Long-term policy and infrastructure decisions under deep uncertainty

Solution

To address this challenge, we move beyond average scenarios and isolated peak events and focus on persistent system dynamics. Our approach models renewable utilization as a persistent stochastic process calibrated to observed temporal patterns in historical data. This allows us to represent realistic system trajectories rather than idealized, statistically independent hours.

Redispatch is sampled from empirically observed distributions conditional on the simulated system state. In this way, both the level and variability of renewable utilization are directly linked to operational grid stress in a data-driven manner. The resulting simulations capture not only expected outcomes, but also the accumulation of risk over extended stress periods.

By systematically varying the average level and volatility of renewable utilization, we derive a sensitivity surface that quantifies how annual redispatch volumes scale under different system regimes. This transforms complex, path-dependent dynamics into a transparent decision space.

Instead of asking whether a single scenario is “acceptable”, the analysis reveals where operational risk grows rapidly, where the system remains robust, and where trade-offs between renewable integration and system stability become critical. This enables planners and decision-makers to identify resilient strategies, prioritize network reinforcement, and evaluate investments under realistic uncertainty.

Water Supply Planning under Hydrological Uncertainty

This example illustrates how long-term water supply decisions change when uncertainty is treated as persistent and path-dependent rather than averaged over.

Challenge

Water supply systems operate under a combination of high climatic variability, growing demand pressures, and strict operational constraints. For instance, in California large surface reservoirs play a central role in balancing seasonal inflows, interannual drought risk, and downstream water demands for municipalities, agriculture, and ecosystems.

The figure below illustrates this challenge using Lake Oroville, one of California’s largest reservoirs, which is primarily supplied by the Feather River. The time series shows historical monthly inflow to the reservoir, observed storage levels, and a simulated aggregate water demand that must be met through reservoir releases. This demand represents the operational control variable in the system and reflects the volume of water supplied to downstream users under different management policies.

A defining challenge for reservoir management arises from rare and persistent events, such as multi-year droughts, delayed snowmelt, or unusually dry winters. Periods of sustained high demand further reduce system resilience, especially when they coincide with unfavorable inflow sequences. These conditions are not well represented by average hydrological years.

Historical records from California’s reservoir Lake Oroville show that inflows and storage levels evolve smoothly most of the time, yet critical shortages emerge during relatively short episodes. During these periods, reservoir storage can decline rapidly, and recovery may take multiple seasons or years. Planning approaches based on long-term averages or “typical” years therefore may systematically underestimate the corresponding risk.

At the same time, future hydrological conditions are deeply uncertain. Climate change affects not only mean precipitation but also its timing, persistence, and sequencing. Snow-dominated systems, such as those feeding California’s reservoirs, are particularly sensitive to shifts in seasonal patterns. As a result, assigning reliable probabilities to future inflow sequences is often not defensible.

This creates a fundamental planning dilemma:

Demand management policies must be decided today, even though future inflow sequences, drought persistence, and demand pressures cannot be characterized by a single probabilistic forecast.

Note: The analysed data are publicly available on the website of the U.S. Geological Survey (USGS).

Solution

Simple forecasts based on averaged future conditions fail to capture the complexity of real-world water supply systems. The key question is therefore not what happens in an “average” future, but which demand management strategies remain reliable across many plausible futures under hydrological uncertainty.

Using historical observations of inflow to Lake Oroville, we generate many alternative future inflow trajectories that preserve key temporal characteristics such as seasonality, persistence, and drought clustering. These futures do not represent forecasts, but rather stress tests of the system. For each future, reservoir storage is simulated through a simple water balance, while demand is treated as the controlled decision variable. We then evaluate alternative demand management strategies by modifying how much water is released from the reservoir over time. Two broad classes of strategies are considered: Static and adaptive demand management.

Static demand policies apply a fixed adjustment to demand throughout the planning horizon. Adaptive demand policies, in contrast, respond dynamically to system conditions: demand is reduced only when reservoir storage falls below predefined thresholds and relaxed again when storage recovers. The figure below summarizes system performance across all simulated futures using reliability, defined as the fraction of time that reservoir storage remains above a critical minimum level. Each curve shows the cumulative distribution of reliability outcomes across futures for a given policy.

Curves further to the right indicate more robust strategies: a larger share of futures achieve high reliability. The static policies exhibit substantial spread and overlap, indicating that fixed demand adjustments can perform well in some futures but fail severely in others. In contrast, the adaptive policies are consistently shifted toward higher reliability, particularly in the lower tail of the distribution.

This illustrates a key insight: adaptivity matters more than static scaling. While static demand reductions improve average performance, adaptive strategies substantially reduce the risk of prolonged shortages by responding to unfolding conditions rather than committing to a single assumption about the future. This approach reveals where strategies fail and to what extent. This enables decision-makers to identify demand management policies that remain effective across deep uncertainty.