Amazon dams database

Geographic location, elevation and technical data including installed capacity and flooded area for proposed and existing dams were obtained from published databases on existing and proposed Amazon dams3,45. Our database incorporated information from recent national government databases for countries where updated inventory data were readily available46,47. We calculated the level of branching in the river network using the Strahler stream order method48.

There are 158 existing dams, either operating or under construction, with over 1 MW of installed capacity in the Amazon basin, totaling 32,608 MW of electricity generation capacity with an average of 206 MW per dam (range: 1–11,233 MW). We identified 351 proposed dams in various stages of inventory, planning and licensing (installed capacity >1 MW). The proposed dams have a combined electricity generation capacity of 91,887 MW, on average 262 MW per dam (range: 1–6133 MW). Watershed areas above each dam were estimated from a digital elevation model of the region. Existing and proposed dams were categorized as upland or lowland using a cutoff of 500 m a.s.l.49. In some cases (26% of dams), information on flooded areas was unavailable. For existing reservoirs without reported flooded areas, we quantified flooded areas from satellite imagery (Google Earth Pro 7.3.2.5776). For proposed dams with missing information, we used available flooded areas as a training dataset to develop a multiple regression model including country, watershed area, installed capacity, and elevation as covariates to estimate flooded areas (Supplementary Fig. 3a). The predictive power of the regression model was high; however, we also ran sensitivity analyses to confirm that our main conclusions were robust to the inclusion of estimated flooded areas for the subset of dams with missing data (Supplementary Fig. 3b).

Time horizon of the analyses

To compare the radiative forcing effects of GHGs with different warming potentials and atmospheric residence times, an index termed Global Warming Potential (GWP) is typically used. The GWP measures the relative amount of energy the emission of a gas will absorb over a given period of time in relation to the same amount of CO 2 . The most widely used time horizon for GWP of atmospheric gases is 100 years, but shorter time frames are particularly appropriate for interpreting the climate effects of certain activities when short-lived gases are to be prioritized. This is the case of CH 4 , which remains in the atmosphere for approximately a decade but has a large radiative forcing effect. Therefore, all of our analyses also consider a 20-year time horizon in addition to the commonly used 100-year time horizon. In terms of radiative forcing, CH 4 is the predominant GHG emitted from hydropower reservoirs, and the general temporal pattern of GHG emissions from dams indicates that emissions peak in the first decade after damming and then fall to lower levels that remain somewhat constant over time13. Therefore, the high potential of dams to cause warming over short timescales gets underrepresented when the GHG footprint of dams is assessed only over long time horizons. We converted CH 4 emissions to CO 2 -equivalents using a GWP of 34 over 100 years and 86 over 20 years50.

Carbon intensity estimates

The carbon intensity (also referred to as emission intensity or emission factor) of power sources measures the net GHG emission per unit electricity generated (kg CO 2 eq MWh−1). We combined project-specific data on flooded areas and installed capacity from our Amazon dams database with 48 CO 2 and 38 CH 4 published flux estimates for tropical and subtropical reservoirs12 to calculate carbon intensity ranges for all existing and proposed Amazon dams. To calculate the carbon intensity of a given dam, we first calculated total GHG flux as follows:

$${\mathrm{TE}}_{{\mathrm{dam}}} = A_{{\mathrm{dam}}} \times \left( {{\mathrm{net}}_{{\mathrm{CO}}_{2}} \times F_{{\mathrm{CO}}_{\mathrm{2,dam}}} + {\mathrm{net}}_{{\mathrm{CH}}_{4}} \times F_{{\mathrm{CH}}_{\mathrm{4,dam}}} \times {\mathrm{GWP}}_{{\mathrm{CH}}_{4}}} \right) \times \left( {1 + R_{{\mathrm{downstream}}}} \right)$$ (1)

where TE dam is the total GHG flux (kg CO 2 eq d−1), with positive values denoting emission (water-to-atmosphere flux) and negative values denoting uptake (atmosphere-to-water flux); A dam is the reservoir flooded area (km2); F CO2,dam is the CO 2 flux (kg CO 2 km−2 d−1); F CH4,dam is the CH 4 flux (kg CH 4 km−2 d−1); GWP CH4 is a conversion factor for the global warming potential of CH 4 over the corresponding time horizon (20 or 100 years) to transform kg CH 4 km−2 d−1 to kg CO 2 eq km−2 d−1; R downstream is a constant representing the ratio of downstream emissions to reservoir-surface emissions, estimated to be 17%51. We multiplied CO 2 fluxes by a discount factor of 0.25 (net CO2 ) and CH 4 fluxes by 0.90 (net CH4 ) to account only for the net (anthropogenic) change in GHG emissions associated with reservoir creation (see details below). We then calculated total electricity generation as follows:

$${\mathrm{EG}}_{{\mathrm{dam}}} = {\mathrm{Cap}}_{{\mathrm{dam}}} \times 24 \times P_{{\mathrm{Cap}}}$$ (2)

where EG dam is the total electricity generation of a given dam over a day (MWh d−1); Cap dam is the installed capacity (MW), which was multiplied by 24 to obtain the energy output in 24 h and to have numerator and denominator units of Eq. (3) in the same time unit; and P Cap is a constant representing the capacity factor (0.5727), which denotes the effective electricity generation as a proportion of installed capacity, and was derived from an empirical relationship between data in our database on existing Amazon dams. Carbon intensity (CI dam , kg CO 2 eq MWh−1) is then calculated as:

$${\mathrm{CI}}_{{\mathrm{dam}}} = \frac{{{\mathrm{TE}}_{{\mathrm{dam}}}}}{{{\mathrm{EG}}_{{\mathrm{dam}}}}} + {\mathrm{CI}}_{{\mathrm{construction}}}$$ (3)

where CI construction is a constant representing the carbon intensity associated with construction and infrastructure of hydropower dams (19 kg CO 2 eq MWh−1 for a 100-year time horizon)7.

Uncertainty in estimated carbon intensities for proposed Amazon dams is largely influenced by variability in the GHG flux input data (i.e., F CO2,dam and F CH4,dam in Eq. (1)). Thus, for each Amazon dam, we generated 10,000 carbon intensity predictions through the implementation of a bootstrapping procedure that randomly resampled with equal probability from the dataset of published CO 2 and CH 4 fluxes from tropical and subtropical reservoirs12. CH 4 fluxes from these reservoirs included both ebullition (bubbles rising directly from sediments) and diffusion. Our bootstrapped ranges of carbon intensities therefore reflect project-to-project variability in GHG flux rates as observed for existing tropical and subtropical dams. The CO 2 and CH 4 fluxes measured for single dams12 were found to be uncorrelated (r = 0.19, p = 0.16), which allowed us to combine independently resampled CO 2 and CH 4 fluxes. Variation in calculated carbon intensity among dams is essentially driven by two parameters: installed capacity and flooded areas. Supplementary Fig. 4 shows examples of the bootstrapping output for two existing dams with contrasting power densities. Emissions results presented in the main text are based on mean and 95% confidence intervals for bootstrapped values.

Our calculations incorporate the net change in GHG fluxes resulting from the transformation of a riverine landscape into a reservoir by dam construction. The most comprehensive review on GHG emissions from reservoirs, which we used to support our analysis, reported gross fluxes12. To assess the net change in GHG fluxes resulting from the creation of a reservoir, emissions that would have existed under pre-impoundment conditions have to be discounted from the gross fluxes. Although conceptually simple, disentangling natural and anthropogenic reservoir emissions is a complex task with limited empirical support13. A recent review suggested that it is reasonable to assume that practically all CH 4 emissions from global reservoirs are new and therefore anthropogenic, whereas the majority of CO 2 emissions (perhaps ≈ 75%) over a 100-year time horizon would take place even without the reservoir creation13. In our analysis, we conservatively assumed that 75% of reservoir CO 2 emissions and 10% of CH 4 emissions reflect natural pre-impoundment emissions, and thus we incorporated these corrections in Eq. (1) (net CO2 and net CH4 ). For a particular reservoir, the percentage of CH 4 emissions that can be attributed to reservoir creation depends in part on the preexisting environments that become inundated; floodplains and other wetlands would have higher CH 4 emissions rates than non-wetland environments52,53. We use the 10% estimate in our analysis because preexisting land cover information for all of the existing and proposed reservoirs in the Amazon is not available. We ran sensitivity analyses to verify how much these assumptions affect our results (Supplementary Fig. 5). Emissions of nitrous oxide (N 2 O) can also occur in reservoirs; however, this gas was not considered in our analysis because N 2 O emissions generally represent < 5% of the total gross CO 2 -equivalent emissions from impoundments12, and because Amazon soils have naturally high rates of N 2 O emission, such that net increases in N 2 O emissions associated with dams are expected to be relatively low54.

Previous studies indicate that reservoir GHG emissions vary as a function of temperature18 and therefore latitude17, with low-latitude dams generally emitting more GHG per unit area. Thus, we used flux information only from tropical and subtropical dams in the global reservoir emissions database to represent the latitudinal range of dam projects proposed in the Amazon12. Sensitivity analyses indicated that carbon intensities would not change substantially if fluxes from tropical dams only or dams from all climates (with most dams being located in northern temperate zones) were utilized instead of the subset that we adopted (Supplementary Fig. 6).

The increased rate of GHG emissions varies over the lifetime of a hydropower dam, with peak fluxes occurring in the first years after damming due to the decomposition of flooded biomass, followed by a protracted period of lower fluxes due to decomposition of soil organic matter, continuing river inputs, and new aquatic primary production9,14,19. The reported GHG flux measurements for tropical and subtropical dams12 refer to dams on average > 30 years old, which means that they reflect GHG fluxes that miss the large pulse of emissions anticipated when dam reservoirs are first flooded. To account for the initial pulse of emissions from a hydropower project, we applied multiplier factors to the reported emissions associated with the first 5 years post-damming (300% for years 1–3, 200% for years 4–5) for a given dam for which we predict a carbon intensity, based upon the emissions profile from an existing Amazon reservoir19,20.

Validation of estimated carbon intensities

To assess the validity of our approach to generating predicted carbon intensities for Amazon dams, we compared our estimated carbon intensities against intensities calculated using reported measurements of CO 2 and CH 4 fluxes for operational Amazon dams in ref. 12 (n = 6). Our predictions were in reasonable agreement with observed carbon intensities (Supplementary Fig. 7), which was supported by a paired t-test between observed and mean modeled values (t = −1.0, two-tailed P = 0.34, degrees of freedom = 5).

Carbon intensity of electricity sources

The International Energy Agency (IEA) releases an annual report on the status and trends of global energy (World Energy Outlook), which includes carbon intensities anticipated under a range of global energy development scenarios23. To place proposed hydropower dams in the Amazon in a global energy production context, we used benchmarks from the IEA 2040 Sustainable Development Scenario, which portrays a decarbonized global electricity sector to meet the United Nations 2030 Agenda for Sustainable Development goals55. The IEA report suggests that a decarbonized global electricity sector should emit about 80 kg CO 2 eq MWh−1 in 2040, which is representative of a power mix sustained by renewables such as solar and wind power, as well as low-carbon hydropower plants. We also directly compared our calculated carbon intensities for Amazon hydropower dams against those reported for alternative energy technologies by the Intergovernmental Panel on Climate Change (IPCC), including coal-fired, combined-cycle natural gas-fired, and solar power plants7. The carbon intensities reported by the IPCC are for a 100-year time horizon. Owing to CH 4 emissions, carbon intensities of natural gas and coal are at least 37 and 4% higher over a 20-year time horizon, respectively, compared with a 100-year time horizon56. We applied 37 and 4% correction factors to obtain carbon intensities for natural gas and coal over 20 years.

Tradeoff analysis and computation of the Pareto frontier

To analyze the tradeoffs between electricity generation capacity and GHG emissions, we computed the Pareto frontier with respect to the two criteria. The Pareto frontier is a function that identifies for a given installed capacity target the portfolio (or combination) of dams with the lowest amount of GHG emissions, or conversely, for a given GHG emission target, the portfolio of dams with the highest installed capacity. In our case, considering the 351 proposed dams in the Amazon basin, the possible portfolios of dams are: the empty portfolio that builds none of the proposed dams, 351 singleton portfolios with only one dam, 61,425 portfolios with two dams each \(\left( {\begin{array}{*{20}{c}} {351} \\ 2 \end{array}} \right)\), 7,145,775 portfolios with three dams each \(\left( {\begin{array}{*{20}{c}} {351} \\ 3 \end{array}} \right)\), and so on, until we reach the final portfolio comprising all 351 dams.

The application of the Pareto frontier is illustrated in the following scenarios. In Scenario 1, portfolio A has an installed capacity of 20,000 MW and carbon intensity of 90 kg CO 2 eq MWh−1, whereas portfolio B has an installed capacity of 20,000 MW and carbon intensity of 100 kg CO 2 eq MWh−1; we say that portfolio A dominates portfolio B since portfolio A has a lower carbon intensity for the same electricity generation capacity. In Scenario 2, portfolio A has an installed capacity of 20,000 MW and carbon intensity of 90 kg CO 2 eq MWh−1, whereas portfolio B has an installed capacity of 18,000 MW and carbon intensity of 100 kg CO 2 eq MWh−1; in that case we say that portfolio A dominates portfolio B since portfolio A has lower carbon intensity and higher electricity generation capacity. In Scenario 3, portfolio A has an installed capacity of 20,000 MW and carbon intensity of 90 kg CO 2 eq MWh−1, whereas portfolio B has an installed capacity of 18,000 MW and carbon intensity of 85 kg CO 2 eq MWh−1; in this scenario neither portfolio dominates the other. The Pareto frontier is then defined as the set of all portfolios of dams that are not dominated by any other portfolio.

Computing the exact Pareto frontier is a challenging computational problem, referred to as non-deterministic polynomial-time hard (NP-hard) problem, which means that in the worst case the computational time increases exponentially as a function of the number of dams27. Our framework for computing the exact (i.e., provably optimal) and approximate (with optimality guarantees) Pareto frontier exploits the tree structure of river networks26,27, extending previously proposed algorithms for single-objective optimization stochastic network design in bidirected trees57,58 to multi-objective optimization and computation of the Pareto frontier. In this approach, the river network is converted into a more abstract tree structure, whereby a node corresponds to a continuous section of the river uninterrupted by existing or proposed hydropower dams and an edge represents a proposed or an existing dam. This abstract tree structure is used by our dynamic-programming algorithm for the sequence of the merging and pruning of Pareto-optimal solutions.

The dynamic-programming approach recursively computes the Pareto-optimal partial solutions from leaf nodes up to the root26,27. The key insight is that at a given node u, we only need to keep the Pareto non-dominated partial solutions and we can therefore eliminate suboptimal (dominated) solutions. To increase incremental pruning, we convert the original tree into an equivalent binary tree. Given a binary tree, we first compute non-dominated Pareto solutions for the two children of the given parent node u, enumerate the partial solutions from the children and consider the four possible different combinations of whether to include each of the dams associated with each edge from the children. We then compute the objective values for the different extended partial solutions and add them to the set of overall partial solutions. Finally, we remove all dominated partial solutions from this set, so that the remaining partial solutions are Pareto-optimal for the parent node. This procedure allows us to systematically explore the entire search space of possible Pareto-optimal solutions. To prevent memory overflow in response to the large number of partial Pareto solutions considered, the algorithm batches partial solutions at each node and is parallelized to speed up the approach. We do not assume spatial dependencies among reservoirs when optimizing hydropower for GHGs, but consideration of spatial dependence may be critical for other environmental criteria (e.g., fish migrations or sediment retention), and our algorithm has the ability to solve problems where spatial dependence is important to consider.

In addition to computing the exact Pareto frontier, our dynamic-programming approach can provide a fully polynomial-time approximation scheme (FPTAS) by applying a rounding technique to the exact algorithm. The FPTAS finds a polynomially succinct solution set, which approximates the Pareto frontier within an arbitrary small factor ε and runs in time that is polynomial in the size of the instance and 1/ε26,27. The exact algorithm guarantees to find all optimal portfolios on the Pareto frontier. The approximate algorithm finds fewer portfolios but guarantees that every portfolio on the exact Pareto frontier is ε-approximately dominated by one of the portfolios on the approximate Pareto frontier. The algorithm used in our framework adapts and parallelizes a dynamic-programming based algorithm for the exact and approximate Pareto frontier. More computational details concerning our approach can be found in ref. 26,27, and the code is publicly available (see Code Availability section).

Compared with previous approaches used to compute the Pareto frontiers for dam placement, our algorithm provides coverage optimality guarantees and runs faster. Importantly, we also show that the approximate version of our algorithm is guaranteed to run in polynomial time (Supplementary Fig. 2). The computation of the exact Pareto frontier for the 351 proposed dams takes 8.6 min (wall-clock time, 8 threads; ≈1 h CPU time) and produces 83,108 non-dominated portfolios. Computing the ε-approximate Pareto frontier with 99% accuracy (i.e., ε = 0.01) for the 351 proposed dams takes 1.5 min wall-clock time (8 threads, ≈7 min CPU time) and produces 66,312 non-dominated portfolios. Except for Supplementary Fig. 2, all results presented here are based on the exact Pareto frontier. Finally, we also generated random suboptimal portfolios to compare with the Pareto-optimal ones. Due to the large number of all possible portfolios (≈10105), we show only a subset of the suboptimal portfolios.