Climate change significantly impacts the natural systems, accelerating the global water cycle, and impacting various ecosystem services. However, the expected effects of climate change on the frequency and severity of extreme events on hydrological systems vary significantly with location. The present study investigates the uncertainties engulfed in hydrological predictions for the Tungabhadra River Basin. The ensemble streamflow projections were generated using four hydrological models, five climate models, and four climate scenarios to illustrate the associated uncertainties. The uncertainty in hydrological components such as streamflow (QQ), water availability (WA), and potential evapotranspiration (PET) was analysed in the future period (2015–2100). The results suggest that, in the monsoon period, precipitation projections increase by about 10.43–222.5%, whereas QQ projections show an increment between 34.50 and 377.7%. The analysis of variance (ANOVA) technique is used to further quantify the contribution of different sources to the total uncertainty. Furthermore, the ensemble spread is optimized using quantile regression forests (QRF), and the post-processed flows are likely to decrease up to 7% in June and increase up to 70% in September. This study is envisaged to give insights into the quantification of uncertainties in the prediction of future streamflow for rational and sustainable policymaking.

  • Hydrological assessment of the Tungabhadra Basin using CMIP6 GCMs and multiple hydrological models.

  • Diagnostic evaluation of performance of hydrological models were estimated.

  • Uncertainty in the ensemble flows decomposed using the analysis of variance (ANOVA) technique.

  • The ensemble spread is optimized using quantile regression forests (QRF), and the post-processed flows were generated using the QRF method.

Global climate change has altered the intensity and frequency of hydro-climatological extremes (Yuan et al. 2015; Piras et al. 2016). Accordingly, reliable streamflow prediction under climate change is imperative for better water resources planning and management (Steinschneider et al. 2012; Singh et al. 2016). A typical approach for this purpose is to generate future streamflow by forcing future projections obtained from climate models under varying climate scenarios into a calibrated hydrological model. However, the obtained projections suffer from inherent biases in both climate and hydrological models (HMs) (Her et al. 2019; Wang et al. 2020). It is essential to account for and quantify these uncertainties to improve the skill of future hydrologic projections. As projections from a single climate model cannot address the non-linear interactions researchers employed multi-model projections (Georgakakos et al. 2004; Harding et al. 2012; Hagemann et al. 2013; Tegegne et al. 2017; Keteklahijani et al. 2019; Adib et al. 2020).

Future climate projections are generally obtained from the outputs of state-of-the-art tools called global climate models (GCMs), which represent the atmospheric processes through distinct mathematical expressions (Gouda et al. 2018). The Coupled Model Intercomparison Project Phase 6 (CMIP6) initiated by the Intergovernmental Panel on Climate Change (IPCC) has coordinated and compiled the simulation from climate model experiments obtained from various modelling teams worldwide. The simulations in CMIP6-based climate models were generated under a set of scenarios using combinations of various radiative forcing levels and shared socioeconomic pathways (Meinshausen et al. 2020). The uncertainties in the future streamflow projections generated with the help of climate model outputs propagate from model structures, sub-grid parameterizations and their simplification of processes, various forcing scenarios, initial conditions, and choice of downscaling methods (Zhang et al. 2015b; Anil et al. 2021). Many of the studies reported so far address the uncertainty in the future streamflow projections due to uncertainties in model structures, initial conditions, scenarios, and downscaling methods (Knutti et al. 2010; Chen et al. 2011; Wang et al. 2019; Alam et al. 2021). The uncertainty corresponding to the climate models has been reduced in the latest CMIP6 bundle of GCMs due to the advancement in understanding the underlying physics of atmospheric processes over the last couple of decades (Gusain et al. 2020; Priestley et al. 2020). However, the climate model uncertainty is considered a major contributor to the future streamflow projections’ uncertainty (Kwon et al. 2012). Moreover, it is essential to note that the hydrological model structure uncertainty has received comparatively less emphasis so far than the former (Poulin et al. 2011; Steinschneider et al. 2012). The uncertainties associated with hydrological modelling include uncertainty in model structure, the spatial scale of the model, initial hydrologic conditions, parameter equifinality, and uncertainty in the calibration data (Jakeman & Hornberger 1993; Beven 2006; Kirchner 2006; Ludwig et al. 2009; Her & Chaubey 2015).

Basin-level hydrological studies assist policymakers and end-users in implementing better adaptation strategies for improved water resources management under climate change. In this article, the uncertainty in the future ensemble streamflow projections of the Tungabhadra Basin is studied considering the projected hydrological alterations and low water use efficiency. The future projections of the Tungabhadra Basin, a tributary to Krishna River, predicted severe drought and alterations in hydrological variables such as streamflow, soil moisture, and evapotranspiration (Gosain et al. 2006; ACIWRM & WRD 2012; Chanapathi et al. 2020). Singh et al. (2016) assessed the parametric uncertainty in simulating the extreme peak and low flows in the Tungabhadra Basin using Soil Water Assessment Tool (SWAT). The results suggested the reliability of SWAT performance in simulating the observed peak and low flows. Meenu et al. (2013) calibrated Hydrologic Engineering Center Hydrologic Modeling System version 3.4 (HEC-HMS 3.4) and forced future climate projections obtained from a single GCM to assess the impact of climate change on streamflow. The results of the study suggest increasing precipitation and runoff, with decreasing evapotranspiration. In contrast, a recent study by Facer-Childs et al. (2021) shows a reduction in the streamflow projections in the Tungabhadra Basin because of the increased frequency and severity of droughts due to climate change. Their study addressed the necessity to adapt ensemble streamflow prediction strategies to increase the reliability of the design and operation of water resources systems. Moreover, the water usage in the Tungabhadra Basin is low leading to unreliable allocation to all the users. Furthermore, the groundwater levels in Vedavati sub-basin are depleting due to over-exploitation attributable to scanty rainfall and surface water availability (WA). Bejagam et al. (2020) reported that precipitation from CMIP5-based models projects a decline of about 1.31–14.57% in the Tungabhadra Basin. Hence, understanding the future streamflow projections from recent CMIP6-based climate models is quintessential for hydrological applications such as reservoir operation, hydropower production, and irrigation in the Tungabhadra Basin. To the best of the authors' knowledge, very few studies have been reported so far on the hydrological modelling of the Tungabhadra Basin and assessing the uncertainty in the ensemble streamflow projections (Meenu et al. 2013; Singh et al. 2013, 2016; Goyal & Khan 2017). However, no study has been reported on assessing the uncertainty in the future streamflow at the Tungabhadra Basin using multiple GCMs and HMs.

The main objective of this study is to account for the uncertainties in the future streamflow projections of the Tungabhadra Basin generated from multiple GCMs and multiple HMs for different future scenarios. For this purpose, five CMIP6-based GCMs were selected based on their performance in replicating the historical statistics. A detailed description of the methodology used for the selection of best-performing GCMs is mentioned in the succeeding sections. The climate projections obtained from the five selected GCMs for four different scenarios were forced into four HMs (with varying model structures) to generate ensemble streamflow. Consequently, this study also shows how the uncertainty in future precipitation and temperature projections are translated into hydrological variables such as streamflow, potential evapotranspiration (PET), and WA. The total uncertainty in the generated ensemble streamflows is further decomposed using ANOVA to estimate the contributions of three different sources (GCMs, HMs, and SSPs). An ensemble post-processing method is also employed to correct the ensemble spread of the simulated flows during the future period.

Study area

Tungabhadra River, a tributary of the Krishna River, is formed by the conjunction of the rivers Tunga and Bhadra. Both rivers originate at Gangamoola in Varahaparvatha hills located at the Western Ghats, at an elevation of 1,198 m above mean sea level (MSL). They flow separately and later merge near Koodli village in Shivamogga district, where the river Tungabhadra starts. Tungabhadra dam, an interstate multipurpose project, is located at Munirabad, Koppala district of Karnataka near Hosapete, and the basin is located between 74°46′52″ E to 78°01′29″ E longitude and 13°8′60″ N to 16°13′35″ N latitude. The catchment area of the river is 69,552 km2 up to its confluence with the Krishna River. In this study, the catchment with Haralahalli as a gauge point with an area of 14,490 km2 is considered as the study area, where the observed streamflows are available. The average annual rainfall in the basin is nearly 1,100 mm and the runoff due to the southwest monsoon is predominant in the catchment (Bisht et al. 2018). The location map along with the digital elevation model (DEM) of the study area is shown in Figure 1.
Figure 1

Location map of the Tungabhadra River Basin along with digital elevation model.

Figure 1

Location map of the Tungabhadra River Basin along with digital elevation model.

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Observed data

The gridded daily precipitation, maximum temperature, and minimum temperature data are obtained from the Indian Meteorological Department (IMD). The daily precipitation dataset is available at a spatial resolution of 0.25° × 0.25° (Pai et al. 2014), and the daily maximum and daily minimum temperature data are available at a resolution of 1° × 1° (Srivastava et al. 2009). The gridded precipitation and temperature data were collected for the study area from 1975 to 2010 to set up HMs. The observed daily streamflow of the Tungabhadra Basin at Haralahalli gauge station was collected from 1975 to 2010, from India Water Resources Information System (India-WRIS).

GCMs and emission scenarios

The future projections of precipitation and daily maximum and minimum temperature were obtained from the latest bundle of CMIP6-based GCMs. A new set of five scenarios were considered in CMIP6-based GCMs, namely ‘shared socioeconomic pathways’ (SSPs). These scenarios were developed based on socioeconomic factors such as urbanization, economic growth, population, education, and the rate of technological development (Riahi et al. 2017). However, the raw GCM projections are simulated at coarser spatial resolutions (>200 km2) that cannot be used in basin-scale climate change impact studies. Moreover, they are prone to inherent biases that should be corrected. Hence, bias-corrected projections are used in this study to generate future ensemble streamflow. Mishra et al. (2020) developed a bias-corrected dataset for six countries in South Asia using empirical quantile mapping (EQM) at a spatial resolution of 0.25° for the daily time step. In this study, future climate projections (precipitation, maximum, and minimum temperature) obtained from CMIP6-based, bias-corrected 13 GCMs for all 4 scenarios (i.e., SSP-126, SSP-245, SSP-370, and SSP-585) for the future period of 2015–2100 and historical projections for the period 1975–2010 were also extracted for the study area (Mishra et al. 2020). The selected CMIP6 GCMs used in this study and their originating institute, spatial resolutions, and country are tabulated in Table 1.

Table 1

CMIP6-based GCMs used in the study and their specifications

SI NoModel NameInstitution NameResolution (Lat × Lon)Country
ACCESS-CM2 Commonwealth Scientific and Industrial Research Organization 1.25° × 1.875° Australia 
ACCESS-ESM1-5 Commonwealth Scientific and Industrial Research Organization 1.25° × 1.875° Australia 
BCC_CSM2-MR Beijing Climate Centre 1.12° × 1.13° China 
CanESM5 National Centre for Atmospheric Research, Climate and Global Dynamics Laboratory 2.79° × 2.81° The United States 
EC-EARTH3 EC-EARTH consortium published at Irish Centre for High-end Computing 0.7° × 0.7° Netherlands/Ireland 
EC-EARTH3-VEG EC-EARTH consortium published at Irish Centre for High-end Computing 0.7° × 0.7° Netherlands/Ireland 
INM-CM4-8 Institute for Numerical Mathematics 1.5° × 2° Russia 
INM-CM5-0 Institute for Numerical Mathematics 1.5° × 2° Russia 
MPI-ESM1-2-HR Max Planck Institute for Meteorology 0.94° × 0.94° Germany 
10 MPI-ESM1-2-LR Max Planck Institute for Meteorology 1.85° × 1.88° Germany 
11 MRI-ESM2-0 Meteorological Research Institute 1.12° × 1.13° Japan 
12 NorESM2-LM Centre for International Climate and Environmental Research 1.89° × 2.5° Norway 
13 NorESM2-MM Centre for International Climate and Environmental Research 0.94° × 1.25° Norway 
SI NoModel NameInstitution NameResolution (Lat × Lon)Country
ACCESS-CM2 Commonwealth Scientific and Industrial Research Organization 1.25° × 1.875° Australia 
ACCESS-ESM1-5 Commonwealth Scientific and Industrial Research Organization 1.25° × 1.875° Australia 
BCC_CSM2-MR Beijing Climate Centre 1.12° × 1.13° China 
CanESM5 National Centre for Atmospheric Research, Climate and Global Dynamics Laboratory 2.79° × 2.81° The United States 
EC-EARTH3 EC-EARTH consortium published at Irish Centre for High-end Computing 0.7° × 0.7° Netherlands/Ireland 
EC-EARTH3-VEG EC-EARTH consortium published at Irish Centre for High-end Computing 0.7° × 0.7° Netherlands/Ireland 
INM-CM4-8 Institute for Numerical Mathematics 1.5° × 2° Russia 
INM-CM5-0 Institute for Numerical Mathematics 1.5° × 2° Russia 
MPI-ESM1-2-HR Max Planck Institute for Meteorology 0.94° × 0.94° Germany 
10 MPI-ESM1-2-LR Max Planck Institute for Meteorology 1.85° × 1.88° Germany 
11 MRI-ESM2-0 Meteorological Research Institute 1.12° × 1.13° Japan 
12 NorESM2-LM Centre for International Climate and Environmental Research 1.89° × 2.5° Norway 
13 NorESM2-MM Centre for International Climate and Environmental Research 0.94° × 1.25° Norway 

Multiple hydrological models

To consider the uncertainty induced by hydrological modelling in the streamflow projections, three lumped conceptual and physics-based semi-distributed HMs were used in this study. They are Hydrologiska Byråns Vattenbalansavdelning (HBV), simple hydrology (SIMHYD); identification of unit hydrographs and component flows from rainfall, evaporation, and streamflow data (IHACRES), and soil and water assessment tool (SWAT). The varying complexities of these models in terms of model structures and spatial scale appraise the hydrologic predictive uncertainty. These models were calibrated and validated for 1975–2010 at daily time steps to simulate the future flows in the basin for 2015–2100. A brief description of the selected HMs is presented in the succeeding sections.

HBV

HBV is a lumped conceptual rainfall-runoff model, developed by the Swedish Meteorological and Hydrological Institute (SMHI) for runoff simulation and hydrological forecasting in the early 1970s (Bergstrom 1975). The runoff generation process is controlled through a set of 15 parameters, out of which 5 parameters address the snow routine and the remaining parameters account for soil moisture, response, and routing routines (Mendez & Calvo-Valverde 2016). This model has been widely used around the world attributable to its strong scientific foundation (Chen et al. 2012), and the model requires minimal inputs such as basin-averaged precipitation, PET, and temperature (Ashagrie et al. 2006; Jin et al. 2009; Chen et al. 2012; Seibert & Vis 2012).

SIMHYD

SIMHYD is a simple lumped conceptual rainfall-runoff model and different hydrologists have tested the applicability of the model on various catchments (Chiew et al. 2009; Vaze et al. 2010). It consists of seven parameters and three storages to account for interception losses, soil moisture, and groundwater. The simulated runoff in SIMHYD consists of three components: surface runoff, interflow, and base flow. The surface runoff is generated through the infiltration excess mechanism (simulated using the negative exponential function of soil wetness), whereas the interflow is generated based on the saturation excess mechanism. The surface runoff is estimated using a negative exponential function of soil wetness, and the interflow and base flow are estimated as linear functions of soil wetness and groundwater storage, respectively.

IHACRES

IHACRES is a six-parameter lumped conceptual rainfall-runoff model based on the principle of unit hydrograph, developed by the Integrated Catchment Assessment and Management Centre (iCAM), Australian National University, and the Institute for Hydrology, Wallingford, UK (Jakeman et al. 1990; Chiew et al. 1993; Post & Jakeman 1996). A different version of this model has been widely used in multiple applications across the globe (Croke & Jakeman 2004). Basically, the model identifies unit hydrograph and flow components from rainfall, evaporation, and streamflow. The unit hydrographs corresponding to quick and slow flows are defined to generate total runoff. The runoff generation mechanism consists of a non-linear and linear module, where the former converts rainfall to effective rainfall, and the latter routes the effective rainfall. A detailed description of the underlying equations in the IHACRES model can be found in Post & Jakeman (1996).

SWAT

SWAT is a physics-based semi-distributed hydrological model with a wide variety of applications and it was developed by the United States Department of Agriculture–Agricultural Research Services (USDA–ARS) and Agricultural Experiment Station in Temple, Texas. It efficiently performs long-term simulations (Singh et al. 2013). The SWAT model uses physically based inputs such as the DEM, Land use and Land cover, Soil Map, and weather parameters for runoff simulation. The model divides the entire catchment into sub-basins and these sub-basins are further divided into Hydrological Response Units (HRUs) based on unique combinations of elevation, soil, and land use. The principle behind the SWAT model is the basic water balance equation given in Equation (1).
(1)
where is the soil water content at the end of the day i, is the amount of initial soil water content on an ith day, t is the time in days, is the amount of precipitation on day i, is the amount of surface runoff on day i, is the amount of evapotranspiration on day i, is the amount of water entering the vadose zone from the soil profile on the day i, and is the amount of return flow on the day i.

All three lumped models were calibrated using the genetic algorithm and the SWAT model was calibrated with the help of SWAT-CUP software using the Sequential Uncertainty Fitting (SUFI-2) algorithm. The parameters of the HMs are fine-tuned to match the observed discharge during the period 1975–1993. The calibrated parameters were validated for the period 1994–2010. A diagnostic evaluation of the performance of all the selected HMs is conducted using a set of metrics. The metrics were chosen such that they emphasize distinct features of hydrograph such as low flows, high flows, and overall water balance (Manikanta & Vema 2022). The selected metrics along with their equation ranges and ideal values are mentioned in Table 2. The calibrated parameters were used to generate the future projections during 2015–2100, using the best-performing GCMs under four climate scenarios.

Table 2

Performance evaluation metrics along with equation, range, and ideal values

Sl NoPerformance evaluation metricEquationRangeIdeal value
Percent Bias (PBIAS)  −∞ to +∞ 
Nash–Sutcliffe Coefficient of Efficiency (NSE)  0 to ∞ 
Logarithmic Nash–Sutcliffe Coefficient of Efficiency (logNSE)  −∞ to 1 
Mean Absolute Error (MAE)  0 to ∞ 
Fourth Root Mean Quadrupled Error (R4MS4E)  0 to ∞ 
Skill Score (SS)  0 to 1 
Sl NoPerformance evaluation metricEquationRangeIdeal value
Percent Bias (PBIAS)  −∞ to +∞ 
Nash–Sutcliffe Coefficient of Efficiency (NSE)  0 to ∞ 
Logarithmic Nash–Sutcliffe Coefficient of Efficiency (logNSE)  −∞ to 1 
Mean Absolute Error (MAE)  0 to ∞ 
Fourth Root Mean Quadrupled Error (R4MS4E)  0 to ∞ 
Skill Score (SS)  0 to 1 

where and represent the observed and simulated discharge values, respectively, and is the mean observed discharge, n represents the total sample size of data, represent the frequency of simulated and observed streamflows for a particular bin. bn represents the total number of bins selected to analyse the match between PDFs between simulated and observed flows.

Selection of best-performing GCMs

Previous studies reported that the performance of GCMs is region specific. Hence, employing a large ensemble of GCMs with models that do not perform well in the study area plausibly impacts the projected streamflow (Srinivasa Raju et al. 2017; Chhin & Yoden 2018; Raju & Kumar 2020). In this regard, a set of best-performing GCMs are chosen for climate change impact assessment studies by evaluating the performance of GCMs in replicating the observed data during the historical simulation period. In this study, a Multi-Criteria Decision-Making method is adopted to rank the performance of GCMs (Raju & Kumar 2014; Srinivasa Raju et al. 2017). Three performance evaluation measures that yield distinct information about the match between observed and simulated data were chosen, namely, NSE, skill score (SS), and PBIAS. A payoff matrix () is populated with the computed three metrics as criteria and each GCM as an alternative. Considering that the ranges of criteria are different, they are normalized using the linear sum normalization technique and a normalized payoff matrix () is generated using Equation (2).
(2)
where x denotes the GCM and y represents the indicator. X represents the total number of GCMs.
The entropy technique was used to obtain the weights of the three indicators in the normalized payoff matrix. The entropy method allocates weights based on the amount of information that is available and how important the indicators are with respect to that information. The entropy for each criterion (column) in the payoff matrix is estimated using Equation (3)
(3)
where is the entropy of the yth metric.
Degree of diversification is computed using Equation (4)
(4)
Weights are assigned for each performance indicator obtained from the entropy method using Equation (5)
(5)
where Y represents the total number of GCMs.
Compromise programming (CP) is used to rank the performance of GCMs based on the computed indices. CP computes the distance between alternatives and the ideal solution using a distance-based measure metric is given by Equation (6)
(6)
where is the normalized ideal value of the indicator y; p is a parameter whose value is set as 2 to estimate the Euclidean distance.

The ranking is given to the GCMs at each grid and the ranking pattern in each grid is plausibly different. Hence, to facilitate impact assessment studies for a region, a group decision-making approach is used to extract the suitable set of GCMs for the entire study area. A detailed description of group decision-making methodology can be found in Srinivasa Raju et al. (2017). The group decision-making in this study is performed over all three variables at all grids to obtain five best-performing GCMs for carrying out further study. From the analysis, it was found that models CanESM5, INM-CM5-0, MPI-ESM1-2-HR, MPI-ESM1-2-LR, and MRI-ESM2-0 were found to be the best-performing models. The complete analysis is carried out using these selected five models in the subsequent section.

Quantification of uncertainty from multiple GCMs and multiple HMs

The difference between maximum and minimum values (ranges) of projected climate variables (precipitation and temperature) and hydrological components (QQ, DR, SS, etc.) was calculated as a measure of the amount of uncertainty contained in ensemble predictions made using multiple GCMs and multiple HMs. Uncertainty in ensemble hydrological components obtained from the multiple GCMs and multiple HMs were first quantified. Then, the uncertainty amount was quantified for two different sources, multiple GCMs, and multiple HMs.

One of the popular approaches to overcome the uncertainty in model prediction is to pool the ensemble members from all the models, also known as equal weighting. It is challenging to assign weights to individual GCMs based on past performance and create a weighted ensemble mean. Assigning weights based on the representation of history requires a comprehensive knowledge of the model's performance (Curry & Webster 2011). However, the weights will highly depend on the evaluation procedure, ground truth data, region of interest, and parameters evaluated. Hence, in this study, a simple ensemble mean is employed to maintain the information about the spread of the ensemble. Uncertainty in ensemble projections due to each GCM is quantified by estimating the range (difference between maximum and minimum) and rank given to individual GCMs in the contribution of overall uncertainty among the selected GCMs. GCM with higher uncertainty given the first rank and GCM with the least uncertainty given the last rank. Then, flow duration curves (FDCs) were drawn from the ensemble streamflows obtained to quantify the uncertainty in multiple HMs. In addition, the relationships between the quantities of uncertainty in the ensemble projections of the climate variables and hydrological components were then investigated to see which climate variables (precipitation, maximum, and minimum temperature) exerted the most significant influence on the hydrological prediction uncertainty.

To quantify the uncertainty present in future streamflows, the ANOVA technique was used in the present study. The ANOVA approach quantifies the contributions of various sources and their interactions to the total uncertainty by splitting the overall variance into its several origins (Aryal et al. 2019). The total variance, calculated as the sum of squared errors, is split into two parts: individual effects and interaction effects. Three-way ANOVA has been carried out in the present study, which splits up the total uncertainty into seven fractions, out of which, the first three fractions represent the individual contributions and the remaining four fractions belong to their interactions as shown in Equation (7). In this study, an ensemble of 80 streamflow projections were obtained using 5 best-performed GCMs, 4 HMs, and 4 climate scenarios (SSPs). The uncertainties in the future streamflows due to the three sources were quantified using ANOVA for two time periods: near future (2021–2060) and far future (2061–2100).
(7)
where , , and represent the total sum of squares corresponding to the hydrological model, climate scenarios, and climate models, respectively. A detailed flowchart depicting the workflow of the present study in the generation of ensemble streamflow is given in Figure 2.
Figure 2

Flowchart representing the workflow of the present study.

Figure 2

Flowchart representing the workflow of the present study.

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QRF for post-processing technique

The future streamflows generated using multiple GCMs, multiple HMs, and multiple scenarios are highly uncertain with a high ensemble spread. However, it is worth noting that the ensemble spread plays a vital role in decision-making under uncertainty. Hence, the correction of ensemble spread to reduce the uncertainty bands assists the policymakers in better decision-making (Zhang et al. 2022; Manikanta et al. 2023). For this purpose, QRF, a non-parametric method, is used to post-process the ensemble streamflows (Meinshausen 2017). In QRF, conditional quantiles and median values of the response variable are estimated for high-dimensional predictors. The conditional quantiles are estimated using binary regression trees known as classification and regression trees (CARTs). Sequentially, in each tree, iterative binary splitting is employed to determine a new vector of predictors and its associated leaf. This iterative binary splitting between predictors aggregates the observations according to their forecasts. Therefore, for every generated streamflow event, an ensemble of observations is restored to create an empirical cumulative distribution function (CDF). The final CDF is estimated as the weighted mean of the CDFs obtained from all the trees, from which the predictive quantiles are determined. For more details on QRF methodology, the readers are encouraged to refer to Taillardat et al. (2016). In this study, 20 ensemble members generated by 5 GCMs and 4 HMs were forced as predictors for post-processing the spread of historical ensemble streamflows under each SSP. The hyper-parameters such as the maximum terminal node size are set to 20 with a tree size of 1,000. The model established during the historical period is used to correct the ensemble spread of generated future streamflows. The post-processing of future ensemble streamflows using QRF is performed with the help of an R package called ‘quantregForest’ (Meinshausen 2017).

Diagnostic evaluation of the performance of HMs

The model structural uncertainty plays a key role in a hydrological prediction system (Moriasi et al. 2007). Hence, using multiple model structures is essential to account for the uncertainties in future streamflow projection. In this study, four different HMs (SWAT, HBV, IHACRES, and SIMHYD) were calibrated and validated in simulating the observed streamflow. The ranges of parameters and their fitted values are presented in Table 3. Nash–Sutcliffe Efficiency (NSE) is used as an objective function to calibrate the selected HMs. The NSE values for HBV, IHACRES, SIMHYD, and SWAT were 0.71, 0.65, 0.59, and 0.73, respectively, during the calibration period (1975–1993) and 0.76, 0.72, 0.71, and 0.73, respectively, during the validation period (1994–2010). The performance of selected models during both calibration and validation periods in terms of NSE was reasonably acceptable (Moriasi et al. 2007, 2015). However, it is necessary to understand the performance of the simulated streamflow in capturing different flow segments of the observed hydrograph. The performance metrics such as fourth root mean quadrupled error (R4MS4E), Logarithmic Nash–Sutcliffe coefficient of efficiency (logNSE), percentage bias (PBIAS), SS, and mean absolute error (MAE) are estimated to evaluate the performance of simulated flows from the calibrated HMs.

Table 3

Parameters used in the selected hydrological models along with their range and fitted value

Model NameParametersRangeFitted value
HBV SCF – Snow correction factor 0.9 to1.5 1.27 
DDF – Degree day factor (mm/°C/time step) 0 to 5 2.77 
Tr – Threshold temperature above which precipitation is rain (°C) 1 to 3 1.86 
Ts – Threshold temperature below which precipitation is snow (°C) −3 to 1 −1.17 
Tm – Threshold temperature above which melt starts −2 to 2 0.11 
LPrat – Parameter related to the limit for potential evaporation 0 to 1 0.96 
FC – Field capacity, i.e., max soil moisture storage (mm) 0 to 600 194.36 
BETA – The non-linear parameter for runoff production 0 to 20 0.18 
k0 – Storage coefficient for very fast response (time step) 0 to 2 0.39 
k1 – Storage coefficient for fast response (time step) 2 to 30 19.79 
k2 – Storage coefficient for slow response (time step) 30 to 250 47.66 
Lsuz – Threshold storage state, i.e., the very fast response starts if exceeded (mm) 1 to 100 46.04 
cperc – Constant percolation rate (mm/time step) 0 to 8 0.28 
bmax – Maximum base at low flows (time step) 0 to 30 5.94 
Croute – Free scaling parameter (timestep2/mm) 0 to 50 38.29 
SIMHYD Insc – Interception store capacity (mm) 0.5 to 5 0.53 
Coeff – Max infiltration loss (mm) 50 to 400 290.75 
Sq – Infiltration loss exponent 0 to 6 1.21 
Smsc – Soil moisture store capacity (mm) 50 to 500 122.15 
Sub – Constant of proportionality in interflow equation 0 to 1 0.03 
Crak – Constant of proportionality in groundwater recharge equation 0 to 1 0.99 
K – Baseflow linear recession parameters 0.003 to 0.3 0.21 
IHACRES f – Catchment Moisture Deficit (CMD) stress threshold as a proportion of d 0.01 to 3 0.44 
e – Temperature to PET conversion factor 0.01 to 1.5 0.05 
d – CMD threshold for producing flow 50 to 800 334.80 
tau_s – Recession coefficient for Soil Storage discharge (days) 0 to 3 2.99 
tau_q – Recession coefficient for quick flow (days) 0 to 3 2.80 
v_s – Fraction of effective rainfall that goes to groundwater 0 to 1 0.96 
SWAT R_CN2.mgt – Initial SCS Curve number −0.2 to 0.2 −0.18 
V_ALPHA_BF.gw – Baseflow alpha factor (day−10 to 1 0.31 
V_GW_DELAY.gw – Groundwater Delay from soil to channel (days) 0 to 500 30.06 
V_GWQMN.gw – Threshold depth of water in the shallow aquifer required for return flow to occur (mm of H2O) 0 to 5,000 1,026.73 
V_ESCO.hru – Soil evaporation compensation factor 0 to 1 0.58 
V_ALPHA_BNK.rte – Baseflow alpha factor for bank storage. 0 to 1 0.67 
V_CH_N2.rte – Manning's n value for the main channel −0.01 to 0.3 0.02 
V_CH_K2.rte – Hydraulic conductivity of the main channel (mm/h) −0.01 to 500 70.89 
R_SOL_K.sol – Saturated hydraulic conductivity −0.2 to 0.2 0.18 
V_GW_REVAP.gw – Groundwater revap coefficient 0.02 to 0.2 0.11 
Model NameParametersRangeFitted value
HBV SCF – Snow correction factor 0.9 to1.5 1.27 
DDF – Degree day factor (mm/°C/time step) 0 to 5 2.77 
Tr – Threshold temperature above which precipitation is rain (°C) 1 to 3 1.86 
Ts – Threshold temperature below which precipitation is snow (°C) −3 to 1 −1.17 
Tm – Threshold temperature above which melt starts −2 to 2 0.11 
LPrat – Parameter related to the limit for potential evaporation 0 to 1 0.96 
FC – Field capacity, i.e., max soil moisture storage (mm) 0 to 600 194.36 
BETA – The non-linear parameter for runoff production 0 to 20 0.18 
k0 – Storage coefficient for very fast response (time step) 0 to 2 0.39 
k1 – Storage coefficient for fast response (time step) 2 to 30 19.79 
k2 – Storage coefficient for slow response (time step) 30 to 250 47.66 
Lsuz – Threshold storage state, i.e., the very fast response starts if exceeded (mm) 1 to 100 46.04 
cperc – Constant percolation rate (mm/time step) 0 to 8 0.28 
bmax – Maximum base at low flows (time step) 0 to 30 5.94 
Croute – Free scaling parameter (timestep2/mm) 0 to 50 38.29 
SIMHYD Insc – Interception store capacity (mm) 0.5 to 5 0.53 
Coeff – Max infiltration loss (mm) 50 to 400 290.75 
Sq – Infiltration loss exponent 0 to 6 1.21 
Smsc – Soil moisture store capacity (mm) 50 to 500 122.15 
Sub – Constant of proportionality in interflow equation 0 to 1 0.03 
Crak – Constant of proportionality in groundwater recharge equation 0 to 1 0.99 
K – Baseflow linear recession parameters 0.003 to 0.3 0.21 
IHACRES f – Catchment Moisture Deficit (CMD) stress threshold as a proportion of d 0.01 to 3 0.44 
e – Temperature to PET conversion factor 0.01 to 1.5 0.05 
d – CMD threshold for producing flow 50 to 800 334.80 
tau_s – Recession coefficient for Soil Storage discharge (days) 0 to 3 2.99 
tau_q – Recession coefficient for quick flow (days) 0 to 3 2.80 
v_s – Fraction of effective rainfall that goes to groundwater 0 to 1 0.96 
SWAT R_CN2.mgt – Initial SCS Curve number −0.2 to 0.2 −0.18 
V_ALPHA_BF.gw – Baseflow alpha factor (day−10 to 1 0.31 
V_GW_DELAY.gw – Groundwater Delay from soil to channel (days) 0 to 500 30.06 
V_GWQMN.gw – Threshold depth of water in the shallow aquifer required for return flow to occur (mm of H2O) 0 to 5,000 1,026.73 
V_ESCO.hru – Soil evaporation compensation factor 0 to 1 0.58 
V_ALPHA_BNK.rte – Baseflow alpha factor for bank storage. 0 to 1 0.67 
V_CH_N2.rte – Manning's n value for the main channel −0.01 to 0.3 0.02 
V_CH_K2.rte – Hydraulic conductivity of the main channel (mm/h) −0.01 to 500 70.89 
R_SOL_K.sol – Saturated hydraulic conductivity −0.2 to 0.2 0.18 
V_GW_REVAP.gw – Groundwater revap coefficient 0.02 to 0.2 0.11 

For instance, the indicator R4MS4E puts more emphasis on peak flows, whereas logNSE is sensitive to low flows. The volumetric error is measured using PBIAS and the match between observed and simulated frequencies is measured using SS, and MAE yields the unbiased error estimate. The computed performance evaluation metrics for the calibration and validation periods are tabulated in Table 4. From the R4MS4E values, it is clear that the SWAT and HBV models perform well in capturing high flows in both calibration and validation periods. The logNSE values show that the HBV model performance in simulating the low flows is best in both calibration and validation periods. The PBIAS value of SWAT is lower (between ±5%) than that of other models, whereas the bias in HBV simulated flow is within acceptable limits. In terms of SS, all four models exhibit similar performance during both calibration and validation periods, with the HBV model exhibiting slightly better performance. The performance of HBV and SWAT in terms of MAE is found to be good during calibration and validation. The SIMHYD simulated flows are highly underestimating the observed flows leading to declined performance. SWAT being a physics-based semi-distributed model, and the inclusiveness of spatial variability in rainfall and physical characteristics of the catchment, is the reason behind its better performance (Singh et al. 2013). The process description of the HBV model structure is the plausible reason for its better performance.

Table 4

Performance evaluation metrics of hydrological models during the calibration and validation periods

ModelsR4MS4ENSELogNSEPBIASSSMAE
Calibration (1975–1993) 
 HBV 546.24 0.71 0.61 −12.00 0.70 96.24 
 IHACRES 563.83 0.65 −2.40 −21.17 0.64 121.92 
 SIMHYD 623.08 0.59 −25.96 −35.03 0.66 128.80 
 SWAT 489.83 0.73 0.36 −5.17 0.71 95.62 
Validation (1994–2010) 
 HBV 539.79 0.76 0.25 0.75 0.79 90.07 
 IHACRES 553.22 0.72 −3.17 −9.04 0.73 107.14 
 SIMHYD 577.88 0.71 −27.61 −23.52 0.75 105.62 
 SWAT 536.28 0.73 −0.31 −0.78 0.73 108.86 
ModelsR4MS4ENSELogNSEPBIASSSMAE
Calibration (1975–1993) 
 HBV 546.24 0.71 0.61 −12.00 0.70 96.24 
 IHACRES 563.83 0.65 −2.40 −21.17 0.64 121.92 
 SIMHYD 623.08 0.59 −25.96 −35.03 0.66 128.80 
 SWAT 489.83 0.73 0.36 −5.17 0.71 95.62 
Validation (1994–2010) 
 HBV 539.79 0.76 0.25 0.75 0.79 90.07 
 IHACRES 553.22 0.72 −3.17 −9.04 0.73 107.14 
 SIMHYD 577.88 0.71 −27.61 −23.52 0.75 105.62 
 SWAT 536.28 0.73 −0.31 −0.78 0.73 108.86 

Changes in projected precipitation and temperature

The precipitation and temperature projections obtained from selected GCMs for four climate scenarios were averaged over months to examine the future climate in the study area. However, maximum precipitation in the basin is received during the monsoon season (June to October); the projected changes in the monsoon precipitation were analysed in this section. The average increment in the monsoon precipitation was analysed by considering the ratio of projected to historical values of total precipitation, variance, and maximum precipitation for each scenario. It is noticed from Figure 3 that the total precipitation, variance, and maximum precipitation is likely to increase during the future period and the increment is varying across months. The increased variability and maximum precipitation indicate the intensification of precipitation patterns in June for all future scenarios (Katzenberger et al. 2021). The increment in total mean precipitation component during August and October is more (more than 2.5 times greater than historical values), with minimal variation in variance. July and September have the least variability concerning total mean precipitation. It can be observed from the figure that there is more than a two-fold increment in precipitation present for the future except for June in all scenarios. Precipitation projections were highly variable under four climate scenarios, SSP-585 shows a greater increment with SSP-126 being minimal increment during the entire monsoon period. October shows a greater spread in total, variance, and maximum precipitation in all the SSPs.
Figure 3

Variations in projected changes of precipitation (projected/historical) for monthly mean, monthly maximum, and monthly variance for the monsoon period for all SSPs.

Figure 3

Variations in projected changes of precipitation (projected/historical) for monthly mean, monthly maximum, and monthly variance for the monsoon period for all SSPs.

Close modal
Figure 4 represents the difference between historical and projected monthly mean values of maximum and minimum temperatures from the selected GCMs for all SSPs. The difference between the monthly averaged future (2015–2100) and historical values of Tmax and Tmin ranges from −3.0 to +3.4 °C and −1.8 to +1.8 °C, respectively. Tmax projections would decrease for the future period under all scenarios except for June, July, and August. Tmax projection shows a positive increment for June having a maximum increment (more than 2 °C) in all the climate scenarios and maximum variation (spread) being observed in the monsoon period. It is also observed from Figure 4 that the variation of Tmin (means spread in boxplot) in the study area is more as compared to Tmax. When Tmin variability along month-wise is considered, the minimum temperature is highly variable in all the months except May. SSP-370 and SSP-585 scenarios show a positive increment in Tmin projections, whereas SSP-126 and SSP-245 show a decrement. The climate projections over the basin under the future period are highly subjected to GCM uncertainty.
Figure 4

Variations in projected changes of monthly maximum and minimum temperature (projected–historical) for all SSPs.

Figure 4

Variations in projected changes of monthly maximum and minimum temperature (projected–historical) for all SSPs.

Close modal

Changes in projected hydrological variables

The change in the future projections of various hydrological components like precipitation (PR), streamflow (QQ), WA, and PET over the basin concerning the historical data (i.e., observed data) are shown in Figure 5 for the monsoon period. The mean monthly values of hydrological components for the future period are obtained by computing the average mean monthly values of all 20 ensembles (obtained by forcing selected 5 GCMs into 4 HMs) for each SSP. The ratio of projected values of hydrological components to that of historical values in the monsoon period for each scenario is computed and presented in Figure 5. It could be noticed that the components like PP, QQ, and WA are expected to increase throughout the monsoon season in the basin in the future period in all scenarios except WA in June under all scenarios, with the highest increment being observed in the SSP-585 scenario and variation among scenarios is slightly variable. The decrease in PET values in September and October might be the possible reason for the increase in PP and QQ projections. For SSP-126, the PP projections are likely to increase from 10.43 to 180%, and for QQ projections, the increment is about 56 to 307%. In the case of SSP-245 and SSP-370, the PP projection shows an increase of up to 207.60%, and the increment in QQ projection ranges between 34.50 and 364%. Maximum increment in PP projections is noticed in the SSP-585 scenario, ranging between 21.70 and 222.5% and a similar trend can be noticed in QQ projection with an increment of 78.6–377.70%. Though both PP and QQ projections tend to increase in the future for all scenarios, the increment in QQ projections is comparatively higher. This is due to the fact that there is a reduction in PET projections in future scenarios. A study by Fu et al. (2007) revealed 20% precipitation increase might result in a streamflow increment of 48%, provided that the projected long-term mean temperature is only 1 °C lower than the long-term historical mean. However, the increase in the streamflow will only increase to a meagre 4% if the projected long-term mean temperature is 1.8 °C higher than the long-term historical mean. WA projections were likely to increase under all SSP scenarios, except in June, with increments being observed along months with a maximum increment in October of about 41.40%. It could be noted that the PET values in June are high due to an increment in Tmax projections and show decrement up to 9.4% in October.
Figure 5

Mult-GCM and multi-hydrologic model projections of overall changes of hydrological components of the study area for four climate scenarios.

Figure 5

Mult-GCM and multi-hydrologic model projections of overall changes of hydrological components of the study area for four climate scenarios.

Close modal

Uncertainty introduced by the climate models

In order to assess the uncertainty induced by each individual GCM to the uncertainty in the GCM ensemble, each GCM was given a rank based on the amount of uncertainty (Figure 6). GCMs with higher uncertainty are given top rank. It can be noticed from Figure 6 that the contribution of individual GCM to the uncertainty in the obtained ensemble is varying with respect to the hydrological components. Overall, projections obtained from the model CanESM5 subjected to the least uncertainty and uncertainty contributed by the MPI-ESM1-2-HR, MPI-ESM1-2-LR, and MRI-ESM2-0 are higher in PP, QQ, and WA projections for the basin, whereas CanESM5 and INM-CM5-0 models contribute least. Similarly, for Tmax and PET projections, MRI-ESM2-0 and MPI-ESM1-2-HR induce larger uncertainty and CanESM5 exhibits the least uncertainty. In the case of Tmin projections, models INM-CM5-0 and MPI-ESM1-2-HR uncertainty contribution are higher, and CanESM5 and MRI-ESM2-0 models contribute the least uncertainty. Identifying the individual GCM uncertainty contribution is necessary to select the most suitable GCMs to reduce the uncertainty under the climate change impact study. The GCMs with unrealistic projections will be screened first for reliable hydrological projections under climate change when multiple GCMs outputs are available. Therefore, at the initial stages, this analysis will reward the user in minimizing the translation effect of uncertainty in climate variables to various hydrological components.
Figure 6

The contribution of GCM to the uncertainty in the multi-GCM ensemble projections composed of hydrological components and climate variables. The numbers on the right-side colour bar represent the ranks of GCMs’ contributions to the overall uncertainty (the GCM with the largest contribution is given the highest rank and vice versa).

Figure 6

The contribution of GCM to the uncertainty in the multi-GCM ensemble projections composed of hydrological components and climate variables. The numbers on the right-side colour bar represent the ranks of GCMs’ contributions to the overall uncertainty (the GCM with the largest contribution is given the highest rank and vice versa).

Close modal

Relation between uncertainty in climate variables and hydrological variables

The correlation between the uncertainty of different climate variables projection and hydrological components of the HBV model at a monthly scale was plotted (Figure 7) under all scenarios. The figure shows that the correlation between PP and hydrological components QQ and WA is greater than 0.9 for all SSPs. These results indicate the translation of uncertainty in PP projection into QQ and WA projections, indicating that substantial efforts are needed to enhance the accuracy of precipitation projections for reliable hydrological simulations under changing climate. In the same way, a moderate correlation can be noticed between PET and Tmax which is greater than 0.70 in all scenarios. The correlation between QQ and WA projections for all scenarios in the HBV model is greater than 0.9, whereas the correlation varies for other models (refer to Supplementary Figures S1–S3). The varying correlation among the HMs indicates the model's structural uncertainty in simulating the WA.
Figure 7

Correlation between the uncertainty in climate variable and hydrological components for HBV model for all four scenarios.

Figure 7

Correlation between the uncertainty in climate variable and hydrological components for HBV model for all four scenarios.

Close modal

Uncertainty in the streamflow projections

The frequency distribution of flows can be graphically visualized using FDCs at the outlet point. The historical FDC is plotted in Figure 8 in a red line along with uncertainty (shaded polygon between maximum and minimum) in the FDCs of the ensemble streamflow. Projections generated by forcing the climate variables of selected five GCMs into four calibrated HMs. The high flows (exceedance probability between 0 and 20%) were found to be increasing in the future period for all the scenarios for all HMs except SWAT. Similarly, the low flows (exceedance probability between 80 and 100%) were found to be decreasing in all scenarios except for HBV. The plausible reason for this is the intensification of precipitation patterns in future projections. The slope of FDC for streamflow projections simulated by SIMHYD and IHACRES models is high in all the scenarios indicating the flashiness of the flows. The variation of FDCs simulated through multiple model structures shows slight variation with respect to scenarios except for SSP-370 where high flow variability is less than all other scenarios. The results in Figure 8 can be understood in a better way than the results obtained in Section 4.1. The SWAT and HBV simulated FDCs were slightly deviating from the observed flows at higher exceedance probabilities when compared to FDCs simulated by the other two HMs. Hence, it is highly recommended to generate ensemble streamflows using multiple HMs to account for the uncertainty in the streamflow projections in a more reasonable way.
Figure 8

Flow duration curves for multiple GCMs and multiple hydrological model ensemble projections for four climate scenarios. (The y-axis of the main figure is plotted on the logarithmic scale and the y-axis of the inset figure is plotted on the normal scale). Please refer to the online version of this paper to see this figure in colour: https://dx.doi.org/10.2166/wcc.2023.272.

Figure 8

Flow duration curves for multiple GCMs and multiple hydrological model ensemble projections for four climate scenarios. (The y-axis of the main figure is plotted on the logarithmic scale and the y-axis of the inset figure is plotted on the normal scale). Please refer to the online version of this paper to see this figure in colour: https://dx.doi.org/10.2166/wcc.2023.272.

Close modal

Uncertainty decomposition

The uncertainty contribution of different sources obtained from 3-way ANOVA for the near future (2021–2060) and far future (2061–2100) is plotted in Figure 9(a) and 9(b), respectively. In summary, the contributions of HMs and SSPs as individual and their interaction is found to be negligible in both time periods. The contribution of uncertainty in GCMs' output and their interaction with HMs and SSPs accounts for the major portion of the total uncertainty. The interaction between SSPs and GCMs is the highest contributor among all other sources ranging from 44.19 to 58.62% in the near future and 40.24 to 59.37% in the far future. The second highest contributor corresponds to the combined effect of HMs, SSPs, and GCMs with a share ranging between 29.18 and 38.79% in the near future and 30.14 to 40.85% in the far future. It is worth noting that the individual contributions of GCMs (5.04–9.48% in the near future and 5.06–9.26% in the far future) and SSPs (0.57–0.82% in the near future and 0.57–1.03% in the far future) to the total uncertainty is very low. Contrastingly, their interaction is the major contributor to the uncertainty.
Figure 9

Contribution of various sources of uncertainty in terms of variance fraction for (a) near future (2021–2060) and (b) far future (2061–2100).

Figure 9

Contribution of various sources of uncertainty in terms of variance fraction for (a) near future (2021–2060) and (b) far future (2061–2100).

Close modal
Figure 10

FDC of ensemble streamflows before and after post-processing during the validation period (1994–2010). The coloured envelope represents 0.25 and 0.75 interquartile values.

Figure 10

FDC of ensemble streamflows before and after post-processing during the validation period (1994–2010). The coloured envelope represents 0.25 and 0.75 interquartile values.

Close modal

Post-processing of ensemble spread of streamflows

The ensemble streamflows generated by forcing the GCM outputs for the calibration period (1975–1993) are post-processed using QRF to reduce the ensemble spread and to capture the observed streamflow. The model fitted during the calibration period is extrapolated to post-process the ensemble streamflows during the validation period. Figure (10) represents the FDC plotted using the ensemble streamflows before post-processing (hereby referred to as EnSF) and after post-processing (QRF-EnSF) during the validation period (1994–2010). In summary, the ensemble spread is highly optimized in the QRF-EnSF, where the ensemble spread captures observed FDC between the exceedance probabilities of 0.05 and 0.8 efficiently with minimal spread. It can also be noticed that the spread in EnSF is comparatively high. Moreover, the FDC by EnSF tends to overpredict the high flows and underpredict the low flows. The performance of both EnSF and QRF-EnSF is not satisfactory in capturing the streamflow extremes (extremely low and high values of streamflows). The results of the analysis suggest that QRF post-processed flows efficiently capture the majority of the flows and can be used to reduce the uncertainty in the generated streamflows.

The QRF post-processing is further applied to the generated future streamflows for 2020–2100 under all SSPs and the changes obtained after and before the post-process are shown in Figure 11. From the figure, it is found that mean flows in the monsoon period in the QRF post-processed flows are comparatively lower than the values obtained before post-processing (refer to Section 4.3). The mean flows after post-processing are likely to be reduced up to 7% in June and increase up to 70% in September under all scenarios. The increment in the mean flows was found to be highest in October in un-post-processed flows, whereas the results from QRF post-processed flows show that August is likely to have the highest increment.
Figure 11

Changes in hydrological component QQ before and after application of QRF post-processing technique.

Figure 11

Changes in hydrological component QQ before and after application of QRF post-processing technique.

Close modal

The Tungabhadra River serves as an essential source of irrigation, hydropower generation, and water supply in major portions of Karnataka regions. Hence, assessing the WA under changing climate scenarios is a crucial issue in this basin. Limited studies have been reported so far assessing the impact of climate change on the streamflow of the Tungabhadra Basin (Meenu et al. 2013; Singh et al. 2013, 2016; Janga Reddy & Nagesh Kumar 2020; Venkatesh et al. 2020b). Moreover, no study was reported so far considering the hydrological model uncertainty along with GCM uncertainty in the future streamflow projections in the Tungabhadra Basin. Hence, the present study comprehensively measured the influence of uncertainty in climate projections and hydrological model structure uncertainty on different hydrological variables for the Tungabhadra Basin. The total uncertainty in the future streamflows is decompounded as the contribution of individual sources (GCMs, HMs, and SSPs) and their interactions using the ANOVA technique. Furthermore, a statistical post-processing method is used to calibrate the ensemble spread intended to reduce the uncertainty in the streamflows. From previous studies, it was suggested that the selection of suitable GCMs is based on the past performance (Srinivasa Raju & Nagesh Kumar 2015; Anil et al. 2021), which is also followed in the present study using a widely accepted approach such as CP (Srinivasa Raju et al. 2017). Four HMs (SWAT, HBV, SIMHYD, and IHACRES) were calibrated and validated in simulating the observed streamflow at the Haralahalli gauge point. The performance of all the calibrated models was found to be satisfactory. SWAT is s physics-based semi-distributed model and the previous studies supported the results for the hydrological assessment of the basin (Singh et al. 2013, 2016; Venkatesh et al. 2020a), proved its efficiency again with better performance in the present study. From Section 4.1, conceptual model HBV performance is equally good with SWAT in simulating future streamflow. Models IHACRES and SIMHYD performance might not match well with the other models mentioned before but their performance in simulating future streamflow cannot be ignored owing to the fact that model structure is one of the major sources of uncertainty.

The analysis shows that all the streamflow projections project an increase in the higher streamflow values and a decrease in the lower streamflow values which is in line with the previous studies (Zhang et al. 2015a). The results obtained from the ANOVA method demonstrated that the contribution of interaction between GCMs and SSPs to the total uncertainty was found to be significantly higher (between 44.19 and 58.62% in the near future and 40.24 and 59.37% in the far future). Despite having lower individual contributions, i.e., GCMs (5.04–9.48% in the near future and 5.06–9.26% in the far future) and SSPs (0.57–0.82% in the near future and 0.57–1.03% in the far future), their interaction has a major share in total uncertainty. It is also important to note that the uncertainty in the future ensemble streamflows is also due to the temporal uncertainty in the GCMs. It implies that the daily projections obtained from the GCMs vary drastically leading to high variations in the projected streamflow values. The uncertainty in the climate projections obtained from GCMs varies over different months, recommending improved GCM simulations for reliable basin-level impact assessment studies (Her et al. 2019). However, the current study using multiple HMs yields better insights into the uncertainties in the streamflow projections (Her et al. 2019; Wang et al. 2020). Since the inherent complexity is present among various parameters in the modelling chain, it is difficult to generalize a single hydrological model for a catchment. From higher QQ projections, it is understood that more intense precipitation is expected in the future with fewer rainy days (Meenu et al. 2013). The QRF post-processing technique was applied to reduce the uncertainty bands in the ensemble streamflow projections. The post-processed ensemble streamflows were found to be efficiently capturing the observed streamflows during the validation period with lower ensemble spread. The post-processed future streamflows also project increment in the future streamflows, but the increment is significantly lower than the ensemble streamflows before post-processing. The results of the present study are useful in framing adaptation strategies such as enhancing irrigation efficiency, managing water demand, and installing water harvesting schemes considering the future WA in the Tungabhadra Basin.

This study focuses on quantifying the uncertainty in the ensemble streamflow projections introduced by multiple GCMs and multiple HMs. The conclusions are as follows:

  • The performance of selected HMs was found to be satisfactory with an acceptable NSE value (>0.6) during both calibration and validation periods and diagnostic evaluation of model performance indicates that SWAT and HBV performed better in simulating low flows.

  • The ability of SWAT to account for rainfall spatial variability and spatial heterogeneity of catchment characteristics is attributable to its better performance, which agrees with previous studies (Singh et al. 2013). The performance of HBV, being a lumped model, was equally good as SWAT in simulating streamflows.

  • Uncertainty in climate projections during the monsoon period was appraised and results show that the overall increment in PP projections ranges from 10.43 to 222.5% and QQ projections range from 34.50 to 377.7% in the monsoon season. Both Tmax and Tmin were found to be increasing with respect to scenarios. It was found that the changes in projected Tmax range from −3.0 to +3.4 °C, and Tmin ranges from −1.8 to +1.8 °C.

  • • FDCs obtained from the models HBV, IHACRES, and SIMHYD show that the frequency of high flows is likely to be increased under all SSPs, and the frequency of low flows is expected to decrease in the future scenarios for SIMHYD and IHACRES models. The above results indicate that the flashiness of the catchment (slope of flow duration curve) may increase indicating higher variability of flows in future scenarios.

  • Uncertainty decomposition using 3-way ANOVA suggested that the interaction between SSPs and GCMs is the highest contributor among all other sources ranging from 44.19 to 58.62% in the near future and 40.24 to 59.37% in the far future. The second highest contributor corresponds to the combined effect of HMs, SSPs, and GCMs with a share ranging between 29.18 and 38.79% in the near future and 30.14 and 40.85% in the far future. SSPs and HMs individual contributions are negligible.

  • The mean flows after post-processing are likely to be reduced up to 7% in June and increase up to 70% in September under all scenarios. The increment in the mean flows was found to be highest in October in un-post-processed flows, whereas the results from QRF post-processed flows show that August is likely to have the highest increment. The ensemble spread has been reduced after the QRF post-processing application.

All relevant data are available from an online repository or repositories: https://www.imdpune.gov.in/cmpg/Griddata/Rainfall_1_NetCDF.html - For gridded precipitation data, https://www.imdpune.gov.in/cmpg/Griddata/Max_1_Bin.html - For gridded temperature data, https://indiawris.gov.in/wris/#/ - For observed streamflow data, https://swat.tamu.edu/data/ - India dataset for SWAT model, https://esgf-node.llnl.gov/projects/cmip6 - future climate dataset.

The authors declare there is no conflict.

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