Global risk pooling mitigates financial risk from drought in hydropower-dependent countries

Domain: earth_science
Published: 2026-01-16
Editorial outcome: minor_revision

Abstract
More than 50 countries rely on hydropower for over 25% of their electricity generation, making them vulnerable to drought and resulting revenue losses. Governments can offset financial losses for publicly-owned hydropower generators, but this can create fiscal pressures and lead to negative consequences, such as lower bond ratings. Index-based financial instruments, used to manage weather-related risk, offer an alternative, though data collection and index design are challenging. Using remotely sensed hydrometeorological data, we develop index insurance contracts to manage drought-related financial risk for hydropower-dependent countries. Low correlations in drought across these countries allow cost reductions when risks are pooled. Pooling the contracts yields average savings of 54% compared to individual risk management via reserves. These findings indicate that pooled index insurance can strengthen financial resilience in countries dependent on hydropower and support governments in mitigating drought-related economic risks.

Introduction
Hydropower accounts for the majority of global renewable energy, a share expected to grow through 2030 as countries attempt to meet net zero emissions targets and energy-related Sustainable Development Goals (SDGs)1. For 56 countries, however, hydropower already provides more than 25% of domestic electricity generation2 and, for some, hydropower sales are also an important source of government revenue (Fig. 1). Yet hydropower’s advantages are undermined by its vulnerability to hydrometeorological variability-the first half of 2023 alone saw an 8.5% decline in global hydropower generation due to droughts3, though individual countries experienced far larger drops (e.g., China –20%4). Corresponding reductions in revenues of this scale may impact a hydropower supplier’s financial stability, as hydroelectric dams require large, upfront capital expenditures that are usually repaid at constant rates. Sufficiently large drops in hydropower revenue can lead to financial losses, undermining a supplier’s ability to meet these fixed debt service obligations.

For the governments that rely on hydropower, reductions in generation and the commensurate loss of revenues may yield budget deficits5, which are most difficult to manage for low and lower-middle income countries (LICs/LMICs). The need to purchase more expensive, compensatory sources of electricity to meet firm contractual obligations can compound these revenue losses by simultaneously increasing costs6. And, in many regions, droughts and heatwaves are at least somewhat correlated7, further exacerbating the impacts of reduced generation as heatwaves lead to increased electricity demand (e.g., for air conditioning). Such variable revenues and the increased potential for financial losses at the national level can lead to sovereign credit rating downgrades, driving interest rates on government borrowing higher, and thus increasing the costs thereof. This is particularly important for LICs/LMICs, of which less than 5% hold investment-grade credit ratings8. For example, Fitch credit rating agency (Fitch Ratings) noted in its analysis of Zambia, which uses hydropower to generate over 80% of its electricity9, that the country would face substantial costs to import electricity during a drought10. Fitch expected this increase would be large enough to adversely impact the national budget, negatively influencing the country’s credit rating.

For these reasons, hydropower suppliers at all scales have developed various strategies to manage their hydrometeorological financial risk (Fig. 2). A traditional risk reduction strategy might involve building larger reservoirs to store more water for use during drought, or diversifying the energy mix. Such approaches typically require large capital outlays for capacity which will be seldom used and which may ultimately fail to provide the expected level of risk management under uncertain future climate conditions. Another category of management techniques is risk retention, which often involves holding cash reserves to protect against low revenue and/or high-cost periods (self-insurance). However, reserves must be maintained in a relatively liquid form to be available for unpredictable events, and therefore earn little return. Given the sums necessary to protect against the most extreme events, these low returns can lead to prohibitively high opportunity costs associated with holding large reserves for long periods—the foregone returns when holding funds as opposed to investing them—especially in LICs/LMICs where capital is scarce.

Risk transfer techniques are often better suited for managing larger, more infrequent losses11. This approach typically involves paying a third party (or parties) to take on the risk of losses in exchange for payment. Transfer is often conducted through financial contracts, such as index insurance, whose payouts are triggered when a threshold of some pre-established metric correlated with financial losses (”the index”) is crossed. Such index-based contracts can link weather-based losses to payouts intended to compensate for them. In comparison to traditional, indemnity-based insurance, which involves the filing and individual adjudication of every loss claim, index insurance can provide faster and less contentious payouts. The pre-set trigger and payment structure can also reduce administrative costs for the insurer and, therefore the buyer. Contracts using weather-based indices can be compared to weather-based derivatives12–14, which emerged in the 2000s to mitigate risk for power utilities and generators experiencing fluctuations in electricity use (and revenues) based on daily temperatures.

If the risks in question are spatially uncorrelated or negatively correlated, insurance and other risk transfer tools can be pooled across regions. Establishment of risk pools consisting of parties with uncorrelated losses can reduce the reserves required to offset a given level of losses, relatively to each pool member individually maintaining adequate reserves, thereby lowering the costs of insurance11,15,16. Several regional and global risk pools take advantage of this strategy, including the Caribbean Catastrophe Risk Insurance Facility (CCRIF), the Pacific Catastrophe Risk Insurance Facility (PCRIF), and African Risk Capacity, each of which provide insurance to countries as a means to mitigate household-level property and agricultural losses resulting from hurricanes, tropical storms, and/or droughts. Empirical evidence from these organizations suggests that pooling hydrometerological financial risks reduces the cost of insurance by 27% to 65%11,17,18, values that are dependent on the level of correlation in losses across pool members. However, despite the advantages to pooling, such an approach has not yet been applied to insuring the hydropower sector.

One challenge to developing risk pooling strategies at the global level is data availability, as the design of robust risk transfer instruments and risk pools requires historical data to characterize the probability and severity of droughts, and limited on-site historical data are available in many hydropower-dependent countries19. In previous works, satellite-based measurements of vegetation, elevation, temperature, and precipitation have been used to characterize the severity of drought20,21; crop growth and yields22–24; land use/land cover change25,26; flooding27; and streamflow28,29, as well as to generate seasonal streamflow forecasts for hydropower generation30. Such data can be used to develop multivariate indices that correlate with financial losses from reduced hydropower generation, facilitating the development of new risk transfer tools such as a risk pool to combat drought-related losses for hydropower.

We use increasingly available remotely sensed data to do so, designing index insurance contracts which form the basis of a global risk pool that can cost-effectively manage drought-related financial risk in countries that rely on hydropower. First, country-level index contracts are designed using remotely sensed data, which while limited, provide greater temporal and spatial coverage than alternative data, such as streamflow reanalysis datasets (e.g., 31). The contracts are then individually evaluated and priced. Second, these contracts are pooled, with each country experiencing savings on the cost of the insurance contract based on the degree to which their inclusion in the pool influences the magnitude of, and level of correlation in, payouts.

Results
Index insurance contracts

Monthly data for four hydrometeorological conditions are used as inputs to indices that correlate with annual national hydropower generation (Table 1). Precipitation, retrieved from the Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement Mission (IMERG), is a proxy for water supply32. Snow cover extent (Normalized Difference Snow Index, NDSI) and vegetation indices (Normalized Difference Vegetation Index, NDVI and Enhanced Vegetation Index, EVI) similarly provide information on water availability, with the former most important in basins where streamflow is driven by snowpack. Available snow and vegetation index data33,34 are produced from observations of the Terra Moderate Resolution Imaging Spectroradiometer (MODIS). Finally, land surface temperature (LST) data from MODIS35 provides insight into both water supply, as it is influenced by on-the-ground moisture, and electricity demand, as electricity use is linked to high temperatures36.

The multivariate indices, designed using linear regressions for each of the 56 hydropower-reliant countries, form the basis of the index insurance contracts. In order to be effective, the indices on which these contracts are based must be reasonably correlated with hydropower generation and revenues. Of the countries considered, 15 have indices with r2 values ≥0.35 (see Fig. 3) and trigger at least one payout during the 21-year historical timeseries (2002–2023). This threshold corresponds to the low end of commercially available index insurance contracts37–39. Notably, 67% of the 15 countries in our pool have three or fewer dams whose ‘Main’ or ‘Major’ purpose is to generate hydroelectricity (as categorized in the Global Reservoir and Dam Database (GRaND) database). The remaining five participants (Norway, Austria, Albania, Croatia, and Georgia) have a greater number of dams, though only Norway and Austria have dams on more than 5 rivers, as designated by the GRaND database. This suggests that future efforts to form risk pools might initially focus on countries with concentrated hydroelectric facilities. The minimum r2 threshold for the fitted model limits basis risk, which represents the ability of an index to trigger payouts when losses occur and at an appropriate amount. Additional leave-one-out cross-validation provides further confidence in these indices, as all indices have mean absolute errors of ≤0.11 across a range of training and testing set combinations, relatively to the capacity factor range of 0–1. The Normalized Nash-Sutcliffe Efficiency for each index lies between 0.57 and 0.74, indicating adequate fit. Supplementary Information Table 2 (Section “Additional Statistical Tests”) provides results for additional statistical tests. The indices are also limited to four or fewer indicator variables, making them relatively transparent to buyers, a factor important for increasing insurance uptake40. The remainder of this analysis exclusively focuses on the 15 countries whose indices meet these criteria.

Ten indices utilize data aggregated at the subbasin level, which takes into consideration the outsized impact of large dams clustered in a single subbasin and/or disparate climatic zones across a country. For example, Chile’s hydropower capacity is concentrated in a single regional though the country spans nearly 40 degrees of latitude. Five indices exclusively use annually aggregated hydrometeorologic conditions as predictor variables, while the remainder have at least one seasonally aggregated predictor (e.g., average fall temperature). Variables aggregated at different seasonal timesteps provide information related to the timing of hydropower generation—an important consideration given that periods of high supply may not align with periods of high demand. Temperature and precipitation—variables that act as proxies for both electricity demand and hydropower generation—dominated index inputs. Snow cover extent and EVI—both indicators of water supply and therefore hydropower generation—were also included. Less than half of the indices rely on either temperature or water supply indicators alone to predict hydropower generation.

Insurance contracts are designed to pay out when indices fall below the twentieth percentile of a country’s historical capacity factors. Payouts are capped at the worst 0.5% of losses, also referred to as the 99.5% Value at Risk (VaR). The expected annual payout for the individual contracts is $20 million (cumulatively $301 million). This value, however, varies widely for individual countries. Slovenia (1172 MW), the country with the least installed hydropower capacity in the pool, has an expected annual payout of $4.3 million, while Chile has far larger hydropower capacity (6934 MW) and an expected annual payout of $42 million.

Contract premiums are a function of these expected payouts and a loading factor, which represents the portion of the premium in excess of the expected payouts and accounts for the costs of contract design, administration, and the insurer’s return. The loading coarsely represents the cost of insurance (ignoring the time value of money), as it is the fraction of the premium that does not statistically return to the buyer over the long-term. Here, we use the Wang Transform41 to price contracts, which applies a risk adjustment factor (λ) to modify the distribution of payouts in order to more heavily weigh infrequent, but high magnitude payouts, such that the mean of the modified distribution represents the expected payout and loading (see “Methods”, Section “Index insurance”).

Large variability in payouts, along with their magnitudes, is reflected in individual country premiums, which vary between $1.7 million for Latvia and $107 million for Norway, as well as the loading (see Table 2). While the range of premiums reflects the magnitude of payouts required for different countries, a function of absolute hydropower capacity and generation, differences in loading (37–64% in our sample) attest to the variability in payouts for each country. Austria and Croatia, for example, experience low levels of variability, as measured by the ratio of the standard deviation to mean payout value (coefficient of variation), and correspondingly have lower levels of loading than other countries in the pool (37% and 39%, respectively). In contrast, Pakistan and Latvia both exhibit high levels of variability and experience higher proportionate loading (64%).

The cost-effectiveness of the individual contracts can be compared to the opportunity cost of self-insurance via a reserve fund, i.e., foregone returns from holding liquid funds large enough to cover losses equivalent to the maximum insurance payouts (see “Methods”, “Index insurance”). As seen in Fig. 4A, risk transfer via individually purchased insurance provides the same level of risk mitigation as reserves at 65% of the average cost. The benefits of purchasing individual insurance versus holding reserves vary by country with some countries experiencing cost savings of over 50% (Table 2 and Fig. 4B). However, self-insurance can be more cost-effective than individually purchased insurance. In this pool, the costs of risk management for Croatia increases when purchasing individual insurance. That said, the relative cost-advantage of purchasing insurance is contingent on the rate of returns. Figure 5 (Section “Index insurance”) shows historical rates of return under which self-insurance is more or less attractive than purchasing individual insurance; higher rates of return generate higher opportunity costs, making insurance more attractive.

Savings from pooling reserves and insurance

The risks of the individual countries and the individual insurance contracts can be pooled, with premiums modified to reflect the new, aggregate risk of the pool. The impact of pooling insurance contracts mirrors the reductions in costs when reserves are pooled instead of individually held.

This is because as the number of pool participants grows, the coefficient of variation associated with the aggregate payout falls, even as the overall, annual expected payouts increase. This phenomenon can be attributed to the relatively low levels of correlation between the losses experienced by pool members. This correlation drives the difference between the reserves necessary to compensate for the 99.5% VaR of the pool and the sum of the reserves countries would need to individually hold in order to independently manage their risk. Figure 6 shows the reduction in reserves achievable with multiple countries in the pool, whose cumulative reserves across all potential participants, if held individually, would amount to $4 billion. Instead, when reserves are jointly held within a pool, the necessary amount falls by ~33% ($1.3 billion) to $2.7 billion. This corresponds to the smaller reserves that an insurer would need to maintain as well, and in a competitive market lower costs for an insurer should lead to lower loading for purchasers42.

The reduction in necessary reserves manifests itself as the difference between premiums for individually insured countries versus premiums charged when they are members of the pool. Were the 15 countries analyzed in this work to purchase individual insurance contracts, the sum of their premiums would equal $447 million with an average loading of 50% ($146 million total). In contrast, the overall premium for the risk pool is $405 million, with an average loading of 29% ($104 million total). This overall annual saving of $42 million is distributed across pool members by calculating each participant’s Shapley value (Methods “Global risk pool”), which capture the changes in contract loading attributable to each country’s participation in the pool.

Using the Shapley value to allocate savings from participation in the pool with all 15 participants, individual participants see reductions in loading between 8% and 94% (see Table 2 and Fig. 4B), with the greatest savings going to countries whose payouts are uncorrelated with others in the pool (e.g., Latvia and Zambia) and therefore bring more value in terms of diversification (see Fig. 7B). The smallest reductions in loading occur for the countries with the highest payouts or those most correlated to the pool, e.g., Norway and Austria. The reduction in contract loading from establishing a risk pool are such that insurance is more cost-effective than holding a reserve fund for all countries in the pool and remains cost-effective for most countries even as the opportunity cost of holding reserves falls (Fig. 5, Section “Index insurance”).

Methods
This work involves the design and testing of individual, country-level index insurance contracts in terms of their ability to offset severe hydropower losses and their cost, followed by an examination of the potential for aggregating them into a global risk pool (Fig. 8). Index-based contracts are designed with the use of remotely sensed hydrometeorological data. The following sections describe the data used in this analysis (Section “Remotely sensed data”); the design of the indices (Section “Index insurance”); and the creation of the risk pool (Section “Global risk pool”). Analysis was undertaken using Python 3.7 using the geopandas (version 0.10.2), shapely (version 1.8.0), statsmodels (0.13.2), scikit-learn (version 1.0.2), and scipy (version 1.7.1) packages62.

Remotely sensed data

Data acquired via remote sensing can be used to overcome the paucity of on-the-ground observations in many countries, providing more spatially and temporally complete information on hydrometeorological conditions such as precipitation, snow cover extent, enhanced and normalized vegetation index, and LST. With respect to this analysis, the first three relate to water availability and hydropower supply, while temperature has a strong relationship with electricity demand36,63 as well as with evapotranspiration and other water supply indicators (e.g., vegetation indices). Each of the remotely sensed datasets is globally available between 2000 and 2023 at various time steps ranging from sub-daily to monthly. These data are complemented by information on watershed boundaries and data on global dam/reservoir locations and sizes which are used for aggregation of hydrometeorological inputs at different spatial scales during the index design process. Brief descriptions of the datasets are provided here, though readers are referred to the Supplementary Information, Section 2 and the original dataset documentation for more details on how the data are collected and processed.

The Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement Mission (IMERG) algorithm integrates precipitation data collected from passive microwave estimates, microwave-calibrated infrared estimates, and precipitation gauges. This analysis utilizes the “Final” monthly 0.1×0.1 degree product, version 0664, which is summed to a monthly timestep from half-hourly observations.

Snow cover extent can provide a complementary measure of snowmelt magnitude and timing when paired with the IMERG measurements for precipitation levels. In many parts of the world, snowmelt accounts for a large fraction of streamflow65, and its influence on hydropower can outweigh that of rainfall, making it important to isolate. We use monthly NDSI data at the 0.05×0.05 degree spatial scale (MOD10CM)33, produced from daily MODIS observations. The NDSI, the normalized difference of green and shortwave infrared wavelengths, captures the relative percentage of high reflectance values typical of snow in visible bands, thereby producing an estimate of snow cover extent. It should be noted that NDSI can also capture variations in surface water extent, not just snow, meaning that NDSI may show variation even in areas that do not experience snowfall. Indices are thus manually screened to ensure NDSI is only used for countries with snowfall.

Vegetation indices reflect hydrologic conditions by describing vegetation density, a proxy for water availability. The vegetation index data used in this analysis (MOD13C2)34 is produced from 16-day composites of the same MODIS observations as the NDSI data, aggregated to the monthly timestep. The NDVI is similar to the NDSI in that it measures the difference between the red and near-infrared wavelengths. The EVI improves on the NDVI in areas with dense vegetation by accounting for soil and atmospheric influences, thereby “decoupling” the vegetation from the background canopy signal. In regions with dense vegetation, EVI has improved sensitivity that can more accurately characterize vegetation levels. On the other hand, EVI is very sensitive to topography and so may produce error-laden index values in areas with variable topographies. This analysis includes both NDVI and EVI in index creation to improve accuracy for countries with either of these features.

Finally, LST data, which measures the emissivity and “brightness” temperature of the surface in Kelvins is also derived from MODIS. The MODIS LST data (version 6) is collected daily at a 1 km×1 km scale but this analysis uses the 0.05 ×0.05 degree, monthly aggregation (MOD11C3)35. These five datasets are aggregated at several temporal (i.e., seasonal and annual) and spatial scales. Temporal averaging is undertaken at the seasonal (i.e., winter, spring, summer, fall) and annual timestep. Spatial averaging is based on hydrologic unit boundaries from the HydroBASINS dataset66, which delineates subbasins by the location where two river branches meet, given a minimum upstream area of 100 km2. Units are categorized into 12 levels ranging from the continental to the local watershed levels, with sub-continental and regional level basin scales used for this analysis. Data are additionally averaged within country borders. See Supplementary Information, Section 2 for more detail on spatial and temporal averaging, as well as for a map of the level 4 subbasins used for each country.

Additional data are obtained from the US Energy Information Administration for historical hydropower generation from 1980 to 202367 and from the International Renewable Energy Agency (IRENA) for generation capacity, from 2000 to 202368.

Index insurance

Index insurance emerged as a tool to manage hydrometeorological financial risk as early as 1920 in India69. Unlike indemnity-based insurance, which requires quantification and on-site verification of losses, payouts from index insurance contracts are triggered when a pre-defined threshold of some established metric (the “index”), measured at a specific time and place, is crossed. Payouts may be fixed or vary according to the difference between the index threshold, or strike, and the observed value (i.e., the larger the gap, the larger the payout). This index-based structure typically reduces administrative costs and concerns over moral hazard because damages and payouts are not directly linked. Additionally, less reliance on lengthy and subjective judgements over losses can increase the speed of payouts70.

Though index insurance has long been associated with weather-based perils impacting agriculture69–75, its potential has been explored across many other economic sectors, including shipping and inland navigation76–78; urban water supply79,80; and energy81–86. Other perils that have been covered by index insurance include wildfires, earthquakes, hurricanes, cyclones, windstorms, and floods11,44,87,88. The most notable example of index insurance related to hydropower is the 2013 index insurance contract written to cover the hydropower-dependent, publicly-owned Uruguayan electricity utility, UTE, which provides up to 75% of the country’s electricity via hydropower2. In this case, reinsurer Swiss Re collaborated with the World Bank to underwrite the contract, which triggered a payout to UTE when rainfall fell below an agreed upon level as measured in a prescribed manner5. The goal of this contract was to offset the increased costs of generating and/or importing electricity from alternative sources during periods of low hydropower generation.

This work aims to design index-based contracts for countries dependent on hydropower to offset the lost value of hydropower generation during years with shortfalls, but to do so while pooling the risks of multiple countries. The primary challenge when developing such a contract is identifying an index that is sufficiently correlated with the insured party’s losses (i.e., with low basis risk), a process that can be limited by data availability89. Designing a strong index requires consistent and reliable data to identify triggers for payouts and to characterize the relationship between hydrometeorological conditions, hydropower generation and financial outcomes. A poorly designed index lead to high basis risk, meaning a low level of correlation between losses and payouts such that payouts are not be triggered when losses occur, or are triggered when losses are minimal. The former results in ineffective risk management and the latter in more expensive contracts.

The remotely sensed data described in Section “Remotely sensed data” are used to meet this requirement. Indices are designed using precipitation, LST, NDVI, EVI, and snow cover extent data as inputs to multivariate linear regressions predicting national average hydropower capacity factor, or the ratio of actual electricity generated to maximum potential generation. Use of the capacity factor accounts for changes in hydropower generation capacity over time, as countries build new hydropower infrastructure or, in some cases, remove it. Data are split into training (80%) and testing (20%) sets. Only countries whose indices have less than four statistically significant predictor variables (two-tailed p-values ≤0.05) and an r2≥0.35 are considered when correlating losses with payouts. The restriction on the number of inputs to each index is an attempt to limit overfitting, especially important considering the limited time series (21 years) on which indices are based, but also to increase transparency, an important consideration for buyers of index contracts40. The second condition is intended to ensure a commercially viable level of agreement between the index and reduced generation (and sales revenue). Existing index insurance instruments capture less than 30% of financial variation37–39, suggesting that 35% would be acceptable to contract buyers in terms of basis risk. Index-based contracts are designed only for hydropower-reliant countries, defined here as relying on hydroelectricity for at least 25% of domestic generation, those which would face substantial financial consequences during periods of hydropower shortfalls. Additional statistical tests for normality, heteroscedasticity, and accuracy were conducted, and can be found in the Supplementary Information, Section 1.

A key component of index-based instruments is the strike, which is the threshold that when crossed leads to payouts. There is no single method to set a strike, but different probabilistic measures of risk can provide useful guidelines, including use of VaR, the value below which a given percent of outcomes (e.g., generation, net revenues) fall based on the historical distribution of losses. The strikes in this analysis are set to each country’s 80% VaR of capacity factor, indicating the worst 20% of outcomes in terms of annual generation, with the assumption that less severe losses can be compensated for using other tools, such as tariff adjustments and reserve funds. The capacity factor is translated into generation by multiplying it against 2020 installed hydropower capacity (Eq. (2)).

Generation is converted into a financial value using the global average levelized cost of electricity (LCOE) for hydropower (Eq. (1)). The LCOE takes into account both operating and capital expenses throughout the lifetime of an electricity generator, and in 2022 was $44/MWh for hydropower90. Use of the average levelized cost provides a consistent evaluation of the value of hydropower generated globally and avoids reliance on national electricity tariffs that may be heavily subsidized and which are not consistently available. In practice, this value may be adjusted according to the LCOE of hydroelectricity in any given country. Historical capacity factor data is used to set a cap on payouts, using the 99.5% VaR:

v i($) = (avg cf i,y) * capacity * 8760 * LCOE (1)

payout i,y ($) = 0 ≤ v i,y ≤ cap i, if cf i,y < k i (2)
0, otherwise

where v is the predicted value for the financial shortfall country i faces in year y; cf is the capacity factor as calculated by the index; and capacity (MW) is a country’s hydropower capacity in 2020. Because there are no negative capacity factor values, the hydropower shortfall is calculated as the difference between the average capacity factor (avg) and the index-calculated capacity factor for a given year. This value is multiplied by maximum annual potential hydropower generation—the product of hydropower capacity (MW) and the number of hours in a year (8760)—and by the LCOE ($/MWh) to calculate (v), which is intended to offset the hydropower shortfall. The final payout is triggered by the strike, k (set to the twentieth percentile of capacity factor) and capped using the 99.5% VaR for capacity factor ($).

The premiums for the index insurance contracts are the sum of a country’s expected payouts and loading. The first component, the expected payouts, is intended to offset payouts for the insurer over the long-term. Loading then accounts for the costs an insurer accrues in developing and administering the contract, as well as a reasonable return for accepting the risk of losses (e.g., opportunity cost of holding large liquid reserves). The loading loosely represents the cost of an insurance contract to the buyer of the insurance because the buyer will, statistically, receive the value of the expected payouts from the insurer over the long-term, but there is no accounting for the true value of money held by an insurer.

Though historical data on losses can be used to calculate expected payouts, there are various ways to estimate loading and full premiums. For example, the CCRIF, which insures Caribbean nations against hurricane-related losses, fits limited historical data to loss exceedance curves, which are used to assess the probability of a loss greater than a given threshold. Information on the probability and magnitude of payouts informs premium calculation for a contract providing a given level of insurance coverage. The distribution of payouts can also be altered to more heavily weigh the tail (higher payouts) using a risk adjustment factor to generate a risk-adjusted distribution for which the expected payout represents the premium. The Wang Transform41 has been used to make this risk adjustment and has been applied to insurance pricing in several sectors16,82,83,91–93:

F*(xi) = Φ[Φ-1(F(xi)) + λ] (3)

v i = E(F*(xi)) (4)

where Φ is a standard normal distribution, x($) are the payouts for country i, and λ is the risk adjustment factor used to approximate the market price of risk and generate a risk-adjusted distribution of payouts. The market price of risk, λ is set to 0.25 for this analysis, a benchmark value used for pricing weather derivatives in the original work41. The expected value of this risk-transformed distribution is the premium (v i), and the loading is the difference between the expected payout and the final premium.

When comparing the costs of risk transfer via insurance with risk retention via reserves, loading on the insurance contract (the annual cost) can be compared to the opportunity cost of holding reserves in some accessible (liquid) form. This analysis uses the average returns (6.03%) on 20-year US Treasury bonds between 1974 and 202494. Fig 5 shows results using historical rates from a high return period (1974–1999, 8.5%) and a low return period (2000–2024, 3.3%). It highlights the influence of investment returns on the relative cost-effectiveness of purchasing insurance.

Global risk pool

While index insurance can be effective for individual people or countries, bundling the uncorrelated (or negatively correlated) risks of several parties can reduce the costs of insuring all pool participants relative to a scenario in which each is independently insured or chooses to manage its risk via reserves (risk retention). As the degree of correlation between losses experienced by pool participants declines, the total reserves required by the pool to cover collective losses similarly falls far below what the parties in the pool would have to maintain independently42.

Thus, one important factor in determining the effectiveness of a risk pool is the level at which losses are uncorrelated across participants. The degree to which the pool diversifies the risk of losses depends on this lack of correlation, and benefits from negative correlations15. Figure 7 shows correlations between annual hydropower capacity factors in hydropower-dependent countries. Although some countries experience correlations of up to 0.89, others experience correlations as negative as −0.83, with a median correlation of 0.07. Though this work attempted to design indices for all countries depending on hydropower, only indices for 15 countries met the criteria of r2≥0.35, less than four indicator variables, and triggered payouts in at least 1 year. This subset of countries exhibits a range of bilateral correlations similar to the full set, with a range of 0.78 to −0.69 and a median correlation of 0.06. For individual countries, median bilateral correlations range between 0.15 and −0.16. The low, and often negative, median level of correlation suggests that a risk pool could be effective in reducing the aggregate reserves necessary to provide a defined level of risk management.

The pool comprises the individual country contracts, meaning that the annual pool payout is equivalent to the sum of annual payouts for all pool participants. The pooled premium is a single sum, priced by applying the Wang Transform to overall pool payouts. The difference between the premium for this pooled contract and the sum of individual premiums for all countries within the pool yields the savings from pooling countries’ risk.

This pooled premium must then be disaggregated into individual premiums for pool participants. An important question then becomes how the savings associated with pooling should be distributed amongst pool members. In this work, savings are allocated according to each participant’s average marginal contribution to the risk and diversification advantage that they contribute to the pool, in line with the literature on pricing individual components of a portfolio95–100. The marginal contribution is calculated as the Shapley value101.

The Shapley value quantifies the average contribution of each pool participant to the cost of insurance, i.e., how the loading for the pooled contract changes based on a participant’s addition to possible pool subsets. It incorporates changes in loading across all potential pool combinations, i.e., changes in loading were a country added to a pool of any size. Consideration of the average contribution allows the distribution of savings such that all members of the pool experience savings relative to the purchase of individual contracts or participation in a smaller pool (see Supplementary Information, Section 3). For example, a country that experiences payouts that are strongly correlated with other pool members will see a smaller relative reduction in its premium as a result of pooling compared to a country whose payouts are negatively correlated with other participants, even if their expected losses are equal. This is because the latter country provides greater diversification advantages to the pool.

Premiums within the pool are thus a function of the individual loadings calculated via the Wang Transform, and the Shapley value (φ i(N,v)), which is the new loading value, accounting for the savings made possible by each pool participant:

φ i(N,v) = Σ C⊆N (|C|-1)!(n-|C|)! / n! [v(C) - v(C\{i})]

where N is the full set of pool participants, C is a permutation of that set, i is a single participant, and v is the loading associated with the set of pool participants as calculated via the Wang transform. Once the savings from the risk pool are allocated to individual participants, the cost of the pooling strategy can be evaluated in comparison to (1) the opportunity cost of holding liquid reserves sufficient to offset generation losses up to the maximum insurance payout (payout cap= 99.5% VaR) and (2) premiums that would be charged to pool members if they were to independently purchase insurance contracts.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Dear Authors,\nThanks for this interesting submission which is methodologically robust and very policy relevant. I hope you will engage with\nrelevant international bodies (e.g., International Hydropower Association) and financiers (e.g., World Bank) to share your\nframework and apply it in practice. I made a few minor suggestions in the attached file for your consideration.\nBest regards,\nEdoardo Borgomeo\n(Remarks on code availability)\nLibrary is well structured and readme file is ok.", "reviewer_2": "Dear Authors,\nThe study described in the manuscript titled ‘Using Remote Sensing to Develop a Global Risk Pool for Hydropower-\ndependent Countries” develops hypothetical index insurance contracts to insure hydropower-dependent countries against\nfinancial risks associated to drought.\nThe study analyzes the potential benefits of these contracts for individual countries and within a global risk pool in\ncomparison with self-insurance via a reserve fund. The results indicate that reasonably accurate contracts could be\ndeveloped for 16 countries out of the 56 hydropower-dependent countries. For these 16 countries, pooling the index-\ninsurance contracts could lead to relevant average savings (68%) relative to individual country risk management using\nreserves. Less significant comparative advantages are also estimated with individual index-insurance contracts, but the\nbenefit is contingent on the level of average returns (interest rates) used to calculate the opportunity cost of reserves.\nThe topic of this study is certainly of interest for the disaster risk financing research and professional global community from\nan operational perspective. However, the paper misses a clear review of the state of the art of scientific research related to\nthe specific topic and does not clearly highlight what the cutting-edge innovative scientific contribution of the study is, and\nwhy this can be relevant for a broad scientific audience. This is a major drawback.\nThe overall technical quality and readability of the manuscript is good, and results are presented and discussed in a clear\nway.\nHowever, there are some major methodological issues to highlight:\n- It is clear that for most hydropower-dependent countries considered (40 out of 56) the contract accuracy in predicting\nhydropower generation and revenues does not meet even the low requirements (i.e. model R2 > 0.35 and one historical\npayout triggered) set in this study to assess the contract suitability for commercial implementation. This topic is barely\ndiscussed and analyzed.\n- The requirements for index-insurance contract acceptability set in this study are low and, according to Authors, all contracts\nare “in the low end of acceptability of commercially available contracts”. To support the choice of the requirements, the\nAuthors cite selected paper from the index-insurance literature. However, these papers are all related to crop index-\ninsurance and it is not very clear how the threshold was ultimately set. It seems that contracts which such a high uncertainty\nmight not be easily acceptable for index-insurance schemes adopted at country level for a strategic and economically\nrelevant sector like hydropower, especially for countries having access to relatively high-quality data. This uncertainty is also\nnot taken into account in the comparison between index-insurance and self-insurance, while it might be a relevant factor to\nconsider for the insurance pricing (as well for the willingness to purchase by countries). While the Authors correctly\nrecognize that the quality of the proposed contract is a limitation of the study, a more in-depth analysis of basis risk would be\nessential to support the findings of this study and the broad suggested implications (i.e. that a pooled index-insurance\nproduct can be an effective tool for improving the financial stability of hydropower-dependent countries)\n- In addition to the previous consideration, the description of the contract design is limited and R2 is the only performance\nindicator presented to compare multivariate models. This is a strong limitation, especially considering that multiple linear\nregression models are developed using a data limited time series (18 years), with risk of overfitting and violation of\nregression assumptions. A much more in-depth analysis of the model uncertainty would be important to support the potential\neffectiveness and commercial value of the proposed contracts.\n- Remaining in statistical methods, the analysis of correlations between national level capacity factors is also unclear (Figure\n4). In the text the Authors state that -0.84 is “a low correlation”, while it is a high negative correlation. Then it seems that the\naverage between negative and positive correlations is done, while the absolute values should be considered. Perhaps this\nis just a misunderstanding.\n-It is also not very clear how the different remote sensing indicators were processed and aggregated spatially and\ntemporarily for each of the country models. Some information is provided in Appendix A, but the details provided do not\nallow reproducing the indices and evaluating specific technical choices made in the contract technical design. This is a very\ncritical step that can affect the overall quality of the index-insurance contract and should be presented and discussed in more\ndetail.\nBest regards,", "reviewer_3": "The manuscript is well written, relevant, and valuable and provides a useful analysis for the audience.\nI have two items for the authors to address:\n1) My understanding is that there is an active weather derivatives market for hydropower, and note power derivatives in the\nearly 2000s was part of the motivation for index insurance. In a quick search, I see that EEX European Hydro Power Go\nappears to be an active product. It may be that derivatives are a more appropriate mechanism for hydropower than\ninsurance, but since the math stays the same, their paper is just as relevant. The authors should reference these markets,\ndiscuss their gaps and relevance, and connect their work to the derivatives market.\n2) The key driving factor for price savings is how much of the total payouts in the portfolio are covered by the premiums from\nother reservoirs, as the remainder must be financed by the insurance company. The formulas and assumptions used in the\npaper are reasonable, but are not completely illustrative of this fundamental driver. They should highlight in their discussion\nhow much of the payouts would come from provided through other reservoirs premiums, and how much would need to be\nfinanced by insurance companies comparing pooled and non-pooled setups based on historical burn, prior to assuming\nloading and distributional weighting."}, "author_response": "Response to Reviewers for: Using Remote Sensing to Develop a Global\nRisk Pool for Hydropower-Dependent Countries\nWe would like to express our appreciation to the reviewers and editors for their time and\ninsights. The comments and questions have helped hone the message of the manuscript and\nclarify the original takeaways.\nThe responses below show reviewer comments in blue font and the authors’ responses in\nregular black font. Reviewer comments refer to the line, section, and figure numbers of the\noriginal manuscript while references to changes made refer to the newly revised manuscript,\nwithout tracked changes. Any articles mentioned in the responses below are cited in a separate\nbibliography at the end of this document. Revised excerpts show added text in red and deleted\ntext as red, with a strikethrough .\nReviewer #1\nDear Authors,\nThanks for this interesting submission which is methodologically robust and very policy\nrelevant. I hope you will engage with relevant international bodies (e.g., International\nHydropower Association) and financiers (e.g., World Bank) to share your framework and apply\nit in practice. I made a few minor suggestions in the attached file for your consideration.\nBest regards,\nEdoardo Borgomeo\nThank you Dr. Borgomeo – it is indeed our hope that this paper (at least the ideas underlying\nit) can be of practical use to international organizations, and we are grateful for this affirmation.\nReviewer #1 (Remarks on code availability):\nLibrary is well structured and readme file is ok.\nThe paper ‘Using remote sensing to develop a global risk pool for hydropower-dependent\ncountries’ presents an innovative framework to mitigate financial risks to hydropower\nproduction worldwide. The paper presents a significant advancement to the field, it’s very well\nwritten, clear and methodologically robust. Having worked at the World Bank for a good part\nof the last decade, I can attest that this type of work has tremendous relevance for\ngovernments in low-income countries that rely on hydropower (or other renewable energy\nsources, as this framework can also be applied to wind production, for example). I think the\npaper should be accepted pending some minor revisions and clarifications. Below I provide\nsome minor comments for the authors’ consideration.\n• Title. Titles are important and I think the current title does a disservice to the paper.\nCould the authors use a more direct title to convey the essence of the findings? For\nexample, ‘Global risk pooling helps mitigate climate-related financial risks for\nhydropower-dependent countries’ or something like that.\nWe appreciate the point on the title and have modified it to:\nGlobal Risk Pooling Can Mitigate Drought-Related Financial Risk for Hydropower-Dependent\nCountries\n• Input data. I have gone through the data and methods section, and find the proposed\ndata sets and approach appropriate given the global scope of the study. However, I was\na bit surprised that the authors did not include any global streamflow dataset. For\nexample, reanalysis datasets (e.g., Alfieri et al. 2020; Bosmans et al. 2022 for projections)\nor other hydrological datasets being developed for machine learning type of analysis\n(E.g., Chen et al. 2023). It would be great if the authors could explain briefly why they\ndecided not to use streamflow data. I understand the focus is on remote sensing, but I\nthink we agree that an index should be developed on best available evidence,\nirrespective of the data collection approach.\nWe did consider the use of reanalysis data but ultimately decided that it was important\nto use data that extended until at least 2020 to provide more recent overlap with other\ncritical datasets used in this work. The reanalysis dataset constructed by Alfieri et al.\n(2020), for example, provides data from 1980, but ends in 2018. The Global Runoff Data\nCentre has additional useful hydrologic data, but it ends in 2019. Chen et al. (2023a)\ndeveloped another notable dataset, but of the countries included, only 6 have data for\nstreamflow stations between 2000 and 2020. Considering that the remotely sensed\nhydrometeorological data is consistently available from 2002 onwards, inclusion of any\nof these datasets would have reduced the length of our usable historical data.\nIn general, the satellite data used here has the advantage of being consistently and\nglobally available for a longer coincident time period, thereby allowing for the\ndevelopment of indices that capture multiple conditions simultaneously. However, we\nrecognize (and hope) that a future risk pool designed in partnership with participant\ncountries would have access to more recent, higher resolution data. To reflect this\nreasoning in the text, we have added the following:\no Page 5, lines 122-124: First, country-level index contracts are designed using\nremotely sensed data which, while limited, provide extensive, coincident\nhistorical data with greater temporal and spatial coverage than alternative\nsources, including streamflow reanalysis datasets (e.g., Alfieri et al. (2020)).\no Page 15, lines 331-349: This work has several limitations. First is the level of basis\nrisk and the number of countries in the pool (32% of hydropower-dependent\ncountries), associated with the index insurance contracts. both of which can be\nattributed to the dearth of recent, coincident historical data. Though streamflow\nreanalysis datasets, e.g., Alfieri et al. (2020) or Chen et al. (2023b), can provide\nadditional data, they offer poor geographic coverage and/or are limited to a few\nyears, factors hindering the design of a global pool. In contrast, remotely sensed\ndata provides greater spatial and temporal coverage. The dataset remains limited,\nhowever, meaning that it is unsurprising that indices have high levels of basis risk.\nExisting index insurance products similarly face substantial challenges in managing\nbasis risk, some of which can be mitigated by dynamically adjusting triggers and\nindices throughout the duration of an insurance contract (Palwishah et al., 2023;\nViergutz, 2024). This was the approach taken by CCRIF, whose self-described\n“undesirable” levels of basis risk were improved with continued iterations of its\nmodels (CCRIF, 2023). In the context of this analysis, Whilethe indices\ndeveloped serve as useful starting points; the use additional financial and\nhydrometeorological data available within country is likely to may lead to\nstronger indices, lower basis risk, and more effective insurance contracts. Other\nemerging data sources may serve the same function. For example, the Surface\nWater and Ocean Topography Mission (SWOT) directly measures surface\nwater, and early results suggest that it is able to capture even small variations in\nsurface water extent and elevation (Fu et al., 2024), which could greatly improve\nindex accuracy.\n• Assumption that drought risks are uncorrelated globally. While I would generally agree\nwith the statement made by the authors that drought risks to hydropower are\nuncorrelated globally, there is also lots of research that examines joint occurrence of\nextremes globally, particularly focusing on food production (e.g., Gaupp et al. 2020;\nHasegawa et al. 2022). These papers suggest that risks of simultaneous breadbasket\nfailures cannot be ignored. I would therefore suggest that the authors reflect on this\nissue in their discussion and perhaps suggest refinements to their methodology that will\nimprove the representation of potentially simultaneous hydropower failures.\nThank you for raising this issue, which will likely become even more pressing with a\nchanging climate. Simultaneous hydropower shortfalls would present challenges for\ninsurers, as correlated failures undermine the benefits of risk pooling. From an insurer’s\nperspective, simultaneous failures would increase the level of liquid capital needed to\nprotect against a simultaneous failure. However, so long as there is not a strong\ncorrelation between hydropower shortfalls among all countries, pooling is still a valuable\nand cost-saving approach. In our subset of countries, bilateral correlations based on the\nhistorical data range between -0.66 and 0.83, but the median bilateral correlations for\neach country range between -0.17 and 0.22. The lower range of bilateral correlations\nsuggests that even if national hydropower generation were slightly more correlated than\nthe data show, pooling would still have value.\nTo address these comments, we have added the following text into the discussion\no page 14, lines 327-329: A final consideration may be including countries that are\ndependent on hydropower imports, on which a drought in a hydropower-\ndependent country may have cascading financial impacts.\no Page 15, lines 382-390: A second avenue for future work may explore the\npotential for simultaneous or sequential streamflow shortfalls and hydropower\nfailures. Insurers calibrate the appropriate level of liquid reserves they hold based\non the distribution of potential losses for any given year and this in turn\ninfluences premiums. Were the modeled distribution of losses to prove\ninaccurate (e.g., because of climate change), premiums collected could be\ninsufficient to fully offset payouts. This challenge would be particularly acute if\nperiods of simultaneous shortfalls across the pool, or sequential shortfalls that\ndrew down reserves year-on-year, occurred more often than projected.\n• Other aspects of the water-energy nexus. The approach proposed here would be very\nrelevant also for thermal power generation, which in places like the US is very\nvulnerable to droughts (e.g., Van Vliet 2016). The authors might wish to mention similar\nadditional applications.\nThe reviewer is correct in noting that this approach could be replicated across many\nsectors and locations. To that end, we have added text into the discussion page 14, lines\n319-325:\nThermal generators are also impacted by extreme weather, including by droughts and\nheatwaves, as these can reduce access to cooling water and thereby inhibit power\ngeneration and lead to economic losses (Byers et al., 2020). Inclusion of thermal\ngenerators in the risk pool would further grow the size thereof. That said, the sources’\nparallel vulnerability to drought may impact a country's risk contribution to the pool by\nincreasing the magnitude of payouts during drought years.\n• Conceptual figure. The authors might wish to consider including a summary figure at the\nstart of the paper that shows how financial risks to hydropower from drought can be\nmanaged, including through a global risk pool (such as Figure 1 in Mechler et al. 2014).\nThis could expand what is currently Figure 5 of the methods.\nThank you for this suggestion. We have added a new figure on page 4 to illustrate\ndifferent risk management approaches.\nFigure 2. The risk of high probability, low impact events is typically managed using risk\nreduction or risk retention. Risk transfer via either individual insurance or risk pooling is\nbest suited for low probability, high impact events. Dams represent hydropower-\ndependent countries.\n• Figure 1. Did the authors search for any more recent data from the international energy\nagency on total generation from hydropower?\nThere is IEA data available through 2024 on hydropower generation, but it is only\navailable upon payment. Our intent was to exclusively use open access data, recognizing\nthat a pooling strategy, if implemented by an international finance institution in\npartnership with individual countries, would rely on more data than is publicly available\non a consistent basis. That said, we realize that the data had not been updated since we\ninitiated the work, and the International Renewable Energy Agency has released\nelectricity generation data through 2023 as of the time of this review (IRENA, 2024).\nThe revisions to this analysis now include the updated data through 2023. Each index\nwas refined and updated using the new data points, as can be seen in the revised Figure\n3. Though two indices were dropped (Namibia and Sweden), we were able to develop\nindices for three additional countries (Norway, Panama, and Pakistan). All results have\nbeen updated accordingly, though the tables and figures are not highlighted in red. Note:\nto make the data consistent, we have opted to update all of the land surface\ntemperature data to 0.05 degrees\nFig. 3 Performance of indices along with regression formula. Variables are averaged at\nthe country level or, when ending with \"_4\", at the subbasin scale, using the subbasin\nwith the greatest number of hydroelectric dams. Seasons reflect Northern Hemisphere\nmonths (e.g., winter indicates December-February).\n• Link between r2 and hydropower characteristics. Figure 2 and section 2.1 show that r2\nis >0.35 only for some countries. Is there any particular pattern behind the countries for\nwhich r2 is >0.35? Are these countries where there are just a few, large hydropower\nfacilities (e.g. Kariba in Zambia, Itaipu in Paraguay). It could be interesting for the authors\nto assess whether there is any correlation between number/size of hydropower facilities\nand the performance of the indices.\nWe were also interested in identifying whether index creation was more successful in\nsome groups of countries or not. We attempted to break countries into groups based\non which variable most closely correlated with generation, or what season was most\ncommon, but there was no discernable pattern. We had not considered the\nnumber/size of hydropower facilities, which is an interesting question. The point proves\ntrue – 13 of the 17 countries for which indices were developed have fewer than three\ndams whose ‘Main’ or ‘Major’ purpose is to generate hydroelectricity (as categorized in\nthe Global Reservoir and Dam Database database). One exception to this rule, Albania\nhas a greater number of dams, but on fewer than three rivers. Of the pool participants,\nonly Norway has both a large number of hydroelectric dams and a large geographic\nspread of these dams. Together, the number of hydroelectric dams and the number of\nrivers can be used in a logistic regression to predict the significant countries, with an\naccuracy of 80% and an area under the receiver-operating characteristic curve (ROC) of\n66%. These metrics suggest the two factors are indicative of whether an index can be\nformulated for a country, though they are not conclusive; 14 additional hydropower-\ndependent countries have fewer than three hydroelectric dams though no viable index\nwas created for them. Many thanks to the reviewer for raising this point.\nTo reflect on this point, we have added the following text (page 6, lines 159-169):\nOf the countries considered, 176 have indices with r2 values > 0.35 (see Figure 2) and\ntrigger at least one payout during the 21 year historical timeseries (2002-2023). This\nthreshold with r2 > 0.35 (see Figure 2), a level corresponding corresponds to the low\nend of commercially available index insurance contracts (Gong et al., 2023; Jensen et al.,\n2016; Tsay & Paulson, 2024), and trigger at least one payout during the 18-year historical\ntime series (2002-2020). Notably, 77% of the 18 countries in our pool have fewer than\nthree dams whose ‘Main’ or ‘Major’ purpose is to generate hydroelectricity (as\ncategorized in the Global Reservoir and Dam Database (GRaND) database). The\nremaining four participants (Norway, Albania, Croatia, and Georgia) have a greater\nnumber of dams, though only Norway has dams on more than 5 rivers, as designated by\nthe GRaND database. This suggests that future efforts to form risk pools might initially\nfocus on countries with concentrated hydroelectric facilities.\nReviewer #2\nThe study described in the manuscript titled ‘Using Remote Sensing to Develop a Global Risk\nPool for Hydropower-dependent Countries” develops hypothetical index insurance contracts\nto insure hydropower-dependent countries against financial risks associated to drought.\nThe study analyzes the potential benefits of these contracts for individual countries and within a\nglobal risk pool in comparison with self-insurance via a reserve fund. The results indicate that\nreasonably accurate contracts could be developed for 16 countries out of the 56 hydropower-\ndependent countries. For these 16 countries, pooling the index-insurance contracts could lead\nto relevant average savings (68%) relative to individual country risk management using reserves.\nLess significant comparative advantages are also estimated with individual index-insurance\ncontracts, but the benefit is contingent on the level of average returns (interest rates) used to\ncalculate the opportunity cost of reserves.\nThe topic of this study is certainly of interest for the disaster risk financing research and\nprofessional global community from an operational perspective. However, the paper misses a\nclear review of the state of the art of scientific research related to the specific topic and does\nnot clearly highlight what the cutting-edge innovative scientific contribution of the study is, and\nwhy this can be relevant for a broad scientific audience. This is a major drawback.\nThe overall technical quality and readability of the manuscript is good, and results are presented\nand discussed in a clear way.\nHowever, there are some major methodological issues to highlight:\n- It is clear that for most hydropower-dependent countries considered (40 out of 56) the\ncontract accuracy in predicting hydropower generation and revenues does not meet\neven the low requirements (i.e. model R2 > 0.35 and one historical payout triggered)\nset in this study to assess the contract suitability for commercial implementation. This\ntopic is barely discussed and analyzed.\nThe reviewer makes a good point, and we have added the following text to address\nthese concerns (pages 14-15, lines 330-348). We would also like to note that use of two\nadditional years of data enabled us to refine the pool, such that the total number of\ncountries included is now 17. Greater availability of data, offered by host countries or\ncollected over time, will continue to strengthen the indices and extend the effectiveness\nof the pool.\nThis work has several limitations. First is the level of basis risk and number of countries\nin the pool (32% of hydropower-dependent countries), associated with the index\ninsurance contracts. both of which can be attributed to the dearth of recent, coincident\nhistorical data. Though streamflow reanalysis datasets, e.g., Alfieri et al. (2020) or Chen\net al. (2023b), can provide additional data, they offer poor geographic coverage and/or\nare limited to a few years, factors hindering the design of a global pool. In contrast,\nremotely sensed data provides greater spatial and temporal coverage. The dataset\nremains limited, however, meaning that it is unsurprising that indices have high levels of\nbasis risk. Existing index insurance products similarly face substantial challenges in\nmanaging basis risk, some of which can be mitigated by dynamically adjusting triggers and\nindices throughout the duration of an insurance contract (Palwishah et al., 2023;\nViergutz, 2024). This was the approach taken by CCRIF, whose self-described\n“undesirable” levels of basis risk were improved with continued iterations of its models\n(CCRIF, 2023). In the context of this analysis, Whilethe indices developed serve as\nuseful starting points; additional financial and hydrometeorological data available within\ncountry is likely to may lead to stronger indices, lower basis risk, and more effective\ninsurance contracts. Other emerging data sources may serve the same function. For\nexample, the Surface Water and Ocean Topography Mission (SWOT) directly measures\nsurface water, and early results suggest that it is able to capture even small variations in\nsurface water extent and elevation (Fu et al., 2024), which could greatly improve\nindex accuracy.\n- The requirements for index-insurance contract acceptability set in this study are low\nand, according to Authors, all contracts are “in the low end of acceptability of\ncommercially available contracts”. To support the choice of the requirements, the\nAuthors cite selected paper from the index-insurance literature. However, these papers\nare all related to crop index-insurance and it is not very clear how the threshold was\nultimately set.\nThe minimum r2 requirements for the indices are based on available literature on\nimplemented contracts. While the examples cited are indeed related to crop index\ninsurance, that is because index insurance is most commonly used in agriculture, with\nmajor sub-national and international programs including from the US Department of\nAgriculture’s Risk Management Agency, the Global Index Insurance Facility, the\nCaribbean Catastrophe Risk Insurance Facility, and the African Risk Capacity. Part of the\nnovelty of this paper is applying index insurance to hydropower at the national level, an\napplication with very few historical examples. The primary example in the hydropower\nsector, is the insurance contract offered by the World Bank and Swiss Re for\nhydropower in Uruguay (Swiss Re, 2018; The World Bank, 2013). However, we have\nbeen unable to find detailed information on the index or the contract’s efficacy. A final\npoint is that even with the levels of basis risk seen in our analysis, the pool is still able to\nprovide payouts and reduce premiums (loading) for participant countries, a proof of\nconcept that may justify countries’ interest in insurance and a pool. Put into practice,\nthe insuring party would most likely have access to higher quality data from individual\ncountries, which would reduce basis risk and further increase the value of the pool.\nWe would also like to clarify the meaning of the quote referenced by the reviewer:\nOf the countries considered, 16 have indices with r2 > 0.35 (see Figure 2), a level corresponding\nto the low end of commercially available index insurance contracts (Gong et al., 2023; Jensen\net al., 2016; Tsay & Paulson, 2024), and trigger at least one payout during the 18-year\nhistorical time series (2002-2020).\nOur reference to the low end of commercially available index insurance contracts is\nlinked to the minimum r2 (0.35), not to each of the contracts designed. The contracts in\nthis work have r2 values ranging from 0.43 to 0.81. To clarify this, we have modified the\nsentence:\nOf the countries considered, 176 have indices with r2 values > 0.35 (see Figure 2) and\ntrigger at least one payout during the 21 year historical timeseries (2002-2023). This\nthreshold with r2 > 0.35 (see Figure 2), a level corresponding corresponds to the low\nend of commercially available index insurance contracts (Gong et al., 2023; Jensen et al.,\n2016; Tsay & Paulson, 2024), and trigger at least one payout during the 18-year historical\ntime series (2002-2020).\nIt seems that contracts which such a high uncertainty might not be easily acceptable for\nindex-insurance schemes adopted at country level for a strategic and economically\nrelevant sector like hydropower, especially for countries having access to relatively high-\nquality data. This uncertainty is also not taken into account in the comparison between\nindex-insurance and self-insurance, while it might be a relevant factor to consider for\nthe insurance pricing (as well for the willingness to purchase by countries). While the\nAuthors correctly recognize that the quality of the proposed contract is a limitation of\nthe study, a more in-depth analysis of basis risk would be essential to support the\nfindings of this study and the broad suggested implications (i.e. that a pooled index-\ninsurance product can be an effective tool for improving the financial stability of\nhydropower-dependent countries)\nThe reviewer makes a fair point that basis risk is a major challenge for parametric and\nindex insurance products. The pool we propose provides an illustrative case of the\npotential of pooling. Were countries to join a risk pool, it is natural that they would\ncontribute higher resolution and quality data, thereby reducing the basis risk involved.\nYet even with the notable levels of basis risk for some of the indices, the cost of pooled\ninsurance is ~30% of the opportunity cost of holding reserves, when the strike is set to\ncover the same level of financial losses (seen in Figure 4 of the original manuscript, now\nFigure 5). The addition of higher quality data would only make index insurance more\nattractive, as the basis risk associated with the contracts falls. One long-running risk\npool protecting against hurricane-related financial losses, the Caribbean Catastrophe\nRisk Insurance Facility (CCRIF), explicitly describes this evolution. A CCRIF report\nnotes that the original models and indices had “undesirable” levels of basis risk\n(unquantified in the report), which were improved with each iteration of the insurance\nproducts (CCRIF, 2023).\nThe following text has been modified to address the reviewer’s comment:\no Pages 14-15, lines 330-348 This work has several limitations. First is the level of\nbasis risk and number of countries in the pool (32% of hydropower-dependent\ncountries), associated with the index insurance contracts. both of which can be\nattributed to the dearth of recent, coincident historical data. Though streamflow\nreanalysis datasets, e.g., Alfieri et al. (2020) or Chen et al. (2023b), can provide\nadditional data, they offer poor geographic coverage and/or are limited to a few\nyears, factors hindering the design of a global pool. In contrast, remotely sensed\ndata provides greater spatial and temporal coverage. The dataset remains limited,\nhowever, meaning that it is unsurprising that indices have high levels of basis risk.\nExisting index insurance products similarly face substantial challenges in managing\nbasis risk, some of which can be mitigated by dynamically adjusting triggers and\nindices throughout the duration of an insurance contract (Palwishah et al., 2023;\nViergutz, 2024). This was the approach taken by CCRIF, whose self-described\n“undesirable” levels of basis risk were improved with continued iterations of its\nmodels (CCRIF, 2023). In the context of this analysis, Whilethe indices\ndeveloped serve as useful starting points; additional financial and\nhydrometeorological data available within country is likely to maylead to\nstronger indices, lower basis risk, and more effective insurance contracts. Other\nemerging data sources may serve the same function. For example, the Surface\nWater and Ocean Topography Mission (SWOT) directly measures surface\nwater, and early results suggest that it is able to capture even small variations in\nsurface water extent and elevation (Fu et al., 2024), which could greatly improve\nindex accuracy.\n- In addition to the previous consideration, the description of the contract design is\nlimited and R2 is the only performance indicator presented to compare multivariate\nmodels. This is a strong limitation, especially considering that multiple linear regression\nmodels are developed using a data limited time series (18 years), with risk of overfitting\nand violation of regression assumptions. A much more in-depth analysis of the model\nuncertainty would be important to support the potential effectiveness and commercial\nvalue of the proposed contracts.\nAlthough we omitted mention of this in the original text, we also conducted leave-one-\nout cross-validation, judging accuracy using mean absolute error (MAE). Only two\ncountries had a MAE > 0.10 (Zimbabwe – 0.14, Uruguay – 0.10) with respect to the\nprediction for capacity factor, which ranges from 0 to 1.\nWe have added text to that effect on page 6, lines 171-174:\nAdditional leave-one-out cross-validation provides further confidence in these indices, as\nall indices have mean absolute errors of < 0.14, relative to the capacity factor range of\n0-1. The Normalized Nash-Sutcliffe Efficiency for each index lies between 0.51 and 0.72,\nindicating adequate fit.\nWe have added additional statistical tests for normality in Appendix B. Most countries\nfail to reject the null hypothesis of normality in all tests, although some fail one out of\nthree tests. While this adds uncertainty to the analysis, we do not believe it alters the\nconclusion that bundling the risk faced by hydropower-dependent countries can lead to\nreduced cost of risk management.\nAppendix B Additional Statistical Tests\nIndices were developed using a criteria of r2 > 0.35 in the training and testing datasets as\nwell as overall. Additional metrics were used to evaluate normality, heteroskedasticity,\nand accuracy, as seen in Table B1. Generation data for most countries shows evidence\nof normality, though some fail one out of three tests. While this adds uncertainty to the\nanalysis, we do not believe it alters the conclusion that bundling the risk faced by\nhydropower-dependent countries can lead to reduced cost of risk management.\nTable B1. Metrics evaluating hydropower capacity factor data normality and\nhetereoscedasticity as well as index performance. The Anderson-Darling test\nis evaluated with respect to p = 0.01\nD'Agostino- Anderson- Normalized\nWhite Breusch- Shapiro- Pearson Darling Nash-Sutcliffe\nTest Pagan Test Wilk Test Test Test MAE Efficiency\nAlbania 0.69 0.36 0.44 0.59 normal 0.07 0.52417\nAngola 0.20 0.12 0.02 0.31 normal 0.07 0.57\nChile 0.38 0.45 0.09 0.32 normal 0.05 0.737\nCosta\nRica 0.67 0.62 0.19 0.06 normal 0.03 0.66284\nCroatia 0.19 0.40 0.28 0.43 normal 0.05 0.72864\nEcuador 0.40 0.81 0.51 0.40 normal 0.04 0.70617\nGabon 0.16 0.76 0.01 0.18 normal 0.08 0.62\nGeorgia 0.53 0.30 0.87 0.88 normal 0.02 0.67732\nLatvia 0.71 0.80 0.73 0.55 normal 0.03 0.62356\nNorway 0.64 0.23 0.37 0.27 normal 0.02 0.63348\nPakistan 0.46 0.63 0.04 0.26 normal 0.05 0.57454\nPanama 0.26 0.54 0.04 0.21 normal 0.04 0.62603\nParaguay 0.31 0.42 0.05 0.18 normal 0.05 0.69738\nSuriname 0.63 0.42 0.24 0.13 normal 0.06 0.58846\nTajikistan 0.28 0.06 0.01 0.17 normal 0.03 0.52542\nUruguay 0.69 0.32 0.22 0.17 normal 0.11 0.61503\nZambia 0.48 0.76 0.88 0.95 normal 0.04 0.52928\nZimbabwe 0.17 0.14 0.06 0.21 normal 0.14 0.52\n- Remaining in statistical methods, the analysis of correlations between national level\ncapacity factors is also unclear (Figure 4). In the text the Authors state that -0.84 is “a\nlow correlation”, while it is a high negative correlation. Then it seems that the\naverage between negative and positive correlations is done, while the absolute values should be\nconsidered. Perhaps this is just a misunderstanding.\nThank you for pointing out this misrepresentation – the average of the absolute values\ndoes not adequately convey the existence or lack of correlations. To be more clear, we\nhave modified the text in two places:\no Pages 21-22, lines 592-606): Thus, one important factor in determining the\neffectiveness of a risk pool is the level at which losses are uncorrelated across\nparticipants. The degree to which the pool diversifies the risk of losses depends\non this lack of correlation, and benefits from negative correlations (Ciullo et al.,\n2023)., and therefore the degree of diversification of risk achieved by the pool\n(Ciullo et al., 2023). Figure 7 shows correlations between annual hydropower\ncapacity factors in hydropower-dependent countries. Although some countries\nexperience correlations of up to 0.89, others experience correlations as negative\nlow as -0.83 4, with a median correlation of 0.75. an average correlation of 0.06.\nThough this work attempted to design indices for all hydropower-dependent\ncountries, only indices for 1816 countries met the criteria of r2 > 0.35, with less\nthan four indicator variables, and triggered payouts in at least one year. This\nsubset of countries exhibits a similar range of bilateral correlations compared to\nthe full set has comparable levels of correlations, ranging from 0.89 to -0.72\nwith a range of 0.83 to -0.66 and, with a median correlation of 0.1. of n average\nof -0.05. For individual countries, median bilateral correlations range between\n0.22 to -0.17 . The low, and often negative, median level of correlation suggests\nthat a risk pool could be effective in reducing the aggregate reserves necessary\nto provide a defined level of risk management.\n- It is also not very clear how the different remote sensing indicators were processed and\naggregated spatially and temporarily for each of the country models. Some information\nis provided in Appendix A, but the details provided do not allow reproducing the indices\nand evaluating specific technical choices made in the contract technical design. This is a\nvery critical step that can affect the overall quality of the index-insurance contract and\nshould be presented and discussed in more detail.\nThanks to the reviewer for pointing this out. An explicit listing of the steps is provided below\nand has now been added to the appendix with a parenthetical comment in the main body of the\ntext pointing the reader toward the appendix (page 26, lines 701-716).\nIn summary, the indices were designed using the following steps:\n1. Calculate the annual capacity factor for each hydropower-dependent country\n2. Extract the average precipitation, land surface temperature, snow cover extent,\nand vegetation indices across two spatially bounded areas at the temporal level\nof the data (monthly). Data was not additionally filtered after download.\na. Within country (political borders)\nb. Within the boundaries of the Level 4 subbasin in which the majority of a\ncountry’s dams reside\n3. Temporally aggregate the spatially aggregated data in two ways:\na. Aggregate at the seasonal level (i.e., winter, spring, summer, fall)\nb. Take the annual average of the spatially aggregated data\n4. Evaluate the accuracy of a linear regression using any combination of variables. A\ntraining/test set split of 80/20 was used. This process was done automatically\nusing a Python script that saved the combination meeting the test criteria of >\n0.35 r2 and less than four input variables.\n5. Manually verify the accuracy of each index\nOther aggregations were tested. For example, the maximum of the hydrometeorological\nvariables as opposed to the average and a seasonal aggregation\n(fall/winter/spring/summer), but these aggregations did not result in more accurate\nindices, and so they were omitted in the final analysis.\nTo clarify the process used to aggregate each indicator, we have also added the\nfollowing:\no Pages 19-20, lines 534-549, description of payout equation (note, the equation\norder has been reversed):\nThe hHistorical capacity factor dataset is used to set a cap on payouts, using the\n99.5% VaR:\n𝑣 ($) = (𝑎𝑣𝑔 −𝑐𝑓 )∗𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 ∗8760∗𝐿𝐶𝑂𝐸\n𝑖,𝑦 𝑖 𝑖,𝑦 𝑖\n0 ≤ 𝑣 ≤ 𝑐𝑎𝑝 , 𝑖𝑓 𝑐𝑓 < 𝑘\n𝑖,𝑦 𝑖 𝑖,𝑦\n𝑝𝑎𝑦𝑜𝑢𝑡 = {\n𝑖,𝑦\n0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒\nwhere v is the predicted value for the financial shortfall country i faces in year y;\ncf is the capacity factor as calculated by the index; and capacity (MW) is a\ncountry's hydropower capacity in 2020. dollar value of the insurance contract's\npayout; cap ($) is the maximum payout for country i, set using the 99.5% VaR for\ncapacity factor; cf is the capacity factor as calculated by the index in year y; k is\nthe strike (set to the 20th% of capacity factor); and capacity (MW) is a country's\nhydropower capacity in 2020. Because there are no negative capacity factor\nvalues, the hydropower shortfall is calculated as the difference between the\naverage capacity factor (avg) and the index-calculated capacity factor for a given\ni\nyear. This value is multiplied by maximum annual potential hydropower\ngeneration -- the product of hydropower capacity (MW) and the number of\nhours in a year (8760) -- and by the LCOE ($/MWh) to calculate the insurance\npaymentv, which is intended to offset the hydropower shortfall. The final payout\nis triggered by the strike, k (set to the 20th% of capacity factor) and capped using\nthe 99.5% VaR for capacity factor cap ($).\no Pages 17-18, lines 449-458, in reference to the snow cover extent,\nvegetation index, land surface temperature, and precipitation\ndatasets): These five datasets are aggregated at several temporal (i.e., seasonal\nand annual) and spatial scales. Temporal averaging is undertaken at the seasonal\n(i.e., winter, spring, summer, fall) and annual timestep. Spatial averaging is based\non hydrologic unit boundaries from the HydroBASINS dataset (Lehner & Grill,\n2013), which delineates subbasins by the location where two river branches\nmeet, given a minimum upstream area of 100 km2. Units are categorized into 12\nlevels ranging from the continental to the local watershed levels, with sub-\ncontinental and regional level basin scales used for this analysis. Data is\nadditionally averaged within country borders. See Appendix A for more details\non spatial and temporal averaging, as well as for a map of the level 4 subbasins\nused for each country.\no Pages 25-26, lines 682-700): The above hydrometeorological data is aggregated\ntemporally and spatially to provide possible inputs to an index. Temporally, data\nis averaged over the monthly and seasonal timescales. Use of the maximum and\nminimum values for each variable were also tested, but use of these variables\nprovided no improvement on the indices. The data is then spatially aggregated in\ntwo ways: using country borders and subbasin boundaries. The HydroBASINS\ndataset developed by (Lehner & Grill, 2013) identifies different sizes of subbasins\nusing the location where two river branches meet, given a minimum upstream\narea of 100 km2. SubbasinsUnits are categorized into 12 levels according to the\nPfafstetter system, ranging from the continental to local watershed levels. Level\n4, which represents regional level basins, is used in this analysis.\nHydrometereological variables are averaged at each of these hydrologic\nunits.The single level 4 basin within each country withthat has the largest\nconcentration of hydroelectric dams is identified in order to spatially aggregate\nenvironmental condition inputs. The Global Reservoir and Dam Database\n(GRanD) is used for this purpose (Lehner et al., 2011). It includes records on\nnearly 7,000 reservoirs and their dams, as well as information on their purposes.\nOnly dams whose primary purpose is hydropower generation are included in the\nanalysis. Once the level 4 subbasin of interest is identified, available, pixel-level\nhydrometeorological data (i.e., temperature, precipitation, snow cover, and\nvegetation indices) is averaged across the entire subbasin. The variables are\naveraged within country borders as well, providing a single average\nhydrometeorological value at two spatial scales and two temporal scales. In\nsummary, two spatial scales are used as inputs to the indices: average\nenvironmental conditions at the national level and at the subbasin level.\nFigure A1. Map with level 4 subbasins used to spatially aggregate remotely sensed data inputs\nhighlighted in purple.\nReviewer #3\nThe manuscript is well written, relevant, and valuable and provides a useful analysis for the\naudience.\nI have two items for the authors to address:\n1) My understanding is that there is an active weather derivatives market for hydropower,\nand note power derivatives in the early 2000s was part of the motivation for index\ninsurance. In a quick search, I see that EEX European Hydro Power Go appears to be an\nactive product. It may be that derivatives are a more appropriate mechanism for\nhydropower than insurance, but since the math stays the same, their paper is just as\nrelevant. The authors should reference these markets, discuss their gaps and relevance,\nand connect their work to the derivatives market.\nAs the reviewer notes, the math underlying derivatives and insurance is, in practice, identical.\nAn important distinction between the two, however, might be that weather derivatives are\npublicly traded, while index-based insurance contracts are sold on an individual basis either as\nbespoke contracts or through individual agencies (e.g., the US Department of Agriculture’s Risk\nManagement Agency).\nThank you for bringing the EEX Hydro Power GO product to our attention. The GO\n(Guarantees of Origin) products are used to attribute the generation source used for a given\nunit of electricity meeting demand for buyers seeking to source a certain percentage of\nelectricity from renewable energy sources. Their stated purpose is to track energy production\n(eex group, 2024), and so they appear to fulfill a different purpose than insurance or similar\nderivatives.\nTo address some of these points, we have added the following to the Introduction (page 4,\nlines 92-95):\nThe pre-set trigger and payment structure can also reduce administrative costs for the insurer\nand therefore the buyer. Contracts using weather-based indices can be compared to weather-\nbased derivatives (Hertzler, 2004; The World Bank, 2023; Zeng, 2000), which emerged in the\n2000s to mitigate risk for power utilities and generators experiencing fluctuations in electricity\nuse (and revenues) based on daily temperatures.\n2) The key driving factor for price savings is how much of the total payouts in the portfolio are\ncovered by the premiums from other reservoirs, as the remainder must be financed by the\ninsurance company. The formulas and assumptions used in the paper are reasonable, but are\nnot completely illustrative of this fundamental driver. They should highlight in their discussion\nhow much of the payouts would come from provided through other reservoirs premiums, and\nhow much would need to be financed by insurance companies comparing pooled and non-\npooled setups based on historical burn, prior to assuming loading and distributional weighting.\nAs the reviewer surmised, this analysis assumes sufficient initial capital to provide payouts for\ncountries in year 1, when premiums paid may be insufficient to cover payouts. In addition, we\ndo not model time-dependent changes in premia, which can be triggered by the previous year’s\npayouts when/if the total capital available to insurers falls (Heinrich et al., 2022). We believe the\nanalysis remains reasonable and significant regardless because a risk pool of this magnitude (the\nnational scale) would most likely be implemented by large international (re)insurers, perhaps in\nconjunction with international finance institutions like the World Bank. This category of\n(re)insurer has large, extant capital supplies and a well-diversified portfolio, able to absorb the\nrisk of an additional, uncorrelated loss (i.e., drought for hydropower). The 2018 index\ninsurance contract deployed to manage the impacts of droughts on Uruguay’s hydropower\nfollowed this model, as it was developed by Swiss Re and the World Bank (Swiss Re, 2018).\nSwiss Re similarly worked with the Government of Mexico and the World Bank to insure\nnatural perils via The Fund for Natural Disasters of Mexico (FONDEN) (Difiore & Drui, 2020;\nWorld Bank, 2020). We have added the following on pages 13-14, lines 291-303:\nCountries are heeding these recommendations, joining regional risk pools like CCRIF and\nPCRIF or purchasing index-based instruments to manage the risk of natural hazards such as\ndroughts, earthquakes, floods, tsunamis, and windstorms (Cooney et al., 2022; InsuResilience,\n2021). Partnerships between a large international finance institution (e.g., the World Bank) and\nlarge (re)insurers (e.g., Swiss Re) have enabled the development of these tools, taking advantage\nof the financial stability of the former in combination along with the access to capital and well-\ndiversified portfolio of the latter. This type of partnership has been applied to insure Uruguay's\nhydropower sector against the risk of drought (Swiss Re, 2018), as well as to insure against\nmultiple natural hazards in Mexico, via The Fund for Natural Disasters of Mexico (FONDEN)\n(Difiore & Drui, 2020; World Bank, 2020). At a broader level, national- and regional-level risk\npools are exploring joint reinsurance facilities to further diversify their risk (Evans, 2023)\nreducing the levels of needed reserves and therefore lowering costs of risk management to\npool participants."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Dear authors,\nI have reviewed your responses and revised manuscript, and I don't have any further comments.\nThanks for Figure 2, which I think will help readers immediately understand the value of what's\nbeing proposed here.\nIt has been a great pleasure reading this work, and I wish you all the best with the\ndissemination. Thanks for your excellent submission.\nBest regards,\nEdoardo\n(Remarks on code availability)\nThe code is available and the readme file well structured. Authors need to make sure they\nupdate the file names with the latest manuscript title.", "reviewer_2": "Dear Authors,\nThank you for addressing my comments in a careful manner. The manuscript quality and clarity\nhave improved.\nI have a couple of remaining points to clarify:\n- On the cross-validation, the Authors mention they have used a leave one out cross-validation.\nHowever, in the Appendix A a 80%-20% splitting approach is mentioned. It is also unclear if the\nR2 presented in Figure 3 refers to cross-validated models or fitted models.\n- The choice of a fixed season for temporal aggregation is somewhat questionable, especially in\nterms of rainfall distribution. The concept of spring, summer, fall, winter works mainly for mid-\nlatitude countries, while it can be very different for tropical or equatorial countries. In addition,\nthere are major geographic changes in seasonality due to a number of factors. Improving the\ntemporal aggregation by defining the correct seasonality for each country might significantly\nimprove the model performance.\nSpecific comments\nLine 107: 27%\nLine 181: 17 countries\nLine 241: increases", "reviewer_3": "The authors have addressed my points adequately for moving forward.\nAlthough the requested analysis on risk pooling was not performed (as far as I could see), an\nadequate discussion was included.\nI do believe that the manuscript would be of more value to the audience (including the re-insurrers and risk pools now cited) if there was analysis on the reduction in risk costs if the reservoirs were pooled together verses priced individually.\nI do not think that the time-dependent changes mentioned in the authors response are an important connection to this\nquestion."}, "author_response": "Response to Reviewers for: Global Risk Pooling Can Mitigate Drought-\nRelated Financial Risk for Hydropower-Dependent Countries\nDear reviewers,\nThank you for reviewing our paper once more. We are glad we were able to address most of\nyour comments and hope you will find the additional revisions satisfactory. Your comments\ncontinue to strengthen the manuscript and its future utility.\nThe responses below show reviewer comments in blue font and the authors’ responses in\nregular black font. Reviewer comments refer to the line, section, and figure numbers of the\noriginal manuscript while references to changes made refer to the newly revised manuscript,\nwithout tracked changes. Any articles mentioned in the responses below are cited in a separate\nbibliography at the end of this document.\nReviewer #1 (Remarks to the Author):\nDear authors,\nI have reviewed your responses and revised manuscript, and I don't have any further comments.\nThanks for Figure 2, which I think will help readers immediately understand the value of what's\nbeing proposed here.\nIt has been a great pleasure reading this work, and I wish you all the best with the\ndissemination. Thanks for your excellent submission.\nBest regards,\nEdoardo\nThank you Edoardo! We appreciate your comments. The figure was an excellent idea and we\nexpect it will be useful for many a presentation in addition to this paper.\nReviewer #1 (Remarks on code availability):\nThe code is available and the readme file well structured. Authors need to make sure they\nupdate the file names with the latest manuscript title.\nThe title on the GitHub has been updated – thank you for catching that!\nReviewer #2 (Remarks to the Author):\nDear Authors,\nThank you for addressing my comments in a careful manner. The manuscript quality and clarity\nhave improved.\nI have a couple of remaining points to clarify:\n- On the cross-validation, the Authors mention they have used a leave one out cross-validation.\nHowever, in the Appendix A a 80%-20% splitting approach is mentioned. It is also unclear if the\nR2 presented in Figure 3 refers to cross-validated models or fitted models.\nThank you for the suggestions to clarify our process. We first fit a model using the 80%-20%\ntraining-testing approach. Once the model was fit, we then used LOO cross-validation to\nensure that model accuracy remained acceptable across any 80/20 split. The r2 refers to the\nfitted model while the MAE score is the average across the LOO cross-validated models.\nSection 2.1 has been edited to clarify that the minimum r2 threshold refers to the fitted model,\nwhile the leave-one-out cross-validation refers to a range of training and test set combinations.\nThe minimum r2 threshold for the fitted model limits basis risk, which represents the ability of an index\nto trigger payouts when losses occur and at an appropriate amount. Additional leave-one-out cross-\nvalidation provides further confidence in these indices, as all indices have mean absolute errors (MAE)\nof ≤ 0.14 across a range of training and testing set combinations, relative to the capacity factor range\nof 0-1. The Normalized Nash-Sutcliffe Efficiency for each index lies between 0.52 and 0.74, indicating\nadequate fit.\n- The choice of a fixed season for temporal aggregation is somewhat questionable, especially in\nterms of rainfall distribution. The concept of spring, summer, fall, winter works mainly for mid-\nlatitude countries, while it can be very different for tropical or equatorial countries. In addition,\nthere are major geographic changes in seasonality due to a number of factors. Improving the\ntemporal aggregation by defining the correct seasonality for each country might significantly\nimprove the model performance.\nWe also struggled with how to temporally group data such that we could capture seasonal\neffects without creating an excessive number of potential inputs, especially because we\nexpected that annual values would be more reflective of hydropower capacity factor than\nseasonal alone. We settled on the three-month chunks (seasons) noting that while the label\n“winter” for the months of December-February refers to the Northern hemisphere, the three-\nmonth chunk could remain relevant even where it is in reality summer, and where two seasons\nmattered (e.g., fall into winter), those could be captured as two input variables to the index.\nHowever, as the reviewer notes, the three-month chunks do not necessarily reflect\nhydrometeorological patterns. To that end, we re-evaluated the seasonal groupings for Angola,\nCosta Rica, Ecuador, Panama, Suriname, Zambia, and Zimbabwe – the countries in our pool\nwith dry/rainy seasons that do not align with the four-season aggregations previously used in\nthe analysis. None of the indices improved performance with use of a dry/rainy aggregation,\nneither in terms of r2 nor in terms of statistical significance. Some worsened to a degree. We\nsee two intuitive reasons for this. First, in many cases, the dry versus wet season split is\nequivalent to the average of a winter + spring versus summer + fall (e.g., Costa Rica’s\nDecember – April dry season and May – November rainy season). In these cases, a country’s\nindex might contain inputs aggregated by two seasons. Second, in countries with substantial\nreservoir storage, annual values for precipitation may capture hydropower potential adequately,\nsince the timing of hydropower generation is not dependent on the timing of rainfall.\nSpecific comments\nLine 107: 27% corrected\nLine 181: 17 countries corrected\nLine 241: increases corrected, as “the costs of risk management…increase”\nReviewer #3 (Remarks to the Author):\nThe authors have addressed my points adequately for moving forward.\nAlthough the requested analysis on risk pooling was not performed (as far as I could see), an\nadequate discussion was included.\nI do believe that the manuscript would be of more value to the audience (including the re-\ninsurrers and risk pools now cited) if there was analysis on the reduction in risk costs if the\nreservoirs were pooled together verses priced individually.\nI do not think that the time-dependent changes mentioned in the authors response are an\nimportant connection to this question.\nThank you, Reviewer #3, for your feedback during both rounds of revisions. Your suggestions\nimproved the paper and gave us inspiration for future directions. We have made edits to\nSection 2.2. (below) in order to more clearly address how the magnitude of necessary reserves\nchanges when they are held individually versus pooled, as we agree this is an important point\ndriving the remainder of our findings.\nThe risks of the individual countries, and individual insurance contracts, can be pooled, with premiums\nmodified to reflect the new, aggregate risk of the pool. The impact of pooling insurance contracts\nmirrors the reductions in costs when reserves are pooled instead of individually held.\nThis is because as the number of pool participants grows, the coefficient of variation associated with the\naggregate payout falls, even as the overall, annual expected payouts increase. This can be attributed to\nthe relatively low levels of correlation between each country’s hydropower generation and drives the\ndifference between the reserves necessary to compensate for the 99.5% VaR of the pool and the sum\nof the reserves countries would need to individually hold in order to independently manage their risk.\nFigure 5 shows the reduction in reserves achievable with multiple countries in the pool, whose\ncumulative reserves across all potential participants, if held individually, would amount to $3.9 billion.\nInstead, when reserves are jointly held within a pool, the necessary amount falls by approximately 33%\n($1.3 billion) to $2.6 billion. This corresponds to smaller reserves that an insurer would need to\nmaintain as well, and in a competitive market lower costs for an insurer should lead to lower loading for\npurchasers (Bollmann & Wang, 2019).\nFig. 5: Pooling reserves reduces the levels needed to meet the 99.5% VaR of participating countries\nwhen compared to these countries individually holding reserves. Increasing the number of participants in\na pool leads to greater savings. Values by pool size are calculated as the average savings across\ndifferent combinations of pool participants.\nBibliography\nBollmann, A., & Wang, S. S. (2019). International Catastrophe Pooling for Extreme Weather: An\nIntegrated Actuarial, Economic and Underwriting Perspective. Society of Actuaries."}]

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