 6 GCMs. Therefore, downscaling of more GCMs to the regional level for climate change assessment will result in considerably large ensemble and more reliable outcomes. Therefore, the inclusion of non-stationarity in hydrological parameters, more number of GCMs and evaluating the differences in possibility value with the passage of time provide a direction to pursue studies in the future.

5 Summary and Conclusions

Two different methodologies, namely REA and possibility approach to model the GCM and scenario uncertainties are presented in this paper. VIC-3 L hydrological modelling is used to project the monthly streamflow using the dynamically downscaled outputs from the COREX. The non-parametric quantile mapping is used to correct the bias in the precipitation based on the baseline period (1978–2002). REA is performed to model the GCM uncertainty in precipitation, maximum temperature, minimum temperature, and wind velocity based on the performance and convergence criteria. Based on the weight assigned through REA, a weighted ensemble of these variables is given as input to the calibrated VIC-3 L model to project the streamflow. However, in possibility approach, weights are assigned to different GCMs and scenarios based on their ability to capture the climate forced recent past (2006–2015) streamflows. Based on the possibility values most probable experiment and weighted mean possible CDF for the future periods are obtained. The critical outcomes from the present investigation are as follows.
  • Precipitation dataset shows highest inherent bias than other meteorological variables (i.e., maximum and minimum temperature, wind speed) and hence bias correction should be incorporated.

  • There is no significant difference in the streamflow is observed after assessing the uncertainty using REA and possibility theory. However, the uncertainty associated with GCM is more significant than the scenario uncertainty.

  • The predicted low and medium flows are likely to increase during the annual, monsoon, and non-monsoon periods and the primary cause of the increase in flow is due to the increase in precipitation.

  • However, the flows (high to low) during the non-monsoon period are projected to increase significantly over the river basin.

  • Moreover, it is observed that streamflow generation not only depends on the change in precipitation but also depends on the previous state of physical characteristics of the region.

It is worth mentioning that appropriate modelling of the cloud systems, robust computation of evapotranspiration, and proper understanding of the forcing-feedback relationship in the GCMs can provide more reliable projections of climate and hydrologic variables in future. An important limitation of the study presented in this paper is that the meteorological variables are dynamically downscaled by CORDEX and the uncertainty in the downscaling method is not addressed in the study. Hence, incorporation of such uncertainty may result in more robust and effective approach for assessing the climate change impact.



A previous shorter version of the paper has been presented in the 10th World Congress of EWRA “Panta Rei” Athens, Greece, 5-9 July 2017. The authors sincerely thank Dr. Subimal Ghosh, Associate Professor, Department of Civil Engineering, Indian Institute of Technology Bombay for sharing the observed meteorological data for the recent past (2006-2015).

Compliance with Ethical Standards

Conflict of Interest Statement



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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Civil EngineeringNational Institute of TechnologyWarangalIndia

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