Stochastic Model

Discrete Event Simulation Mode

Overview

The Stochastic mode simulates realized damage from a specific sequence of storm surges. Each simulation run produces a different outcome because dike failure is sampled stochastically.

How It Works

For each year in the simulation:

  1. Sample surge: Read the next surge height from the time series
  2. Compute effective surge: Apply wave runup and subtract seawall height
  3. Sample dike failure: Draw from Bernoulli(\(p_{fail}\)) – the dike either fails or holds
  4. Compute damage: Sum zone-level damages based on flood depth and dike status
  5. Apply threshold: Add catastrophic damage amplification if total exceeds \(d_{thresh}\)

The total outcome is the discounted sum of investment costs and realized damages over all years.

Key Feature: Stochastic Dike Failure

Unlike EAD mode (which analytically averages over dike failure), Stochastic mode samples whether the dike fails for each surge event. This means:

  • The same policy + same surge sequence can produce different outcomes depending on the RNG seed
  • Dike failure is a Bernoulli event with probability \(p_{fail}(h_{surge}, D)\)
  • When the dike fails, Zone 3 damage is amplified by \(f_{failed} = 1.5\) instead of \(f_{intact} = 0.03\)

This stochasticity is essential for understanding tail risk and the variance of outcomes.

When Variance Matters

Two policies with equal expected damage can have very different outcome distributions. A dike-heavy strategy concentrates risk: it performs well unless the dike fails, in which case losses are catastrophic. A diversified strategy (withdrawal + resistance + small dike) spreads risk across mechanisms, producing less extreme tails. Stochastic mode is the only way to see this distinction.

When to Use Stochastic Mode

Stochastic mode is the right choice when:

  • You care about tail risk (e.g., 95th or 99th percentile losses)
  • You want to analyze the distribution of outcomes, not just the mean
  • You are doing robustness analysis across many scenarios
  • You want to design adaptive policies that respond to observed storms

Comparison with EAD Mode

Property Stochastic EAD
Dike failure Sampled per event Integrated analytically
Output Realized damage Expected damage
Deterministic? No (varies with RNG) Yes (with quadrature)
Variance info Yes No
Speed per evaluation Fast Fast (quadrature adds overhead)
Ensemble needed? Yes (many seeds) No (one evaluation suffices)
Note

For static policies, the mean of many Stochastic runs converges to the EAD result by the Law of Large Numbers. The variance across runs reveals the risk that EAD mode hides.

Tip

See Details for worked examples showing damage distributions and policy comparisons with visualizations.

References