Climate change projects an increase in extreme weather events in the coming decades, which could significantly affect Brazil's water and energy security. Thus, this study sought to analyze possible impacts of climate change on the projections of naturalized streamflows and Affluent Natural Energy (ANE) for the Brazilian hydropower sector utilizing five models of the Coupled Model Intercomparison Projects version 6 (CMIP6), based on SSP-4.5 and SSP-8.5 scenarios for the 21st century. Naturalized streamflows for the 24 stations representing the National Interconnected System (NIS) were estimated through the concentrated hydrological model SMAP (Soil Moisture Accounting Procedure), while the streamflows for the other stations that comprise the NIS were obtained by linear regression. The streamflows, as well as the productivity of the reservoirs, were used to calculate the ANE. The results showed that most of the models project possible reductions in annual naturalized streamflows and ANE for the three periods analyzed and for the North, Northeast, and Southeast/Midwest sectors of Brazil. Meanwhile, the Northern and Southern sectors, for the period 2080–2099, most of the models indicated an increase of annual, precipitation, naturalized streamflows and ANE.

  • Most of the CMIP6 models showed that the NIS reservoirs are sensitive to increasing greenhouse gas emissions.

  • The medians of the standardized anomalies of annual naturalized streamflows and ANE indicated an increase for the South and North sectors of the country.

  • In the Northeast subsystem, most of the CMIP6 models indicated a reduction in naturalized streamflows and ANE.

Climate change in the coming decades indicates significant impacts on the hydrological cycle with the intensification and higher frequency of extreme weather events that can be divided into three main categories: too little water (with longer periods of severe droughts), too much water (with torrential rainfalls and floods), and too dirty water (with pollution) (Babel et al. 2020). As a consequence of these impacts, studies point out that several essential sectors for society may be affected, and among the main ones is the electric power generation (Silveira et al. 2017; Hasan & Wyseure 2018; Qin et al. 2020; Silva et al. 2021).

In the modern world, the need for reliable and affordable electric power for society grows every year due to population growth and economic development. In the year 2018, the global electricity demand increased by 2.3%, which was the highest annual growth in the last decade, and for the first time in history, the population with no electricity access rate fell to less than one billion (IEA 2020). On the other hand, the same year saw a 1.7% increase in global CO2 emissions, reaching an all-time high of 33.1 Gt (billion tons) (IEA 2020).

The Intergovernmental Panel on Climate Change (IPCC), through the fifth Assessment Report (AR5), stated that the climate system warming is evident and largely caused by the increasing concentration of CO2 in the atmosphere, with anthropogenic factors being the main causes (IPCC 2014).

Therefore, there is a climate, water, food, and energy nexus where one may influence the other in the same proportion, i.e., energy generations that emit CO2 into the atmosphere are positive feedback for climate change, which in turn intensifies extreme events, such as heat waves and severe droughts, causing changes in runoff and streamflow, and may significantly influence water availability, which directly impacts irrigation, urban water supply systems, and hydroelectric power production (Guimarães et al. 2016; Silveira et al. 2017; Silva et al. 2021). Thus, meeting the economic needs for electricity and protecting the environment from climate change impacts have become one of the main challenges of the modern world.

Renewable energy, including solar, wind, water, biofuels, and others, is part of the new, less carbon-intensive and more sustainable electric power system in transition. According to the IEA (2020), the net additions increase in renewable electricity capacity will be almost 4% higher in the year 2020 than in the year 2019. In quantitative totals, this represents a total of 198 GWh of installed renewable capacity in the year 2020, breaking another record and accounting for almost 90% of the total power capacity increase. Higher additions from wind (+8%) and hydropower (+43%) are expected in 2020, while photovoltaic solar growth remains stable (IEA 2020).

In Brazil, the water demand growth, especially for agriculture, threatens electricity generation, since the country's hydroelectric power plants are the main power generation source (Cunha et al. 2019; Silva et al. 2021). In 2019, for example, hydroelectric generation was responsible for 58% of the electricity generated by the sector, with the rest, approximately 17% coming from other renewable sources (except hydro, wind, and solar), 5% from fossil fuels, 8% from wind, 2% from nuclear, and 1% from solar sources. This is different from the reality found in the year 2000 when hydroelectric generation accounted for 87% of all electricity generated in the country (IEA 2020).

Therefore, the analysis of possible climate change impacts on the hydrological cycle, and consequently on the hydroelectric power generation in the next decades, is important information for the management of these resources. It brings subsidies for the elaboration of adaptation and mitigation strategies of these possible impacts in order to preserve the water and energy security, making the hydroelectric system more resilient.

The IPCC releases ARs on the possible climate change impacts, releasing projection scenarios based on the Greenhouse Gas emissions, using the Global Climate Models (GCM – General Circulation Model) (IPCC 2014). These models follow a pattern among various institutions which operate them, called Coupled Model Intercomparison Project (CMIP) (IPCC 2014). The last released AR by the IPCC, the AR5 in 2014, used the GCMs of the fifth phase of CMIP, called CMIP5.

Recently, updated data from the GCMs referring to the sixth phase of the CMIP, the CMIP6, were made available. CMIP6 climate projections differ from those of CMIP5's because they are not only produced with updates of the GCMs versions, but also generated with new scenarios. The scenarios combine socioeconomic and technological developments, called Shared Socioeconomic Pathways (SSP), with future radiative forcings (RCP) scenarios based on updated data on 26 emission tendencies, in a matrix scenario architecture (Eyring et al. 2016; Gidden et al. 2019).

There are five different SSPs with quantifications of models that cover future sustainable or fossil fuel-powered growth potentials, SSP1 and SSP5, respectively; high inequality among or within countries, SSP3 and SSP4, respectively; and the SSP2 scenario, which is the ‘halfway point’ of the above-mentioned scenarios. For each SSP, a different RCP scenario can be achieved depending on the policies implemented, locally or globally, throughout the century (Eyring et al. 2016; Gidden et al. 2019).

According to Gidden et al. (2019), this new structure permits to standardize all socioeconomic premises (e.g., population, Gross Domestic Product, and poverty, among others) in the modeled representations of each scenario, and also permits a more subtle investigation of the variety of paths which climate results can follow.

However, Kundzewicz et al. (2018) point out several sources of uncertainty in the projections of climate change impacts on hydrological resources, including emissions and socioeconomic development scenarios, input data, and the hydrological models. The same studies show that in order to minimize these uncertainties, the authors indicate the use of multiple GCMs and the removal of biases, since GCMs are usually highly biased towards the current climate. Making use of multiple GCMs and applying bias removal techniques, that several studies show the possible impacts of climate change on water and energy resources.

Among these studies, the work of Ribeiro Neto et al. (2016) evaluated the impacts of climate change on water resources and hydrological processes throughout the Brazilian territory through the coupling of a hydrological model for large basins to a forced regional climate model with the HadGEM2-ES and MIROC5 models of CMIP5. The RCP4.5 and RCP8.5 scenarios were analyzed, and the results showed that water availability decreases almost entirely in the study area (except for the South) and the main hydroelectric power generation basins are affected.

The work of Silveira et al. (2017) analyzed the climate change impact on the estimated streamflow projections with the Soil Moisture Accounting Procedure (SMAP) hydrological model for 24 relevant hydrographic basins in the Brazilian hydropower sector from monthly precipitation projections of the IPCC-AR5 global models from 2010 to 2098 for the RCP4.5 and RCP8.5 scenarios. Their results showed streamflow reductions in the southeast/central-west regions with reduction magnitude ranging from 15 to 30% depending on the hydrographic basin in the RCP8.5 scenario. On the other hand, for the Southern sector, the results showed a streamflow increase over the extreme south of Brazil and a decrease at the intersection between the south and southeast regions.

On the other hand, works that analyze the entire National Interconnected System (NIS), with approximately 200 stations, have not yet been applied using the new CMIP6 scenarios. Therefore, this study aimed at evaluating the CMIP6 projections of the temperature, precipitation, naturalized streamflows, and Affluent Natural Energy (ANE) of the hydroelectric plants' reservoirs for the Brazilian electricity sector, based on the SSP2-4.5 and SSP5-8.5 scenarios. Results should help decision-makers prepare better for future scenarios and reduce climate change impacts on water and energy resources.

In order to evaluate CMIP6 climate change projections for Brazil's hydroelectric plants usage, naturalized streamflows and ANE based on SSP-4.5 and SSP-8.5 scenarios were analyzed. The methodology consisted of choosing the basins representing the NIS, obtaining naturalized streamflows data, and ANE calculation. Such a process was divided in six steps, according to Figure 1.

Figure 1

Flowchart of the methodology steps.

Figure 1

Flowchart of the methodology steps.

Close modal

In step 1, the choices of the hydrographic plants representing the NIS were made. For this, 24 stations of some hydroelectric plants were used to determine the 24 hydrographic basins (see Figure 2).

Figure 2

Region of study with the hydrographic basins representing the NIS.

Figure 2

Region of study with the hydrographic basins representing the NIS.

Close modal

In step 2, mean, minimum, and maximum time series of precipitation and surface air temperatures (SAT) were extracted from the basins representing the NIS of the CMIP6 models related to the historical scenarios (1901–2000, 20th century), SSP-4.5 and SSP-8.5 (2015–2100, 21st century), and observation of precipitation of the Global Precipitation Climatology Centre (GPCC) and the mean, maximum, and minimum SAT of the Climate Research Unit (CRU), both in the period of 1931–2018. With the mean, minimum, and maximum SAT series of the CMIP6 models and observation of the CRU, time series of potential evapotranspiration (PET) were estimated using the Hargreaves–Samani method (Hargreaves & Samani 1985).

In step 3, statistical corrections for bias removal were performed using the Gamma distribution function of data precipitation and PET from CMIP6 scenarios based on the observational data.

In step 4, PET and unbiased precipitation data from CMIP6 were used as input by the SMAP hydrological model to generate naturalized streamflow data of the 24 basins representing the NIS. For that, the SMAP model had its parameters calibrated via an objective optimization procedure based on the Nash–Sutcliffe coefficient, which compares the streamflow series obtained by SMAP with the series provided by the National Power System Operator (ONS, in Portuguese). Further details are described in the subtopic ‘Estimation of the naturalized streamflows of the CMIP6 models’.

Step 5 consisted of estimating streamflow data for the remaining stations, which do not have the calibrated SMAP model. The NIS, responsible for the Brazilian energy matrix, has 206 streamflow time series, divided into 185 stations of hydroelectric use, 161 natural stations, and 24 natural and artificial stations. Out of these 185 utilization sites, 16 started only in 2015 (ONS 2019). Therefore, it was decided to divide them into two groups: one has 24 stations and the other has 161, respectively. The 24 stations were used as predictors of the other station's streamflows, and thus, it was possible to obtain the regression parameters of the 185 stations by using stepwise. That would not be possible with the SMAP model alone, as there are missing data and many of the stations are nearby – with most of the 161 stations located within the 24 basins, and the downstream of the 24 predictor stations (see Figure 2).

In step 6, ANE was calculated through natural streamflows and productivity equivalent to 65% of the useful storage volume of hydroelectric plant reservoirs.

All steps, as well as the description of the study area, data used, and statistical analyses performed, will be discussed in the next topics.

Study area

The NIS is divided into four subsystems, namely Southwest/Midwest, South, Northeast, and North (see Figure 2), which are interconnected by an extensive transmission network, permitting surplus energy to be transferred, and favoring the optimization of the stocks stored of the hydroelectric plant's reservoirs. The Northern region produces 8% of the energy in GWh and demands 7%, the Northeastern region produces 11% and demands 18%, the Southern region produces 18% and demands 16%, the Southeastern/Midwestern region produces 47% and demands 61% (ONS 2019). From these reservoirs, 24 hydrographic basins of the NIS were generated, as illustrated in Figure 2. In addition to the stations of the reservoirs of the 24 hydrographic basins above mentioned, another 161 stations spread throughout the Brazilian territory were used. In total, 185 stations of the NIS were analyzed for streamflow and 120 for the ANE.

In this study, the 24 main reservoirs of the NIS were selected by the energy storage capacity of the basin/reservoir in relation to the subsystem, considering all reservoirs full, as shown in Table 1.

Table 1

Area, annual precipitation, annual streamflow and installed capacity for the basins representing the NIS

BasinsArea (km2)Annual precipitation (mm)Annual streamflow (m³/s)Installed capacity (MW)
Emborcação 29,000 1,341 483 1,192 
Nova Ponte 15,300 1,505 532 510 
Itumbiara 51,011 1,432 1,548 2,280 
São Simão 85,729 1,420 2,363 1,710 
Furnas 50,464 1,754 929 1,312 
Água Vermelha 89,436 1,357 2,089 1,396 
Nova Avanhandava 62,300 1,300 747 347 
Porto Primavera 190,760 1,300 7,130 1,540 
Rosana 100,799 1,212 1,281 372 
Itaipu 149,000 1,650 10,027 14,000 
Santa Cecília 16,694 1,608 297 
Salto Caxias 57,000 1,824 1,260 1,240 
Itá 44,500 1,830 1,022 1,450 
Dona Francisca 14,014 1,200 182 125 
Três Marias 50,600 1,400 686 396 
Sobradinho 447,825 1,000 2,706 1,050 
Xingó 110,275 957 2,810 3,162 
Serra da Mesa 50,975 1,500 784 1,275 
Lajeado 134,543 1,500 2,484 902 
Tucuruí 572,482 2,500 10,948 4,125 
Belo Monte 480,000 1,971 8,045 11,233 
Teles Pires 90,707 2,000 2,414 303 
São Luiz do Tapajós 362,293 2,123 1,068 8,040 
Santo Antônio 988,873 1,750 1,431 3,568 
BasinsArea (km2)Annual precipitation (mm)Annual streamflow (m³/s)Installed capacity (MW)
Emborcação 29,000 1,341 483 1,192 
Nova Ponte 15,300 1,505 532 510 
Itumbiara 51,011 1,432 1,548 2,280 
São Simão 85,729 1,420 2,363 1,710 
Furnas 50,464 1,754 929 1,312 
Água Vermelha 89,436 1,357 2,089 1,396 
Nova Avanhandava 62,300 1,300 747 347 
Porto Primavera 190,760 1,300 7,130 1,540 
Rosana 100,799 1,212 1,281 372 
Itaipu 149,000 1,650 10,027 14,000 
Santa Cecília 16,694 1,608 297 
Salto Caxias 57,000 1,824 1,260 1,240 
Itá 44,500 1,830 1,022 1,450 
Dona Francisca 14,014 1,200 182 125 
Três Marias 50,600 1,400 686 396 
Sobradinho 447,825 1,000 2,706 1,050 
Xingó 110,275 957 2,810 3,162 
Serra da Mesa 50,975 1,500 784 1,275 
Lajeado 134,543 1,500 2,484 902 
Tucuruí 572,482 2,500 10,948 4,125 
Belo Monte 480,000 1,971 8,045 11,233 
Teles Pires 90,707 2,000 2,414 303 
São Luiz do Tapajós 362,293 2,123 1,068 8,040 
Santo Antônio 988,873 1,750 1,431 3,568 

Electricity generation in Brazil went from approximately 200,000 Giga of kilowatts per hour (GWh) in 1990 to approximately 600,000 GWh in 2017, with an average growth rate of approximately 17% for every 5-year period, as shown in Figure 3. It is observed that hydraulic energy has always been predominant in the country, but it started to suffer a reduction in the participation of the energy power generation matrix especially in 2015, with 62%. This deficit in hydroelectric generation was replaced, mainly, by the wind and fossil energy with 3.7% and 23%, respectively (IEA 2020).

Figure 3

Electricity generation in Brazil. Data source: IEA (2020).

Figure 3

Electricity generation in Brazil. Data source: IEA (2020).

Close modal

Observational data

For the calibration and validation of the SMAP and linear regression models and for the monthly Gamma statistical correction of the CMIP6, observed data in the period from 1901 to 2018 regularly spatialized on 0.5° × 0.5° grid of precipitation from the GPCC (Schneider et al. 2017), and mean, minimum, and maximum SAT of the CRU were used. The choice of this data set was due to its high consistency and reliability when compared with data measured from meteorological stations (Limberger & Silva 2018; Eini et al. 2019). In addition, due to Brazil's extensive area, in some regions – such as the northern region – there are still low density of meteorological stations and short periods of time series (less than 30 years). Thus, reanalysis and satellite data, as in the case of CRU and GPCC, respectively, emerge as an excellent source of global data, and because they are regularly specialized, it is an excellent option for hydrological modeling of hydrographic basins, as reported by several studies (Jong et al. 2018; Eini et al. 2019). The affluent natural streamflow data obtained for the period 1951–2008 from the National Power System Operator (ONS) were also used in the calibration and validation process of the SMAP and linear regression models.

CMIP6 data

CMIP6 prevenient data are results of simulations of five GCMs, conforming to Table 2.

Table 2

CMIP6 models with institutions, countries and citations where they talk about them

ModelsInstitute (country)Grid
CanESM5 Canadian Earth System Model 5nd generation (Canada) 2.81° × 2.81° 
IPSL-CMSA-MR Institut Pierre-Simon Laplace (France) 2.5° × 2.5° 
MIROC6 Atmosphere and Ocean Research Institute, National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology (Japan) 1.41° × 1.41° 
BCC-CSM2-MR Beijing Climate Center climate system model version 2 (China) 1.13° × 1.13° 
MRI-ESM2.0 Meteorological Research Institute Earth System Model version 2 (Japan) 1.13° × 1.13° 
ModelsInstitute (country)Grid
CanESM5 Canadian Earth System Model 5nd generation (Canada) 2.81° × 2.81° 
IPSL-CMSA-MR Institut Pierre-Simon Laplace (France) 2.5° × 2.5° 
MIROC6 Atmosphere and Ocean Research Institute, National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology (Japan) 1.41° × 1.41° 
BCC-CSM2-MR Beijing Climate Center climate system model version 2 (China) 1.13° × 1.13° 
MRI-ESM2.0 Meteorological Research Institute Earth System Model version 2 (Japan) 1.13° × 1.13° 

This study used the precipitation variables, monthly mean, minimum, and maximum SAT for the historical scenario (1901–2000, 20th century), and projection scenarios SSP2-4.5 and SSP5-8.5 in the period from 2020 to 2100. In the coming decades, these results might serve as a parameter to measure in which scenario we find ourselves, if optimistic, with more satisfactory results than the SSP2-4.5; intermediate, with results close to those obtained in SSP2-4.5; or pessimistic, with results close to the SSP5-8.5 scenario, since the other scenarios, except for SSP1 and RCP2.6, are obtained from variations of the two chosen scenarios.

SSP2 is called the ‘halfway’ scenario, with moderate population growth and slower convergence of the income levels among countries (Gidden et al. 2019). Regarding the greenhouse gas emissions, it is expected that in the SSP2, electric power generation keeps on depending on fossil fuels close to the current rates, resulting in continuous growth of those gases (Gidden et al. 2019). Concerning pollution, according to Gidden et al. (2019), for SSP2, it is expected a decrease in polluting emissions – associated with efforts in continuing to diminish air pollution and with the developing economies reaching high-income countries. For SSP5, a world with strong economic growth with the use of fossil fuels is expected, with a substantial increase in income worldwide and a reduction in social inequality among countries. However, this growth occurs at the expense of potentially large impacts on climate change (Gidden et al. 2019).

PET estimation through the Hargreaves–Samani Method

PET was estimated using the Hargreaves–Samani Method with the observational data of the CRU and CMIP6 of the mean, maximum, and minimum SAT variables (in degrees Celsius) through Equation (1):
(1)
where PET is given in mm/month, and Ra is the average external radiation, which was estimated from the latitude and month of the year, according to the work of Hargreaves & Samani (1985).

The reason why the Hargreaves–Samani method was chosen is that, among the PET estimation methods that use SAT as an input variable, the studies of Gurski et al. (2018) and Valle Júnior et al. (2020) pointed out the Hargreaves & Samani (1985) method as the one with the best performance for different Brazilian regions.

Statistical correction using the Gamma Cumulative Distribution Function

GCM's results have systematic errors when compared with the observational data. Hence, it is common to apply techniques which aim at correcting those errors, and among the most used ones is the statistical correction via Gamma Cumulative Distribution Function (CDF) (Silveira et al. 2017; Silva et al. 2021). The Gamma CDF was used in this study to correct the bias of the precipitation data and the PET of the CMIP6 models in the historical SSP2-4.5 and SSP5-8.5 scenarios. A CDF Gamma is expressed as:
(2)
where x is the variable (precipitation or PET in this case); is the scale parameter; is the shape parameter; and is the Gamma function.
In this study, the process of bias correction of data can be mathematically expressed in the following five steps (Equations (3)–(7)):
(3)
where and are shape and scale parameters, respectively, for GCM's simulated historical data (20th century), and is GCM-simulated historical data.
(4)
where is Gamma CDF.
(5)
where and are shape and scale parameter, respectively, for observed data (20th century), and is GCM-observed data.
(6)
(7)
where is inverse of Gamma CDF, and is historic bias-corrected data.
The following steps (Equations (8)–(10)) were then used to correct bias in future GCM's simulated data from SSP2-4.5 and SSP5-8.5 scenarios.
(8)
where and are shape and scale parameters, respectively, for GCM's simulated future data (21th century, SSP2-4.5 and SSP5-8.5 scenarios), and is GCM-simulated future data.
(9)
(10)

is future bias-corrected data.

Estimation of the naturalized streamflows of the CMIP6 models

In this study, the naturalized streamflows for the 24 reservoirs representing the NIS were estimated through the SMAP hydrological model, while the naturalized streamflows for the 161 remaining stations were obtained by the linear regression model. These models have been widely used in several studies for the Brazilian electricity sector (Silveira et al. 2017; Gondim et al. 2018; Silva et al. 2021).

The rain streamflow-type SMAP conceptual hydrological model was developed by Lopes et al. (1982) in order to estimate streamflows in a hydrographic basin, having precipitation and PET as input variables. For this purpose, it seeks to represent water flows in the hydrographic basin via two fictional reservoirs, one superficial or soil and the other subterranean , as shown in Figure 4.

Figure 4

Operation scheme of the monthly SMAP model. Source: Lopes et al. (1982).

Figure 4

Operation scheme of the monthly SMAP model. Source: Lopes et al. (1982).

Close modal

In the SMAP initial version, the hydrological processes encompassed daily time paces, that is, it had the daily information of precipitation about the basin as entry, the fictional reservoirs were updated, and the daily streamflows for the basin were obtained. In this version, SMAP presents a monthly time pace.

Transfers between reservoirs are governed by theoretical equations and calibrated deterministic parameters which represent the soil saturation (SAT) capacity in mm, the surface runoff through the exponent of the exponential equation (PES), the coefficient of recharge of the underground reservoir in %, and the recession equation of base runoff (K) in months. Besides, there are two initialization parameters of the initial soil moisture rate which determines the initial level of the , and the initial surface runoff (EBin) defines the initial value of the which was manually adjusted based on calculated values for the Nash—Sutcliffe Efficiency (NSE) coefficient (NSE) on each simulation. NSE is expressed in Equation (11):
(11)
in which N is the number of samples, is the observed data, is the modeled data, and the average observed data (Nash & Sutcliffe 1970). The maximum value corresponds to 1, which indicates a perfect adjustment between the modeled and observed data.

Table 3 presents the SMAP model parameters calibrated for the NIS basins.

Table 3

Parameters of the SMAP model calibrated for the basins representing the NIS

BasinsArea (km2)TuEb (mm)SAT (mm)PESCrec (%)K (month−1)
Emborcação 29,000 55 96 900 3.2 20 
Nova Ponte 15,300 52 70 1,100 25 
Itumbiara 51,011 52 170 2,000 3.1 
São Simão 85,729 60 349 2,100 4.6 
Furnas 50,464 48 221 1,400 2.2 26 
Água Vermelha 89,436 55 449 1,200 3.3 20 
Nova Avanhandava 62,300 67 352 1,200 4.6 10 
Porto Primavera 190,760 54 1,071 1,400 3.3 20 
Rosana 100,799 65 1,149 1,300 3.4 22 
Itaipú 149,000 59 2,204 1,000 2.9 50 
Santa Cecília 16,694 63 110 2,000 3.5 
Salto Caxias 57,000 61 762 400 1.8 70 
Itá 44,500 78 513 600 3.7 15 
Dona Francisca 14,014 92 120 1,900 
Três Marias 50,600 45 85 1,300 2.3 18 
Sobradinho 447,825 31 541 1,800 2.5 50 
Xingó 110,275 22 500 2.5 
Serra da Mesa 50,975 63 107 1,800 3.7 
Lajeado 134,543 59 163 1,350 3.9 4.5 
Tucuruí 572,482 59 919 1,200 
Belo monte 480,000 72 588 2,580 10 0.54 
Teles pires 90,707 61 382 1,300 3.8 9.3 
São Luiz do Tapajós 362,293 56 1,684 1,300 3.8 
Santo Antônio 988,873 71 3,283 2,700 6.4 1.64 
BasinsArea (km2)TuEb (mm)SAT (mm)PESCrec (%)K (month−1)
Emborcação 29,000 55 96 900 3.2 20 
Nova Ponte 15,300 52 70 1,100 25 
Itumbiara 51,011 52 170 2,000 3.1 
São Simão 85,729 60 349 2,100 4.6 
Furnas 50,464 48 221 1,400 2.2 26 
Água Vermelha 89,436 55 449 1,200 3.3 20 
Nova Avanhandava 62,300 67 352 1,200 4.6 10 
Porto Primavera 190,760 54 1,071 1,400 3.3 20 
Rosana 100,799 65 1,149 1,300 3.4 22 
Itaipú 149,000 59 2,204 1,000 2.9 50 
Santa Cecília 16,694 63 110 2,000 3.5 
Salto Caxias 57,000 61 762 400 1.8 70 
Itá 44,500 78 513 600 3.7 15 
Dona Francisca 14,014 92 120 1,900 
Três Marias 50,600 45 85 1,300 2.3 18 
Sobradinho 447,825 31 541 1,800 2.5 50 
Xingó 110,275 22 500 2.5 
Serra da Mesa 50,975 63 107 1,800 3.7 
Lajeado 134,543 59 163 1,350 3.9 4.5 
Tucuruí 572,482 59 919 1,200 
Belo monte 480,000 72 588 2,580 10 0.54 
Teles pires 90,707 61 382 1,300 3.8 9.3 
São Luiz do Tapajós 362,293 56 1,684 1,300 3.8 
Santo Antônio 988,873 71 3,283 2,700 6.4 1.64 
Both reservoirs are updated from month 1 to month i + 1 through Equations (12) and (13):
(12)
(13)
in which is the surface runoff in mm, P is the precipitation in mm, is the initial moisture content, is the actual evapotranspiration in mm, is the PET in mm, is the surface runoff parameter, is the recharge coefficient, is the base runoff in mm, K is the recession constant in month−1, and is the underground recharge.
The first parameter of the model is , which, by definition, receives as maximum value the same as the SATs. In turn, SAT can be expressed by Equation (14):
(14)
is also calculated via and (which is one of the input variables) using Equation (15):
(15)
The recharge, which appears in Equations (12) and (13), is expressed by Equation (16):
(16)
is expressed by Equation (17):
(17)
is expressed by Equation (18):
(18)
and constitute together with the area and the affluent streamflow of the basin (Q) in m³/s, given by Equation (19):
(19)
With the estimated naturalized streamflows for the 24 basins representing the NIS, the linear regression model was used to estimate the naturalized streamflows for the other hydroelectric plant stations. To this end, the first stage consisted in the standardization of the naturalized streamflow monthly series of the ONS utilizing Equation (20):
(20)
in which Z is the normalized streamflow, the number of months (ranging from 1 to 12), k the number of years (ranging from 1931 to 2008), j the number of stations (in total 185), naturalized streamflow of station j in the month i in the year k, is the matrix which represents the average of all months and stations, and is the matrix which represents the standard deviation of the monthly series of all stations.
With the standardized time series, the linear regression of the naturalized streamflows observed in the ONS was used, and the parameters of each of the 161 stations that did not have the SMAP were obtained, considering the 24 basins representing the NIS as explanatory variables, as it is expressed in Equation (21):
(21)
in which pk are the streamflows of the 24 basins obtained by the SMAP model (ranging from 1 to 24), pj are the stations that do not have the calibrated SMAP (ranging from 1 to 161), and the regression coefficients.

The 24 stations were used as predictors of the other station streamflows, and thus, it was possible to obtain the regression parameters of the 185 stations by using stepwise. In this method, predictors are iteratively added and removed in the predictive model in order to find the subset of variables in the data set to have a better model performance, which is a method that reduces the prediction error.

The ANE calculation

With the naturalized streamflow data and the usage of 120 hydroelectric stations, it was possible to calculate the ANE by using Equation (22):
(22)
in which t is the time interval of the ANE calculation, i is the usage belonging to the usage system of the considered basin, Qnat is the natural streamflow of the usage in the considered time interval, p is the average productivity of the turbine-generator set of the hydroelectric usage, related to the drop obtained by the difference between the level of amount, corresponding to a storage of 65% of the useful volume, and the average level of the escape channel; j is the usage belonging to the usage system of the considered subsystem; and m is the number of existing usages in the system (ONS 2019).

Statistical analysis of the projections

For the statistical analysis of projections, two methods were used, they are (i) the calculation of the annual anomalies and (ii) the non-parametric Mann–Kendall–Sen trend test.

The annual anomaly calculation of the SAT, precipitation, naturalized streamflow, and ANE of the CMIP6 model data for the projections related to the SSP2-4.5 and SSP5-8.5 scenarios from 2020 to the end of the 21st century was performed considering 20-year intervals, that is, from 2020 to 2039, 2040 to 2059, 2060 to 2079, and 2080 to 2099 in comparison to the historical scenario for the 20th century (period from 1901 to 2000), conforming Equation (23):
(23)
where is the annual average of the projection variables for the 21st scenarios and is the annual average of the 20th century variables.

In this study, the non-parametric Mann–Kendall–Sen test was applied in the series of naturalized streamflows and ANE of the projections of the SSP2-4.5 and SSP5-8.5 scenarios for the 21st century to verify trends.

In an analogous way to the calculation of the anomaly, for the Mann–Kendall–Sen trend tests, the 21st century projections were compared with the 20th century characteristics. For this, they were standardized according to Equation (24):
(24)
where Z is the series of the 21st century scenarios standardized; is the annual average series of the SSP2-4.5 and SSP5-8.5 scenarios for a year j; is the average of the annual average series of the 20th century; and the is the standard deviation of the annual average series of the 20th century.
The standardized series of the naturalized streamflows and ANE were submitted to the Mann–Kendall test given by Equation (25):
(25)
where S is the value of the series in annual time intervals; i and j are time indexes, and n is the number of elements of the series (Moreira & Naghettini 2016). The signal term (ZjZi) results from Equation (26):
(26)
The null hypothesis (H0) – referring to the absence of trend – is considered as accepted, when the test is less than a critical value named α, which for this study was α = 0.05 (for a statistical significance of 95%), that is, for TAU < α, the series has no positive trend. Otherwise, that is, for TAU ≥ α, the ST has a positive trend. In another way, the p-value of the S-statistic considers the H0 true, for p-value > α and false for p-value ≤ α (Moreira & Naghettini 2016). The TAU variable is related with the classification and correlation coefficient and quantifies the monotonic association, being given by Equation (27):
(27)
where n is the series size.
The estimator of sem provided the magnitude of the trends detected through the Q statistic, which is given by Equation (28):
(28)
where Xi and Xj are related to the values of the variable under study in times i and j (Moreira & Naghettini 2016). The positive or negative value for Q indicates increasing or decreasing trends, respectively.

Temperature and precipitation

The median of the annual anomalies of the model projections for the 21st century in relation to the 20th century (1901–2000) indicates an increase in the SAT for the entire Brazilian territory, in all four periods and for both projection scenarios, as shown in Figure 5. The increase in SAT is more intense in the SSP5-8.5 scenario in contrast to the SSP2-4.5 scenario, with the 2060–2079 period showing anomaly magnitudes above 4% for part of the Northern and Southeast/Midwest sectors, and above 4% for the entire Brazilian territory in the 2080–2099 period. In addition, the median of the annual anomaly projections for the 21st century in relation to the 20th century from the models indicates a precipitation reduction for most sectors and for all periods and scenarios analyzed with anomaly magnitudes ranging from less than −50% to −10%, as per Figure 6.

Figure 5

Median of the average annual percentage anomalies of the SAT of the CMIP6 models in the SSP2-4.5 and SSP5-8.5 scenarios in relation to the 20th century.

Figure 5

Median of the average annual percentage anomalies of the SAT of the CMIP6 models in the SSP2-4.5 and SSP5-8.5 scenarios in relation to the 20th century.

Close modal
Figure 6

Median of the average annual percentage anomalies of the precipitation of the CMIP6 models in the SSP2-4.5 and SSP5-8.5 scenarios in relation to the 20th century.

Figure 6

Median of the average annual percentage anomalies of the precipitation of the CMIP6 models in the SSP2-4.5 and SSP5-8.5 scenarios in relation to the 20th century.

Close modal

Part of the coast of the Northeast sector and virtually the entire Southern sector are exceptions, for which the median of the models indicates a precipitation increase for most periods and scenarios analyzed. The precipitation increase indicated by the models for the Southern sector is greater than that shown in the northern Northeast sector, reaching a magnitude of 40% in the SSP5-8.5 scenario over the period 2080–2099, while, in the northern Northeast sector, the magnitude of the anomalies ranged from −5% to 30%.

These results coincide with several studies that have analyzed SAT projections and precipitation of previous versions of CMIP project models and regional models for various regions in Brazil (Guimarães et al. 2016; Jong et al. 2018; Silveira et al. 2019). Among them, the study by Jong et al. (2018), using the ensemble of three regional models, showed that for the period 2071–2100 in the RCP8.5 scenario, the projections for SAT in inland cities of the Northeast sector are projected to increase by about 4–5 °C, and the precipitations might decrease by about 25–50% in the semi-arid areas of Bahia and up to 80% in the coastal areas. Silveira et al. (2019), using the CMIP5 models, also showed a possible precipitation reduction for the periods 2015–2044, 2045–2074, and 2075–2098 in relation to the 1984–2003 period for most sectors of the NIS, except for the Southern sector where the models indicated a possible increase in rainfall.

Figure 7 shows the model trends for the SSP2-4.5 and SSP5-8.5 scenarios for the SAT using the Mann–Kendall–Sen test.

Figure 7

Trends, according to the Mann–Kendall–Sen method, of the annual average temperature, referring to the SSP2-4.5 and SSP5-8.5 scenarios of the CMIP6 for the period from 2020 to 2100.

Figure 7

Trends, according to the Mann–Kendall–Sen method, of the annual average temperature, referring to the SSP2-4.5 and SSP5-8.5 scenarios of the CMIP6 for the period from 2020 to 2100.

Close modal

The set of models indicates a significant and positive trend for all NIS subsystems. There is clear evidence that increased greenhouse gas emissions suggest a greater impact on SAT, as in all cases the module of the trend magnitude is always larger for the SSP5-8.5 scenario over the SSP2-4.5 scenario. The CanESM5 and IPSL-CM6A-LR models have demonstrated to be more pessimistic, showing a trend with an increase of more than 0.6 °C for the 21st century (2020–2100) for all subsystems in the SSP5-8.5 scenario.

Unlike the SAT, in which the models were unanimous in indicating a possible increase in the SAT for the NIS according to the Mann–Kendall–Sen test, for precipitation, the models presented divergent results, both spatially and in relation to the trend declivities for most subsystems (Figure 8). For the regions that presented significant trends, the MIROC6 and MRI-ESM2.0 models indicated a positive trend of precipitations above 6 mm/year for most subsystems, while the rest of the models indicated a negative trend of precipitation for most of the subsystems. However, even with the divergence among the models, all of them agreed with the possible increase of precipitation for the Southern subsystem for the SSP5-8.5 scenario, presenting a significant and positive trend with a value above 6 mm/year.

Calibration and validation of the SMAP and the linear regression model

Figures 9 and 10 present, respectively, the linear regression and SMAP model performance in the streamflow estimations of the 185 stations for the calibration and validation process through the NSE.

Figure 8

Trends, according to the Mann–Kendall–Sen method, of the standardized annual average precipitation, referring to the SSP2-4.5 and SSP5-8.5 scenarios of the CMIP6 for the period from 2020 to 2100.

Figure 8

Trends, according to the Mann–Kendall–Sen method, of the standardized annual average precipitation, referring to the SSP2-4.5 and SSP5-8.5 scenarios of the CMIP6 for the period from 2020 to 2100.

Close modal
Figure 9

Performance of the SMAP and linear regression model in estimating the affluent natural streamflow of stations of the NIS through the NSE.

Figure 9

Performance of the SMAP and linear regression model in estimating the affluent natural streamflow of stations of the NIS through the NSE.

Close modal
Figure 10

SMAP model performance in estimating the affluent natural streamflow of the following stations: (a) Tucuruí, (b) Sobradinho, (c) Furnas and (d) Dona Francisca through the NSE.

Figure 10

SMAP model performance in estimating the affluent natural streamflow of the following stations: (a) Tucuruí, (b) Sobradinho, (c) Furnas and (d) Dona Francisca through the NSE.

Close modal

For this purpose, the streamflows' annual time series in the period from 1951 to 1990 were used for calibration and the period from 1991 to 2005 was used for validation. It is possible to observe that the stations calibrated with the SMAP model showed NSE values greater than 0.8 compared with the ONS naturalized flows, while the stations calibrated with the linear regression model showed NSE values between 0.4 and 0.8. In the validation, most stations had a decrease in the NSE value, but continued to perform well with values equal to or above 0.4. Among the sectors, the Northern one presented the worst performance in the validation, with most stations presenting values equal to 0.4. The Tucuruí station presented the highest NSE value, even though it was much lower compared with the stations of the other sectors calibrated and validated with the SMAP model, with a value equal to 0.43099. This could be associated with the smaller number of rainfall measuring stations and SAT in this region, used by GPCC and CRU to generate their grids, respectively. Thus, for this region, one may be more uncertain regarding these data.

Even though the NSE indicates a good performance of the SMAP and linear regression models, due to the fact that it prioritizes maximum extreme values, this might cause the streamflows estimated by the models to have poor performance in representing minimum values.

Streamflow and ANE

The behavior of the mean percentage anomalies of the annual naturalized streamflows and ANE shown by the CMIP6 models for the periods 2020–2039, 2040–2059, 2060–2079, and 2080–2099, indicated projections with more intense modules in the SSP5-8.5 scenario than in the SSP2-4.5 scenario for the four analyzed periods and for most of the sectors, as shown in Figures 11 and 12. Such a fact suggests that most of the stations of the NIS reservoirs are sensitive to the increasing emissions of greenhouse gases.

Figure 11

Median of the average annual percentage anomalies of the naturalized streamflows of the CMIP6 models, referring to the SSP2-4.5 and SSP5-8.5 scenarios.

Figure 11

Median of the average annual percentage anomalies of the naturalized streamflows of the CMIP6 models, referring to the SSP2-4.5 and SSP5-8.5 scenarios.

Close modal
Figure 12

Anomalies of the average annual ANE for the subsystems of the Brazilian electrical sector.

Figure 12

Anomalies of the average annual ANE for the subsystems of the Brazilian electrical sector.

Close modal

In the North subsystem, for instance, most of the CMIP6 models indicated an increase in the naturalized streamflows and ANE for all the analyzed periods and scenarios. With emphasis on the magnitude of the median percentage anomalies in the naturalized flows of some reservoirs, they are: Santo Antônio, Tucuruí, and Belo Monte, with values above 5, 25, and 45%, respectively. This result is contrary to that obtained from SAT and precipitation, because with the SAT increase and the precipitation decrease for the northern sector, a streamflow and ANE decrease was expected. Such fact may be associated with the poor performance of the linear regression and SMAP hydrological models during the validation of the stations of this sector, as demonstrated previously.

In the South subsystem, most of the CMIP6 models indicated a reduction in the naturalized streamflows and ANE for the first period analyzed in the SSP5-8.5 scenario. However, this projection changes in the last period analyzed, with most of the CMIP6 models suggesting an increase in the naturalized streamflows and ANE, with emphasis on the magnitudes of the average annual anomalies of the ANE, which presented values above 20% with the MIROC6 and MRI-ESM2-0 models. The projections of the possible increase in precipitation and naturalized streamflows had already been demonstrated in previous studies, using data from the CMIP3 and CMIP5 models (Ribeiro Neto et al. 2016; Silveira et al. 2017; Jong et al. 2018; Silva et al. 2021). Hence, similar results among the CMIP3, CMIP5, and CMIP6 databases show the cohesion in the methodologies adopted for the projection of climate variables. This way, recent studies like this one end up contributing to the confirmation of results obtained in previous studies, respecting the uncertainties associated with the process.

In the Northeast subsystem, most of the CMIP6 models indicated a reduction in naturalized streamflows and ANE. The CanESM5 and IPSL-CM6A-LR models, for example, indicated reductions in the average annual anomalies of the ANE of less than −10%. On the other hand, there was a variation in the magnitudes of the average annual anomalies of the naturalized streamflows of the Xingó and Sobradinho reservoirs, which showed magnitudes lower than −5% in the SSP5-8.5 scenario for the first period, non-significant in the periods 2040–2059 and 2060–2079, and higher than 5% in the period 2080– 2099.

This fact might be related to the greater increase in SAT projected by the SSP-8.5 scenario, resulting in a greater increase in PET projected for the 21st century, as demonstrated in this study and in previous studies with the use of previous versions of CMIP (Guimarães et al. 2016; Jong et al. 2018). The possible PET increase impacts directly on significant reductions in the naturalized streamflows for most of the stations from these sectors and consequently on the ANE.

In the Southeast/Midwest subsystem, there is a slight spatial dispersion between the response of reservoir streamflows and climate change. The reservoirs located further to the Midwest presented positive magnitudes of percentage anomalies during all the analyzed periods and scenarios, while there were variations in the values for the reservoirs located further to the Southeast. In those, during the periods 2020–2039 and 2040–2059, most reservoirs presented non-significant anomalies for both scenarios, in the period from 2060 to 2079 some reservoirs presented average percentage anomalies below −5% in both scenarios. In the period from 2080 to 2099, for the SSP5-8.5 scenario, the models suggest a greater possibility of reduction in streamflows or a slight increase, since the anomalies in the annual streamflow projections for this subsystem are between 5 and −25%.

These results, as in the Northern sector, also have contradictions with the SAT results of a possible increase and a possible decrease in precipitation for the sector. Thereby, streamflows and ANE reductions might also be expected, rather than values ranging from 5 to −25%. This may be associated with the calibration and validation process of the SMAP hydrological model using the NSE coefficient. Once it prioritizes maximum values, and with this, it may end up softening streamflows and, consequently, ANE results.

The naturalized streamflows and ANE trends, with the Mann–Kendall–Sen method, for the CMIP6 models in the SSP2-4.5 and SSP5-8.5 scenarios, reinforce that the climate change impact on the NIS is sensitive to the increase in the greenhouse gas emissions, since the magnitude of the trend declivities is more significant in the SSP5-8.5 scenario than in the SSP2-4.5 scenario, as shown in Figures 13 and 14.

Figure 13

Trends, according to the Mann–Kendall–Sen method, of the standardized annual average streamflow, referring to the SSP2-4.5 and SSP5-8.5 scenarios of the CMIP6 for the period from 2020 to 2100.

Figure 13

Trends, according to the Mann–Kendall–Sen method, of the standardized annual average streamflow, referring to the SSP2-4.5 and SSP5-8.5 scenarios of the CMIP6 for the period from 2020 to 2100.

Close modal
Figure 14

Trends, according to the Mann–Kendall–Sen method, of the standardized annual average ANE, referring to the SSP2-4.5 and SSP5-8.5 scenarios of the CMIP6 for the period from 2020 to 2100.

Figure 14

Trends, according to the Mann–Kendall–Sen method, of the standardized annual average ANE, referring to the SSP2-4.5 and SSP5-8.5 scenarios of the CMIP6 for the period from 2020 to 2100.

Close modal

Most of the CMIP6 models indicated a reduction in naturalized streamflows and ANE in the two analyzed scenarios for all the analyzed subsystems, except for the MIROC6 and MRI-ESM2-0 models, which indicated an increase for both scenarios.

Even with the uncertainties attributed to the GCMs, from the observed data used, the bias correction method, the calibration and validation of the SMAP, and linear regression models, it was possible to achieve consistent results with the reality shown in observational studies, which already show significant impacts of climate change in the last years in Brazil (Jong et al. 2018; IEA 2020), mainly over the Northeast and South regions of Brazil. In addition, new results were brought, covering not only the main hydroelectric stations in the NIS, but with the use of SMAP and linear regression models, it was possible to estimate and project the streamflows and ANE for the almost 200 stations that constitute the NIS. These results are of great importance for government agencies and society, as they provide subsidies for the development of mitigation plans for the possible climate change impacts on the water and energy sectors.

The analyses proposed by this study aimed at identifying patterns of projections for SAT, precipitation, streamflows, and ANE for the NIS about the impacts associated with climate change of the CMIP6 models. Such information is of great importance to aid government agencies and society in making decisions concerning extreme hydrological events (floods and droughts), since climate has a strong influence on the development of society, interfering directly in the environment, agriculture, air quality, economy, energy sector, among others.

Most of the CMIP6 models showed that the NIS reservoirs are sensitive to increasing greenhouse gas emissions, as the climate change impacts were more intense in the SSP5-8.5 scenario than in the SSP2-4.5 scenario both in annual anomalies as in trend magnitudes.

The medians of the standardized anomalies of annual, precipitation, naturalized streamflows, and ANE indicated an increase for the South sector of the country for most of the models and periods analyzed.

The increase in the average annual precipitation, naturalized streamflows, and ANE in the South and North sectors of the country is not unanimously reflected in the trend of the Mann–Kendall–Sen test by the models. The CanESM5 and IPSL-CM6A-LR models, for example, signaled that most reservoirs might present negative trends for all the analyzed subsystems and scenarios, while the MIROC6 and MRI-ESM2-0 models signal positive trends. This dispersion in the results in the trend declivities might be associated with the greater occurrence of hydrological extremes in these regions.

In the Northeast subsystem, most of the CMIP6 models indicated an increase in SAT and a reduction in rainfall, naturalized streamflows, and ANE. The CanESM5 and IPSL-CM6A-LR models, for example, indicated reductions in average annual ANE anomalies of less than −10%. In the Southeast/Midwest sector, for the period from 2080 to 2099, in the SSP5 8.5 scenario, the models suggest a greater possibility of reducing flows or a slight increase, since anomalies in annual flow projections for this subsystem are between 5 and −25%.

The reduction in water availability in the Northern sector and possible reduction in the Southeastern/Midwestern sector, added to the increase in SAT shown in this work, reveal possible impacts due to conflicts among multiple uses, a possible slowdown of the economy due to water reduction for agriculture and industry, as well as shortage of cities. Thus, added to the possible growth in demand for electricity in Brazil in the next few years, it could lead to a crisis in the Brazilian electricity sector.

Therefore, investments in other forms of electricity generation will be necessary for the next decades. One of the forms of energy are nonrenewable ones that cause negative feedback for climate change and, consequently, increase its damage to the entire climate system. This compensation of hydroelectric energy is the one currently used, with the activations of thermoelectric plants – which make use of fossil fuels – and emit large quantities of CO2 into the atmosphere.

Alternatively, and more beneficial, it could be the investment in renewable sources (wind and solar, for example), so that they can achieve a greater participation in the Brazilian electricity matrix. However, for the latter, a very complex policy is needed with investments in technology and labor qualification, so that in the long term the cost of this generation becomes cheaper for the country.

All relevant data are included in the paper or its Supplementary Information.

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