Insights · Climate-Informed Asset Management · Part 4 · Appendix

Exposure analysis appendix: EAE, climate PoF, and the CNAIM framework

CNAIM's probability of failure has exposure baked in — but statically, generically, and backward-looking. Reconciling it with the IPCC climate risk framework shows exactly where forward-looking, probabilistic climate hazard modeling plugs into traditional asset risk.

2026-01-11 · 4 min read

This supplementary article accompanies Part 4 and clarifies a common point of confusion: the distinction between the IPCC Climate Risk Framework and the CNAIM Risk Framework familiar to many utility asset managers.

How IPCC Climate Risk Framework, EAE, and CNAIM Risk frameworks actually relate:

┌──────────────────────────────────────────────────────────────────────┐
│                COMPLETE RISK FRAMEWORK RECONCILIATION                │
├──────────────────────────────────────────────────────────────────────┤
│                                                                      │
│  IPCC AR6:   Risk = f(Hazard, Exposure, Vulnerability) × Consequence │
│                        ↓         ↓            ↓              ↓       │
│                       f(x)      E(x)      Fragility(x)      CoF      │
│                        │         │            │              │       │
│                        └────┬────┘            │              │       │
│                             ↓                 │              │       │
│  EAE Step:          ∫ f(x)·E(x) dx            │              │       │
│                     = Expected Annual         │              │       │
│                       Exposure                │              │       │
│                             │                 │              │       │
│                             └────────┬────────┘              │       │
│                                      ↓                       │       │
│  PoF Step:              ∫ f(x)·E(x)·V(x) dx                  │       │
│                         = Annual Probability                 │       │
│                           of Failure (Climate)               │       │
│                                      │                       │       │
│                                      ↓                       │       │
│  CNAIM:                     PoF_total × CoF = Risk           │       │
│                                ↑                             │       │
│                                │                             │       │
│                    ┌───────────┴───────────┐                 │       │
│                    │                       │                 │       │
│              PoF_baseline            PoF_climate ←───────────┘       │
│              (Condition,Age,         (From hazard ×                  │
│               Environment)            fragility)                     │
│                                                                      │
└──────────────────────────────────────────────────────────────────────┘

Breaking Down Each Framework

1. IPCC Climate Risk Framework (Conceptual)

Formula stating risk equals a function of hazard, exposure and vulnerability, multiplied by consequence

This is a conceptual framework—it tells you the components, but not the math.

2. Expected Annual Exposure (Quantifying Exposure)

Formula defining expected annual exposure EAE as the integral of the hazard PDF f of x times the exposure response E of x

  • f(x) = Hazard PDF (how often does intensity x occur?)
  • E(x) = Exposure response (what stress/demand at intensity x?)
  • EAE = Expected annual exposure (NOT failure probability)

Example interpretation: EAE = 0.09 means "9% expected stress utilization per year" or "equivalent to 0.09 damaging events per year"

3. Climate PoF (Adding Vulnerability/Fragility)

To get actual probability of failure, you need the fragility curve:

Formula for climate probability of failure as the integral of the hazard PDF times the fragility function of intensity x

Or if E(x) represents stress ratio:

Formula for climate probability of failure as the integral of the hazard PDF times the probability of failure given the exposure response E of x

This is where the "vulnerability" component enters.

4. CNAIM Framework (Traditional Asset Management)

CNAIM formula stating risk equals probability of failure times consequence of failure

Where CNAIM's PoF includes:

  • Health Index (condition, age, defects)
  • Environmental factors (generic: corrosion, pollution)
  • Loading factors (utilization)

Critical insight: CNAIM's PoF does NOT explicitly model climate hazard distributions. It uses average historical failure rates, not probabilistic climate projections.

The Reconciliation: Where is Exposure in CNAIM?

Exposure is partially "baked into" CNAIM, but incompletely.

Table comparing how CNAIM and the climate risk approach treat hazard, exposure, vulnerability and consequence

CNAIM captures exposure through:

  • Location environment category (coastal, industrial, rural)
  • Distance from coast (corrosion proxy)
  • Pollution level (insulator degradation)

But this is:

  • Static - doesn't capture changing climate
  • Non-probabilistic - not based on hazard intensity distributions
  • Generic - not specific to each hazard type
  • Backward-looking - based on historical conditions

The Complete Formula: Integrating Both Approaches

For climate-informed asset risk:

Complete integrated formula set where total risk equals baseline plus climate probability of failure times consequence, with the climate term summed over hazards as hazard frequency times an integral of the hazard PDF and fragility, or equivalently a sum of per-hazard EAE converted to failure probability

Clarifying E(x) Interpretation Options

The interpretation of E(x) determines what EAE means:

Table of three interpretations of E of x, stress ratio, damage ratio and fragility curve, with what EAE then represents and its relationship to PoF, plus the special case where E of x is a fragility curve and EAE equals climate PoF directly

This is the special case where EAE directly equals the climate-driven probability of failure.

Summary Table: Framework Reconciliation

Summary table reconciling the IPCC, EAE, climate PoF, CNAIM and integrated frameworks by formula and their treatment of hazard, exposure, vulnerability and consequence

Visual Summary

                          CNAIM (Traditional)
                         ┌─────────────────────┐
                         │   PoF_baseline      │
                         │   (Age, Condition,  │
                         │    Environment)     │
                         └──────────┬──────────┘
                                    │
                                    ↓
                         ┌──────────┴──────────┐
                         │                     │
     Climate Risk        │    PoF_total        │         Consequence
    ┌──────────────┐     │         ×           │     ┌──────────────┐
    │  PoF_climate │ ──→ │                     │ ←── │     CoF      │
    │              │     │                     │     │              │
    │ = ∫f(x)·V(x) │     └──────────┬──────────┘     │ (Customers,  │
    │              │                │                │  Safety,     │
    └──────┬───────┘                ↓                │  Financial)  │
           │                  ┌─────────┐            └──────────────┘
           │                  │  RISK   │
           │                  └─────────┘
           │
    ┌──────┴───────────────────────────────┐
    │                                      │
    │   f(x) = Hazard PDF (GEV/GPD)        │
    │          ×                           │
    │   V(x) = Vulnerability (Fragility)   │
    │          ×                           │
    │   [Spatial Exposure: is asset here?] │
    │                                      │
    └──────────────────────────────────────┘

Key Takeaways

  • f(x) is hazard intensity PDF, not PoF — it answers "how often does intensity x occur?"
  • E(x) is exposure response, not PoF — it answers "what happens to the asset at intensity x?"
  • Fragility/Vulnerability converts exposure to failure probability — P(failure | intensity x)
  • CNAIM's PoF has exposure baked in implicitly through generic environment factors, but this is static, backward-looking, and non-probabilistic
  • Climate risk adds explicit, forward-looking, probabilistic hazard modeling on top of the CNAIM baseline
  • Complete integration: Risk = (PoF_CNAIM + PoF_climate) × CoF