Risk Metrics

Introduction

Risk metrics quantify the expected losses and consequences from seismic hazards over time. This section provides interactive tools to compute and visualize key risk indicators for cities across 12 global regions.

The following risk metrics are computed:

Structural AALR: Expected annual structural damage as a fraction of replacement cost
Non-Structural AALR: Expected annual non-structural damage
Contents AALR: Expected annual contents damage
Building AALR: Combined structural and non-structural losses
Total AALR: Combined structural, non-structural, and contents losses
Fatalities AALR: Expected annual fatality rate per building
Average Annual Collapse Probability (AACP): Annual probability of structural collapse

All AALR metrics use the efficient intensity measure for each building class — the IMT that minimises average dispersion across damage states, reducing uncertainty in the estimates.

Methodology

Risk Calculation

The Average Annual Loss (AAL) is computed by integrating the product of the vulnerability function and the hazard curve:

\[AAL = \int_0^{\infty} V(IM) \cdot \left| \frac{d\lambda(IM)}{dIM} \right| \, dIM\]

where:

\(V(IM)\) is the mean loss ratio from the vulnerability function at intensity \(IM\)
\(\lambda(IM)\) is the annual rate of exceedance from the hazard curve
The derivative represents the annual rate of occurrence at each intensity level

Numerical Integration

The integral is approximated using the trapezoidal rule:

\[AAL \approx \sum_{i=1}^{n} \frac{V(IM_i) + V(IM_{i-1})}{2} \cdot |\lambda(IM_{i-1}) - \lambda(IM_i)|\]

For collapse probability, the calculation integrates the collapse fragility function with the hazard curve:

\[AACP = \int_0^{\infty} P(C|IM) \cdot \left| \frac{d\lambda(IM)}{dIM} \right| \, dIM\]

Interactive Viewer

Use the interactive viewer below to explore precompiled risk metrics for a specific building class within a selected region. The bar charts show values across cities.

Model:

Region:

Building Class:

Occupancy:

Intensity Measure:

Data Requirements

The risk calculations require:

Hazard Curves: Annual exceedance probabilities for each intensity measure level, stored in in/hazard/hazard_curves_{mosaic}_{IMT}.csv
Vulnerability Functions: Mean loss ratios and coefficients of variation as a function of intensity measure
City Database: Geographic and regional information for cities, including hazard mosaic assignments

Regional Coverage

Risk metrics are available for the following 12 regions:

Regional Coverage
Region	Description
North America	United States, Canada, Mexico
Europe	EU member states and surrounding countries
Oceania	Australia, New Zealand, Pacific Islands
South America	All South American countries
Caribbean & Central America	Caribbean islands and Central American countries
Middle East	Gulf states and Levant region
Africa	All African countries
Southeast Asia	ASEAN member states
East Asia	China, Japan, Korea, Taiwan
South Asia	India, Pakistan, Bangladesh, Nepal, Sri Lanka
Central Asia	Former Soviet Central Asian republics, Afghanistan
North Asia	Russia and northern territories