The Hurricane Damage Index (HurDI)

Abstract

Statistical hurricane risk assessments make long-term multi-decadal stationary climate assumptions, but there is large hurricane variability in the risk. It would be useful to also better estimate the “current” risk. The hurricane damage index (HurDI), is proposed as a measure of the underlying non-stationary risk. The HurDI is defined as the normalised annual average damage calculated with a stochastic wind only model, a single damage function, and uniform exposure across the continental U.S. The stochastic model is climate conditioned by weighting the historical basin hurricane counts, potential intensity, and tracks. The weights are chosen to give the best persistence forecast for each parameter for the next five years. There has been a substantial increase of the hurricane risk as measured by the HurDI. In 2024, the index was at a record high of 188, with a reference value of 100 in 1989. The HurDI is a dynamic view of risk based on the hurricane variability only and can be compared to U.S. property catastrophe reinsurance rates. There are periods of varying difference between the rates and the HurDI reflecting the volatile market cycles.

Key Points

• A Hurricane Damage Index, the HurDI, is proposed.
• Time series of the risk can be calculated and updated annually to provide a view of current risk.
• The current risk is the largest since 1989.

1.0 Introduction

The formulation of statistical hurricane hazard and catastrophe models for risk assessment often uses stationary assumptions based on long-term observed behaviour. This makes it difficult to navigate an inherently non-stationary environment as that assumption may be no longer valid. What is the “current” risk? It would thus be desirable to also capture shorter-term variability with a probabilistic risk perspective, rather than just noting observed landfall wind speeds or losses. This current risk would help disentangle the variability around any longer-term anthropogenic climate change. Here we present an approach to estimate the variability of hurricane damage risk and propose a Hurricane Damage Index (HurDI) for the continental U.S.. Such an index could then also be used to contrast the underlying physical risk with the reinsurance pricing cycles. The prices often strongly respond to actual large loss events which may or may not reflect changes in the physical risk.

A distinct spatial and temporal pattern of increasing hurricane frequency is reported over the North Atlantic (e.g. Murakami et al, 2020). There is much debate about the causes of decadal variability, such as the phase changes of the Atlantic Meridional Oscillation (AMO), and/or the effect of volcanic eruptions and decreasing North Atlantic anthropogenic aerosols (e.g. Zhang and Delworth, 2006; Dunstone et al. 2021). There have also been reported shifts in tracks (e.g. Cao et al. 2025), lifetime maximum intensity (Kossin et al., 2020) and number of major hurricane landfalls (Wang and Toumi, 2022). It is argued that the hurricane damages in the United States have increased primarily because of increased exposure (Muller et al., 2025). It remains problematic to disentangle the hurricane variability from the exposure and vulnerability drivers of losses.

The hurricane variability can be described by several observations such as the basin count, the landfall rate or losses. However, these observations by themselves do not capture the underlying probabilistic hazard or risk because they exclude the counterfactual, and do not directly quantify changes in probability of damage. Stochastic event sets are arguably the best way to capture the full range of possible outcomes, and thus inform the risk (e.g. Emanuel et al. 2006, Lee et al., 2018, Bloemendaal et al. 2020, Sparks and Toumi, 2024). These models, however, often assume a longer-term stationary state, which may not reflect shorter term variations.

In this paper we first describe the climate conditioning of the stochastic wind model for three input variables. Secondly, we simulate annual losses and calculate the HurDI. Thirdly, we diagnose the behaviour of the key drivers in the wind model simulation. Finally, we compare the HurDI to market reinsurance prices.

2.0. Method

2.1. The wind model

To capture the full range of plausible landfall wind speeds we use the stochastic Imperial College Storm Model (IRIS), to simulate 10,000 years of synthetic landfall winds and damages for the continental U.S. The IRIS model is described in detail by Sparks and Toumi (2024). The IRIS is a global tropical cyclone wind hazard model. The number of hurricanes in the basin is specified as a model input from IBTrACS (Knapp et al., 2010, Gahtan, et al., 2024). It recognises that the key step for estimating landfall wind speed is the decay process and identifying the location and value of the lifetime maximum intensity (LMI). The LMI is assumed to be physically constrained by the thermodynamic state as defined by PI, the potential intensity (Emanuel, 1986). IRIS takes a PI field calculated from ERA5 variables (Hersbach et al., 2023) and observed (IBTrACS),  “parent” tracks as inputs which it perturbs to create  “child”' tracks. These child tracks have their own stochastic LMI generated using the PI field. From this LMI the tropical cyclone (TC) decays according to a decay model with a stochastic decay rate. The maximum wind speed is the last ocean value before landfall, which is when the track intersects the U.S. coasts (defined by polygons). The model simulates wind only and not explicitly flood or surge. To calculate the wind footprint, a symmetric wind speed is calculated using the Holland et al. (2010) radial wind speed model. The storm translation vector is added to a scaled symmetric wind speed.

IRIS has several innovative features that allow studies on climate change attribution (Sparks and Toumi, 2025a; Clarke et al., 2025) and climate change scenarios (Sparks and Toumi, 2025b). The model is flexible in that it can be conditioned by a choice of the three inputs (basin counts, PI and tracks) and we make use of this to calculate the HurDI.

2.2. Climate Conditioning of IRIS

Conditioning of IRIS is essential as we want to capture the evolution of the hazard and its component drivers. We achieve this conditioning by combining a historical weighting with a forecast. This allows us to constrain the historical weighting for each of the key drives in the IRIS model.

The first challenge is to choose an appropriate minimum time frame to define “current”. The problem is reframed here by considering that it is desirable to have an index that captures both recent history and also provides a potential forecast. We are trying to represent a time scale that is between the strong influence of El Niño-Southern Oscillation (ENSO) and other decadal climate modes, as well as being business relevant. The forecast lead time we choose to determine the optimal historical weighting of the three IRIS inputs is the next five-year mean. The reason for choosing the five-year mean is that it is weakly affected by the ENSO cycle (see 3. Results). It is perhaps the minimum time scale one could consider as a “baseline” current state which is not sensitive to the strong impact of ENSO, but also short enough to enable business planning.

Persistence is the simplest forecast. It assumes the future is the same as the past and the most widely used benchmark in meteorology. The history of the variable needed for the persistence forecast is constructed by applying an exponential weighting or smoothing. In a simple average, the past observations are weighted equally. Instead here we assign exponentially decreasing weights over time. This weighting is a more flexible method than a simple block time average; to enable climate conditioning of the IRIS inputs we can assign a higher weight to the current state, but also include much older data. The weighting may be physically justified in the case of, for example, the potential intensity; it is plausible that older data is increasingly less physically relevant. On the other hand, for older tracks, pre-satellite data may still be informative, but perhaps less reliable. When applying weighting, the older tracks would thus have a smaller impact but are not completely eliminated, as they would be with a block time. By back testing we find the exponential time constant, t, that minimises the root mean square error (RMSE) of the persistence forecast for each variable. Each variable will have its optimal time constant reflecting its variability and predictability. The different weightings are applied to the observations and become the three IRIS inputs: basin count, potential intensity, and tracks.

2.3. The Hurricane Damage Index (HurDI)

The HurDI is defined as the annual average damage simulated with a uniform exposure where every grid point over land has the same economic value. We apply a single damage function proposed by Emanuel (2011). The sigmoid-like shape is defined by a damage minimum wind speed of 24.7 m/s and a wind speed of half damage of 74.7 m/s (Eberenz et al., 2021). However, the damage function is for total economic loss and thus includes surge and flood only indirectly. We also perform simulations of the annual economic damage using a realistic exposure. The LitPop method (Eberenz et al., 2020) was used to generate a realistic exposure of asset value of 2014 at horizontal resolution of approximately 1 km². The method uses the population density and night-time light as a proxy of economic value. We also simulate the annual average damage with this exposure (a simulation we call EXP). The HurDI is a unitless index normalised to 1989 with a value of 100.

3.0 Results

3.1. Climate Conditioning of IRIS

3.1.1. The Basin Hurricane Count

The hurricane basin shows substantial inter-annual variability and long-term increase since 1950. Over the period 1950-2024, the ENSO (the Niño3.4 Index) is very significantly correlated with the annual North Atlantic hurricane basin count (p<0.01), but not significantly correlated with the five-year mean (p=0.3). The lack of correlation justifies the choice of the five-year mean as a minimal “climate” timescale. Climate conditioning of the three input IRIS parameters (counts, PI, and tracks) is achieved by evaluating the time constants that minimise the persistence forecast error for the five-year mean.

For the hurricane basin count since 1950, the best exponential weighting with a time constant, t, of five years is the best persistence forecast, but explains only about 12% of the variance (r=0.3), because of the inherent lagging in the persistence method (Figure 1). It is also important in our application to focus on the hurricane basin count error. The persistence forecast has an error (RMSE) of 1.3 y^-1 or 19%. With the time constant of five years, the forecasts have r=0.6 and RMSE=1.3 y^-1 for the entire period (1900-2024), but we have low confidence in the earlier counts. The AMO is a known strong predictor of the basin hurricane count. Since 1950, the five-year AMO mean only explains about 43% (r=0.7) of the variance of basin-wide hurricane counts. This illustrates the limitations of forecasts, even when hypothetically “knowing” a predictor, like the AMO, perfectly. In the case of a perfect AMO hindcast count, the RMSE would be 0.9 y^-1 or 15%. Given that we never have perfect knowledge of the future five year mean AMO, the persistence forecast error of 1.3 y^-1 is not much larger. Results are not very sensitive to similar time constants (three to 10 years).

Figure 1: Time series of +five-year mean hurricane basin counts (blue line) and five-year time constant weighted count (t=5 y) since 1900 (orange line).

3.1.2. The Potential Intensity

The potential intensity is evaluated at the position of LMI. The best exponential weighting is with a time constant of three years to optimise the persistence forecast. Persistence captures 61% (r=0.8) of the variance with an RMSE of 0.8 m/s (Figure 2). Perfect knowledge of the AMO is also a good predictor of the potential intensity, but accounts for only 53% of the variance underperforming persistence. Results are not very sensitive to similar time constants (two to five years).

Figure 2: PI (m/s) with a three-year time constant weighting (t=3 y) vs mean PI (m/s) of the next five year mean at the LMI position since 1980.

3.1.3. The Tracks

The position of the LMI is used to condition the tracks in the model. We do not directly condition the landfall probability. The annual mean LMI position has undergone substantial shifts since 1900, but also more recently. Some of these LMI changes are likely due to observational bias. The weighting of tracks is very important because we need to keep older landfalls, albeit weighting them less, that are locally infrequent when we build the model. By exponentially weighting the annual historical tracks with a time constant of 21 years, we can best capture the past evolution (Figure 3). The weighted approach can explain 27% (r=0.5) of the variance of the annual mean latitude of LMI and 9% (r=0.3) of the variance of the annual mean longitude of LMI since 1980. The rate of Cat1+ at landfall has an RMSE of 0.7 y^-1. The relatively larger time constant, compared to the PI and basin counts, means we only characterise the long-term LMI position. The large variability of the tracks/probability causes the need for many more observations to estimate a robust mean state. Results are not very sensitive to similar time constants (15-30 years).

Figure 3: Time series of annual mean LMI latitude and longitude with +five-year mean (blue line) and weighted track (t=21 y) mean since 1950 (orange line).

3.2 The HurDI

We can now condition the IRIS model for the three inputs, simulate 10,000 years, and update the “current” risk as defined by the HurDI index. The IRIS inputs and HurDI change annually.

Figure 4: HurDI, PI, landfall rate (LR) and basin count (N) time series (1989-2024) using the weighting PI (t=3 y; RMSE=0.8 m/s), count (t=5 y; RMSE=1.3 y^-1), tracks (t=21 y; combined with N giving the LR RMSE=0.9 y^-1) to evaluate the “current” risk. RMSE is the error in the persistence forecast of the five-year mean of the three variables with time constant, t. HurDI is a normalised index referenced to 1989. Every “year” corresponds to a 10,000-year simulation of HurDI.

Figure 4 shows the HurDI time series normalised to the 1989 loss with a value of 100 and the important model drivers. The HurDI shows a substantial increase over the 35 years with a big increase in 2005, the year of Katrina. A period of decreasing HurDI started in 2005, and HurDI reverted to near reference values in 2013-2019. There has been another very rapid increase in the last five years, notably a jump in 2020 before Ian (2022). The HurDI in 2024 was at a record 188 or +88% above the 1989 reference year.

The time evolution and inherent variability is different for the drivers in the IRIS model. The changes of the drivers play different roles in the HurDI at different times. The long-term basin count uplift from about 5 to 8 is the biggest single driver of the long-term rise in HurDI (r=0.84). We find no correlation of the annual landfall probability and basin hurricane count. The PI increase also appears to contribute by generating more damage through more intense hurricanes, particularly recently. Apart from these multi-decadal changes, there is also substantial shorter-term variability. The landfall rate accounts for 89% of the historical HurDI variance and its variability is the biggest driver of HurDI forecast uncertainty. During the declining phase of 2005-2015 it is instructive to note that the landfall rate dropped off even more dramatically than the basin count. This suggests that the low index during that period was caused mostly by the drop-in basin activity – but also “lucky misses”. These lucky misses are captured by the track weighting. The PI continued to climb during this period but did not control the HurDI. The recent dramatic increase of HurDI over the last five-10 years is caused by both an uptick in the landfall rate, the landfall probability, and the increased basin count. Most recently, the HurDI is at a record high, although the landfall rate is similar to that in 2005. This is due to the impact of the record PI, which is driving stronger intensity at landfall and causing more damage.

Figure 5: The normalised HurDI (black) and EXP (blue) using the exponential weighting for PI (t=3 y), count (t=5 y), tracks (t=21 y) to evaluate the “current” risk for 1989-2024. Reference 1989=100. The average relative standard deviation of 125-year samples in the 10,000-year simulation “year” for HurDI and EXP is 18 % and 22 % respectively.

Figure 5 shows the time series of the simulations with the two different exposures. EXP tends to be lower than HurDI. The heterogeneous nature of EXP enables more misses, reducing the 10,000-year average and causing less damages than HurDI. The differences in time are due to different track weightings. However, EXP generally follows the same pattern as HurDI but has larger sample variability within the 10,000-year simulation. The similarity in the time series confirms both the utility of the uniform exposure assumption in HurDI, and that the 10,000-year event set is sufficient to capture the full range of possible landfalls – otherwise we would have more substantial divergence.

Figure 6: The HurDI (black) and the U.S. Property Catastrophe Rate on Line, ROL (blue), Guy Carpenter Index, 1989 = 100.

We compare the HurDI with the U.S. property catastrophe reinsurance rate indices as published by Guy Carpenter (Figure 6, Appendix). These rates are updated annually (January) and normalised to an index level of 1990. For convenience, we have therefore shifted the reference year to 1989. Clearly visible are three peaks in the rates corresponding to Hurricane Andrew (1992), Katrina (2005) and Ian (2022). These peaks do not align readily with the HurDI. It is important to note that the IRIS model only includes the tracks of events and not their actual landfall intensity or damage. The HurDI is designed to capture the underlying five-year average risk, which often does not change during the year of the loss.

We define the difference between the HurDI and the Guy Carpenter reinsurance rate index as a premium. The average premium since 1989 is 57. An interpretation could be that there has been a systematic uplift of the premium since 1989 as the rates pre-Andrew may have been too small i.e. at a discount and thus the risk was under-priced. Nevertheless, there have been brief periods, for example 2004, when the premium was close to 1990 levels. The lack of an immediate large rate uplift after Irma (2017) may have been due to abundant available reinsurance capital (Paul Wilson private communication). The peak premiums after Hurricanes Andrew, Katrina and Ian were 144, 94, and 123 respectively. The last peak premium suggests that the market may not be becoming much more resilient to large losses, albeit that this assertion is based on a very small sample size of large losses. The premium in 2024 was 75 and above the average by 18.

4. Discussion and Conclusion

A new hurricane damage index, the HurDI, has been developed. It is the annual average damage from a conditioned model with a damage function and uniform exposure for the continental U.S. The HurDI has been increasing over the last 35 years and is at record levels. The increase has been caused by mostly the increasing basin counts. The landfall probability has not made a substantial contribution to the long-term increase. The current record HurDI points to the impact of increased potential intensity, due to substantial warming in the North Atlantic, making more intense hurricane landfall much more likely. In a warming world, it is no longer sufficient to just consider the landfall rate. Including a changing intensity distribution gives a more accurate picture of the risk. The HurDI enables a dynamic view of risk rather than assuming a long-term stationary view.

A uniform exposure for the entire continental U.S. is a suitable choice for a general understanding of the risk evolution, but an index with any specific or local exposure may evolve differently. We have chosen the annual average loss as it is perhaps the most common metric. We find that it also has a larger variability compared to fixed return period loss (e.g. one in 20-year loss) and thus highlights the potential benefit of the HurDI. There are clearly opportunities to create other variants including ones with a regional focus. The HurDI does depend on the reliability of the IRIS model. The IRIS construction with observed inputs makes the calculation of the HurDI straightforward, but other modellers may be encouraged to make similar simulations.

Reinsurance rates can be compared to observed losses or observed landfall wind speeds. The HurDI now also allows an overlay of a probabilistic dynamic view of the risk on losses or insurance rates. The difference between the HurDI and reinsurance rates can be defined as a premium. It can be useful to think of a “hardening” or “weakening” market as one of increased or decreased premium. The large premium after major losses suggests that the market is not very resilient or efficient in the sense that large losses are to be expected. The extensive use of catastrophe models since the 1990s should have caused the market to price risk and it should by now be less prone to large loss price reaction. The response in rates to large loss events may also be due to capital supply/demand rather than the industry assuming a change in risk. A lack of additional capital (e.g. from Insurance Linked Securities) after a large event will maintain a premium compared to HurDI. There is also the sentiment of clawing back funds from insurers after large losses.

There are, of course, a multitude of factors affecting the rates which are not directly connected to the hurricane hazard. These market factors may include the supply of reinsurance capital, non-hurricane large losses, and interest rates. Nevertheless, the HurDI provides a robust way to define the underlying physical hurricane risk and helps to place these market cycles in some context.

References

Appendix

Guy Carpenter U.S. Property Rate-on-Line Index – this is the proprietary index of U.S. property catastrophe reinsurance Rate-on-Line (ROL) movements, on brokered excess of loss placements, that has been maintained by Guy Carpenter since 1990. The index covers U.S. property catastrophe renewals. It is updated following January 1st renewals and July 1st renewals reflecting the full year, by calculating the change in the ROL year on year across the same renewal base. The Guy Carpenter ROL index is a measure of the change in dollars paid for coverage year on year on a consistent program base. The index reflects the pricing impact of a growing (or shrinking) exposure base, evolving methods of measuring risk, changes in buying habits, as well as changes in market conditions. Unlike risk-adjusted measurements, the index is not dependent on the model or method used to measure the amount of perceived risk in a programme, which can vary widely.

Quotation from https://www.artemis.bm/us-property-cat-rate-on-line-index/

Acknowledgements

This work was supported by the Lighthill Risk Network. We thank anonymous reviewers for insightful comments.

Declarations

Handling Editor: Thomas Loridan, Co-Founder and Chief Science Officer, Reask

The Journal of Catastrophe Risk and Resilience would like to thank Thomas Loridan for his role as Handling Editor throughout the peer-review process for this article. We would also like to extend our thanks to the chosen academic reviewers for sharing their expertise and time while undertaking the peer review of this article.

Received: 18th February 2025
Accepted: 26th June 2025
Published: 6th August 2025

Rights and Permissions

Access: This article is Diamond Open Access.
Licencing: Attribution 4.0 International (CC BY 4.0)
DOI: 10.63024/k2gm-2j0m
Article Number: 03.05
ISSN: 3049-7604
Copyright: Copyright remains with the author, and not with the Journal of Catastrophe Risk and Resilience.

Article Citation Details

Toumi, R., & Sparks, N., 2025. The Hurricane Damage Index (HurDI), Journal of Catastrophe Risk and Resilience, (2025). https://doi.org/10.63024/k2gm-2j0m

Share this article: https://journalofcrr.com/research/03-05-toumi-sparks/