# Translating the internal climate variability from climate variables to
hydropower production

Divya Upadhyay
Discipline of Civil Engineering,
Indian Institute of Technology Gandhinagar, India
&Sudhanshu Dixit
Discipline of Civil Engineering,
Indian Institute of Technology Gandhinagar, India
&Udit Bhatia
Discipline of Civil Engineering,
Indian Institute of Technology Gandhinagar, India
<EMAIL_ADDRESS>
###### Abstract

Quantifying uncertainties in estimating future hydropower production directly
or indirectly affects India’s energy security, planning, and management. The
chaotic and nonlinear nature of atmospheric processes results in considerable
Internal Climate Variability (ICV) for future projections of climate
variables. Multiple initial condition ensembles and multi-model ensembles of
earth system models are often used to analyze the role of ICV and model
uncertainty in precipitation and temperature. However, there are limited
studies focusing on quantifying the role of internal variability on impact
variables, including hydropower production. In this study, we analyze the role
of internal variability and model uncertainty on three prominent hydropower
plants of India using multiple initial condition ensembles of the EC-Earth3
and multiple models from CMIP6. We estimate the streamflow projections for all
ensembles using the Variable Infiltration Capacity (VIC) hydrological model
for four time periods, historical (1985-2014), near-term (2015-2044), mid-term
(2045-2074) and far-term (2075-2100). We estimate maximum hydropower
production generated using monthly release and hydraulic head available at the
reservoir. We also analyzed the role of bias correction in hydropower
production. The results show that ICV plays a significant role in estimating
streamflow and hydropower estimation for monsoon and throughout the year,
respectively. Model uncertainty contributes more to total uncertainty than ICV
in estimating the streamflow and potential hydropower. However, ICV is
increasing towards the far-term. We also show that bias correction does not
preserve the internal variability in estimating the streamflow. Although there
is an increase in uncertainty for estimated streamflow, mean hydropower shows
the decrease towards the far-term for February to May, more prominent for MICE
than MME. The results suggest a need to incorporate uncertainty due to
internal variability for addressing power security in changing climate
scenarios.

_K_ eywords Internal climate variability $\cdot$ model uncertainty $\cdot$
hydropower production $\cdot$ streamflow estimation $\cdot$ bias correction

##  1 Introduction

Sustaining an optimal reservoir operation under various uncertainties is
challenging in changing climate for hydropower production. The increasing
population, urbanization and industrialization raise the demand for the energy
consumption of fossil fuels, water, material, and available natural resources,
which further poses the issue of energy security and clean environment [1, 2].
The large energy requirement in India is fulfilled by non-renewable sources,
which is fast depleting [3]. Hydropower is a vital source of renewable energy,
which provides over 72 % of all renewable energy globally [4]. However, only
about 17 % of hydropower potential of 150,000 MW has been tapped in India [5].
For India, hydropower and small hydropower are the second-highest contributors
towards renewable energy consumption, which is close to 12 % of the total
capacity [6]. The impacts of climate change on hydropower production affect
energy generation in the near term and by the end of the 21st century [7, 8,
9, 10]. Thus, tremendous opportunities in hydropower generation and its future
expansion exist, which help us meet the soaring energy demands. However,
hydropower production is directly related to the water availability in
reservoirs that depends on streamflow, which is characterized by uncertainties
of the processes that result in streamflow [7]. The uncertainty associated
with precipitation, temperature and wind pattern of a region affects the
streamflow uncertainty [11, 12]. [13] have analyzed the effects of
precipitation uncertainty on discharge calculations for 294 river basins
worldwide and shown that average precipitation uncertainty (about 30 %) can
lead to higher uncertainty in discharge (about 90 %). Quantification of
uncertainties associated with future projections of streamflow is a critical
challenge for climate change impact studies [14] as it necessitates obtaining
the range of possible future variations in streamflow projections [15].

Characterizing and quantifying uncertainty projection of streamflow and
hydropower potential considering the climate change projections is important
to plan for adaptation and mitigation [16]. It is essential to quantify and
discuss the role of different uncertainties and their propagation to future
hydrological projections as it is a fundamental characteristic of prediction
[17]. The estimated variables’ uncertainty sources are forcing uncertainty,
model uncertainty and internal climate variability [18, 16, 19]. The relative
importance of different uncertainty sources varies depending on the type of
variable, temporal and spatial scales, and specifically its nature [18, 16,
20]. For example, model uncertainty reflects our lack of knowledge or
inability to encapsulate the existing knowledge within the climate models, and
it is considered as potentially reducible as models improve [16]. The Multi-
Model Ensembles (MMEs) are generally used to estimate the model uncertainty
[21]. Whereas, Internal Climate Variability (ICV), which refers to natural
variability that arises from processes in the coupled land, biosphere, ocean,
atmosphere, and cryosphere system in the absence of external forcing [22, 23],
considered as irreducible [24, 25, 26, 27, 28, 29]. ICV dominates climate
uncertainty over decadal prediction horizons at regional to local scales,
where stakeholders are more interested [30]. It is typically handled by
considering Multiple Initial Condition Ensembles (MICE), assuming that it
satisfactorily captures the internal variability [22, 31]. The MICE are
generated by applying minor perturbations to the initial state of the model
such that the different climate projections behave as surrogates of climate
variability [26, 32, 33, 30, 34].

The importance of ICV has received considerable attention recently from
scientific community [16, 35, 22, 29, 28, 31]. Several studies have explored
the role of internal variability to assess future climate outcomes such as
surface air temperature, a vertical profile of recent tropical temperature
trends and precipitation [16, 26, 35, 22, 29, 36]. A few studies have
quantified role of ICV in estimating streamflow [37, 38], extreme
precipitation [28, 31], sea-level rise [39], air quality and associated health
risks in a warming world [40]. [41] have criticised initial condition large
ensembles as they are resource-intensive, redundant, and biased. Despite this
criticism, they have shown that large ensembles provide unique information
consistent with the insights and support robust adaptation decision-making
regarding freshwater resources. Climate variability may cause large
uncertainties in climate at regional scale [18, 16, 35]. Recently, [31] have
quantified the relative contribution of uncertainty due to ICV and model
uncertainty in the depth and volatility of Indian summer monsoon rainfall
extremes. They have shown that ICV is comparable and even higher than model
uncertainty in estimating extreme precipitation indices in central India.
However, the understanding role of ICV in various meteorological variables and
its translation to streamflow and hydropower estimation has received
relatively less attention for India. A few researchers have considered the
translation of different uncertainties of climate variables to hydropower and
analyzed it using hydrological models [42, 17, 43]. Here, we consider the
uncertainties associated with precipitation, maximum temperature ($T_{max}$),
minimum temperature ($T_{min}$), wind and its impact on streamflow estimation
and subsequently on hydropower production, as the range of uncertainty in
input data, has a significant influence on the output, which may not be
neglected in the communication of results [13].

Several studies have analyzed the impact of climate change on hydropower
production and shown that it affects energy generation in the near term and by
the end of the 21st century [7, 8, 9, 44, 10]. [45] have assessed the
sensitivity of hydropower production using 40 multi-model ensembles and shown
that annual hydroelectric power production ranges between $-55$ and +39 % of
the mean historical outputs for the period 2071–2100. For seven large
hydropower projects of India, [10] have assessed climate change impacts on
hydropower production and analyzed model uncertainties and projected increase
in mean hydropower production and annual streamflow in non-snow dominated
areas. Similarly, [46] have evaluated the impact of climate on hydropower
using 21 GCMs and quantified the role of model uncertainty of 134 hydropower
plants of South America. However, studies on the role of ICV in estimating
hydropower has rarely been studied using large ensembles. For example, [17]
have examined uncertainties due to internal variability, which is
intrinsically sampled by assessing the interannual variability within the
projected 28-year duration. The role of the ICV using large ensembles in
estimating hydropower production in India is still unexplored, despite
exploring the impact of climate change on hydropower production.

This study attempts to translate the meteorological variables’ uncertainties
due to ICV and model uncertainty to hydropower production at a regional scale.
We analyze the role of model uncertainty and ICV in estimating streamflow and
hydropower generation. We analyze the effect of bias correction of
meteorological variables such as precipitation, $T_{max}$, $T_{min}$ and wind
data on streamflow estimation and its translation to hydropower production
estimation. Our study may help scientists and policymakers to understand and
communicate the role of internal variability at a regional scale and provide a
way to assimilate multiple sources of information to justify actions in
climate change adaptation.

The following section of the paper shows the study area and data set used for
the analysis, followed by the methodology section. In the methodology section,
we first discuss a flowchart for uncertainty analysis. Then, the subsection
provides details of streamflow and potential hydropower estimation. We discuss
the uncertainty analysis in this paper’s result and discussion section.

##  2 Study area and data

India has experienced significant changes in temperature and precipitation
over the past few decades, which is likely to change by the end of the twenty-
first century [47, 48, 49]. India is the fifth-largest producer of
hydroelectric power globally, with a 50.07 GW capacity [50]. India’s power
grid is divided into northern, western, eastern, southern, and northeastern
regions [51]. The western region covers Maharashtra, Gujarat, Madhya Pradesh,
and Goa states of India, with the highest capacity for hydroelectric potential
[52, 51, 53]. This study considers the three major hydropower plants such as
Sardar Sarovar, Ukai, and Kadana, located in Gujarat, India. The details of
these hydropower plants are given in the appendix (Table A1), and more details
can be obtained from India Water Resources Information System (India-WRIS)
(https://indiawris.gov.in/wris/). Gujarat is the fifth largest Indian state
located in the western region of India and the ninth largest state by
population with approximately 60.4 million [54]. The study area and location
of the three basins are shown in Figure 1. We consider the hydropower plants
with greater than 100 MW capacity for our analysis. The Sardar Sarovar Project
has six River Bed Power House (RBPH) with 200 MW capacity and five Canal Head
Power House (CHPH) with 50 MW capacity [55]. The Ukai and Kadana dam has
hydropower with an installed capacity of 305 MW and 240 MW, respectively [56,
57].

We use 50 Multiple Initial Condition Ensembles of the CMIP6-EC-Earth3 to
analyze the role of internal variability, which are available from the Earth
System Grid Federation (https://esgf-data.dkrz.de/projects/esgf-dkrz/) [58,
59]. We use eight Multi-Model Ensembles from Climate Model Intercomparison
Project Phase-6 (CMIP6) to analyze model uncertainty. The models considered
for the model uncertainty analysis are ACCESS-CM2, CanESM5, EC-EARTH3, GFDL-
ESM4, INM-CM4-8, INM-CM5-0, MRI-ESM2-0, NorESM2-LM, which are available from
World Climate Research Program Coupled Model Intercomparison Project
(https://esgf-node.llnl.gov/projects/cmip6/). The resolution of each model is
given in the appendix (Table A2). We consider low-to-moderate emission
scenarios Shared Socioeconomic Pathway (SSP) SSP2-4.5 (approximately
corresponding to the RCP-4.5 scenario) for the analysis [60, 61]. We selected
models from CMIP6 based on data availability of precipitation, maximum
temperature ($T_{max}$), minimum temperature ($T_{min}$) and wind for the
historical period (1985–2014) and the future period (2015–2100) under SSP2-4.5
(SSP245). We use one initial condition realization (r1i1p1) to analyze model
uncertainty.

For hydrological modelling, we use the observed daily gridded precipitation,
minimum and maximum temperature from the India Meteorological Department (IMD)
[62] at $None$ X $None$ resolution. Observed daily wind speed data were
obtained from [63, 10] at $None$ X $None$ resolution. All model (MICE/MME)
data are interpolated at $None$ x $None$ gridded daily precipitation,
$T_{max}$, $T_{min}$ and wind dataset over Narmada, Tapi and Mahi basins using
linear interpolation. We use observed monthly streamflow data from India-WRIS
to calibrate and validate Variable Infiltration Capacity (VIC) Macroscale
Hydrologic Model [64]. We used vegetation parameters from advanced very high-
resolution radiometer global land cover information at a 1-km spatial
resolution [65, 66, 67] and soil data from the Harmonized World Soil Database,
version 1.2 (http://www.fao.org/soils-portal/soil-survey/soil-maps-and-
databases/harmonized-world-soil-database-v12/en/). The storage and height of
the reservoir are obtained from Sardar Sarovar Narmada Nigam Ltd.
(https://sardarsarovardam.org/hydrology.aspx) for Sardar Sarovar reservoir.
For the ukai and kadana reservoir, we obtained data of storage and height
relationship from India-WRIS to compute hydropower potential.

Figure 1: Study Area: Location of three basins of India are shown with the
basin watershed. The red triangle shows the dam’s location, and the green
circle shows the location of gauges considered for calibration and validation
of the VIC hydrological model. Mahi, Narmada and Tapi basins are given from
top to bottom in the second column, respectively. The shaded part represents
the catchment area contributing to the dam location.

Figure 2: Flowchart of the study: Quantification of uncertainty arising from
internal variability and model uncertainties in the estimation of streamflow
and hydropower production, using different steps involved including bias
correction, streamflow estimation, hydropower estimation and uncertainty
analysis.

We have analyzed the role of ICV and model uncertainty in estimating
streamflow and hydropower production for three hydropower plants. The
methodology considered for the proposed work is as shown in Figure 2, divided
into three sections.

First, the data collection and preprocessing section show the different data
used for the analysis. We use observed precipitation (P), $T_{max}$,
$T_{min}$, wind (W) and streamflow of different gauges as shown in Figure 1
for calibration and validation of the VIC hydrological model. We use Earth
System Models (ESMs) outputs (P, $T_{max}$, $T_{min}$ and W) for estimation of
streamflow and potential hydropower. ESM outputs have large systematic biases
relative to observational data sets owing to the imperfect representation of
the model’s physical processes [68, 31]. Thus, it should not be directly used
to develop climate change adaptation policies without some form of prior bias
correction [69, 70, 68]. The objective of bias correction is to adjust the
statistical properties of climate simulations with observations. Several
studies have used Quantile Mapping (QM) bias correction and shown that it
substantially reduces the biases [71, 72, 73, 74, 75]. Recently, [76] have
compared bias-corrected climate model outputs and post-process model output
for streamflow estimation and recommended use of bias correction. [77] have
analyzed the effects of bias correction of radiation, humidity and wind
estimates on evapotranspiration and runoff estimates and shown that estimates
are relatively similar. Differences between simulated and observed radiation,
humidity and wind values are smaller than for temperature and precipitation
for the bias and non-bias corrected hydrological projections. Bias correction
may affect the consistency between the ESM output variables such as P,
$T_{max}$, $T_{min}$ and W [78, 77, 79, 80]. The use of bias-corrected data is
an open question and unresolved issue among scientists, especially for climate
change impact studies such as hydropower production and agricultural
production [79, 81, 82]. Thus, the effect of bias correction on estimated
streamflow and potential hydropower is explored in this study.

We use observed and climate data for each variable such as daily P, $T_{max}$,
$T_{min}$, and W of each ensemble (MICE/MME) to analyze the effect of bias
correction. We perform quantile-quantile mapping [71] for bias correction for
each variable separately. We use the ’qmap’ library of Rpy2 in python for data
from 1985 to 2014 and try to match quantiles at intervals of 0.01. We estimate
parameters for bias correction using observed and historical ensemble data
(1985-2014). These parameters are then applied to historical and SSP245 data
to obtain bias-corrected historical and SSP245 data. We perform analyses for
bias and non-bias corrected data separately.

The modelling and calculation section shows the flowchart to estimate
streamflow and potential hydropower production. First, we calibrate and
validate the VIC hydrological model using different gauge streamflow data to
obtain calibrated hydrological parameters. Streamflow estimated using
calibrated parameters and climate data (bias and non-bias corrected data).
These streamflow estimates and storage-height relationships are used to
calculate potential hydropower. The last section of the flowchart shows the
data and duration used for uncertainty analysis. The details about streamflow
estimation and potential hydropower estimation are given below.

###  2.1 Streamflow estimation

We estimate streamflow using the VIC hydrological model [64] at the reservoir
for three hydropower plants. The VIC is a semi-distributed model developed
based on energy and water balance equations solved for individual grid cells.
The VIC generate baseflow and streamflow using Arno model conceptualization
[83] and the infiltration mechanism utilized in the [84]. We use observed
daily data of precipitation, $T_{max}$, $T_{min}$, wind data vegetation
parameters, soil parameter files, and observed streamflow data to calibrate
and validate the model. In the VIC model, the assumption is that water can
only enter through the atmosphere, and water entering the channel can not flow
back to the soil [85]. The observed meteorological forcing data such as P,
$T_{max}$, $T_{min}$, and W are fed as input data. We first simulate baseflow
and surface runoff from each grid cell. Then, runoff from individual cells is
routed to gauge location using the routing model, developed by [86]. Channel
routing based on the linearized Saint-Venant equation is used to simulate the
discharge at the gauge location by assuming that all runoff exits a cell flows
in a single flow direction [87, 88].

We have calibrated and validated the model using the Handia, Mandleshwar and
Sandia gauge station for the Narmada basin. Similarly, we consider Sarangkheda
and Burhanpur for the Tapi basin; Mataji and Khanpur for the Mahi basin. The
calibration and validation results for three basins are shown in Table 1. The
time-series of observed streamflow and VIC simulated monthly streamflow is
given in the appendix (Figure A1). We use Nash–Sutcliffe model efficiency
coefficient (NSE) [89] and coefficient of determination (${R}^{2}$) [90]
performance criteria, which are commonly used metrics in hydrological and
climate impact studies. We use simulated monthly data and observed data for
calculation of NSE and ${R}^{2}$ to analyze the performance of the VIC. We
estimate streamflow using the bias and non-bias corrected data of each
ensemble of MICE and MME separately using parameters obtained after
calibration and validation. We also performed separate analyses for
historical, near-term, mid-term and far-term data. We route the streamflow to
the dam location to calculate potential hydropower.

###  2.2 Potential Hydropower Estimation

We calculate hydropower production for all the ensembles using the estimated
streamflow. We calculate Developed Hydropower Potential (DHP), the maximum
possible hydropower generated using the available water and existing
hydroelectric facilities [8]. First, we calculate the monthly releases using
estimated streamflow and generic regulation rules described by [91], which
contain the effect of yearly and monthly variability. We calculate monthly
release $R_{m}$ $(m^{3}/s)$ using Equation 1, given by [91], which can be used
where irrigation is not considered. [91] has developed a reservoir operation
scheme for global river routing models, which uses reservoir specifications,
global runoff data sets, and water demand downstream. Here, we note that DHP
does not represent the actual hydropower production as it does not consider
socioeconomic factors such as water use variability, power consumption
variation, and consumer behaviour. We assume that the reservoir is primarily
used for hydropower production. The monthly release from the reservoir is
generally not influenced by monthly inflow when storage capacity is large
compared to the mean annual inflow. However, monthly release fluctuates if
storage capacity and mean annual inflow are of the same order [10].

$\displaystyle
R_{\mathrm{m}}=\left\\{\begin{array}[]{l}\left(\frac{c}{0.5}\right)^{2}k_{y}i_{\mathrm{a}}+\left[1-\left(\frac{c}{0.5}\right)^{2}\right]i_{\mathrm{m}},\>\>\>\>0<c<0.5\\\
k_{y}i_{\mathrm{a}}\>,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\>\>\>\>\>\>c>0.5\end{array}\right.$
(1)

Where c is the ratio of maximum storage capacity to mean total annual inflow,
$c=C/Ia$. C is the maximum storage capacity of the reservoir ($m^{3}$),
$I_{a}$ is the average total annual inflow ($m^{3}/year$). $k_{y}$ is the
release coefficient that considers water stored in the reservoir at the
beginning of the operational year [92, 10]. It is calculated as
$k_{y}=S_{beg}/{\alpha}\times{C}$, $S_{beg}$ is the storage available at the
beginning of the operational year, ${\alpha}$ is an empirical coefficient
suggested based on sensitivity analysis. In this study, ${\alpha}$ value
considered is 0.85 as suggested by [92], $i_{m}$ is monthly inflow ($m^{3}/s$)
and $i_{a}$ is mean annual inflow ($m^{3}/s$). Two constraints are considered
for the analysis. The first is that monthly release should not be less than 10
% of the monthly inflow to the reservoir. The second is that at any point, the
storage in the reservoir should not be greater than storage capacity, and a
minimum of 10 % of storage capacity is maintained for flood control and
maintaining minimum water levels. We calculated the storage using the
continuity equation and compared calculated storage with observed storage
(Billion Cubic Meters: BCM), which was downloaded from India-WRIS to ensure
the method’s accuracy. We observe that the calculated storage values are
slightly higher than those observed, as we have not considered irrigation
demands and other demands for the analysis. Then we calculate the height using
the storage height relationship. DHP can be calculated based on monthly
release, storage capacity, and Installed Hydraulic Capacity (IHC) [8]. The
equation to calculate DHP is given by Equation 2, which ensure that it will
not exceed IHC.

$\mathrm{DHP}=\min\left(\mathrm{R}_{\mathrm{m}}\times\mathrm{h}\times\mathrm{g},\mathrm{IHC}\right)$
(2)

where $R_{m}$ is monthly release, $h$ is a hydraulic head (m) and $g$ is an
acceleration of gravity ($m/s^{2}$). We analyze the uncertainty resulting from
internal variability and model uncertainty in estimating hydropower generated
for four different periods: historical, near-term, mid-term, and end-term. The
monthly power production and uncertainties resulting from internal variability
and model uncertainties are analyzed for each period. We also analyze
percentage change with respect to the historical period of streamflow and
hydropower production to analyze uncertainties and their translation from
streamflow to hydropower production.

Table 1: Calibration and validation results Basin |  Station name | Calibration | Validation
---|---|---|---
NSE | R-square |  Period | NSE | R-square |  Period
Narmada |  Handia | 0.90 | 0.92 |  Jan-1985-Dec-1999 | 0.86 | 0.94 |  Jan-2000-Dec-2014
Mandleshwar | 0.94 | 0.94 |  Jan-1985-Dec-1999 | 0.71 | 0.86 |  Jan-2000-Dec-2014
Sandia | 0.86 | 0.88 |  Jan-1985-Dec-1999 | 0.86 | 0.89 |  Jan-2000-Dec-2014
Tapi |  Sarangkheda | 0.90 | 0.92 |  Jan-1978-Dec-1986 | 0.88 | 0.96 |  Jan-1987-Apr-1996
Burhanpur | 0.82 | 0.89 |  Jan-1973-Dec-1980 | 0.84 | 0.89 |  Jan-1981-Dec-1987
Mahi |  Mataji | 0.81 | 0.83 |  June-2005-May-2011 | 0.78 | 0.80 |  June-2011-May-2017
Khanpur | 0.77 | 0.85 |  Jan-1985-Dec-1994 | 0.62 | 0.83 |  Jan-1995-Dec-2004

##  3 Results and Discussions

The calibration and validation results for Narmada, Tapi and Mahi basins are
shown in Table 1. We simulate streamflow using the observed precipitation,
$T_{max}$, $T_{min}$, and wind data in the VIC model and compared it with
observed data. We consider 0.8 as threshold for performance criteria (NSE and
${R}^{2}$) as suggested by previous studies ( [93]. Table 1 shows that values
of NSE and ${R}^{2}$, which are higher than the threshold for all gauge
stations except Khanpur gauge. We analyzed the time series of simulated
streamflow and compared it with observed data, which shows better agreement
with each other (Figure A1). However, simulated streamflow overestimates
observed streamflow for the Mahi basin’s Khanpur gauge. It shows NSE values as
0.77 and 0.62 for the calibration and validation period, respectively (Table
1), which may be due to its location (downstream of the dam Figure 1). We have
not incorporated the reservoir module into the VIC model to simulate the
streamflow [94].

Figure 3: Effect of Bias correction: Bias correction does not preserve the
internal variability in estimating the streamflow. The first and third row
shows the monthly precipitation, $T_{max}$, $T_{min}$, wind, and estimated
streamflow using the non-bias corrected data, respectively. The second and
fourth row shows the monthly variation of the same variables using the bias-
corrected data. Each black line represents the monthly mean average of the
historical period (1985-2014) over an area from the individual ensembles
(MICE/MME) considered in this study. The red line shows observed monthly mean
values averaged over the basin up to the dam location for precipitation,
$T_{max}$, $T_{min}$, wind, and it shows streamflow at dam location. A similar
result for Kadana and Ukai is shown in the appendix (Figure A2). Analysis for
near-term, mid-term and far-term is also shown in the appendix (Figure A3).

We analyze the effect of bias correction of meteorological variables such as
P, $T_{max}$, $T_{min}$, W and its impact on streamflow estimation for each
ensemble from MICE and MME. We compare monthly mean meteorological variables
and estimated streamflow of each ensemble with the observed data. Figure 3
shows variations of meteorological variables of the Narmada basin and
estimated streamflow at Sardar Sarovar dam for the historical data. Non-bias
corrected monthly precipitation from MICE shows lower precipitation than
observed for monsoon (June - September). We observe that bias-corrected
precipitation tries to match for July and increase precipitation values for
August and September with respect to observed data. For $T_{max}$ and
$T_{min}$, bias correction does not significantly improve the performance.
Mean monthly non-bias corrected wind from each ensemble of MICE shows higher
values than observed wind data for all months. The difference between bias-
corrected mean wind data and observed data reduces after bias correction.
Still, the difference between ensemble data and observed data shows that
quantile-quantile mapping does not remove bias effectively for wind data. The
streamflow estimated using meteorological non-bias corrected data
underestimates compared to observed data, while for bias-corrected data shows
better agreement with the observed data (The last column of Figure 3).
However, we observe that streamflow estimated using bias-corrected data
slightly overestimates compared to observed data for August and September.
Overall, mean monthly data from each ensemble of MICE shows better agreement
with each other, indicating lower ICV as shown in the first and second row of
Figure 3. We also observe that bias correction further reduces ICV, indicating
that it cannot preserve the ICV, which is considered irreducible.

The mean monthly variations of P, $T_{max}$, $T_{min}$, wind and estimated
streamflow of ensembles from MME and its comparison with observed data shows
that model uncertainty is higher than ICV. Mean monthly precipitation exhibit
higher model uncertainty for monsoon than $T_{max}$, $T_{min}$ and wind. This
model uncertainty also translates to streamflow and shows the higher model
uncertainty in estimating the streamflow. For example, two ensembles
overestimate streamflow than observed, while other ensembles underestimate for
non-bias corrected data, especially for monsoon. Bias corrected data of MME
shows an improvement for all the variables and tries to match with observed
data. However, we observe high model uncertainties even after bias correction
as quantile-quantile mapping bias correction does not seem able to handle high
variability and seasonality. We performed a similar analysis for Kadana and
Ukai (Figure A2). Meteorological variables show similar behaviour for Tapi and
Mahi basins as the Narmada basin. There is a significant difference between
streamflow estimated using bias and non-bias corrected data for Kadana dam,
which is not observed for Ukai dam. This difference between streamflow
estimated using the bias and non-bias corrected data is observed for other
periods, such as near-term, mid-term and far-term, especially for monsoon
months. (Figure A3).

Figure 4: Uncertainties for streamflow: IQR for estimated streamflow for
historical (1985-2014), near-term (2015-2044), mid-term (2045-2074), and far-
term (2075-2100) using bias and non-bias corrected data of Sardar Sarovar. The
first and second row shows the uncertainties due to ICV in estimating
streamflow, estimated using non-bias and bias-corrected data, respectively,
using Multiple Initial Condition Ensembles. Similarly, the third and fourth
row shows model uncertainty, obtained using the multiple model ensembles. A
similar result for Kadana and Ukai is shown in the appendix (Figure A4).

To analyze the role of ICV and model uncertainty in estimating the streamflow,
we consider different periods such as historical (1985-2014), near-term
(2015-2044), mid-term (2045-2074), and far-term (2075-2100) (Figure 4). We
consider interquartile range (IQR - the difference between the 75th and 25th
percentile) as the measure for uncertainty in estimating the streamflow within
ensembles (MICE/MME) [31]. Figure 4 shows IQR in estimating streamflow at
Sardar Sarovar dam for all four periods. We observe lower internal variability
and model uncertainty for the streamflow estimated using the bias-corrected
data than non-bias corrected data for historical periods, indicating the
effect of bias correction. We also note a significant difference between the
mean monthly streamflow estimated using bias and non-bias corrected data. For
example, mean monthly stream flows are approximately 2000 cumecs and 5000
cumecs when estimated using August’s historical non-bias and bias-corrected
data. This difference further increases from near-term to far-term, as shown
in the appendix (Figure A3). However, Mean streamflow and uncertainty due to
ICV increases from near-term to far-term for MICE. The third and fourth row of
Figure 4 shows that model uncertainty is higher than ICV and increase in mean
streamflow from near-term to far-term for MME. Higher model uncertainty in
estimating streamflow is observed for monsoon months (Figure 4). Model
uncertainty reduces using bias-corrected data, especially for a historical
period. We observe higher mean streamflow, ICV and model uncertainty only for
monsoon and post-monsoon (October-December), which agrees with other studies
([95], [96]). Similarly, we analyze the results for Kadana and Ukai dams as
given in the appendix (Figure A4), which also shows similar patterns of
streamflow uncertainties. Here, We highlight the uncertainty induced due to
ICV increases towards the far-term irrespective of bias correction. Thus, it
is important to internalize the effect of internal variability for planning
and to manage water resources systems.

Figure 5: Uncertainties for power: IQR for estimated power for historical
(1985-2014), near-term (2015-2044), mid-term (2045-2074), and far-term
(2075-2100) using bias and non-bias corrected data for Sardar Sarovar. The
first and second row shows the ICV in estimating the potential hydropower,
estimated using non-bias and bias-corrected data using Multiple Initial
Condition Ensembles. Similarly, the third and fourth row shows the model
uncertainty obtained using the multiple model ensembles. A similar result for
Kadana and Ukai is shown in the appendix (Figure A5).

Figure 6: Percentage change of streamflow and hydropower: Percentage change in
streamflow is not reflected in percentage change in hydropower. The figure
shows the percentage change of mean monthly streamflow and hydropower to
historical data using bias-corrected data for Sardar Sarovar. Uncertainty due
to internal variability and model uncertainty in estimating the streamflow and
hydropower are shown in the first and second row, respectively. A similar
result for Kadana and Ukai is shown in the appendix (Figure A6).

Uncertainty analysis for potential hydropower shows that ICV and model
uncertainty in estimating the mean monthly hydropower production plays a
significant role for all months. Figure 5 shows IQR for mean monthly potential
hydropower estimated using the historical, near-term, mid-term and far-term
streamflow data for Sardar Sarovar dam. Uncertainties in estimating the
hydropower are also lower for bias-corrected data as we observe for
streamflow. The reduction in ICV shows that bias correction does not preserve
the internal variability. A significant increase in mean hydropower production
is observed between June and July for mid and end-term for non-bias corrected
data of MICE, while historical data shows the smooth transition. However, we
observe a similar increase for all periods using bias-corrected data as it
represents the start of the monsoon. MICE data capture the phenomenon due to
starting of the monsoon. We observe uniform and lower internal variability
throughout all months than model uncertainty. There is no significant increase
in uncertainty towards the end of 21 st century (end-term) as calculation
depends on the hydropower plant’s installed capacity and storage capacity.
However, we observe that the lower bound of IQR increases towards the end-
term, while the upper bound remains almost constant for monsoon and post-
monsoon. The third and fourth row of Figure 5 shows the model uncertainty in
estimating the hydropower production. We observe higher model uncertainty in
estimating hydropower production, especially for monsoon for non-bias
corrected data, while bias-corrected data shows higher model uncertainty for
non-monsoon. Similarly, model uncertainty increases towards the end-term for
non-monsoon months, which we do not observe for estimated streamflow. We also
performed a similar analysis for Kadana and Ukai dams as given in the appendix
(Figure A5), which also shows a similar pattern as the Sardar Sarovar dam.
However, uniform hydropower production, model uncertainty and ICV in
estimating hydropower are almost constant throughout the year for Ukai.
Overall, we can say that the uncertainty bounds for hydropower production are
not similar to the streamflow. Hydropower estimation shows a contribution of
internal variability and model uncertainty throughout the year than streamflow
uncertainty.

For further analysis, we performed the percentage change analysis to compare
the role of ICV and model uncertainty in estimating streamflow and hydropower.
Figure 6 shows the percentage change of mean monthly streamflow and hydropower
of near-term, mid-term and end-term with respect to historical bias-corrected
data for Sardar Sarovar. Mean percentage change shows the increase of
streamflow for all months. However, this increase in streamflow is not
reflected in hydropower production. For example, mean hydropower production
decrease towards the far-term for February to May. This decrease is more
prominent for MICE than MME. On the contrary, potential hydropower production
for monsoon and post-monsoon shows an increase in hydropower production. We
observe significant variability in percentage change obtained using MICE for
June, which indicates the starting of the monsoon such as percentage change in
ICV ranges between $-40$ % to 150 % for streamflow and $-20$ % to 40 % for
hydropower (First row of Figure 6). In comparison, model uncertainty does not
show this significant change.

Mean percentage change in model uncertainty in streamflow estimation and
variability increase from near-term to end-term. Similarly, percentage changes
analysis of streamflow and hydropower is also performed for Kadana and Ukai as
given in the appendix (Figure A6). For Kadana, percentage change clearly shows
an increase in mean and uncertainty in estimating streamflow and hydropower
production towards the end of the century (far-term) (Figure A6 (a)). The
percentage change variability in estimated streamflow and hydropower due to
ICV is even higher for June, as observed for Sardar Sarovar. However, a
similar trend is not observed for the Ukai dam. Figure A6 (b) shows higher
percentage change and its variability in estimating streamflow for Ukai dam,
especially for ICV. However, similar variability and increase in mean
percentage change are not observed for potential hydropower. Despite an
increase in streamflow, a decrease in hydropower production is observed for
February to April. Overall, The percentage change for streamflow is
approximate $-48$ % to 240 %, while for hydropower is approximately $-20$ % to
70 % change for all cases, which indicates that increasing streamflow does not
increase hydropower production significantly.

##  4 Conclusions

Hydropower production can help meet the increasing energy demands due to
urbanization and the increasing population in India. Hydropower, the
extensively used renewable energy sensitive to streamflow change, is
characterized by various uncertainties. The improved understanding and better
prediction of hydropower empower the stakeholders for planning and decision-
making, such as to estimate the potential energy production and determine
design parameters such as water level, minimum operation level and
installation capacity of hydropower based on future projections. However, the
crucial role of internal climate variability on hydropower production in India
is still unexplored. The high variability in precipitation, $T_{max}$,
$T_{min}$ and wind, which directly or indirectly affects the streamflow and
hydropower production and acknowledging the importance of internal
variability, motivated us to explore further the role of internal climate
variability in projections of future hydropower production. This study
analyzes the role of internal climate variability, which is irreducible
uncertainty in estimating streamflow and hydropower production. We estimate
streamflow using VIC hydrological model. This study analyzes the role of
internal variability and model uncertainty in estimating the streamflow and
its translation for hydropower estimation. We have also analyzed the effect of
bias correction by comparing the results of bias and non-bias corrected data.
The result shows that bias correction does not preserve the internal
variability in streamflow estimating, which further impacts the potential
hydropower estimation. The other findings from this study are as follows.
Model uncertainty contributes more to total uncertainty than ICV in estimating
the streamflow and potential hydropower for monsoon. However, we observe that
role of ICV is increasing towards the far-term. The estimated mean streamflow
increases during monsoon and post-monsoon only. For non-monsoon, both
uncertainties play a significant role in hydropower estimation, while it is
not evident from estimated streamflow. The uncertainty resulting from ICV and
model uncertainty increases from near-term to far-term for estimated
streamflow, while we have not observed a similar increase for hydropower
production. However, the lower bound of IQR increases towards the far-term
(2075-2100) compared to the historical data for hydropower production. Mean
potential hydropower shows the decrease towards the far-term, especially for
February to May, despite increasing uncertainty for estimated streamflow. This
decrease in hydropower is more prominent for MICE than MME. The higher
percentage change in ICV is observed for streamflow ($-40$ % to 150 %) than
hydropower ($-20$ % to 40 %) for June. In comparison, model uncertainty does
not show this significant change.

This paper uses quantile mapping for bias correction for individual ensembles
of MICE and MME. Recently, [97] have developed ensemble bias correction method
to preserve internal variability. Further study may consider using the
ensemble bias correction approach to understand the role of ICV better. The
present study considers fixed duration data for investigation using a
historical period (1985-2014) and future periods such as 2015-2044 (near-
term), 2045-2074 (mid-term), and 2075-2100 (far-term). The future scope
includes the trend analysis for hydropower production. We use VIC hydrological
model for the estimation of streamflow. We have not considered hydrological
model uncertainty for the analysis, which may play a significant role in
estimating the streamflow. Thus, other studies may consider the combined
effect of climate models, hydrological model uncertainty and internal
variability in estimating hydropower. In this study, we have calculated the
monthly releases using generic regulation rules described by [91]. Further
study may consider applying different reservoir operating policies for
calculating the monthly release by considering the irrigation and municipal
water demand under different demand scenarios. We use 50 multiple initial
condition ensembles from only one model (EC-Earth3) to quantify the internal
variability by assuming that it captures all the variability and represents
the internal climate variability. There are multiple Single Model Initial
Condition Large Ensembles (SMILEs) that are now available, which may provide
new insights for analyzing the role of internal climate variability [29, 98,
22].

## Acknowledgments

This work is supported by DST-SERB Startup Research grant (SRG/2019/000833)
and the DST-SCCC-NMSKCC project (RES/DST/EH/P0137/1920/0005), work for
Establishing/Strengthening the State Climate Change Centre/Cell under NMSKCC
(SCCC-NMSKCC) in the State of Gujarat, India. High-resolution observations
over three basins were distributed by Indian Meteorological Department located
at Pune. Open-source datasets are obtained from PCMDI, NCAR and India WRIS.
The multiple initial condition ensembles of the CMIP6-EC-Earth data is
downloaded from Earth System Grid Federation (https://esgf-
data.dkrz.de/projects/esgf-dkrz/). The multiple models of CMIP6 are downloaded
from World Climate Research Program Coupled Model Intercomparison Project
(https://esgf-node.llnl.gov/projects/cmip6/). The authors thank Prof.
Srikrishnan Subramanian, Pravin, Angana and Raviraj for comments on the
manuscript. The authors would also like to thank Prof. Vimal Misra, Amar Deep
Tiwari, and other members of the Water and Climate Lab of IIT Gandhinagar,
India, for sharing the wind observed data, soil and vegetation parameters and
providing help to set up the VIC hydrological model.

## Author Contributions

Udit Bhatia, Sudhanshu Dixit and Divya Upadhyay designed the experiments.
Sudhanshu Dixit and Divya Upadhyay performed the experiments and analyzed the
data. Divya Upadhyay, Udit Bhatia and Sudhanshu Dixit wrote the manuscript.

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## Appendix

Table A1: Details of Powerplants Dam |  Sardar Sarovar |  Ukai |  Kadana
---|---|---|---
Total installed capacity (MW) |  1450 |  305 |  240
Latitude |  $None$ N |  $None$ N |  $None$N
Longitude |  $None$ E |  $None$ E |  $None$ E
State |  Gujarat |  Gujarat |  Gujarat
River / Basin |  Narmada |  Tapi |  Mahi
Catchment area of Dam (sq. km) |  88,000 |  62,255 |  25,520
Type of Dam |  Gravity |  Earthen,Masonry |  Earthen,Masonry
Full reservoir level (m) |  138.68 |  105.16 |  127.7
Table A2: The list of CMIP6 Models used in this study No |  Modeling Group |  Model Name |  Resolution (Degrees)
---|---|---|---
1 |  Australian Community Climate and Earth System Simulator, Australia |  ACCESS$-$CM2 |  $None$ X $None$
2 |  Canadian Centre for Climate Modelling and Analysis, Canada |  CanESM5 |  $None$ X $None$
3 |  Consortium of European research institution and researchers, Europe |  EC$-$EARTH3 |  $None$ X $None$
4 |  Geophysical Fluid Dynamics Laboratory (GFDL), USA |  GFDL$-$ESM4 |  $None$ X $None$
5 |  Marchuk Institute of Numerical Mathematics, Russia |  INM$-$CM4$-$8 |  $None$ X $None$
6 |  Marchuk Institute of Numerical Mathematics, Russia |  INM$-$CM5$-$0 |  $None$ X $None$
7 |  Meteorological Research Institute, Japan |  MRI$-$ESM2$-$0 |  $None$ X $None$
8 |  Norwegian Climate Centre/Norway |  NorESM2$-$LM |  $None$ X $None$

(a) Narmada Basin (b) Mahi Basin (c) Tapi Basin

Figure A1: Calibration and validation results: Blue line shows the VIC
simulated monthly streamflow at different gauges, and the red line shows
observed monthly streamflow at different gauges

(a) kadana (b) Ukai

Figure A2: Figure shows similar result as shown in figure 3 for Kadana and
Ukai

(a) Near Term (b) Mid Term (c) Far Term

Figure A3: Figure shows similar result as shown in figure 3 using near-term,
mid-term and far-term of Sardar Sarovar

(a) Kadana (b) Ukai

Figure A4: Figure shows similar result as shown in figure 4 for Kadana and
Ukai

(a) Kadana (b) Ukai

Figure A5: Figure shows similar result as shown in figure 5 for Kadana and
Ukai

(a) Kadana (b) Ukai

Figure A6: Percentage change of streamflow and hydropower: percentage change
in streamflow is not reflected in percentage change in hydropower. Figure
shows similar result as shown in figure 6 for Kadana and Ukai