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# Learning about climate change uncertainty enables flexible water infrastructure planning

## Abstract

Water resources planning requires decision-making about infrastructure development under uncertainty in future regional climate conditions. However, uncertainty in climate change projections will evolve over the 100-year lifetime of a dam as new climate observations become available. Flexible strategies in which infrastructure is proactively designed to be changed in the future have the potential to meet water supply needs without expensive over-building. Evaluating tradeoffs between flexible and traditional static planning approaches requires extension of current paradigms for planning under climate change uncertainty which do not assess opportunities to reduce uncertainty in the future. We develop a new planning framework that assesses the potential to learn about regional climate change over time and therefore evaluates the appropriateness of flexible approaches today. We demonstrate it on a reservoir planning problem in Mombasa, Kenya. This approach identifies opportunities to reliably use incremental approaches, enabling adaptation investments to reach more vulnerable communities with fewer resources.

## Introduction

Uncertainty in climate change projections poses a challenge to infrastructure planning for climate change adaptation1. Because of the large expense and widespread need for adaptation investments, planning models play a critical role in targeting resources. Traditional water infrastructure planning accounts for uncertainty by adding a safety factor to new infrastructure2. However, these large projects are typically irreversible, expensive, and last for multiple decades; the same is true across many infrastructure domains3. Preparing for climate change by adding extra capacity, therefore, incurs high risk of expensive overbuilding in resource-scare areas. Flexible infrastructure planning has the potential to manage uncertainty at reduced cost by building less infrastructure up front but enabling expansion in the future if needed2,4,5. However, enabling flexibility often requires substantial proactive planning or upfront investment6. In water resources, it is difficult to know whether recent trends in streamflow are a result of climate change or short-tern variability and therefore whether they are predictive of future trends7. It is therefore difficult for planners to know if and when to trigger adaptive actions. Short-term reliability outages can occur if infrastructure cannot be adapted quickly8. Further, flexibility can ultimately be more expensive by not taking advantage of economies of scale6. Appropriate methods are therefore needed to weigh the risks and benefits of static vs. flexible infrastructure approaches in responding to climate change uncertainty.

Several recent studies provide methods to develop and assess flexible (also called adaptive) infrastructure planning under climate change uncertainty. Robust decision making (RDM) uses iterative scenario development to minimize the regret from both overbuilding unnecessary infrastructure and being unprepared9,10,11. RDM has been used to develop and evaluate adaptive infrastructure planning strategies12,13,14. New policymaking processes design adaptive pathways that allow planners to switch from one action to another if specified thresholds are reached15 and can be combined with optimization approaches to identify adaptive thresholds and actions16. Recent approaches have provided methods for adaptive sequencing of infrastructure investments8,17. Finally, advances in search algorithms18,19 have enabled assessment of adaptive and cooperative approaches against many performance measures using ensembles of streamflow projections20.

Adaptive management requires an ability to learn over time as more information is collected5. A challenge faced by the aforementioned approaches is the difficulty in assessing opportunities to learn in the future. General circulation model (GCM, i.e. climate model) projections provide us with the best available estimates of how the global climate system will evolve under a given emissions scenario. However, as time passes and new climate observations are available, some GCM trajectories will prove to be more reliable than others. For example, suppose current regional projections estimate a range between 0.5 and 1.5 °C of change over the next 20 years. If after 20 years we observe 1.5 °C of change, this suggests the climate is warming in this region more rapidly than expected. We may now shift our projections of change upward for the following 20 years. While existing frameworks provide an iterative process for planners to change course in the future, they do not provide an upfront assessment of the opportunity to learn about climate change in the future. This upfront assessment is critical to deciding whether investments in flexibility are worthwhile or whether a traditional static approach is more appropriate. Existing flexible approaches either assume a priori that flexibility is needed8, assume perfect information about the future21, or rely on thresholds or signposts that are unrelated to learning about climate change13, but do not provide a mechanism for assessing opportunities to learn about climate change in the future. Recent studies have incorporated learning feedback from short-term nonstationary streamflow, but not long-term climate change13,22,23. Note that while this study focuses on water supply infrastructure, the challenge of characterizing learning about climate uncertainty to enable adaptive planning has been highlighted in a range of other disciplines (for example in forest management24).

We develop a planning framework that explicitly models the potential to learn about climate uncertainty over time and uses potential learning to develop and evaluate flexible planning strategies in comparison to static approaches. First, we use GCM projections to develop a wide range of possible future mean regional temperature (T) and precipitation (P) outcomes over a planning horizon. We finely discretize mean annual T and P within that range. This develops a comprehensive set of virtual climate observations of mean T and P that reflect many possible future regional climates, some of which are drier and some of which are wetter. Next, we adapt a Bayesian statistical model25 to update initial climate uncertainty estimates for each virtual climate observation. The updated estimates reflect what we will have learned if the virtual observation comes to pass. These updated uncertainty estimates characterize the transition probabilities in a non-stationary stochastic dynamic program (SDP); each possible change in SDP climate state is equivalent to a virtual climate observation. This SDP planning formulation therefore takes into account all the potential new information that may be learned in the future as it develops optimal planning policies. We use these polices to evaluate flexible infrastructure planning approaches and compare them to static approaches.

The United Nations Environment Program estimates that the cost of climate change adaptation investments in the developing world may reach $500 billion per year by 2050;26 the World Bank estimates that the infrastructure and water sector adaptation costs may be$28 billion and $20 billion per year, respectively27. It is therefore essential to target infrastructure investments efficiently to reach the widest number of vulnerable communities. Flexible planning strategies can substantially reduce the cost of infrastructure investments. To the authors’ knowledge, this is the first framework that values the ability of flexible approaches to respond to climate learning, therefore more comprehensively evaluating the tradeoffs of robust and flexible adaptation strategies. Results show that climate change uncertainty can be reduced over the lifetime of an infrastructure project across different climate change trajectories. Flexibility is effective in preventing unnecessary infrastructure additions while maintaining similar reliability. However, the planning choice is informed by the social context including value of reliability and discount rate. ## Results ### Planning framework and scenarios We demonstrate this planning framework, illustrated in Fig. 1, with an application for Mombasa, Kenya. Mombasa is the second largest city in Kenya with an estimated population of 1.1 million28. Urban water demand is currently estimated at 150,000 m3day−1 and expected to grow to 300,000 m3day−1 by 203529. Mombasa has a warm, humid climate with average annual precipitation of 900 mm year−1 and a mean annual temperature of 26 °C30. Mean annual runoff (MAR) in the nearby Mwache river, the site of a proposed dam, is 113 MCM year−1 31. While GCMs all project warming in the region, there is disagreement on the direction of precipitation change. This creates substantial uncertainty in future runoff and therefore the reservoir capacity needed to meet yield targets over its lifetime. We apply our framework to develop and assess a flexible infrastructure design. The flexible design enables extra storage capacity to be added if the initial dam becomes insufficient due to warmer, drier climates. We assess three planning scenarios, described in Table 1, intended to evaluate the sensitivity of our results to social and technological planning assumptions. In the low-demand scenarios (A and B), we assume a target yield of 150,000 m3 day−1 (54.8 MCM year−1) with 90% reliability from the Mwache dam. We evaluate the two dam sizes proposed by the previous World Bank study21, 80 MCM and 120 MCM, as well as a flexible alternative in which the height of the smaller dam can be raised, increasing the reservoir capacity to 120 MCM. In planning scenario C we assume a target yield of 300,000 m3 day−1 (109.6 MCM year−1) with 90% reliability over the entire planning horizon, reflecting the potential for rapid demand growth on relatively short timescales based on 2035 projections from29. In this scenario, the target yield is greater than observed MAR in the Mwache river, and therefore the dam cannot meet the target yield in today’s climate regardless of its size. Therefore, we model the combination of a 120 MCM dam and a desalination plant that is used to supply demand when reservoir storage is low. Three desalination alternatives are chosen, analogous to the dam design alternatives. A low capacity alternative designed to meet reliability targets in the current and expected future climate with 60 MCM capacity; the large alternative that meets the reliability targets across all projected future climates with 80 MCM capacity; a flexible alternative starts with 60 MCM and can be expanded to 80 MCM. Evaluating this second scenario allows us to compare the value of flexibility across two technology options, earthen dams and desalination, which have unique water supply profiles and cost structures. ### Bayesian learning about climate change uncertainty Figure 2a, b show historical observed regional annual T and P from the Climate Research Unit (CRU)32, as well as individual GCMs’ projected changes in T and P relative to 1990. 90% confidence intervals (CIs) of GCM projections are developed using the Bayesian uncertainty approach, assuming the historical period is prior to 1990, and compared to CIs developed using a traditional democratic weighting. The Bayesian approach weights models based on how well they match historical observed changes in T and P (see Methods). The democratic approach assumes all models perform equally well33. Between these two methods, the Bayesian approach produces smaller CIs because it assigns more weight to a subset of models that best match historical change in this region. While Fig. 2 presents Bayesian CIs based on historical observations, the SDP transition probabilities require Bayesian uncertainty estimates that reflect what will have been learned for many possible virtual future observations. We assume that precipitation change will range between −30% and +30% by end of century; we discretize this range at 2% for a total of 31 unique virtual precipitation change observations. We apply the Bayesian uncertainty analysis to each of these 31 virtual precipitation change observations in each time period. For example, two sample time series of virtual T and P observations and their corresponding updated uncertainty estimates are shown in Fig. 3. An example of strongly increasing P is shown at top; an example of modestly decreasing P is at bottom. For each virtual observation, we simulate 10,000 virtual climate time series from the current observation to the end of the planning period and construct a 90% CI, shown by the shaded regions. This process is repeated for each time step, with darker colors in the plot corresponding to the CIs developed from virtual observations sampled later in the planning period. The darker CIs therefore reflect uncertainty estimates updated with information farther into the future. The sample of virtual observations showing strong increases in P (Fig. 3a–d), leads to high certainty by the end of the century that negligible water shortages will be incurred, assuming the small 80 MCM of dam capacity. Strong asymmetric uncertainty reflects the low-probability, high-severity risk of droughts; shortages occur only when runoff is substantially below MAR for several months. The alternate sample of virtual observations showing modest decreases in P (Fig. 3e–h) demonstrates a reduction in uncertainty in both P and MAR. Expected water shortages increase substantially as more observations are collected, and the uncertainty increases as well due to non-linear relationships between MAR and shortages. While two sample time series of observations are illustrated in Fig. 3, the SDP optimal strategy accounts for a wide range of possible future observations and what would be learned if they were to be observed. This is achieved through the multistage stochastic optimization formulation, which allows for uncertain, rather than deterministic, transitions to new climate states in each period. In the first time period, shown in Fig. 4a, the SDP develops a threshold as a function of T and P during the 2001–2020 time period when the initial infrastructure decision is made. Above the threshold, in hotter and drier climates, the large dam is optimal and below it the flexible dam is. Due to the small cost difference between the flexible and large dam, investing in the large dam option upfront is preferred if the risk of shortages at the outset is high enough. This reduces expected costs by leveraging economies of scale. Panel b shows expansion thresholds for time periods 2–5 for the flexible dam. Expanding infrastructure capacity is optimal in drier and warmer states. In the 2041–2060 time period, the policy threshold shifts right, reflecting the narrowing of uncertainty due to additional information in later time periods. In later time periods, however, it shifts left, reflecting the influence of the end of the planning horizon which disincentivizes investment. Figure 5 shows infrastructure decisions under the optimal policy across 1000 simulated climate time series. In planning scenario A, the flexible alternative is chosen in 90% of simulations, shown in panel a. When the flexible alternative is chosen, the option to expand is never chosen in about 90% of simulations. This highlights the low probability of reaching a climate dry enough to generate shortages beyond 10% of demand. The time period at which expansion is exercised varies; more rapid warming and drying leads to earlier expansion. Panel b shows cumulative distribution functions (CDFs) of the total cost (including shortage damages) of each alternative across the 1000 simulations under planning scenario A. The large static alternative has the same cost across simulations; as designed, no shortage damages are incurred in any feasible climate. The small dam performs better than the large dam in about 70% of simulations, but has substantially higher costs in 30% of simulations due to large damages from water shortages. The flexible dam mirrors the small dam in 70% of simulations, but the reliability risk is substantially mitigated because of the potential to expand. The high-end costs are higher than the large dam because, first, the cost of building the 80 MCM dam and expanding to 120 MCM is higher than building the 120 MCM dam upfront and, second, sometimes the dam is not expanded even when modest water shortages are incurred. The ability of the flexible alternative to mitigate both the risk of overbuilding and the risk of severe shortages demonstrates the high value of flexibility in this case. The value of flexibility changes under planning scenarios B (no discounting; panels c and d) and C (high demand with desalination plant; panels e and f). Without discounting, the large dam is more favorable; it performs best in 60% of simulations, has no cost variability risk, and is chosen in 80% of simulations. Large economies of scale in the dam mean that a 120 MCM dam is only 30% more expensive than an 80 MCM dam for 50% additional capacity. This suggests it is often better to build the large dam upfront even if there is a relatively low probability that it will be needed. Scenario C evaluates a 120 MCM dam combined with a desalination plant. We find a high value of flexibility even without discounting. The flexible alternative is chosen upfront in over 80% of forward simulations. The CDF demonstrates that it outperforms the static alternatives by substantially mitigating the over build risk in comparison to the robust alternative. The flexible alternative also modestly reduces the shortage damage risk in comparison to the small alternative. While the flexible alternative only reduces cost at the 90th percentile and above, this substantially reduces the expected value as the maximum cost of the small plant reaches almost M$400.

Looking across scenarios, the flexible alternative is chosen most often in scenario A because discounting incentivizes delayed capital investments. This is not the case in scenario B because large economies of scale incentivize a single, large investment. In scenario C more modest economies of scale lead to high value of flexibility in the absence of discounting, highlighting differences in the value of flexibility across technologies. Across all scenarios, the flexible dam is expanded in no more than 10% of simulations, highlighting the low probability of reaching a climate that is hot and dry enough to incur substantial shortages.

### Stochastic weather generation

Climate impacts on river runoff depend on changes in month-to-month variability in precipitation and temperature in addition to changes in the mean. We model these two changes separately. To develop monthly time-series of T and P, we follow the k-nearest neighbors (kNN) approach as described in ref. 48 applied to GCM projections. This non-parametric statistical approach allows us to impose the mean T and P from the SDP while also capturing the standard deviation in monthly values and month-to-month autocorrelation projected by the GCMs. This approach was chosen for its simplicity, ease of implementation, and application in long-term water supply; future studies could use other non-parametric approaches such as the local polynomial regression method developed in ref. 49. For each 20-year time period, we employ the kNN approach to generate 100 samples of 20-year long monthly time-series of T and P. The resulting time series are then applied to the rainfall-runoff model presented below.

### Rainfall-runoff model

Next, the synthetic T and P time series are input to a hydrological model to assess the impacts on runoff. We use CLIRUN II, the latest in a family of hydrological models developed to assess the impact of climate change on runoff 50,51,52,53. CLIRUN II is a two-layer, conceptual, lumped-watershed rainfall-runoff model. It averages soil parameters over the watershed and models runoff at one gauge station at the mouth of the basin. It can be run on a monthly or daily time step. Using the kNN generated samples of T and P, CLIRUN II generates a corresponding 100 samples of 20-year long monthly timeseries of runoff.

CLIRUN II is calibrated using 14 years of monthly streamflow data. Only one streamflow gauge, RGS 3MA03, is available in the Mwache basin31. However, it is directly upstream of the dam location, making it representative for this study. The same monthly temperature and precipitation data from CRU used in the Bayesian climate analysis is used to calibrate CLIRUN II for consistency. This temperature and precipitation data is different than the local data used in the previous World Bank study21, leading to different calibration results but similar performance (historical MAR: 113 MCM year−1; World Bank MAR: 133 MCM year−1; our MAR: 103 MCM year−1).

Our analysis using CLIRUN II and the reservoir sizing model confirms that the 80 MCM dam meets the reliability targets in the current and expected future climate but does not meet reliability targets if the climate gets substantially warmer and drier. The 120 MCM dam meets reliability targets across all projected future climates.

### Infrastructure costs and operations

Capex and opex estimates for the small and large dams were developed using the cost tool from the previous World Bank study21. For the flexible dam, the cost per m3 of additional capacity added is assumed to be 50% greater than that of the original capacity. Capex and opex estimates for the RO desalination plants were developed using the Cost Estimator tool from DesalData54.

The infrastructure operation model includes fixed dam operations (and desalination operations when necessary) that seek to meet the specified yield target while accounting for dead storage, net evaporation, and environmental flows. Unmet demand is measured for each of the 100 streamflow time series, and the average 20-year unmet demand is used to characterize U in the SDP formulation in Eq. (8). We acknowledge that assuming reservoir operations that are fixed in time is a limitation given that adaptive reservoir operations would likely reduce the need for additional capacity; future work could optimize the reservoir operations to each climate state.

## Data availability

Historical climate data (CRU TS3. 10) is available here: https://crudata.uea.ac.uk/cru/data/hrg/. GCM projections are publicly available from the respective sources listed in Supplementary Table 1. Streamflow data is available in Supplementary Data 1.

## Code availability

Code is available from the corresponding author upon reasonable request.

Journal peer review information Nature Communications thanks Robert Lempert and the other anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

The authors are grateful for input and feedback from Dara Entekhabi, Olivier de Weck, James Wescoat, Afreen Siddiqi, and Adnan Alsaati. S.F. was supported by a Rasikbhai L. Meswani Fellowship for Water Solutions from the Abdul Latif Jameel Water and Food Systems Lab (J-WAFS) at MIT as well as a National Science Foundation Graduate Research Fellowship. M.L. acknowledges financial support from a Callahan-Dee Fellowship. Additional research funding was provided by the Center for Complex Engineering Systems at MIT and KACST.

## Author information

### Affiliations

1. #### Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 48-216, Cambridge, MA, 02139, USA

• Sarah Fletcher
2. #### Joint Program on the Science and Policy of Global Change, Massachusetts Institute of Technology, 77 Massachusetts Avenue, E19-411, Cambridge, MA, 02139, USA

• Sarah Fletcher
•  & Kenneth Strzepek
3. #### Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 54-1713, Cambridge, MA, 02139, USA

• Megan Lickley

### Contributions

S.F. conceptualized the study. S.F., M.L., and K.S. designed the methodology. S.F. and M.L. performed the analysis. S.F. and M.L. wrote the manuscript. S.F., M.L., and K.S. edited the manuscript.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Sarah Fletcher.