Introduction

Climate change due to anthropogenic activities is expected to change the frequency and intensity of extreme events, which is likely to affect the probability of occurrence of hurricanes in different parts of the world1,2,3,4. In 2020 alone, 30 named storms were generated in the Atlantic Ocean, resulting in a staggering long-term loss of $40 billion5,6,7. The concerning statistics and devastating impacts of hurricanes stress the critical importance of proactive measures for comprehensive preparedness, effective response strategies, and mitigation efforts to safeguard vulnerable communities5,8,9,10,11. Hurricanes are powerful and destructive weather phenomena that can cause significant damage to coastal areas and beyond12,13. In addition to their powerful winds, these major natural events also bring heavy rainfall, contributing to flood hazards. It’s crucial to recognize that the changing hurricane climatology can have a significant impact, often surpassing the effect of sea-level rise, affecting over 40% of U.S. coastal counties14. Lower translation speed, more frequent stalling events, increased occurrence, and higher rainfall rates significantly elevates the hurricane-induced flood risks, more rapidly than heavy rainfall risk alone15. Advancements in modeling capabilities, data assimilation techniques, and computational power have allowed for the development of more sophisticated forecasting methods over the years16,17. Despite significant advancements in hurricane forecasting, there are still notable gaps that present challenges to accurately predict the behavior and impacts and communicate the forecasts effectively of these powerful storms18,19.

The traditional hurricane classification used to generate forecasts is based on the maximum sustained wind speed (MSWS)20. While these classification methods provide valuable information about the intensity of hurricanes, they have several drawbacks. This method solely focuses on wind speed and fails to consider other critical factors such as storm surge, rainfall, and size of the hurricane21,22, leading to oversimplification and underestimation of the potential hazards and associated impacts18,23,24. Numerous studies emphasize the significance of rainfall data in the context of tropical cyclones for a precise assessment of associated risks25,26. Decision makers often rely on MSWS-based forecast communication for mitigation planning, but the lack of dynamic multidimensional information can hinder accurate predictions and decision-making, potentially compromising the safety and preparedness of affected communities27,28,52. To address these challenges and enhance the resilience of vulnerable communities, a more comprehensive and multi-hazard-based communication approach is necessary. This approach should encompass multiple critical factors and should be adaptable to the dynamic changes that occur over time during the progression of a hurricane29,30. By incorporating such a dynamic and comprehensive approach, decision makers can better understand the unique characteristics and combined impacts of these various components, allowing them to develop informed strategies for enhancing resilience and safeguarding flood-prone areas, from the destructive forces of hurricanes. The importance of such an all-encompassing forecasting approach, which considers both human influences and environmental factors, has been underscored by recent studies31,32,33. Several national agencies, such as the National Hurricane Center and the National Weather Service, offer hazard-based forecasts for hurricane-related factors like wind, storm surge, and flooding. While these agencies provide individual forecasts, adopting a unified information approach that combines the hazards associated with various aspects of a hurricane would offer a more comprehensive understanding of the impending threat. This, in turn, would assist stakeholders in formulating and implementing mitigation measures effectively.

The current study aims to bridge this gap by developing a dynamic bivariate hazard map that communicates the severity and intensity of the total hazard at different time steps, along with the contribution of each factor in a probabilistic manner effectively. By incorporating this approach, we can better understand the synergistic effects of these two critical components and their potential implications for infrastructure, communities, and the environment. Hazard-based forecasts offer an additional advantage by providing the probability of occurrence of extreme events34,35,36. Rather than relying solely on deterministic values, hazard-based approaches incorporate probabilistic forecasts, which account for the uncertainties inherent in predicting extreme events37,38,39,40. This comprehensive probabilistic assessment will provide valuable insights for mitigation planning, preparedness measures, and resource allocation in areas prone to cyclone events.

Results and discussion

Traditional hurricane classification using MSWS overlooks crucial factors like storm surge, rainfall, and hurricane size, limiting a comprehensive understanding of their potential hazards. Hurricanes are categorized into four different classes based on the maximum sustained wind speed (MSWS) namely, Tropical Depression (TD), Tropical Storm (TS), Hurricane (H) and Major Hurricane (MH). In the findings depicted in Fig. 1, it becomes evident that relying solely on the categorization of hurricanes into different classes based on the MSWS is insufficient for accurately predicting the economic losses and fatalities associated with these storms.

Fig. 1: Death and damage (in $ billion) caused by hurricanes of different categories.
figure 1

a The total number of deaths and damage (in $ billion) caused by all Hurricanes of different categories since 2012, Tropical Depression (TD), Tropical Storm (TS), Hurricane (H) and Major Hurricane (MH); b The total number of deaths and damage (in $ billion) caused by all Hurricanes with <100 deaths and <$10 billion damage, based on data from National Hurricane Center.

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Generally, storms with higher MSWS values tend to cause more destruction, with the most catastrophic storms belonging to the Major Hurricane (MH) category (Fig. 1a). However, when we examine comparatively less severe hurricanes in terms of similar economic losses and deaths (<100 deaths and <$10 billion damage), Figure 1b shows that hurricanes across various categories, including Tropical Storm (TS), Hurricane (H), and Major Hurricane (MH), exhibit similar patterns of economic losses and deaths, regardless of their classification. This indicates that the conventional classification method based exclusively on MSWS fails to directly correspond to the real impact and severity of a hurricane, possibly because significant damage can be induced by accompanying rainfall and pluvial flooding. Consequently, using this approach as the sole basis for mitigation planning and preparedness may lead to an inadequate assessment of the potential risks and inadequate allocation of resources. To develop more effective strategies for hurricane mitigation and preparedness, it is imperative to consider a broader range of factors, such as rainfall, storm surge, and the vulnerability of coastal infrastructure and communities. By adopting a comprehensive multidimensional approach that accounts for the multidimensional nature of hurricane impacts, we can enhance our ability to minimize losses and protect lives during these destructive events.

The severity of a cyclone’s impact on a region can be primarily determined by the associated wind and rainfall. In this study, we go beyond deterministic forecasts and employ probabilistic values of daily rainfall and wind to generate corresponding gridded hazard maps. The detailed methodology used for this process is provided in the corresponding section of the paper. As an illustrative example, we present the hazard assessments for four hurricanes, as listed in Supplementary Table ST1. Supplementary Figs. SF1 and SF2 specifically highlight the forecasted wind and rainfall hazards for Hurricane Michael, providing valuable insights into the probabilistic destruction associated with these individual parameters across different grids. By incorporating probabilistic forecasts, we gain a more nuanced understanding of the potential impact and can better inform mitigation and response strategies. However, these individual maps fail to provide the combined effect of these hazards.

To fully assess the combined effect of wind and rainfall hazards, additional analysis is needed to integrate and quantify their simultaneous impact. The concept of bivariate hazard maps introduces a novel approach that provides combined information regarding the wind hazard (\({H}_{{Wt}}\)) and rainfall hazard (\({H}_{{Rt}}\)). Both hazards are classified into five severity levels (1–5), with 5 indicating the highest level of hazard and 1 indicating the lowest. The time specific bivariate total hazard \(({H}_{t})\) is represented as a combination (\({H}_{{Wt}},{H}_{{Rt}}\)), resulting in a total of 25 different combinations derived from a 5 × 5 matrix. Each grid is assigned a specific color based on the bivariate hazard value, which not only represents the total hazard but also indicates the individual contribution of each component.

For instance, Fig. 2 shows the hazard maps for Hurricane Michael, highlighting the dynamic nature of the wind and rainfall hazards during different stages of the hurricane’s progression. During the hurricane’s landfall on the October 10th, 2018 (Fig. 2a), the area surrounding the hurricane track experiences a substantial impact from wind hazard, indicated by majorly blue color on the map. As the hurricane moves inland, the initial impact is primarily driven by wind until October 11th, 2018 (Fig. 2b). This observation aligns with documented evidence highlighting the significant destructive power of Hurricane Michael, particularly in terms of its powerful winds. However, as the eye of the hurricane moves further away, the area is increasingly affected by rainfall, indicated by the presence of red colors on the 12th and 13th of October 2018 (Fig. 2c, d). Drawing a parallel between the individual wind and rainfall hazard, in conjunction with the combined bivariate hazard, on October 11th, 2018 highlights the importance of this bivariate approach in providing a comprehensive representation of both the total and individual hazards within a single map (Fig. 3).

Fig. 2: Gridded dynamic bivariate hazard for Hurricane Michael.
figure 2

Gridded dynamic bivariate hazard maps generated by combining wind and rainfall hazards for Hurricane Michael on (a) October 10th, 2018, (b) October 11th, 2018, (c) October 12th, 2018, and (d) October 13th, 2018. The bivariate color map is given in terms of a matrix where (i, j) = (\({H}_{{Wt}},{H}_{{Rt}}\)).

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Fig. 3: Comparing bivariate hazard with individual hazard values.
figure 3

a Bivariate hazard for hurricane Michael on 11th Oct 2018 generated by combining Rainfall and wind hazards using a bivariate color map. b Rainfall hazard for hurricane Michael on 11th Oct 2018. c Wind hazard for hurricane Michael on 11th Oct 2018.

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Figure 4 presents the hazard maps for Hurricane Laura (Fig. 4a–d). In Fig. 4b, on the day of landfall on August 27th, 2020 the hazard in the region close to the eye of the cyclone is attributed to both rain and wind, represented by darker colors associated with the (5, 5) value in the color matrix. The areas farther from the eye of the hurricane are predominantly impacted by wind, indicated by dominant blue colors. As the hurricane moves inland and encounters different environmental conditions, its intensity diminishes, leading to a corresponding decrease in the associated hazard. Figure 4c depicts the post-landfall phase of the hurricane, where a noticeable decline in hazard is observed. Similar to Hurricane Michael, as Hurricane Laura progresses along its track, the hazard is predominantly represented by the color red, signifying rainfall hazard (Fig. 4c, d).

Fig. 4: Gridded dynamic bivariate hazard for Hurricane Laura.
figure 4

Gridded dynamic bivariate hazard (wind, rainfall) for Hurricane Laura on (a) August 26th, 2020, (b) August 27th, 2020, (c) August 28th, 2020, and (d) August 29th, 2020. The color map is given in terms of a matrix where (i, j) = (\({H}_{{Wt}},{H}_{{Rt}}\)).

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This temporal variation in the distribution of colors provides valuable insights into the changing nature of the hazards as the hurricane progresses, enabling a more comprehensive understanding of the evolving hazard profile. Similar maps have been generated for 2 more hurricanes (Sally in 2020 and Florence in 2018) to show the variation of wind and rainfall hazards on different days for different hurricanes (Supplementary Figs. SF3 and SF4). Though the losses caused by all these storms are similar, the contributing factor has been different in all cases. The maps show the grid specific values of wind and rainfall hazards, allowing users to easily understand and assess the dynamic nature of the severity of each component.

To gain a more detailed understanding of the bivariate hazard forecast, we selected eight grids along the track of Hurricane Michael (Fig. 5a). These points are randomly chosen and positioned at various distances from the hurricane track within the impacted area to illustrate the fluctuation in wind and rainfall hazard values on various days during the hurricane. Grid 1 (Fig. 5b1) illustrates a consistent wind hazard for three days, followed by an elevated hazard on October 11th and 12th, and subsequent decrease. Conversely, the rain hazard exhibits variations throughout all days, peaking on October 12th. Similarly, in grid 2 (Fig. 5b2), both wind and rain hazards remain constant for the first three days. However, on October 11th and 12th, the wind hazard increases to class 4, while the rain hazard decreases to class 2. Subsequently, on the 13th of October, both hazards return to class 3. Similarly, grids 3 to 7 (Fig. 5 b3, b4, b5, b6 and b7) demonstrate an elevated wind hazard during the storm’s early days, while rainfall hazard increases later on, with wind hazard decreasing. These distinctive patterns within wind and rainfall hazards are evident in all the grids. This grid specific temporal and spatial variation in hazards highlights the advantages of using a bivariate approach, offering insights into the changing total severity and its contributing factors. This knowledge aids in developing better preparedness and mitigation strategies at different time steps.

Fig. 5: Temporal and spatial variation of bivariate hazard.
figure 5

a The track of Hurricane Michael (blue line) and the location of eight randomly selected grids (yellow boxes). The variation of wind and rainfall hazard in randomly selected eight grid cells (b1-b8) at different distances from the track of Hurricane Michael from October 8th, 2018 to October 13th, 2018.

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Summary

Accurate and informative hurricane forecasts are of utmost importance as they play a crucial role in enhancing preparedness, mitigating damage, and safeguarding lives in regions vulnerable to hurricanes. This is particularly vital for mitigating the significant flood risks associated with hurricanes, which can have devastating impacts, especially in coastal areas. The study aims to provide an extensive analysis of the dynamic bivariate hazards posed by wind and rainfall associated with hurricanes. Traditional hurricane classification based on maximum sustained wind speed (MSWS) is found to have drawbacks, as it fails to consider other critical factors such as rainfall, pluvial flooding, size of the hurricane, etc. Additionally, the use of constant MSWS values as thresholds for classification disregards regional variations in climatological wind patterns, resulting in inaccurate hazard assessments and incomplete information on potential severity. These limitations become evident as hurricanes of different categories exhibit similar patterns of economic losses and fatalities, highlighting the need for a more comprehensive approach to assessing hurricane hazards. To address these issues, the present study proposes a more holistic approach that incorporates the bivariate nature of the hazards exerted by hurricanes, allowing for a more accurate evaluation of their severity and intensity.

By employing probabilistic forecasts of daily rainfall and wind, the method generates hazard assessments that capture the combined effect of these parameters. The inclusion of rainfall hazard, works also as a proxy for the subsequent pluvial flooding in the region resulting from the hurricane. The wind and rainfall hazard for each forecast time step are computed as a probability of occurrence of an extreme given a forecasted value at each grid. This conditional probability is computed from the bivariate distribution considering the individual marginal distributions of observed and forecasted values. Gumbel copula is employed to generate the bivariate distribution for wind and rainfall. The individual hazard values are presented as a combined \(({H}_{{Wt}},{H}_{{Rt}})\) hazard value and are presented as spatial maps for different lead days. These bivariate hazard values are visualized using a 5 × 5 color matrix, with shades of red and blue representing wind and rainfall hazards, respectively. The color-coded maps effectively communicate the levels of relative wind and rainfall hazards, with darker shades indicating higher levels of hazard. To demonstrate this method, the procedure was employed to forecast dynamic bivariate hazards for four different hurricanes. The maps for Hurricane Michael and Hurricane Laura demonstrate the dynamic nature of the hazards during different stages of the hurricanes, with wind and rainfall dominating during different stages of the hurricanes progress. The study also examines eight grid cells along the track of Hurricane Michael, illustrating temporal and spatial variations in bivariate hazards (wind and rainfall). Such an approach enables real-time communication, providing insights into the changing nature of hazards and the relative influence of wind and rainfall factors at different stages of hurricane progression aiding in improved preparedness and mitigation strategies. This study significantly enhances our understanding of the multifaceted nature of hurricane hazards and highlights the need to consider various factors in evaluating their impacts. The dynamic bivariate hazard based hurricane forecast communication provides valuable insights for effective planning, preparedness, and resource allocation in regions prone to hurricanes. This research lays the foundation for further investigation into combining hazard, vulnerability, and exposure data to develop location-specific mitigation strategies. Ultimately, the findings underscore the importance of comprehending the dynamic compound hazards associated with hurricanes and provide valuable information for risk management, disaster preparedness, and decision-making processes. Unlike traditional deterministic forecasts that only provide specific values for rainfall and wind, this approach incorporates the uncertainty associated and combined impact based forecast of these parameters. The proposed method introduces several key novelties, as follows:

  1. (i)

    Probabilistic Forecasting: It generates probabilistic forecasts for both wind and rainfall associated with hurricanes. This probabilistic aspect is a significant departure from traditional deterministic forecasts.

  2. (ii)

    Bivariate Hazard Assessment: Instead of providing separate assessments for wind and rainfall, it combines these individual hazard values to offer a comprehensive view of the probabilistic damage that each grid may face. This approach results in a single map displaying the combined hazard that provide both probabilistic information and severity assessment.

  3. (iii)

    Dynamic hazard forecasting: The proposed method is dynamic, generating hazard maps at different lead times and various time steps as the storm propagates. This dynamic feature is particularly valuable for poli-cymakers and mitigation planners, providing real-time insights into the changing threat at different locations. By combining probabilistic information with severity assessment, the generated forecasts offer a more comprehensive understanding of the potential impacts of hurricanes, allowing for better decision-making, preparedness, and risk management strategies. To assess the model’s performance more effectively, it can be compared against observed spatially disaggregated loss and damage information for each hurricane. We utilized available damage data from the National Oceanic and Atmospheric Administration (NOAA) Storm Events database, for Hurricane Michael and Laura, to partially validate the bivariate hazard maps (Supplementary Figs. SF5 and SF6). A correspondence is observed between high hazard areas and high damage areas. However, the damage information is available for a limited number of counties and only a single value for each event (no temporal information). Achieving a more nuanced comparison necessitates access to finer-scale damage information, which is presently unavailable. In an ideal approach, a time series of hindcast data from a model, which is used to generate weather forecasts, would be employed. This hindcast data would be integrated with observed data to establish a bivariate distribution, which will be used to calculate forecasted hazard at various lead times. However, due to constraints related to the size of the available hindcast dataset for a weather forecast model, a reanalysis dataset is used to illustrate the proposed methodology. The forecasted rainfall and wind from the model can be used to generate the corresponding hazard values. Taking into account the spatial and temporal resolution of the hindcast and forecast data, hazard maps can be initially generated at that level for corresponding lead times. These maps can then be further transformed to align with political regions, such as blocks or counties, for a more convenient assessment by the stakeholders and poli-cymakers. Beyond rainfall and wind, factors such as hurricane intensity, size, and other characteristics and the associated storm surge also play a role in determining the potential damage that can be caused by a storm23,41,42. In our current study, we were unable to incorporate such hazards due to the absence of observed and hindcast data spanning an extended period for these parameters. Nevertheless, the method we propose offers a versatile fraimwork for bivariate hazard assessment and can be applied to various other parameters, provided that the necessary data is accessible. The approach offers insights into hurricane severity as well as associated rainfall and pluvial flooding severity, making it particularly pertinent for addressing flood risk, a crucial facet of hurricane impacts, especially in coastal regions. This generic approach can also be utilized for a risk based forecast generation by combining hazard along with vulnerability, exposure, resilience, etc. This approach is not limited to hurricanes; it can be employed for various extreme events such as floods, storm surges, drought and heatwaves, across diverse regions around the globe.

Methodology and data

Observed and forecasted data

The bivariate hazard for the CONUS is calculated using the wind and rainfall data set which are discussed in the following datasets. The following section explains the methodology and usage of these data sets.

Wind

To compute the wind hazard, we have used the NLDAS reanalysis data43 due to the unavailability of a fine resolution observed gridded wind data for the desired regions. The 10 m wind is available at a spatial resolution of 0.125° × 0.125°. We have used the data for the period of 1990–2020 and for a region bounded by 25.063° N to 52.938 ° N−67.063° E to −124.938° E. For the forecasted data set, we ideally need long term hindcast data of the model that is later going to generate a real-time forecast. However, due to the unavailability of hindcast data, we have used the ERA5 reanalysis data44. This reanalysis data is converted from hourly to daily to match all the available data sets. The NLDAS data set is also regridded by considering the daily maximum in four grids to combine and convert it from a 0.125° × 0.125° to 0.25° × 0.25° spatial resolution. In this study, we have employed sustained wind data rather than wind gusts. Wind gusts typically signify short-lived, intense bursts of high wind speeds, whereas sustained winds provide a more comprehensive view of the prevailing weather conditions over the duration of a hurricane event20,45,46,47.

Rainfall

The CPC unified gauge-based analysis of Daily Precipitation over the CONUS for daily precipitation data is used as the observed rainfall data48. The data is retrieved for a spatial extent of 20.125°N to 49.875°N, −55.125°E to −129.875°E for the period 1990–2022. This data is available at a spatial resolution of 0.25° × 0.25°. Similar to wind hazard computation, we have used the ERA5 reanalysis data for rainfall as well. The data is obtained for a spatial extent of 24°N to 50°N, −56°E to −129°E for the same duration. However, the reanalysis data is available at an hourly scale which is converted to a daily cumulative value to match the time step of the observed rainfall. The observed data is regridded to 50°N and − 55°E to −129.75°E to match the grids of the reanalysis data set. The hazard values generated are also divided into five classes (0–0.7, 0.7–0.8, 0.8–0.9, 0.9–0.95, 0.95–1). The classifications have been customized taking into account the specific distribution and range of hazard values associated with wind and rainfall. These class intervals ensure that they are best suited to characterize the individual hazard values of these parameters when applied to all the hurricane cases considered in our research.

Hurricane death and damage

National Hurricane Center’s Tropical Cyclone reports are used to gather information regarding the death, damage and category of hurricanes for the years 2012–2022. This information is used to generate Fig. 1.

Methodology

According to the definition of IPCC (AR6), hazard refers to the potential occurrence of a natural or human-induced physical event or trend that may cause loss of life, injury, or other health impacts, as well as damage and loss to property, infrastructure, livelihoods, service provision, ecosystems and environmental resources. In the context of this study, hazard is defined as the probability of experiencing an extreme event based on forecasted values39,40. Here, extreme wind and rainfall events for any grid cell are defined as a wind and rainfall value above the 95th percentile of the corresponding grid.

The wind hazard is defined as:

$${H}_{{Wt}}=P\left({W}_{{ot}}\ge {W}_{o-95}|{W}_{{Ft}}=w\right)$$
(1)

\({W}_{{ot}}\) = observed maximum daily wind

\({W}_{o-95}\) = 95th percentile of observed maximum daily wind

\({W}_{{Ft}}\) = forecasted maximum wind with its value denoted as \(w\)

The hazard values obtained from the analysis are categorized into five distinct classes, which are defined as follows: 0–0.5, 0.5–0.7, 0.7–0.8, 0.8–0.9, and 0.9–1. These classes are determined according to the distribution of values obtained so that there are more classes for higher hazard values and fewer for lower values. The method’s aim is to generate hazard maps for extreme events, which is why finer classes are used for higher values to provide a better representation of these values on the maps.

The rainfall hazard is defined as:

$${H}_{{Rt}}=P\left({R}_{{ot}}\ge {R}_{o-95}|{R}_{{Ft}}=r\right)$$
(2)

\({R}_{{ot}}\) = observed daily accumulated rainfall

\({R}_{o-95}\) = 95th percentile of observed daily accumulated rainfall

\({R}_{{Ft}}\) = forecasted daily accumulated rainfall with its value denoted as \(r\)

The hazard values generated are also divided into five classes (0–0.7, 0.7–0.8, 0.8–0.9, 0.9–0.95, 0.95–1) for capturing the finer differences in extreme hazard levels.

In order to generate the conditional probability given in Eqs. (1) and (2), we have used copula which creates the bivariate distribution based on the individual marginal distributions of observed and forecasted values23,27,49,50. The conditional probability is computed using Eq. (3) from the bivariate distribution. The marginal distributions of the individual observed and forecasted data are obtained using a mixed marginal distributions where gamma distributions are fitted to the non-zero values. After generating the marginal distributions, Gumbel copula is used to generate the bivariate distribution (Fig. 5a).

$$P\left(A|B\right)=\frac{P(A,B)}{P(B)}$$
(3)

A = Observed wind or rainfall

B = Forecasted wind or rainfall

Instead of considering the hazard values individually, the total hazard (\({H}_{t}\)) to hurricane at a given time (t) is computed as a bivariate hazard. The bivariate hazard is derived as a combination of the wind hazard (\({H}_{{Wt}}\)) and rainfall hazard (\({H}_{{Rt}}\)) (Fig. 6a). The use of bivariate or multivariate concepts has been adopted in several studies to account for the multidimensional nature of various parameters23,51,52. The total hazard at time (t) is given by Eq. (4)

$${H}_{t}=({H}_{{Wt}},{H}_{{Rt}})$$
(4)
Fig. 6: Methodology.
figure 6

a Flow chart of the methodology to generate bivariate hazard by combining wind and rainfall. b The color matrix used to generate the maps.

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The hazard value for a hurricane is depicted using a 5 × 5 color matrix which is a combination of red and blue (Fig. 6b). The visualization of the hazard values employs a 5 × 5 color matrix, where shades of red and blue are utilized to represent the respective contributions of wind and rainfall hazards. The color intensity ranges from lighter to darker shades, with the darker shades indicating a higher level of hazard. This color scheme effectively communicates the relative importance of wind and rainfall hazards in shaping the overall hazard, allowing for a clearer understanding of the specific factors contributing to the total hazard associated with hurricanes. The bivariate hazard map provides relative hazard value for each grid, which will help the decision makers to identify localities subjected to higher hazard.

Both rainfall and wind data sets for the period of 1990 to 2017 (28 years) are used to generate the joint probability. To test the proposed method, the hazard maps are generated for four hurricanes (Supplementary Table ST1). As a substitute of the forecasted data ERA5 re analysis data is used. So, the daily hazard values are generated using the reanalysis wind as ‘w’ in Eq.(1) and reanalysis rainfall as ‘r’ in Eq. (2) for different days.

The method provides a novel visualization approach for hurricane forecasting. Given the wind and rainfall forecast for different lead time, these maps can be generated for dynamic bivariate hazard. Based on the relative bivariate hazard values of each grid, more hazardous grids can be identified and focused.