Quantifying the potential for reservoirs to secure future surface water yields in the world’s largest river basins

Surface water reservoirs provide us with reliable water supply, hydropower generation, flood control and recreation services. Yet reservoirs also cause flow fragmentation in rivers and lead to flooding of upstream areas, thereby displacing existing land-use activities and ecosystems. Anticipated population growth and development coupled with climate change in many regions of the globe suggests a critical need to assess the potential for future reservoir capacity to help balance rising water demands with long-term water availability. Here, we assess the potential of large-scale reservoirs to provide reliable surface water yields while also considering environmental flows within 235 of the world’s largest river basins. Maps of existing cropland and habitat conservation zones are integrated with spatially-explicit population and urbanization projections from the Shared Socioeconomic Pathways to identify regions unsuitable for increasing water supply by exploiting new reservoir storage. Results show that even when maximizing the global reservoir storage to its potential limit (∼4.3–4.8 times the current capacity), firm yields would only increase by about 50% over current levels. However, there exist large disparities across different basins. The majority of river basins in North America are found to gain relatively little firm yield by increasing storage capacity, whereas basins in Southeast Asia display greater potential for expansion as well as proportional gains in firm yield under multiple uncertainties. Parts of Europe, the United States and South America show relatively low reliability of maintaining current firm yields under future climate change, whereas most of Asia and higher latitude regions display comparatively high reliability. Findings from this study highlight the importance of incorporating different factors, including human development, land-use activities, and climate change, over a time span of multiple decades and across a range of different scenarios when quantifying available surface water yields and the potential for reservoir expansion.


Introduction
Surface water reservoirs help dampen flow variability in rivers while playing a critical role in flood mitigation, securing water supplies, and ensuring reliable hydropower generation. In 2011, total global storage capacity of the largest reservoirs was approximately 6197 km 3 and affected the flow in almost half of all major river systems worldwide (Lehner et al 2011). Changes in natural flow patterns can disrupt local ecosystems (Poff andSchmidt 2016, Richter et al 2012), and inundation of upstream areas during reservoir development can cause conflicts with existing landuses (Richter et al 2010). Reservoirs also require a significant amount of resources to plan, build and operate, with implications for long-term water supply costs and affordability (Wiberg and Strzepek 2005). Quantifying exploitable reservoir capacity is therefore crucial for strategic planning of water, energy and food supplies in the coming decades, particularly with anticipated population growth and exacerbating impacts on hydrological variability due to climate change (Boehlert et al 2015, Kundzewicz and Stakhiv 2010, Soundharajan et al 2016, Stillwell and Webber 2013, Vörösmarty et al 2009. Storage-yield (S-Y) analysis is often used by water resource planners to determine the reservoir storage capacity required to provide firm yield (Rippl 1883, Turner andGalelli 2016). The firm yield represents the maximum volume of water that can be supplied from the reservoir for human purposes (e.g. irrigation, municipal supply, etc.) under a stated reliability. A number of previous studies evaluate different algorithms for modeling the S-Y relationship (Carty and Cunnane 1990), and have included storage-dependent losses (Lele 1987) and generalized functional forms for broader scale application (Kuria and Vogel 2015, Vogel et al 2007, Vogel and Stedinger 1987. For example, McMahon et al (2007) developed six empirical equations to calculate reservoir capacities for 729 unregulated rivers around the world. A number of other previous studies employ S-Y algorithms to provide insight into various water security challenges moving forward. Wiberg and Strzepek (2005) developed S-Y relationships and associated costs for major watershed regions in China accounting for the effects of climate change. Similarly, Boehlert et al (2015) computed S-Y curves for 126 major basins globally under a diverse range of climate models and scenarios to estimate the potential scale of adaptation measures required to maintain surface water supply reliability. Gaupp et al (2015) calculated S-Y curves for 403 large-scale river basins to examine how existing storage capacity can help manage flow variability and transboundary issues. Basin scale S-Y analysis provides estimates on hypothetical storage capacity required to meet water demand, and hence, such analysis helps to identify the need for further infrastructure investments to cope with water stress on a global scale (Gaupp et al 2015). Even though previous analyses of both global and regional energy systems suggest that evaporative losses from reservoirs used for hydropower play a significant role in total consumptive water use (Fricko et al 2016, Grubert 2016, such evaporative impacts are missing from existing global-scale assessments of surface water reservoir potential that consider climate change. Increasing air temperatures and variable regional precipitation patterns associated with climate change will ultimately affect evaporation rates. Moreover, competing land-uses and environmental flow regulations play an important role in large-scale reservoir siting and operations, but have yet to be considered concurrently as part of a global-scale assessment of the ability of future reservoirs to provide sustainable firm yields under climate change. Additional constraints on reservoir operation and siting will reduce firm yields, but these effects could be offset in basins where runoff is projected to increase under climate warming (van Vliet et al 2016). Development of new, long-term systems analytical tools to disentangle the tradeoffs between potential reservoir firm yield, climate change, and competing land-use options is therefore a critical issue to address from the perspective of water resources planning.
The purpose of this study is to assess the aggregate potential for reservoirs to provide surface water yields in 235 of the world's largest river basins, including consideration of climate change impacts on basin-wide runoff and net evaporation (i.e. the difference between estimated evaporation from the reservoir surface and the incident precipitation), as well as constraints on reservoir development and operation due to competing land-uses and environmental flow requirements. Improved basin-scale S-Y analysis tools enabling global investigation are developed for this task, including a linear programming (LP) framework that contains a reduced-form representation of reservoir evaporation and environmental flow allocation as endogenous decision variables. The framework incorporates additional reservoir development constraints from population growth, human migration, existing irrigated cropland, and natural protected areas. We further consider a range of future global change scenarios and measure reservoir performance in terms of yield and corresponding reliability as to maintain a given yield across global change scenarios. The scope of this analysis thus covers a number of important drivers of water supply sustainability neglected in previous global assessments while also providing new insight into the following research questions: • In which basins are surface water withdrawals from reservoirs most affected by future climate change? And how might achieving climate change mitigation targets limit such impact? • What are the impacts of competing land-use activities and environmental flow constraints on the potential of expanded reservoirs to secure freshwater yields?

Method
This study assesses aggregate reservoir storage potential and surface water firm yields at the river basin-scale. River basins represent the geographic area covering all land where any runoff generated is directed towards a single outlet (river) to the sea or an inland sink (lake). The approach builds on previous work that combines basin-averaged, monthly runoff data with a simplified reservoir representation to derive the S-Y relationships for different basins in a computationally efficient way (Wiberg and Strzepek 2005, Boehlert et al 2015, Gaupp et al 2015). Wiberg and Strzepek (2005) tested a similar basin-scale approach to S-Y analysis using a number of simplified geometries for cascaded reservoir systems in the southwest United States and showed relatively good agreement with management strategies simulated with a more complicated model. The resulting basin-scale S-Y relationships quantify the storage capacity needed to achieve a specified firm yield but do not prescribe locations for reservoirs within each river basin, which would require locationspecific S-Y analysis. The basin-scale S-Y relationships provide a metric for understanding how changes in precipitation, evaporation, and land-use across space and time translate into changes in required storage needed at the basin-level to ensure a specified volume of freshwater is available for human use (e.g. irrigation, municipal supply, etc.). The basin-level S-Y indicators enable comparison across regions, and hence, identification of basins with the greatest challenges in terms of adapting to future climate change (Wiberg andStrzepek 2005, Boehlert et al 2015).
A linear programming (LP) model computes the S-Y characteristics (section 2.2) and is applied to the 235 basins delineated in HydroSHEDS used by the Food and Agriculture Organization of the United Nations (www.fao.org/geonetwork/srv/en/ metadata.show?id=38047). The LP model calculates the minimum reservoir capacity required to provide a given yield based on concurrent 30 year average monthly runoff sequences within each basin. This timeframe is selected to mimic existing regional water resource planning practices, which typically take a multi-decadal perspective to include analysis of long-lived infrastructure investments such as reservoir development (Gaupp et al 2015).
Return of extracted groundwater to rivers and long-distance inter-basin transfers via conveyance infrastructure are important parts of the surface water balance in some regions (McDonald et al 2014, Wada et al 2016), but are not included in this current study due to lack of consistent observational data on a global scale and computational challenges preventing application of the LP framework at higher spatial resolutions. The approach also does not consider streamflow routing within basins. Omitting routing in basin-scale S-Y analysis has been adopted in previous studies (Gaupp et al 2015). It is also important to note that in some of the largest basins the hydraulic residence time is on the order of several months, and hence, our analysis is unable to reflect the effects of this time-lag on storage reliability. Similarly, our assessment is unable to address capacity decisions focused on addressing floods, which usually requires assessing flow patterns at higher frequencies (Naden 1992).
In this study, we assume an upper boundary for the maximum reservoir expansion scenario which is defined by the limited availability of land to be flooded due to various restrictions. Availability of land is defined following a spatially-explicit analysis of existing and future land-use in each basin (section 2.3). It is important to emphasize that additional reservoir development constraints not readily quantifiable with existing methods (e.g. soil stability, future habitat conservation, cultural preferences, etc.) are likely to further reduce available area for reservoir expansion.
The overall approach of the global scale assessment is shown in figure 1. The historical period of 1971-2000 and a simulation period of 2006-2099 were analyzed for each of the 235 basins. The 30 year monthly runoff sequences were generated for each decade resulting in eight decadal runoff sequences for each climate scenario. Additionally, the impacts of net evaporative losses from the reservoir surface are estimated for each climate scenario and included in the reservoir capacity calculations.

Model inputs
For this study, we utilized runoff from a state-ofthe-art global hydrological model ( Similarly, net evaporative loss from the reservoir is forced by climate input from the GCM using the general approach of Shuttleworth (1993) (appendix A section 2). This approach originated from the Penman equation (Penman 1948) and is widely used to estimate the potential evaporation of open water and fully-saturated land surfaces (Harwell 2012). Net evaporation is therefore the difference between estimated potential evaporation from reservoir surface and precipitation on reservoir surface.
All model inputs are provided as gridded data at 0.5 • spatial resolution (approximately 50 km by 50 km in the mid-latitudes). Data for each of the four future climate change scenarios from the Representative Concentration Pathways (RCPs) (van Vuuren et al 2011) are available. The four RCPs (2.6, 4.5, 6.0 and 8.5) describe a possible range of radiative forcing values by the year 2100 relative to pre-industrial values, which are consistent with a wide range of possible changes in global climate patterns. For example, the RCP2.6 scenario represents a low-carbon development pathway consistent with limiting the global mean temperature increase to 2 • C by 2100 (van Vuuren et al 2011). Conversely, RCP8.5 represents a world with high population, energy demand, and fossil intensity, and thus the highest carbon emissions (Riahi et al 2011). The inclusion of different global emission scenarios in the S-Y analysis provides insight into the potential interactions with climate change mitigation policy.
Similar to previous research, a simplified geometry for the representative reservoir in each basin is assumed (Wiberg and Strzepek 2005, Boehlert et al 2015, Gaupp et al 2015) (appendix A section 1). The simplification is crucial in the current study for facilitating the long-term global-scale perspective needed to assess impacts of climate change across multiple scenarios. The Global Reservoir and Dam (GRanD) database (Lehner et al 2011) reports the maximum storage capacity and surface area for existing reservoirs with a storage capacity of more than 0.1 km 3 . These data are used to derive an average surface area-volume relationship for each basin (appendix A section 1).

Reservoir storage-yield relationship
Reservoir capacity is defined in this study as the minimum storage capacity c capable of providing a firm yield y across a set of N discrete decision-making intervals, T = {t 1 ,...t N }. Considering average monthly runoff q, releases for environmental purposes r and net evaporative losses v, a simple water balance across basin-wide inflows and managed outflows at the representative basin reservoir results in the following continuity equation for the storage level: where s is the storage level. Evaporation and precipitation are important processes to parameterize in the reservoir water balance due to the feedback with management strategies (Wiberg and Strzepek 2005). Level-dependent net evaporative losses are estimated assuming a linearized relationship between surface area and storage level (Lele 1987): where e is the net evaporation (as equivalent depth), A is the reservoir surface area, is the surface area per unit storage volume (appendix A section 2), and = 1/2 ⋅ e⋅a. The net evaporation and reservoir geometry parameters represent basin-averages.
Combining (1) and (2) generates a continuity equation for the reservoir storage level that incorporates level-dependent net evaporative losses in a simplified way (appendix A section 1). The continuity equation is joined with a number of operational constraints to form the following LP model: where the management variables are defined by the set X = {s,r,c}. The objective function (3a) seeks to minimize the no-failure storage capacity given a certain firm yield. Constraint (3b) is the continuity equation incorporating level-dependent net evaporative losses. Constraint (3c) prevents pre-filling and draining of the reservoir in the model by ensuring the storage level at the final time-step, t , does not exceed the storage level at the initial time step, t 1 . Constraint (3d) ensures the reservoir storage level stays within a maximum fraction of storage capacity, (assumed to be 1), and a minimum dead-storage limit of the installed capacity, . Gaupp et al (2015) adopted of 20% in their study and this value can be as high as 30%-40% (Wiberg and Strzepek 2005). In this study, we assumed a smaller fraction of 15%.
Constraint (3e) ensures the release is maintained between the maximum and minimum environmental flow requirements, r min and r max , which are computed by applying an augmentation factor on monthly natural streamflow. We adopted the environmental flow approach of Richter et al (2012) where the environmental flow allocation is determined by an allowable augmentation from presumed naturalized conditions. We experimented with an augmentation factor of 10%-90% of the naturalized conditions. Results are shown with an augmentation factor of 90%, which serves as a lower bound for illustrative purposes. Hence, r min and r max is 10% and 190% of monthly natural streamflow, respectively. Constraint (3f) limits installed storage capacity to c max and ensures the capacity remains positive. The maximum volume is set based on an assessment of within-basin land-use, which is further discussed in section 2.3.
Solving (3) identifies the minimum storage capacity required to provide the given firm yield subject to the operational constraints. The S-Y relationship is obtained by solving the model for incrementally increasing firm yields. From the S-Y curve, the maximum storage capacity for the reservoir within each basin occurs at the maximum firm yield, i.e. where the marginal gains in firm yield under reservoir expansion approach zero. Maximum reservoir storage potential is therefore equivalent to the maximum storage capacity derived from the S-Y relationship unless such storage capacity is constrained by available land, which is explained in section 2.3. The maximum gain in firm yield is thus the difference between the current firm yield and the maximum firm yield identified from the generated S-Y curve.
An ensemble of S-Y curves is generated for each basin using the climate scenarios and multi-decadal simulations described in section 2.1. The ensemble is assessed to calculate the number of S-Y curves in each basin that reach a given firm yield. This analysis provides an additional reliability-based performance metric that incorporates a measure of climate change uncertainty. Note that to accurately represent the reliability of reservoirs, behaviour simulation of reservoirs with assumptions of operating policy should be implemented (Kuria and Vogel 2015). However, given the computational intensity of behaviour analysis, the reliability in this study represents the probability a certain firm yield can be obtained across the climate scenarios and multi-decadal planning horizons. That is, we assessed reliability in terms of reservoir potential and firm yields across different climate scenarios and decision-making periods.

Exclusion zones
Reservoir expansion, and the associated gains in firm yield, are constrained by the availability of land since not all areas can realistically be used for reservoir expansion. c max in equation 3g is derived for each basin by calculating the storage volume associated with the total available land area (see appendix A section 1). We followed the approach of a number of previous studies on renewable energy potentials ( (3) protected areas (figure S1 and table S1 available at stacks.iop.org/ERL/13/044026/mmedia) (Deguignet et al 2014). We adopted dynamic population trajectories under two Shared Socioeconomic Pathways (SSPs) -SSP1 and SSP3. These scenarios were selected due to their opposing storylines about population growth and urbanization, which introduces human migration uncertainties into the analysis. SSP1 describes a future world with high urbanization and low population growth whereas lower urbanization and higher population growth define SSP3 (O'Neill et al 2014). Total available land area for reservoir expansion in each basin is thus the remaining area outside the exclusion zones. Further discussion of the exclusions zones and the derivation is provided in appendix A section 3.
Other than population, agriculture, and protected land, other physical limitations such as elevation, slope and seismic risk will also constrain the available area for reservoir expansions. It is important to further emphasize that this work does not prescribe actual sites for new reservoirs within basins, which requires a more detailed treatment of the local geography and stakeholder needs. Non-physical constraints such as economic incentives, institutional capacity, and infrastructure readiness would also limit the ability of reservoir capacity expansion. To fully characterize exclusion zones, future work should consider direct use of high-resolution digital elevation model data and alternative metrics for limiting land availability. Without considering non-physical constraints that are difficult to quantify, this study serves as a first-order estimation of reservoir storage and surface water yield expansion potential at global scale. expansion potential (vertical color) and the likelihood of maintaining current firm yields under future climate change (horizontal color). There are large disparities in the potential for reservoir expansion to provide firm yields across basins. For example, the majority of basins in Europe display greater than 2500 m 3 of storage potential per capita, but relatively low reliability (<50%) for maintaining current firm yields due to the projected lower water availability under climate change. Basins in Asia show high reliability (>50%) for maintaining current firm yield yet relatively low storage potential (<2500 m 3 ) per capita associated with large projections in population growth. Basins located at higher latitudes generally display abundant storage potential (>12000 m 3 /capita), but these regions are not usually highly populated or water demanding; hence, there will likely be less of an incentive to plan for reservoir expansion in these regions. To quantify the necessity of building reservoirs to relieve regional water stress, it is necessary to integrate water demand from different sectors into this framework so that the reservoir expansion planning will take into account the severity of water scarcity as well as environmental and socioeconomic development factors.

Results
Maximizing the additional amount of reservoir storage (∼4.3-∼4.8 times greater) results in only a ∼50% increase in firm yield worldwide due to the nonlinear shape of the S-Y curve (ex. figure S3 and S4). Figure 3 shows the marginal gains vary substantially across basins. Gains in storage/firm yield are defined as the ratio between estimated maximum reservoir storage/firm yield and current reservoir storage/firm yield and are computed by analyzing the S-Y curve for each basin of interest. The majority of basins in North America have limited gain in firm yield by maximizing storage as these basins have already been highly developed. Basins in parts of India and Southeast Asia, on the other hand, display relatively greater marginal gain in firm yield by maximizing storage capacity.
By comparing the two types of map products in figure 2 and figure 3, we can identify regions where reservoir expansion will be particularly challenging. For example, current total reservoir storage capacity in the Missouri River Basin, United States is 133 km 3 . There is very little room for further expansion for the Missouri River Basin as the estimated storage potential is almost identical with current reservoir storage (figure S3). Fully utilizing potential storage leads to negligible increases in firm yield, and with a reliability of less than 50% due to the relative instability of future water availability under the tested scenarios (figure S2). In Asia, current total storage capacity in the Mekong Basin is 19 km 3 , and the storage potential is about 300 km 3 (∼16 times current storage) ( figure S3(b)). In contrast, additional storage per capita for the Mekong Basin is 4200 m 3 /capita. By maximizing the potential storage, firm yield increases from 235 km 3 to ∼500 km 3 , which is approximately 2 times the current firm yield. However, the reliability is estimated to be very low due to the projected lower reservoir inflows under climate change (figure S2). As figure 2 and figure 3 illustrate, there exists large regional heterogeneity in marginal gain of firm yield when we fully utilize potential storage and the reliability of maintaining current firm yield varies from basin to basin. In addition to physical feasibility, there are other factors that constrain storage potential and hence gain in firm yield. Additional global maps are included in Supplementary section to help understand current yields for each basin (figure S7) and additional storage needed to maintain current firm yields ( figure S8).  In this study, we experimented with different augmentation factors for environmental flow to show how many basins have already installed a storage capacity that exceeds presumed environmental guidelines. Table 1 shows the percentage of basins that would be overdeveloped if higher environmental flow requirements were assumed.
Results suggest that even at 'poor or minimum' environmental flow condition (Tennant 1976) of 10%, a small portion of the world's largest rivers already have an installed storage capacity that puts river's ability to provide environmental services at risks. With increasing environmental flow guidelines, more river basins would be considered 'overdeveloped' even with current storage capacity. This shows that existing reservoirs are partially causing the deterioration of ecosystem services, and reservoir storage potential would be further constrained by more stringent environmental flow requirements.

Discussions and conclusions
This paper quantified the global potential for surface water reservoirs to provide a firm yield across four different climate change scenarios and two socioeconomic development pathways under a maximum reservoir expansion scenario. Competing land-use activities are found to pose a nontrivial impact on reservoir storage potential worldwide. Approximately 4%-13% of the estimated maximum storage capacity is unavailable due to human occupation, existing irrigated cropland, and protected areas. In addition, net evaporation is non-trivial (∼2.3% of total annual firm yield) and it is anticipated to increase ∼3%-4% under the most extreme climate warming scenario (RCP8.5). Importantly, the impact of climate change on reservoirs differs immensely from basin-to-basin, but the results of this analysis show agreement in terms of its negative role in reservoir reliability. International policies aimed at reducing greenhouse gas emissions would help to reduce this uncertainty, and therefore point to additional co-benefits of climate change mitigation in terms of improving long-term water supply reliability.
Two types of bivariate map products were generated from this study to help decision makers understand the potential benefits of reservoir expansion at the basin-scale and help define regional adaptation measures needed for water security. By linking this framework with anthropogenic water demand for various activities in each basin (e.g. agriculture, electricity, industry, domestic, manufacturing, mining, livestock), regions where water is severely in deficit, and thus, expanding reservoirs would potentially relieve regional water scarcity could be identified. Other than demand for water, alternative metrics that could presumably affect reservoir expansions include, but are not limited to, economic incentives, institutional capacity, and infrastructure readiness.
This paper should not be seen as a call for more large dams, but rather an assessment of where policies and infrastructure investments are needed to sustain and improve global water security. In fact, dam removal activities have become more prominent in the United States since the 2000s, partly due to concerns of deteriorating river ecosystems and degraded environmental services (Oliver 2017). A recent study by the Mekong River Commission tested a scenario of completing 78 dams on the tributaries between 2015-2030, the results of which suggested that it would have catastrophic impacts on fish productivity and biodiversity (Ziv et al 2011). Therefore, it is critical to consider the trade-offs between socioeconomic progress and sustainable development when interpreting results with the tools built from this study.
This study serves as a valuable input to future work connecting water, energy, land and socioeconomic systems into a holistic assessment framework. Future effort will include other metrics described above to further constrain reservoir storage potential. Future work could also examine sensitivity of the results to a wider range of GHMs and GCMs to better capture model uncertainty. Finally, the results of this study provide planners with important quantitative metrics for long-term water resource planning and help explore the implications through integrated modeling of water sector development.