Traditionally, risk is quantified in terms of expected losses using metrics such as average annual losses and probable maximum losses. Risk metrics are calculated considering hazard frequencies, damage probabilities, and consequence exposure (Di Mauro 2014). The National Risk Index approach expands on the traditional expression of risk solely as expected annual losses by accounting for the likelihood of adverse impacts based on a community’s comparative social vulnerability and community resilience. Figure 1 shows the generalized risk equation. The components of this equation are explored in detail in subsequent sections.
See the National Risk Index: Technical Documentation for more information on the detailed methodology used by the Index (FEMA 2021b).
Selection of natural hazards
The 18 hazard types included in the National Risk Index (see Fig. 1) were chosen based on a comprehensive review of hazard risk profiles from available 2016 State Hazard Mitigation Plans. For a hazard type to be included in the index, it had to be profiled by at least half of the State Hazard Mitigation Plans or be considered a significant regional hazard, which is defined as a hazard geographically limited in occurrence but contributing significantly to a region’s risk profile, such as hurricane or volcanic activity. Working groups of hazard identification and risk assessment experts helped identify the best available, nationwide datasets for each hazard type. No man-made hazards, such as dam or levee failure, were included, and the subsidence hazard was excluded due to lack of available data.
Expected annual loss
The objective was to generate accurate, comparable EAL values for all communities (county and Census tract) for each of the 18 hazard types they are susceptible to and a composite EAL, which is the cumulative EAL for all hazard types. There were major challenges to achieving this objective, including, but not limited to:
The nature of hazard types differs significantly, impacting communities with varying frequencies, severities, durations, and geographic extents.
Hazard types contribute orders of magnitude different levels of losses. For example, average annual losses in the US from 1996 to 2019 in the Spatial Hazard Events and Losses Database of the United States (SHELDUS) from Hurricanes were $12.4 billion versus $4 million for Tsunamis (Arizona State University Center for Emergency Management and Homeland Security [ASU CEMHS] 2020).
Hazard occurrence can result in a wide range of consequence types (e.g., injuries, fatalities, property damage, crop and livestock damage, and lifeline disruption).
Available source datasets characterizing historic or expected hazard occurrences vary across hazard types in format, quality, period of record, geographic scope, and resolution.
To address these challenges, the team developed an overarching analytical framework; however, methods specific to hazard types were developed to address and model the variance in hazard nature, magnitude of losses, consequence types, and source data. This approach was unique and iteratively constructed for the specific needs of a national, multi-hazard risk assessment for communities. Characterization of the hazard type in terms of how it would be represented within the model was dependent on how the hazard type’s occurrences were documented in the source data and how historic losses were reported. To ensure consistent EAL results across hazard types, the team ensured alignment among the annualized frequency, exposure, and HLR factors.
Losses were estimated in three consequence types: building, population, and agriculture (crop and livestock). Each hazard type was modeled to have losses in one or more of these consequence types. Impacts to buildings and population were estimated for all hazard types except drought, which only estimated agriculture losses. Additionally, agriculture losses were estimated for those hazard types where agriculture losses contributed greater than 1% of the total historic reported losses (see Fig. 2).
EAL was computed for each hazard type by evaluating the applicable losses in each relevant consequence type. All losses were quantified as an annual dollar amount. While building and agriculture losses were monetary in the source data, impacts on population were monetized into a population equivalence factor by taking fatality estimates from the source data and applying a $7.6 million Value of Statistical Life (VSL) (Zhou et al. 2020; FEMA 2009) and adjusting for inflation to 2020 dollars using the Consumer Price Index Inflation calculator (US Bureau of Labor Statistics [BLS] 2021).EAL was calculated using hazard type-specific annualized frequency and consequence type-specific exposure and HLR factors using the method shown in Fig. 3. Monetization of the population consequences enabled the calculation of a total EAL, which considers all relevant consequence types for the hazard type. (Note: Each EAL factor is explored in detail in subsequent sections.)
For each community, all relevant hazard type EALs were added up to estimate composite EALs for total consequences and each of the three consequence types. Composite EALs represent the expected monetized losses from all hazard types. Hazard types with large EAL values contribute more significantly to the composite EAL than those with lower EAL values. A few hazard types often contribute most of the loss to the composite value of a community. For example, $1.35 billion of the $1.43 billion composite EAL for Los Angeles County, CA, came from Earthquake, while $73 million came from Wildfire.
Natural hazard annualized frequency is defined as the expected frequency or probability of a hazard occurrence per year. Annualized frequency is derived either from the number of recorded hazard occurrences each year over a given period or the modeled probability of a hazard occurrence each year for a given community (Fig. 4).
There were several challenges in maintaining a consistent framework when estimating frequency across hazard types, including:
Available source datasets vary significantly across hazard types in format (e.g., points, polygons, raster), quality, period of record, and geographic scope (e.g., continental US only).
Hazard occurrences not only cause losses over different durations (e.g., Earthquake losses take seconds, Hurricane losses take days, and Drought losses may accumulate over months), but also vary in their geographic extent (e.g., Lightning strikes impact point locations, tornadoes impact paths, and hurricanes can impact multiple states).
Some hazard types occur frequently (e.g., Lightning), while others are rare (e.g., Tsunami).
Some hazard types can occur in places where they have not yet been recorded.
Annualized frequency estimates for the collection of hazard types were derived from multiple authoritative data sources. The team developed a set of techniques to address the challenges for all hazard types that were combined into a tailored approach based on the unique characteristics of each hazard type and its source data. The team had to determine the geographic extent at which event counts should be aggregated to develop representative frequency estimates for a community for each hazard type. For select hazard types, frequency was modeled at the subtype level, for example by the tornado Enhanced Fujita (EF) scale.
To account for different hazard occurrence durations, frequency units were designated for each hazard. For hazard types with shorter durations (generally less than one day), historical event counts were used as the units for annualized frequency (i.e., events per year). For longer duration hazard types (generally more than one day), historical event days were used as the units for annualized frequency (i.e., event-days per year). This distinction in characterizing the frequency basis was important to ensure alignment with the calculation of the HLR, which is discussed later.
For Wildfire, Earthquake, and select Coastal Flooding subtypes, the best available source data were geocoded probabilistic statistics and return period data that were used to compute an annualized frequency. Table 3 in the Appendix identifies the source datasets and approach that was used for each hazard type.
To address challenges with geographic extent, rarity of occurrence, and potential to occur in places where hazards have not yet been recorded, the team developed three major solutions, a combination of which is used for each hazard type:
Hazard Occurrence Buffering Hazard types with widespread and/or unpredictable locations were buffered using expert-determined distances to smooth the representative areas of hazard occurrence. Hazard types using this approach include Hail, Hurricane, Strong Wind, Tornado, and Tsunami.
Geographic Grid Aggregation The team applied a 49-by-49 km fishnet gridFootnote 1 covering the US and counted the number of hazard occurrences (events or event-days) within each cell. Communities within the cell either inherited the count or an area apportionment of the cell count. When communities intersected multiple cells, an area-weighted count was applied. Hazard types using this approach include Hail, Hurricane, Ice Storm, Strong Wind, and Tornado. For select hazards, counts were scaled to prevent overestimation at the community level.
Minimum Annual Frequency A minimum annual frequency was assigned to communities that have not experienced a hazard occurrence recorded by the source data but were determined to be at some risk. Appropriate minimum values were identified by hazard-type subject matter experts. The estimated values are low given that historic occurrences had not been recorded over the period of record. Hazard types using this approach include Avalanche, Hurricane, Ice Storm, Landslide, Riverine Flooding, Tornado, and Tsunami.
Table 3 in the Appendix summarizes the data sources and the hazard occurrence basis used to estimate annualized frequency for each of the hazard types.
Exposure is defined as the representative value of buildings, population (or population equivalence), or agriculture (crop and livestock) in a community exposed to a natural hazard occurrence (see Fig. 5). Each hazard type is associated with a footprint or exposure area in which the hazard can occur and cause loss. Exposure differs across hazard types; so, the team developed three ways to define exposure: (1) widespread, (2) susceptible area, or (3) representative area or values (see Fig. 5 for examples of each). Table 3 in Appendix identifies which approach was used for each hazard type.
A widespread exposure area was used for those hazard types that either impact large, multi-county areas (e.g., Drought) or could happen anywhere in the county with similar likelihood (e.g., Strong Wind). Susceptible area exposures were used for those hazard types where there is a distinct footprint where the hazard type can occur, such as flood zones along a river or areas in proximity to a volcano.
For Tornado, representative areas were estimated using average historic occurrence footprints for three sub-types based on the EF scale: (1) EF-scale 0 and 1; (2) EF-scale 2 and 3; and (3) EF-scale 4 and 5. These representative areas were 0.78 km2, 13 km2, and 79 km2, respectively. For Avalanche, a default value was applied for building and population exposure based on an analysis of historical event occurrences.
As source data varies in its native spatial representation of each hazard type, the team translated each relevant record in the source data into a spatial polygon dataset for each hazard type. Spatial processes were then used to intersect those exposure areas with Census block or Census tract boundaries to determine exposed areas for each hazard type.
Exposure values in the National Risk Index leverage FEMA’s Hazus data (version 4.2 Service Pack 1) (FEMA 2018a) for building value and population estimates at each administrative reference layer (Census block, Census tract, and county). To generate exposure value estimates, the team multiplied exposure areas, either widespread or susceptible, by building and population densities. Depending on hazard type, the calculation used either average density or developed area density. Average building and population densities were calculated by dividing the building and population values by the total area, while developed area building and population densities were calculated by dividing the building and population values by the total developed area within the administrative reference layer. For agriculture, the US Department of Agriculture (USDA) 2017 Census of Agriculture provided an estimated dollar value of crop and livestock within each state (USDA 2019). This value was area-apportioned to each administrative reference layer. Agriculture value density was calculated by dividing the agriculture value by the total agriculture area of the administrative reference layer.
Table 3 in Appendix summarizes the relevant consequence types and the exposure area basis used to estimate exposure for each of the hazard types.
Historic loss ratio
HLR is a hazard- and county-specific estimate of the percentage of the exposed consequence type expected to be lost in a single hazard occurrence (see Fig. 6). This factor is developed using SHELDUS, which provides county-level dataFootnote 2 for each hazard occurrence, including begin and end dates, duration, county, associated hazard and peril, property damage, crop losses, injuries, and fatalities (ASU CEMHS 2020).
As SHELDUS only records events that resulted in losses, hazard occurrences with no losses are not included in SHELDUS. Thus, because the HLR averages needed to consider all events—including those that did and did not result in losses—a number of zero-loss hazard occurrences equal to the difference between the estimated total number of occurrences and the number of occurrences that resulted in loss were added to the dataset as part of the HLR calculation process.
A county’s HLR could be the simple average of loss ratios (losses divided by exposure) from past hazard occurrences. However, because there are often wide variances in loss ratios or not enough hazard occurrences for a statistically significant average, the Bayesian credibility approach (Schnieper 1995) that considers multiple geographic levels was developed. Specifically, averages and variances of the individual hazard occurrence loss ratios are calculated for each consequence type for up to four levels depending on the hazard type: (1) county, (2) surrounding area (196-by-196 km grid), (3) region, and (4) US.
The model used the average and variance values from the four levels to determine each level’s weighting factor and to calculate a final, county-level Bayesian-adjusted HLR for each hazard type and consequence type using the equation in Fig. 7.
HLRBuilding is the county-level Bayesian-adjusted HLR for the building consequence type for a specific hazard type. Note: a similar formula was used to calculate population and agriculture HLRs.
Average Loss RatioX is the average loss ratio for hazard occurrences at X level (national, regional, surrounding area, county) for the consequence type (e.g., building).
WeightX is the weighting factor for hazard occurrences at X level (national, regional, surrounding area, county) for the consequence type based on the variance of X level compared to variances at all other levels.
Figure 8 provides a representation of how loss ratios and variance impact the HLR calculation for four notional neighboring counties. In this example, the HLR for County D would be closer to County D’s average, which has many occurrences of a hazard that resulted in similar loss ratios, than Counties A, B, or C, which have had few or no occurrences and greater variance in their loss ratios. The HLRs for Counties A, B, and C will receive more contribution from the higher geographic levels (e.g., surrounding area, regional, or national) due to the lack of occurrences and/or high variance in loss ratios. Not all geographic levels were used for each hazard type. Table 3 in Appendix identifies which Bayesian levels were applied to each hazard type.
Calculation of EAL
EAL values, quantified as an annual expected dollar loss, were computed at the Census block level for each hazard type and relevant consequence type and summed to a total EAL. The Census block-level EAL values were then aggregated to the parent Census tract and county separately (see Fig. 9). This process was used for all hazard types except for Avalanche and Drought, which used county and Census tract, respectively, as the base EAL calculation level. For Earthquake, county and Census tract EAL values were extracted from FEMA’s P-366 study data (FEMA 2017).
Additionally, a composite EAL value (for total EAL and each consequence type) was calculated by summing the EALs for the 18 hazard types for each census tract and county as shown in Fig. 10.
Comparing EAL to historical losses
To gauge the accuracy of EAL values, historic losses from SHELDUS for the period from 1996 to 2019 were annualized for a national loss estimate for each of the hazard types. When compared to the aggregated total EAL estimate, all hazard types, except Hurricane, Earthquake and Volcanic Activity, were within a factor of two (see Table 1). These exceptions existed because losses for those hazard types are driven by relatively few hazard occurrences. For example, from 1996 to 2019, 75% of all Hurricane consequences were caused by only seven storms. These hazard occurrences are statistical outliers where high-value urban areas were impacted by severe hazard occurrences.
Similarly, from 1996 to 2019, the US had only one earthquake that exceeded one billion dollars in property loss: the 2001 Nisqually earthquake that impacted King, Pierce, and Thurston counties in Washington (ASU CEMHS 2020). Through use of national probabilistic data, the potential for major earthquakes in other parts of the country, such as Los Angeles and San Francisco, was recognized, and the probability that outlier events might occur was included. For this reason, Earthquake EAL estimates are much higher than historic losses for the period. Pursuing the development or integration of probabilistic data for additional hazard types, such as Hurricane and Riverine Flooding, could significantly improve the risk profiles.
Despite these outliers, the relatively high level of agreement between the calculated EAL values and the historical loss records shows that the EAL estimates are well aligned with actual recorded historic losses.
Social vulnerability and community resilience
Communities are impacted differently by natural hazards. To address the inequities of disaster impacts, the National Risk Index includes social vulnerability as a community-specific coefficient that increases risk and community resilience as a community-specific coefficient that decreases risk. The use of these parameters to increase or decrease the community Risk Index scores is consistent with emerging approaches for modeling natural disaster risks (Lavell et al. 2012). The National Risk Index accounts for social vulnerability and community resilience with the University of South Carolina’s Social Vulnerability Index (SoVI) and Hazards and Vulnerability Research Institute’s Baseline Resilience Indicators for Communities (HVRI BRIC) index, respectively.
SoVI is a location-specific assessment that utilizes 29 socioeconomic variables contributing to a community’s reduced ability to prepare for, respond to, and recover from hazards (University of South Carolina 2021a). To construct the index, SoVI converts variable values from this initial set into z-scores and applies a principal components analysis that reduces their dimensionality to a smaller set of statistically optimized components. Then SoVI implements an additive model over these components to adjust their cardinality and arrive at the final result (Cutter et al. 2003). SoVI values range from − 19.944 to 42.589 for Census tracts and from − 9.73 to 15.64 for counties.
The HVRI BRIC dataset includes a set of 49 indicators that represent six types of resilience: social, economic, community capital, institutional capacity, housing/infrastructure, and environmental (University of South Carolina 2021b). To construct the index, HVIR BRIC uses linear min/max scaling to standardize the units of each variable along an interval from 0 (less resilient) to 1 (more resilient). Then HVIR BRIC calculates the mean of these scaled values within each resilience-type and their sum determines the result (Cutter et al. 2014). HVRI BRIC values range from 2.059 to 3.233. HVRI BRIC values are only available at the county level, so each Census tract was assigned the value of its parent county.
These two indices include some related data inputs but are conceptually distinct. While SoVI examines population characteristics to understand vulnerability of individuals to disaster, HVRI BRIC incorporates measures of social, economic, and institutional resilience and community capital (Cutter et al. 2010). At the county level, SoVI and HVRI BRIC index values have low statistical correlation (Pearson’s correlation coefficient of − 0.26), statistically confirming their conceptual distinction.
Individual hazard-type Risk Index scores and a composite Risk Index score were calculated for each Census tract and county using the process shown in Fig. 11. These scores measured the relative risk of a community to that of all other communities at the same level (Census tract or county). EAL, SoVI, and HVRI BRIC values used different scales and units. To combine them, their unit values were independently normalized to a range of 0 (lowest possible value) to 100 (highest possible value). To achieve this range, the values of each component were rescaled using a min–max transformation, which preserves their distribution while making them easier to understand. EAL values can span several orders of magnitude between rural and urban communities. To address this, a cube root transformation was applied before min–max normalization. The cube root transformation controls for this characteristic and provides scores with greater differentiation and usefulness (Hoyle 1973).
EAL ScoreHazard is a score derived from the estimate of expected losses (building value, population equivalence, and agriculture value) each year from the hazard type.
Social Vulnerability Score is derived from an index value of demographic characteristics that measure a community’s susceptibility to the adverse impacts of natural hazards.
Community Resilience Score is derived from an index value of demographic characteristics that measure a community’s ability to prepare for, adapt to, withstand, and recover from natural hazards.
A composite, multi-hazard Risk Index score is calculated using the same process with the EALComposite value. This represented the risk of a community for all hazard types relative to all other communities at the same level (Census tract or county).
Additionally, a five-category qualitative rating was provided that describes the nature of a community’s score in comparison with all other communities at the same level, ranging from “Very Low” to “Very High.” To determine the content of each rating category, an unsupervised machine learning technique known as k-means clustering or natural breaks was applied to each score: Risk Index, EAL, Social Vulnerability, and Community Resilience. For each score, this approach divided all communities into five groups such that the communities within each group were as similar as possible (minimized variance) while the groups were as different as possible (maximized variance).
Since the value ranges associated with each rating category are assessed independently for each component and score, there were no fixed numeric values for each category. For example, a county’s risk score for Tsunami could be 6.2 with a rating of “Very Low,” while its risk score for Riverine Flooding could be 3.3 with a rating of “Relatively Low.” The rating is intended to classify a community for a specific component, relative to all other communities at the same level.
Figure 12 shows the standard color schemes for each rating category, illustrates how component ratings impact risk ratings, and provides several illustrative examples of EAL, Social Vulnerability, Community Resilience, and Risk Index scores and rating categories for ten representative counties.