The major challenge in relying exclusively on “flux-limited” energy sources is to ensure that the varying energy supply can be aligned with the energy demand all the time. “Stock-limited” resources provide both storage and supply by nature and make the alignment of the supply with the demand significantly easier. Although energy flows steadily from the Sun, solar or solar-derived renewable energy sources (e.g., wind) are highly intermittent. The intermittency is due to Earth’s rotation (diurnal) and its tilted axis relative to the orbital plane around the Sun (seasonal) that is exacerbated by the chaotic behaviors of Earth’s atmosphere leading to additional stochastic variabilities. As a result, the energy supplies provided by solar and wind energy sources are highly variable and rarely align with energy demands.

To address the disconnection between energy demand and variable renewable resources, three solutions have been proposed: 1) curtailing loads (that is, modify or fail to satisfy demands), 2) providing supplemental energy sources, or 3) deploying energy storage (Clack et al., 2017). An energy system that fails to satisfy demand, forcing users to accept blackouts or adjust their demand, hardly meets the expectation of reliable services, ruling out the first option as “solution.”

Providing supplemental energy from varying resources can be achieved by installing excess capacity to meet demand all time, but such overbuilding might remain infeasible. For example, at 45° latitude, the incoming solar radiation is three to four times higher in summer than that in winter (these differences are even greater at higher latitudes). Even if winter months were as cloud free as in the summer, solar installation to provide the same power output would require three to four times more solar panels and associated infrastructure to deliver the same energy in the winter.

When the generation of the renewable fails completely, no additional capacity will be able to step in. This situation actually happens in Germany to the extent that they gave a name “Dunkelflaute” (dark lull) referring to the situation that is quite common in October and November, when the sky is covered by thick gray clouds and the air does not move for weeks. In such situation, the only solution left is the deployment of energy storage.

Alternatively, long-distance grid connectivity might allow energy transmission between regions experiencing abundance and shortfalls of renewables at different times and cope with intermittency (Jacobson et al., 2015a; Jacobson et al., 2015b). Interconnected grids can redistribute excess power generated to areas in need. This requires the grid to connect regions experiencing significantly different climate regimes.

Hydropower, while limited in its contribution to satisfying energy demands globally (Fekete et al., 2010), is less affected by intermittency, particularly when substantial water storage behind dams comprises sufficient potential energy to decouple the variation in riverine water fluxes from power generation. Hydropower is expected to partially provide energy at times when solar and wind fall short to meet the demand. Hydropower is much more flexible than solar or wind to the point that hydropower is often operated to assist power generation during peak demands. However, the magnitude that hydropower could be scaled up is poorly understood.

The “capacity factor”—which is the ratio of the power generated at any given time or averaged over a longer time period with respect to the “nameplate capacity” of the installed infrastructure—has a very different meaning for hydropower than for solar or wind. Hydropower plants are not necessarily expected to operate 24/7. They are often built with “nameplate capacity” beyond the energy available if the plant is operated 24/7. Instead, the turbines are purposely left idle and are only turned on when additional power is needed to meet peak demand. This intentionally intermittent operation leads to low “capacity factors.” In contrast, the low-load “capacity factors” of solar or wind generations are unintentional. The low-load “capacity factors” of solar and wind are representing the degree to which they failed to deliver power.

From the perspectives of the grid operator, renewables represent risk that destabilizes power delivery. Although weather forecasts are steadily improving and provide more leeway to prepare for sudden changes in the power supplies, the degree to which grid operators can turn on alternative power sources or alert customers to adjust their power demand is limited. In a truly “fossil fuel-free” energy system that relies exclusively on various renewable energy sources, the only viable means of addressing intermittency is to deploy energy storage.

In preparation for our paper, we compiled a database of publications containing 360+ references from authors dominantly associated with the work of the National Renewable Energy Laboratory (NREL). While our list of publications is unlikely to be fully representative of the entire community researching the transitioning to renewable energy sources, some striking patterns still emerged:

1) Out of the 360+ publications, only few (Doubleday et al., 2019; Kumler et al., 2019; Denholm et al., 2021; Keskar et al., 2023) addressed the seasonal and inter-annual variability of renewables.

Perhaps the most disturbing statement was “Many studies suggest that large (>50%) CO₂ emission reductions will not be possible without carbon capture and sequestration (CCS)” (Loftus et al., 2015; Craig et al., 2017) citing the “Deep Decarbonization Project” (https://ddpinitiative.org). If this is a prevailing sentiment among researchers studying the viability of transitioning the energy sector to renewables, one would wish that they were louder and clearer several decades and trillions of dollar investments ago and informed the public that renewables are not sustainable since they will always require the assistance of fossil fuels.

Without dismissing the tremendous value of the scientific work represented in the 360+ publications, we can confidently state that none of them provided insight into a truly sustainable “fossil fuel-free” future. In these publications, most of the complexities arise from striking a balance between economics, carbon emission targets, and technical feasibility of integrating highly variable energy sources into firm power generation from fossil fuels. These studies are undoubtedly essential for a gradual transition where various renewable energy resources coexist with the current firm generation capabilities.

The prioritization of reducing carbon emission sometimes leads to peculiar outcomes when it comes to energy storage. Numerous publications—attempting to address the integration of various forms of storages into the energy mix—came to the conclusion that the added storage capacity has a) no, b) negligible, or c), sometimes, even negative effects (Huang et al., 2011; Arbabzadeh et al., 2015; de Sisternes et al., 2016; Lin et al., 2016). Given that all papers considered very little storage (hours up to a week at best), these peculiarities are not necessarily surprising. When batteries need to compete with “firm energy sources” (fossil fuels with carbon capture and storage), they are likely to come out as too expensive. One could probably arrive to the conclusion without any sophisticated modeling that 15 GW of added wind capacity even if it is idle most of the time will provide more power than 15 GWh (1 h at a rate of 15 GW power generation) energy storage (Huang et al., 2011).

Another surprising characteristic of the papers was that they expressed energy storage in watts (Johnson et al., 2014; Hodge et al., 2018), which we think is wrong. Some publications ultimately reveal what they mean (e.g., 289[MW] with 289[MWh] storage that could be simply referred to as 1[hr] storage) (Johnson et al., 2014). Some others express storage in complex metrics such as 250 MW/250 MWh for every 500[MW] capacity (Bromley et al., 1997), which means a half an hour storage at best that is stretched out for a full hour by delivering half of the power.

Additionally, it is customary to express energy use over time in some form of Wh (GWh, MWh). Since energy use over time (typically year) is a rate of energy use (or power for short), the reported quantities should be written as Wh/yr (kWh/yr, MWh/yr, GWh/yr, etc.), which could be simplified to W (kW, MW, or GW). We are not alone with this assertion, and the late Sir David J. C. MacKay (a physicist and former science advisor to the UK Department of Energy and Climate Change) also noted this in his book (MacKay, 2009). This might sound nitpicking for those who got used to working with these energy units, but we believe that neglecting to recognize that the annual energy use or supply is a rate of energy transfer leads to quite frequent confusion. Putting aside the fact that non-scientific publications often mix these units, but expressing quantities that technically have the same units, leads to obfuscation. For example, the Tinton Falls Solar Farm in New Jersey that we discuss later has a reported nameplate capacity of 19.88 [MW] and 26,652 [MWh] expected power generation in a year. If the annual energy production was expressed in power units (since it is the rate of energy produced over time), then 26,652 [MWh (yr⁻¹)] = 3 [MW] would make it immediately clear that this solar facility has (3[MW/19.88[MW]) approximately 15% annual average “capacity factor.”

The consideration of only very limited energy storage capacities is probably driven by the absence of long duration storage technologies that could hold energy for months or years. This reality is clearly reflected in the distribution of the existing energy storage facilities around the world depicted by the Global Energy Storage Database (GESDB, https://sandia.gov/ess-ssl/gesdb/public, Figure 1) of the Department of Energy (DOE).

In the DOE database, there are only two entries with over 250 h storage worldwide. The largest among them is the Alto Rabagão Hydro Power Plant in Portugal built in 1964. A large artificial rectangular lake (approximately 4 km wide and 20 km long, where the height of dam is 94 m and the water storage capacity is 1,117,000 m³) on the Rabagão River provides 596 days of storage. The second largest is Vilarinho Furnas Pumped Hydro Station also in Portugal with 46 days of storage. Given the big difference between the largest and the second largest storage facilities, one has to wonder if the data entries are correct. The rest of the storage facilities have less than 10 days of storage capacity. The majority of them appears to be pumped storage, although, this can be only inferred from the names of the facilities, because out of the mostly blank 119 attributes that the GESDB provides, none specifies explicitly the storage technology.

In our view, an accounting of the supply and demand gives robust, first-order estimates about the feasibility of relying entirely on renewable energy. The approach we present is widely used in water resource management. Although, it appears to be absent in most of the energy studies we reviewed, except one (Ryu and Hodge, 2016), which incorporated a similar storage implementation into complex hourly simulation. Wikipedia (https://en.wikipedia.org/wiki/Grid_energy_storage, Figure 2) actually depicts our approach in its general description of energy storage in the grid so its absence in the relevant literature is puzzling.

The goal of this paper is to assess what combination possibilities of

a) building excess power generation capacity,

could lead to a reliable delivery of energy entirely from variable renewable energy sources. This paper carries out a set of computations offering first-order estimates of the problem. Only few studies attempted to address the feasibility of full decarbonization using renewable resources only (Delucchi and Jacobson, 2011; Jacobson and Delucchi, 2011). Notably, there are significant disagreements regarding the viability of these studies (Clack et al., 2017).

Our paper builds on the approach of recent papers exploring the intermittency of solar and wind resources (Tong et al., 2021; Wu et al., 2022). We analyze the spatially distributed solar and wind data for the conterminous United States (CONUS) and its relationship with energy demands. This paper applies normalized cumulative surplus/deficit analysis to estimate the storage needed to align energy demand with production. It also discusses the potential for alternative, renewable energy sources such as hydropower and biomass to alleviate storage needs.

The primary focus of this present paper is the Northeast region of the United States, which is part of the C-FEWS study area (Vörösmarty et al., 2023a; Vörösmarty et al., 2023b), comprising Connecticut, Delaware, Massachusetts, Maine, Maryland, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, Vermont, and West Virginia. These 12 states span over considerably different climate regimes, while they are economically closely connected to each other.

This paper explores the differences between solar and wind energy generation potentials with respect to energy consumption. In addition to highlighting the differences between the selected 12 states, this paper contrasts those differences with the national averages of the 48 lower states of the CONUS territory. The CONUS serves both as a reference and as a guidance to assess the potential to offset the need for energy storage by interconnectivity to the rest of the nation.

The CONUS is used in this section to demonstrate the inner workings of the statistical analysis and the modified, cumulative surplus/deficit analysis. The methods section includes discussions of the interpretation of the statistical analysis and the results from the cumulative surplus/deficit analysis at considerable length to guide the design of the state level experiments in setting the stage for discussion of the results for the selected 12 states.

Energy consumption data for the United States as a whole and by individual states are available from the Energy Information Agency (EIA) of the Department of Energy (DOE) (EIA, 2022). EIA provides detailed annual and monthly time series of both energy production and consumption by energy sectors. The full time series of the monthly total energy consumption (Figure 4) have some characteristics that are important to highlight because they are relevant for the design of the presented experiments.

Figure 4 shows both the monthly time series of the energy consumption of the United States from 1973 to present and the normalized monthly energy consumption, where the monthly values are divided by their respective annual means. Without formal statistical analysis, one could see that the seasonal variability of the energy consumption is relatively modest and the deviation of normalized energy consumption from its annual average (that is 1 by definition) is only 15%–20%. The energy consumption apparently started to stabilize in the last 3 decades. The seasonal variability seems slightly narrowed in the last 2 decades.

The normalized monthly energy use has an apparent shift in the seasonality from pronounced winter peaks in the 70s to lower winter peaks in the more recent years along with increasing secondary peaks in the summer that were almost absent in the 70s (Figure 4). The quantification and attribution of these shifts would need more in-depth statistical analysis that is beyond the scope of our paper, but it is hard to not interpret the winter peak declines and the increasing summer peaks as a sign of climate change via lowering energy use for heating and increasing use for air conditioning.

Unfortunately, monthly total energy consumption data are only available for the entire United States, and at the state level, only electricity generation is available at monthly granularity. At first glance, our expectation was that the monthly electricity use would follow the seasonality of all the energy consumption. A closer look at the state-level data revealed that in most states, the electricity generation differs from the nationwide dynamics seen in Figure 4. The electricity demands peak in summer, while the total nationwide energy demands peak in winter.

In addition to the absence of energy consumption data depicting the seasonal variations state by state, the transitioning to a 100% renewable future will also require a fundamental shift in the energy consumption itself. Both solar and wind energy sources produce electricity; therefore, a 100% renewable future means that all sectors need to be electrified. It is customary to distinguish primary and secondary energy use, where the primary energy use reflects the energy content of the burnt fossil fuels, while the secondary energy use is the electricity produced after the heat to mechanical energy and to electricity conversions. Moving to renewables cuts off the heat to mechanical energy conversion, but considerable portion of our energy use is heat.

Since the seasonal variation in energy consumption is modest and the peaking in the future will likely change over time both as a consequence of climate change and changes in the power system, our team decided to assume seasonally and inter-annually uniform energy consumption in the present study. The proposed method works well with time-varying energy consumption data. We intend to explore the effects of time variations on energy consumption in future studies.

Historical climate data from 1980 to 2019 are from the North American Land Data Assimilation Phase 2 (NLDAS-2 (Xia et al., 2012a; Xia et al., 2012b)), which was used in all studies in the C-FEWS framework (Vörösmarty et al., 2023a). NLDAS-2 data combine energy flux, water flux, and state variables for earth science studies, and the dataset contains 11 primary forcings including long/shortwave radiations and wind speed at 10 m above the surface, which were used in this study.

All 11 primary forcing data within the NLDAS-2 dataset were interpolated from the 3 hourly, 1/8 arc-degree NLDAS-1 dataset. As it concerns this study, the NLDAS solar radiation data were obtained through satellite observation from the Geostationary Operational Environmental Satellite (GOES), and the wind field was simulated from numerical weather prediction (NWP) models (Cosgrove et al., 2003). The dataset has been well studied and validated by the scientific community (Niu et al., 2011; Cai et al., 2014; Barlage et al., 2015; Zhang et al., 2020); thus, the additional validation of NLDAS-2 data was not conducted in this study. The NLDAS-2 data were obtained from the NASA Goddard Earth Sciences Data and Information Services Center (DES DISC, https://disc.gsfc.nasa.gov/, accessed on 05 October 2021), which covers the CONUS from 1980 to 2019.

The gridded, daily solar radiation and wind speed record values from the NLDAS-2 were zonally averaged over the selected states (Connecticut, Delaware, Massachusetts, Maine, Maryland, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, Vermont, and West Virginia), comprising the Northeast study region and over the conterminous 48 states of the United States.

The core statistics of the seasonal cycles, such as the daily minimum, maximum, and 25 and 75 percentiles along median values, were computed for each state and the entire CONUS domain (Figure 5). These statistics show marked differences between solar and wind.

Solar radiation has far greater seasonal variations than wind (considering its median value). Solar radiation goes through a 3.6 times increase between the winter (82.9 [W m^-2]) and the summer seasons (295.5 [W m^-2]). Wind is seasonally much more “steady” peaking at (4.1 [m s^-1]) in April and bottoming out at (2.7 [m s^-1]) in August (Figure 5, right column). While the median values of the daily wind speed appear to be less variable than the solar radiation, the range of wind speed on the same day in different years varies more wildly than solar radiations.

On a daily basis, the range of wind speeds averaged over the CONUS could vary as much as solar radiation and has a similar (2.8 times compared to the 3.6 times of solar) ratio between the highest and the lowest spatially averaged wind speed values. Based on seasonal variability, the only viable means of addressing seasonal variabilities is to install some form of energy storage since otherwise, the “excess installation factor” would be at least three to four times the energy demand.

Annually, the average solar and wind energy potential across the CONUS year by year only deviates by a few percentage points (2% for solar and 6% of wind); therefore, a power system relying solely on wind or solar will need only a minor excess capacity to accommodate inter-annual variability. Modest “excess installation factor” would ensure that the system can meet the annual demands even in years with the least amount of solar radiation or wind on an annual basis. Such an excess capacity is probably easier to install than deploying multi-year energy storage solutions. This finding is fundamental in the design of the cumulative surplus/deficit analysis described in the next section.

It was stated earlier that the NLDAS data represent wind speeds ( u z m ) at z m = 10 m above ground that is significantly less than the height of land-based wind turbines typically at z = 80 m . We applied a speed correction using the Prandtl–von Karman formula, u z = 1 κ u * ln z − z d z 0 , (2) expressing the wind profile of the boundary layer (Dingman, 2015), where z d = 0.7 H veg is the zero-plane displacement and z 0 = 0.1 H veg is the roughness height, H veg is the height of the vegetation, and u * is the friction velocity. The friction velocity can be computed from the wind speed at the reference height ( z m ) given by the NLDAS data so the wind speed at the height of the wind turbine becomes u z = ln z − z d z 0 ln z m − z d z 0 u z m . (3)

In the present study, we assumed that the vegetation height was H veg = 1.5 m in all states and over the CONUS so the velocity increase at the wind turbine height was uniform and we applied the height correction inside our “capacity factor” computation factoring in the “starting” and the “plateauing threshold” for wind turbines.

Cumulative deficit curves were taught to hydrologists for decades to determine the storage capacity requirement of water supply reservoirs (Palotas, 1985). The original graphical method relied on establishing the cumulative S-curve of the incoming flow throughout the year and finding the largest difference between the S-curve and a line with slope representing the integral of steady water demands.

This method is easily extendable to varying demand, by numerically integrating the difference between supply and demand, but carrying out the accumulation only when the supply is less than the demand or the accumulated deficit (the already accumulated difference between demand and supply) is positive. The supply ( I → = i 1 , i 2 , ⋯ , i n , derived from solar and wind speed records) and demand ( O → = o 1 , o 2 , ⋯ , o n , from energy consumption records) were normalized in a manner that incorporates the excess capacity needed via an “excess installation factor” (Figure 6, left column), f = I → a min I → a , (4) which is the ratio of the long-term annual average ( I → a ) and the long-term minimum of the annual means ( min I → a ) of the solar or wind resources. The “excess installation factor” ( f ) ensures that demands are met even in those years when solar or wind energies are below their long-term average (Figure 6, left column).

The cumulative deficit computation can be formalized as follows: d i = ∑ d = 1 i d d − 1 + o d − i d   Δ t > 0 → d d − 1 + o d − i d   Δ t d d − 1 + o d − i d   Δ t < 0 → 0 , (5) where I → = i 1 , i 2 , ⋯ , i n and O → = o 1 , o 2 , ⋯ , o n are time series vectors of energy supply and demand, respectively, while D → = d 1 , d 2 , ⋯ , d n is the time series of cumulative deficit at any time. The initial value of the cumulative deficit time series ( d 0 = 0 ) is zero (0). Δ t is the time step of the time series vectors. Expressing the time step ( Δ t ) in the unit of year ( Δ t = 1 365 y e a r ) and normalizing the demand and supply (i.e., dividing the time series values by their respective long-term mean) ensure that deficit time series can be interpreted as the fraction of the annual energy demand that needs to be stored. The maximum value ( S n e t = max ⁡ ⁡ ( D → )) is equal to the “storage capacity” needed to balance out the mismatch between supply and demand all the time.

This cumulative surplus/deficit analysis is regularly used for water reservoirs, where the water losses during recharging, discharging, and holding the reservoir storage are normally negligible but that is rarely the case for energy storage. Considering efficiency coefficients for recharge ( k R ), discharge ( k D ), and daily storage ( k d S ), equation (5) can be revised as follows: d l i = ∑ d = 1 i o d > i d → d d − 1 + 1 k D o d − i d   Δ t o d < i d a n d d d − 1 > i d − o d → d d − 1 + k R o d − i d   Δ t o d < i d a n d d d − 1 < i d − o d → 0.0 , (6) where D l → = d l 1 , d l 2 , ⋯ , d ln is the adjusted power deficit including the round-trip energy losses and the daily storage loss. The daily storage decay is related to the annual storage decay k a S = k d S 1 Δ t ; therefore, k d S = k a S Δ t , where time step ( Δ t ) is expressed as the fraction of the year (discussed earlier) (Figure 6).

Along with the changes in cumulative deficit, the time series of energy losses ( L → = l 1 , l 2 , ⋯ , l n ) from the combination of the round-trip energy losses (recharge 1 − k R and discharge 1 − k D ) and the storage decay ( k d S ) can be accounted as follows: l i = ∑ d = 1 i o d > i d → d d 1 − k d S + 1 k d o d − i d   Δ t o d < i d → d d 1 − k d S + k R o d − i d   Δ t . (7)

The “total storage capacity” needed to accommodate the storage losses can be computed from the adjusted power deficit D → l as S t o t = max ⁡ ⁡ ( D → l ). The average ( l = ⌈ L → ⌉ ) of the energy losses L → = l 1 , l 2 , ⋯ , l n can be used to adjust the “excess installation factor”: f a d j = f + l . (8)

Since the energy losses are initially not known, the modified cumulative deficit calculations need to be solved iteratively, where an estimate of the “adjusted excess installation factor” ( f a d j ′ ) given as f a d j ′ = f + S n e t 1 − k D + 1 − k R + 1 − k a S (9) can serve as an initial value for the adjusted “adjusted excess installation factor” ( f a d j ).

As a test of the modified cumulative deficit computation, a complementing storage operation algorithm was implemented that practically mirrors the cumulative deficits and starts from a full energy storage system and tracks the state of the energy storage over time. Figure 6, right column, shows the time series of the modified cumulative deficit along with the energy storage variations over time. The cumulative deficits are computed as a fraction of the annual consumption; therefore, “storage capacity” is also represented as a percentage of the computed annual energy consumption that needs to be stored at most to meet the energy demand all the time.

The “(adjusted) excess installation factor” for solar installation ranging between 1.17 and 1.20 (Table 1) in the Northeast region is likely to be a robust metric of the inter-annual variability and the excess power generation capacities needed to weather out years, when solar insolation falls below the long-term average. The Northeast states from West Virginia to Maine have slightly higher “adjusted excess installation factor” than the nationwide average. Therefore, these states would need to deploy marginally more excess solar generation capacity to ensure that the energy demands are always met.

The “adjusted excess installation factors” for wind are slightly lower (in the 1.10–1.24 range, Table 1) in the Northeast states than the national average (1.25, Table 1), indicating that inter-annually, the wind resources are more stable than elsewhere on average in the nation. The proximity of these states to the Atlantic Ocean undermines the feasibility of the deployment of wind turbines since this region is prone to hurricanes and the wind turbines near to the coast or offshore are almost guaranteed to be hit by hurricanes during their 25+ years’ life span (Rose et al., 2012).

The annual averages of both the solar and the wind “capacity factors” appear to follow upward trends (Figures 9, 10) deserving more in-depth analyses in future studies.

The seasonality of solar radiation (Figure 7) is very similar to the nationwide conditions (Figure 5). The summer peak of solar radiation does not vary much between states despite the considerable latitudinal differences. Apparently, the lower Sun angles at higher latitudes are compensated by the increased length of the daylight periods during summer. Summer peaks appear to be quite uniform over the region although less sunny than over the CONUS. The differences are greater during winter, when the states further north have a larger drop than the southern states. These differences are quantified in Table 1, showing the “storage capacity” needed (in the range of 24.1%–28.3%, Table 1) to align power generation with consumption (as a measure of the seasonal variability) is clearly higher in these Northeast states than the national average (22.4%, Table 1).

The seasonal variability of wind is similarly uniform among the 12 states (Figure 8). The summer low and early spring high is more aligned with the consumption regime, so it is clearly better suited for power generation. The median value of the daily wind speeds appears to be closer to the 25 percentile than the 75 percentile (Figure 8), suggesting an asymmetric distribution that is skewed toward the lower values. The median daily values of solar radiation (Figure 7) are closer to the 75 percentile, which is a sign of an asymmetric distribution skewed toward higher values.

Alternative energy sources such as hydropower or biofuels are far behind solar and wind power in abundance. Globally, the total potential energy of runoff landing on the continental surfaces is only 3.5 [TW] (based on the product of the annual discharge to oceans Q ≈ 40,000   k m 3 y r − 1 that is the result of approximately R ≈ 300   m m   y r − 1 runoff from unit area of land (Fekete et al., 2002) and runoff weighted average elevation H r ≈ 275 m multiplied by the density of water and the gravitational acceleration on Earth’s surface (Fekete et al., 2010)). The actual hydropower that can be extracted is much less since some energy has to be left in the rivers to be able to reach the oceans. The 3.5 [TW] pales compared to the global energy use today that is 18 [TW] (Murphy, 2021).

Another way to understand the role that hydropower can play is to consider the aforementioned continental runoff expressed as m ˙ R = 300 k g   m − 2   y r − 1 in the mass flow rate after factoring in the density of water. The potential energy power in that mass flow rate is P = m ˙ R g H r = 0.025 W m − 2 that is much less than the actual P s = 7.3 − 7.3 W   m − 2 solar or P w = 0.2 − 1.4 W   m − 2 wind energy production potentials. In contrast, the current 18[TW] global energy consumption over the A = 148 × 10 6 k m 2 continental area can be expressed as P g = 0.12   W   m − 2 .

One also must realize the poor energy density of hydropower. The energy content of lifting 1 [l] that is 1 [kg] mass by 1 m has a potential energy content of 9.81 [J]. In contrast, warming up the same amount of water by one degree Celsius takes 4,184 [J]. It is worth noting that the heat capacity of liquid water varies more—as a function of its temperature—than its potential energy, but it is normally assumed to be constant. Warming up 1 [l] of water from room temperature (20 [°C]) to boiling (100 [°C]) to make a pot of coffee takes up as much energy as lifting up the same amount of water to H = 80 ° C 4184 J   k g − 1 ° C − 1 / 9.81 [ J m − 1 ] ≈ 33 [ k m . Alternatively, the energy content of 33 [tone] (or 33 [m³]) water lifted to 1[m] height is the same as boiling 1[l] from room temperature to boiling.

In order to estimate national and state-by-state hydropower potentials, water balance/transport models (WBMs) (Vörösmarty et al., 1989; Fekete et al., 2010; Wisser et al., 2010) were carried out for the CONUS domain using the NLDAS forcing data (Xia et al., 2012a; Cai et al., 2014; Zhang et al., 2020) using a gridded network derived from HydroSHEDS (Lehner et al., 2006) 1’ resolution grid on geographic coordinates.

The hydropower potential was computed from monthly mean discharge estimates for each grid cell of the simulated gridded network assuming steady-state flow conditions when the kinetic energy of the flow is constant and the energy loss due to friction is compensated by the loss of potential energy. Under such conditions, the energy that can be extracted is a portion of the lost potential energy by creating impoundments that reduce the flow velocity and in return reducing the frictional energy losses. As an upper estimate of the hydropower of all the rivers, the potential energy loss P = m ˙ g ∆ h = Q   ρ w ∆ h was computed in power terms for each grid cell and summed up for the CONUS and state by state.

Hydropower potential appears to have far more inter-annual variability than solar. The ratio of the median and the minimum annual average hydropower potential (that was termed as excess factor) is f = 1.28 over the CONUS and is significantly higher than the “excess installation factor” solar ( f = 1.02 ) and similar to wind ( f = 1.25 ) power without adjustment for the roundtrip energy losses during energy storage. Figure 13 shows the inter-annual and seasonal variabilities of the normalized hydropower potential in the 12 Northeast states. The seasonality in all 12 states appears to be in line with the national average. Although hydropower potential appears to be the lowest in the summer nationwide and in all 12 states, the states at higher latitudes experience a second drop in hydropower during the winter months when the solar power is the lowest.

Table 2 shows the percentage of the annual consumption that hydropower can provide in the 12 Northeast states and over the CONUS. Maine, New Hampshire, and Vermont stand out with high potential hydropower which is misleading. Although these states are mountainous and in wet regions of the nation, they are also sparsely populated.

In addition to exploring the viability to complement solar and wind power generation with hydropower, plant growth modeling was performed by estimating the biofuel expressed as total energy that could be grown if all suitable croplands were converted to energy crops. This study utilized the crop modeling experiment carried out in this special issue (Lin et al., 2023). Since harvested crops are a form of energy storage, their energy content can be contrasted directly with the annual energy consumption to evaluate how that relates to the energy storage needed according to the cumulative surplus/deficit analysis.

The energy consumption of the CONUS and the 12 states was compared to the amount of biofuel that could be possibly grown in each state along with the hydropower potential (Table 2). It is important to note that the potential energy from biofuel and hydropower represents unrealistic extremes. Converting all croplands to energy crops or impounding all rivers to the point that they have no more potential energy to reach oceans is clearly impossible. It is safe to state that biofuel and hydropower cannot provide the missing energy to eliminate the significant energy storage for 100% reliance on solar or wind power generation. The CONUS value turns out far below the 12 states, which are clearly the wetter part of the country with more hydropower potential and crop production.

In recent decades, Europe advanced aggressively in transitioning to renewable energy sources and reached high renewable penetration. Their experiences could serve as validation of the analyses presented in this paper. Europe in general resides higher north than most of the US territories. Benefiting from the Gulf current, Denmark, Finland, Norway, Scotland, and Sweden are significantly milder than comparable areas in Canada at the same latitude. Consequently, most European countries have less solar resources, particularly in the winter, than the United States.

The impact of the higher latitude is exacerbated further by more clouds in the winter period. Most of the aforementioned countries have 80% or more cloud cover in the winter, while few places reach 70% cloud cover in the United States according to the long-term mean monthly cloud cover from the Climate Research Unit of East Anglia (Mitchell et al., 2004).

Europe also invested heavily in the interconnectivity of the electric grid. European countries form the Continental Synchronous Area, which is the largest electrical grid in the world. This phase-locked electric grid maintains the same 50 Hz frequency across all participating nations and connects 24 countries, serving over 400 million people. The grid is steadily expanding and already has synchronized connections to Algeria, Morocco, Tunisia, and Turkey (Wikipedia, 2022). The expansion to the first three of these countries was motivated by plans to install large solar farms in deserts of Northern Africa where solar resources are far more plentiful than anywhere else in Europe.

The level of connectivity that the Continental Synchronous Area provides is valuable to shift excess power generation to places with power shortages. However, the degree to which it is capable in lowering the need for storage is limited. While the interconnectivity makes the grid more reliable most of the time, a sudden drop in power generation could trigger a snowball rolling event that potentially risks the operation of the entire grid. Europe already experienced such events (most recently on 8 January 2021) (Starn et al., 2021) resulting from a sudden increase in energy demand in Croatia, and similar collapses also happened in the past when renewables failed to deliver power.

The higher level of interconnectivity does not lead to higher energy security when the variabilities of power generation potentials of the connected regions are similar. This appears to be the case for wind resources around the North Sea (Buatois et al., 2014). When wind power generation is low in Scotland, it is often low everywhere else. The same is true for stormy weather such that when wind turbines are stopped around Denmark due to series of storms. They are likely experiencing high winds elsewhere around the North Sea.

The high penetration of renewables in electric power generation in Europe is enabled by fossil fuel (most notable natural gas) backup that is essentially serving as “battery.” This is evidenced by a recent vote in the European Union accepting natural gas (Cliford, 2022) in its “taxonomy of sustainable activities” (European Commission, 2020) in the middle of an energy crisis that is clearly emerging from Europe’s heavy reliance on natural gas imported from Russia.

Accepting natural gas as part of sustainable activities, the Council of the European Union has mandated its member states to maintain natural gas storage capacities that meet 35% of their annual gas consumption and recommended in 2022 to fill up these storages to 80% at a minimum as countries were heading into winter (European Council, 2022). Although this regulation is driven by the current usage of natural gas, the 35% appears to point to the similar magnitude for storage requirements that we found with cumulative deficit computation.

Hungary is among the countries with excess natural gas storage capacity where exhausted natural gas fields are converted into natural storage. While these storage facilities might serve as a sustainable green energy infrastructure in the future in storing hydrogen or some form of synthetic gas produced in the summer from excess power as an NREL study (Denholm et al., 2022) envisioned. Such energy storage likely would endure substantial energy losses, both during the production of the hydrogen or synthetic fuel and during their conversion back to mechanical power as electricity. When hydrogen or synthetic fuel is burned, they are also subject to the Carnot efficiency of thermal power generation; therefore, a hydrogen economy would need to add substantial excess power generation capacities to compensate for these energy losses.

The presented work in our study is more of a proof of concept than a definite accounting that could be used for planning out the exact energy storage infrastructures. We are convinced that our approach is fundamentally solid, and it should be an integral part in future energy studies for outlining our truly “fossil fuel-free” future. Our team envisions three directions to refine the presented work.

First, utilizing the parameterization of the energy storage technologies—via recharge, discharge, and storage decay energy losses—can be applied to different energy storage pathways. For example, lithium batteries have modest recharge, discharge, or decay losses, but they are severely limited by the material requirements. Sodium have similar chemical properties to lithium but more abundant. While the energy density of sodium batteries is lower than lithium batteries, it is acceptable for grid-scale storage. Alternatively, aluminum batteries might also work well at grid scales. Aluminum batteries are not rechargeable, but recycling aluminum batteries might well serve seasonal power storage. In addition to batteries, synthetic fuels or hydrogen might also satisfy the energy storage needs.

The second direction is to study the seasonal variations in energy consumption and explore anticipated changes resulting from the shifting away from using fossil fuels to a full electrification of all the energy sectors. Combined with changing climate and consumer adoption of various technologies such as heat pumps and/or increasing demand for air conditioning, the seasonality of energy demands is likely to change considerably in future.

Third, the variability of renewable energy sources differs significantly spatially. Identifying places where the energy production is more in line with consumption could contribute to a significant reduction of the energy storage capacity needs. While the complete elimination is highly unlikely, any reduction in the energy storage needed by better sitting of the renewable deployment would be a significant step toward sustainable energy production.

In addition to the three directions to refine the present study, our team is also working on a thorough assessment of the roles that hydropower can play in providing energy storage. While the energy density of hydropower pales compared to solar or wind resources, there are a few places around the world where they can play significant roles. The unique geography of Norway allowed the installation of power generation turbines to existing lakes without much if any expansion of the inundated areas. Coastal areas around Scandinavia or Chile appear to be ideal locations for pumped storage possibly relying on sea water if the freshwater resources are limited.

Our plan is to revisit the Global Atlas of Closed-Loop Pumped Hydro Energy Storage (Stocks et al., 2021). This atlas identified 616,000 potential storage sites (with minimum 1 G L = 0.001 k m 3 volumetric storage capacity and 100 − 800 m elevation difference) and claims that these pairs of reservoirs can provide 23 P W h energy storage capacity that is 37 G W h on average that the authors grouped into 2, 5, 15, 50, and 150 G W h energy storage categories. We showed before that the potential energy in runoff globally is only 3.5 T W = 30,660 T W h   y r − 1 . This is only 33% more than the energy storage over these potential sites with a few hundred hectares catchment area upstream (according to the authors). It is unclear how such reservoirs would be filled up in reasonable time.

Assuming 18 h of operations producing 37 G W h energy will require anywhere between 261 − 2095 m 3 s − 1 flow rates passing through the pipes connecting the upper and lower reservoirs that are equivalent to medium to large rivers. The 150 G W h energy generation in 18 h would require 8.3 GW turbine capacity that is the same as the installed capacity of the Tucurul Dam in Brazil, which is the eighth largest hydropower station in the world.

Another team attempting to assess the potential in pumped hydropower arrived to 17.3 P W h potential capacity (Hunt et al., 2020). Their method involved identifying candidate reservoir sites and nearby rivers to support the pumped hydropower operation. At 18 T W global energy consumption, the 17.3 − 23 P W h energy storage estimates translate to 40–50 days of energy storage at best. Our team intends to reproduce these potential storage sites and incorporate them into the hydrological modeling infrastructure discussed earlier and assess the feasibility of their operation for long-term storage.