Time-explicit modelling of disruption, recovery and adaptation of an interdependent road-electricity system

Technical Summary: Time-Explicit Modelling of Disruption, Recovery, and Adaptation of an Interdependent Road-Electricity System

Problem Statement
Large-scale pluvial flooding poses significant risks to critical infrastructure, particularly electricity networks. While previous studies have often relied on static, event-based formulations that focus on direct asset failure, they frequently overlook the dynamic nature of recovery and the cascading effects of interdependencies. Specifically, the interaction between road networks and electricity systems is critical: road flooding can restrict access to damaged electrical assets (substations), delaying repairs and prolonging outages even when the electrical assets themselves are only moderately affected. Existing risk assessments often fail to quantify how dynamic recovery, infrastructure interdependencies, and constrained repair capacity shape societal consequences. Furthermore, there is a lack of insight into how adaptation measures affect impact-based outcomes (economic vs. population service) differently, and whether adaptation priorities remain robust under uncertainty regarding vulnerability and repair capacity.

Methodology
The authors developed a time-explicit disruption and recovery model for an interdependent road-electricity network, applied to the South Holland region of the Netherlands. The model simulates a large-scale pluvial flood scenario (200 mm rainfall over 48 hours) at an hourly timestep.

• Model Structure: The simulation overlays flood depth maps with electricity substation footprints and road networks. It dynamically tracks:

  • Flood Exposure: Flood depths at asset locations.
  • Failure: Substation failure is determined by a stochastic fragility function dependent on flood depth.
  • Accessibility: Road networks are modeled as graphs where flooded segments are removed. Substations are accessible only if connected to a non-flooded road component.
  • Recovery: Repair crews are allocated to accessible, damaged substations. Crew distribution is constrained by road connectivity and total crew availability. Repair times are derived from damage ratios.
  • Impacts: Outage durations are translated into two metrics: Economic Impact (based on Value of Lost Load across land-use sectors) and Population Service Impact (based on affected population counts).

• Adaptation Measures: The study evaluates interventions at four levels:

  1. Hazard-level: Increasing drainage capacity to reduce flood depths.
  2. Asset-level: Elevating substations to reduce failure probability.
  3. Network-level: Prioritizing repair crews based on economic or population impact.
  4. System-level: Providing backup power to industrial and commercial users.

• Uncertainty Analysis: The model employs Latin Hypercube Sampling to vary substation fragility (steepness of the failure curve) and repair capacity (number of crews). This assesses the robustness of impact patterns and adaptation priorities across plausible assumptions.

Key Contributions

1. Dynamic Temporal Modelling: The study moves beyond static exposure mapping by explicitly modelling how disruption and recovery unfold over time, capturing the lag between peak flooding and peak service disruption.
2. Explicit Interdependence: It represents electricity-road interdependence during recovery by accounting for accessibility constraints and limited repair capacity, quantifying how road isolation amplifies electricity outages.
3. Consequence-Based Adaptation: Adaptation measures are evaluated based on their effects on economic and population service impacts rather than hazard reduction alone, revealing diverging priorities between these objectives.

Key Results

• Exposure vs. Impact: Flood exposure alone is an insufficient predictor of societal consequences. The locations with the highest flood exposure do not necessarily coincide with the highest economic losses or population service disruptions. Impact hotspots are determined by the spatial distribution of served users and the duration of outages.
• Temporal Divergence: Peak flooding does not coincide with peak disruption. In the simulated scenario, peak flooding occurred at hour 48, but the maximum number of non-operational substations occurred more than a day later. Impacts continue to accumulate during the recession and recovery phases.
• Role of Repair Capacity and Access: Recovery is strongly shaped by repair capacity. Insufficient crews create backlogs that prolong outages well beyond flood recession. Road-access constraints significantly increase impacts (e.g., increasing economic impacts by ~10% in the "crews-sufficient" scenario) by isolating failed substations from repair crews.
• Adaptation Effectiveness:
  • Pre-event vs. Recovery: Measures implemented before the event (drainage, elevation) reduce impacts more effectively than recovery-stage prioritization alone, as they reduce the total number of failures rather than just redistributing repair order.
  • Targeting: A small, targeted subset of areas or assets accounts for a large share of avoidable impacts. For instance, targeting ~1.6% of substations can avoid up to 70% of impacts.
  • Measure Comparison:
    • Drainage (Hazard-level): Provides broader, more balanced reductions across both economic and population metrics.
    • Elevation (Asset-level): Yields the largest reductions in the targeted metric (e.g., economic or population) but offers limited cross-benefits to the other metric due to the spatial separation of industrial hubs and residential areas.
    • Combination: Combining drainage and elevation allows for larger reductions than drainage alone while mitigating the trade-offs seen in elevation-only strategies.
• Robustness: The identified patterns and adaptation priorities remain stable across variations in substation fragility and repair capacity assumptions.

Significance and Claims
The paper argues that infrastructure adaptation decisions must be grounded in societal impacts and informed by uncertainty, rather than relying solely on hazard footprints. It demonstrates that:

• Risk is temporal: Consequences unfold through disruption and recovery over time; a single snapshot of peak flooding misses critical parts of the event trajectory.
• Interdependence is conditional: Road interdependence is most critical when repair capacity is limited. When crews are abundant, the bottleneck shifts, and the marginal benefit of improving road access diminishes.
• Multi-objective trade-offs exist: No single measure performs best across all objectives. Area-wide drainage offers broader benefits, while asset elevation offers stronger but targeted benefits. This supports the need for combined adaptation strategies.
• Comparative Utility: The results are best interpreted comparatively to identify stable patterns and priorities for adaptation appraisal, rather than as exact forecasts of outage costs.

The study concludes that assessing climate adaptation for critical infrastructure requires consequence-based metrics that consider the full course of an event, from flood build-up to recovery, acknowledging that the greatest societal impacts often emerge long after the floodwaters have receded.