Compound hazard mapping for tropical cyclone-induced concurrent wind and rainfall extremes over India

India is the worst affected region in the world by tropical cyclones (TCs), causing an average 2% annual GDP loss. TCs instigate many other natural hazards that have a compounding effect on the adversely affected population and present signi ﬁ cant challenges to the resilience of emergency response systems and infrastructure. Hence, any risk assessment on TC is inherently multivariate/compound in nature. This study investigates co-occurring wind and rainfall extremes during TCs across India (1979 – 2020) using a novel quasi-Lagrangian approach, focusing on location-speci ﬁ c hazards. Eastern coastal states and adjacent inland areas experience the highest frequency ( ≥ 10 cyclones in 40 years) of concurrent extremes (wind gusts ≥ 16 m/s and rainfall ≥ 18 mm/h). Whereas duration-wise, the eastern coastal states and Gujarat state experience frequent concurrent extremes lasting more than a day annually, with the Krishna – Godavari delta region particularly vulnerable to highly severe events (duration of concurrent extremes ≥ 24 h). This study provides a high-resolution cartographic product of compound hazard from TC-induced extremes for the ﬁ rst time over the entire India, highlighting regional heterogeneity and aiding targeted national-level risk mitigation and adaptation planning.


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Ravi Ranjan 1 & Subhankar Karmakar 1,2,3 India is the worst affected region in the world by tropical cyclones (TCs), causing an average 2% annual GDP loss.TCs instigate many other natural hazards that have a compounding effect on the adversely affected population and present significant challenges to the resilience of emergency response systems and infrastructure.Hence, any risk assessment on TC is inherently multivariate/compound in nature.This study investigates co-occurring wind and rainfall extremes during TCs across India (1979-2020) using a novel quasi-Lagrangian approach, focusing on location-specific hazards.Eastern coastal states and adjacent inland areas experience the highest frequency (≥10 cyclones in 40 years) of concurrent extremes (wind gusts ≥ 16 m/s and rainfall ≥ 18 mm/h).Whereas durationwise, the eastern coastal states and Gujarat state experience frequent concurrent extremes lasting more than a day annually, with the Krishna-Godavari delta region particularly vulnerable to highly severe events (duration of concurrent extremes ≥ 24 h).This study provides a high-resolution cartographic product of compound hazard from TC-induced extremes for the first time over the entire India, highlighting regional heterogeneity and aiding targeted national-level risk mitigation and adaptation planning.
Compound weather and climate extremes, which represent combinations of multiple drivers and/or hazards, have disproportionate impacts on natural environments and social economies compared to individual extremes [1][2][3] .In recent years, a number of compound extremes (particularly concurrent extremes) have been investigated due to their amplified impact on ecologies, economies, and human health 3,4 .Simultaneous or successive extremes weaken emergency response systems at the local to national level and reduce the resilience of natural and human infrastructure systems, leading to "loss amplification" 5,6 .Globally, compound events have recently aroused the interest of several climate researchers in various combinations of extreme events leading to compounded impact 4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20] .
The proportion of intense tropical cyclones (TCs) (category 4-5) and peak wind speeds of the most intense TCs are projected to increase at the global scale with increasing global warming (high confidence), according to the IPCC AR6 report 21 .While the AR6 report does not explicitly address changes in the frequency of cyclones for the Indian Ocean region, studies suggest an increase in heavy precipitation associated with TCs in this region 21 .Additionally, Murakami et al. 22 and Murakami and Wang 23 projected an increase in the frequency of very severe cyclonic storms over the Arabian Sea and the Bay of Bengal by the end of the 21st century under a high-emissions scenario.Notably, the Global Assessment Report on Risk Reduction (GAR) by UNEP/GRID-Geneva depicts the highest TC mortality risk along the Bay of Bengal coast and the Arabian Sea coast (see Supplementary Information, Fig. S1).The National Cyclone Risk Mitigation Project (2021) reported that India is the worst-affected region of the world by TCs, with an average annual loss of about 2% of GDP due to cyclonerelated damage.Furthermore, the power system along the Indian coastline is also highly vulnerable to TC impacts 24 .
TCs invite many natural hazards (extreme wind gusts, torrential rainfall, storm surges, and waves, inland riverine floods, and waterlogging), which have a compounding effect on the adversely affected population 25,26 .Consequently, any risk assessment on TC is inherently compound/multivariate in nature.Surprisingly, despite the extremely high societal relevance, the study of cyclone hazards from a compound event perspective, focusing on affected locations, has received no attention.Numerous studies have been conducted on single events of extreme precipitation and extreme wind speeds [27][28][29][30][31][32] .However, relatively few are compound (or concurrent) events comprised of these single events 13,20 .Multiple studies show that the risk from hydroclimatic compound extremes may be underestimated if the dependence among concerned variables is not considered in hazard estimation 33,34 .
Compound extremes can occur by chance and be causally unrelated, or they can be triggered by the same underlying process or weather system 35 .Simultaneous wind and rainfall extremes are often associated.Concurrent rainfall and wind speed extremes may induce other compound hazards, such as compound coastal flooding due to storm surge and inland extreme rainfall, through a "disaster chain" effect thereby endangering the surrounding society, economy, and health of humans and animals.The maximum wind speed (MWS) at landfall is often employed to represent the wind severity of a TC.Windspeed and rainfall are two representative hazards of TC disasters 36,37 .In coastal areas of India, TCs usually dissipate rapidly after landfall and the wind energy is released in a short period.Thus, the MWS at landfall is often employed to represent the wind severity of a TC.It is notable that MWS can also reflect the potential severity of storm surges and waves, which are mainly driven by strong winds in coastal regions.Similarly, cumulative rainfall is generally selected as a proxy index to reflect the direct impact of TC rainfall as well as its induced effects such as inland riverine flood and waterlogging.While several growing social science literature estimates loss from TCs, almost all have characterized TCs by wind speed alone.In addition, TC-induced concomitant wind and rainfall extremes are of great interest to insurance companies, as the interdependence of extremes and their impacts need to be included in insurance catastrophe loss models.Furthermore, currently, available literature on TC hazards is limited to coastal states/districts only as part of coastal hazards, despite its effects extending deep inland.Bakkensen et al. 36 showed hazard intensity estimation based solely on univariate parameters (e.g., wind) fails to represent the compound hazard severity of TC using a case study for the Korean region.Other studies 13,20,[37][38][39] also highlight the importance of accounting for both wind and rainfall in research and policy, especially in mitigation and adaptation planning.
Literature on cyclone hazard studies over India is based on the total number of cyclones 26,[40][41][42] , probable maximum windspeed 26,[40][41][42] , probable maximum precipitation and storm surge 26,41,42 , and maximum tidal range 26 .The location-specific cyclone hazard studies over India have neither considered the temporal distribution of these variables nor addressed the uncertainty associated with its exceedance probability.Though increasing interest in compound events has been observed in the past decade, the study of compound extremes over India is still at a nascent stage [43][44][45] .India bears substantial economic and other losses from hydrological extremes and needs urgent attention on disaster events, especially concurrent or sequential disasters, to minimize their impact 46,47 .While various studies have explored compound flooding, concurrent droughts and heatwaves, concurrent hot and dry periods, and other related phenomena, India's lack of comprehensive TC severity analysis underscores the pressing necessity for a compound risk assessment framework for TCs over the entire India, including non-coastal regions.While Rajeev and Mishra 44,45 explored TCs as compound events in the North Indian Ocean (NIO), their focus remained solely on cyclone characterization and severity.However, a critical gap exists in addressing the impact locations and associated return levels at any given location.
Here, we aim to provide a comprehensive framework to develop high-resolution maps detailing the spatiotemporal patterns of concurrent wind-rainfall extremes induced by TCs.Through this study, we address the following research questions: (1) Which regions experience the most frequent and longest duration of cyclonic influence annually in India?(2) How long do concurrent wind-rainfall extremes associated with TCs last in different parts of India, and how often can these events be expected to occur?(3) Where are cyclones most likely to cause both extreme wind and rainfall simultaneously for a very long duration?The current study explores the characteristics of concurrent wind and rainfall extremes induced by cyclones and/or low-pressure systems (deep depression) based on 3-hourly rainfall and maximum gust windspeed data from 1979 to 2020 over the entire India.Specifically, the focus is on the concurrent occurrence of wind and rainfall extremes, recognizing that this combination can lead to significant and multifaceted impacts.This study focuses on TCs originating in the Arabian Sea or the Bay of Bengal between 1979 and 2020.Figure 1 depicts tracks of these TCs over the study area.Figure S2 in Supplementary Information can be referred to as the physical map of India and labeled administrative state boundaries for understanding the geographic specificity of findings in the "Results" section.Logistic regression analysis is performed to find an association between extreme rainfall and extreme wind speeds during TC events across India.This study offers a comprehensive evaluation of the compound hazard posed by TCs in India, providing the first high-resolution compound hazard maps for TCs which can serve a crucial role in national-level cyclone risk mitigation and adaptation planning.

Results
Cyclonic events over India A quasi-Lagrangian approach with a 500 km range of influence (i.e., 1000 km × 1000 km square region centered on a cyclone) from the cyclone center is applied over four decades of historical cyclone track data to determine the total number of cyclonic events (Fig. 2a) and average TCinduced extreme exposure durations (Fig. 2b) over India.The sensitivity test conducted to ensure the robustness of our TC influence range definition found that TC rainfall remained relatively insensitive beyond 500 km up to 1000 km (not shown).
The cyclone track data used in the current study is for a total of 275 TCs originating in the Arabian Sea or the Bay of Bengal during 1979-2020.The study reveals eastern coastal and some of the inland states like Telangana, Chhattisgarh, and Jharkhand experience on average two or more cyclones (Fig. 2a) spanning over three or more days every year (Fig. 2b).Entire India below 26°latitude observes on-average at least one cyclone per year.The eastern side of India (≥3 days/year under cyclone influence) is more cyclone-prone than the western side (≤2 days/year under cyclone event).Coastal Odisha is the most cyclone-prone, experiencing on average more than a week of cyclone events each year.The number of cyclones and duration of cyclonic influence exhibit similar spatial variability patterns over India.

Wind extreme
The TC-induced extreme events have been defined as extreme events observed inside the influence range of 500 km from the cyclone center following the quasi-Lagrangian approach (see "Methods", Fig. 8).The 3-hourly maximum 10 m-gust wind speed (see "Methods", Eqs. ( 1), (4)-( 5)) is used to calculate the number of cyclonic events causing wind extremes (Fig. 3b) and the average duration exposure of TC-induced wind extremes (Fig. 3e) across India.The eastern coastal states including non-coastal states like Telangana, Chhattisgarh, Jharkhand, and eastern Maharashtra witnessed more than ten cyclones causing wind extremes in the last four decades (Fig. 3b).Central and western states (like Bihar, Maharashtra, Gujarat, and Madhya Pradesh), despite being less cyclone-prone, encountered more than five cyclones causing wind extremes, mainly from cyclones moving inland or originating in the Arabian Sea.Duration-wise, eastern coastal states including Chhattisgarh encounter an annual average of three or more hours under wind extremes (Fig. 3e).While Maharashtra, Gujarat, and Madhya Pradesh observe more than 1 h of TC-induced wind extremes annually.

Rainfall extreme
TCs significantly contribute to rainfall variability and extremes in India.The number of cyclonic events causing rainfall extremes during 1979-2020 (Fig. 3c) and their average duration exposure (Fig. 3f) at each location is quantified with the 3-hourly cumulative rainfall data (see "Methods", Eqs. ( 2), (4-5)) to understand spatiotemporal patterns of TC-induced rainfall extremes across the country.
It has been observed that the eastern coastal states (Odisha, West Bengal, and Andhra Pradesh) and some adjacent inland states (Jharkhand, Bihar, and eastern Uttar Pradesh) are impacted by more than ten cyclones that produced extreme rainfall events (Fig. 3c) in last four decades.In contrast, some of the central and western states (Telangana, Maharashtra, Gujarat, and Madhya Pradesh) experienced more than five cyclones causing extreme rainfall events.
Analyzing high-resolution rainfall data (may refer to "Methods", Fig. 8) from 1979 to 2020, a substantial spatial variation is observed in the duration of extreme rainfall events (>18 mm/3 h) associated with cyclones across different states.Eastern coastal states (like Odisha and West Bengal) and Bihar experienced more than 6 h of TC-induced rainfall extreme annually, whereas Maharashtra, Gujarat, and Madhya Pradesh experienced more than an hour of extreme rainfall due to TCs each year.

Concurrent wind-rainfall extreme
The simultaneous wind and rainfall extremes induced by cyclones can compound their individual impact by synergistic effects and have amplified potential hazards to human lives and livelihoods with worsened damage and disruption.To quantify the co-occurrence of wind and rainfall extremes induced by TCs, we defined a binary variable that indicates whether a location experiences both wind speed and rainfall above their respective thresholds at the same time.The average duration of TC-induced concurrent wind-rainfall extremes observed each year from 1979 to 2020 was then estimated for the entire India (Fig. 3d). Figure 3a shows the number of TCs that caused concurrent wind-rainfall extremes at a location over India during 1979-2020.
We found that Bihar, Jharkhand, and the eastern coastal states witnessed more than ten cyclones causing concurrent wind-rainfall extremes just within the past four decades.Additional regions including Gujarat, Maharashtra, Telangana, Chhattisgarh, eastern parts of Uttar Pradesh, and southern parts of north-east India also observed concurrent wind-rainfall extremes from TCs. Telangana, Maharashtra, Gujarat, and Madhya Pradesh encountered over five TCs inducing concurrent wind-rainfall extremes.In terms of duration, eastern coastal states observe on average more than 4 h of concurrent wind-rainfall extremes per year induced by TCs, while Maharashtra and Gujarat observe more than 1 h of TC-induced concurrent wind-rainfall extremes annually.
We define the concurrence probability at a location for a TC event as the likelihood that it will produce simultaneous wind and rainfall extremes.Figure 4a shows the spatial distribution of this probability for TCs affecting India.This means that a TC hitting any location has a certain chance, given by the concurrence probability, of causing concurrent wind--rainfall extreme.Gujarat, Maharashtra, Chhattisgarh, Odisha, West Bengal, Bihar, Uttar Pradesh, Tamil Nadu, Meghalaya, Tripura, and Mizoram have a 10-25% probability that a cyclone hitting these states will result in the concurrent wind-rainfall extreme.The return period of a TC event that will induce concurrent extremes is estimated by dividing the mean recurrence interval by the exceedance probability.Figure 4b displays the return period map for TCs causing concurrent extreme for India.Locations that have not experienced any concurrent wind-rainfall extreme in the last four decades are considered very rare and have no assigned return period.

Odd of extreme rainfall given extreme wind gust
We performed a logistic regression analysis (see "Methods", Eqs.(7-8)) to estimate the odds ratio of extreme rainfall events conditional on extreme wind speeds over India (Fig. 5).The results reveal no significant relationship [i.e., log(odd ratio) close to 0] between these variables in regions with very low rainfall [i.e., rainfall climatology < 150 mm/month 48 ].Moreover, a negative association of extreme rainfall with extreme wind speeds is observed for non-cyclonic days in most parts of India, except for the windward side of the Western Ghats, Eastern Ghats, Dandakaranya, Satpura, and Himalayan mountain ranges.This suggests that orographic lifting by extreme wind events may enhance the occurrence of extreme rainfall in these regions.Surprisingly, on the other hand, the odds of extreme rainfall given extreme wind speeds are strongly positive during TC events over the entire country (Fig. 5b), except for some high-altitude regions (eastern plateau and south-central highlands) where the association is moderately positive.

TC-induced extreme wind and rainfall hazards
We assessed the duration of wind and rainfall extremes associated with TCs as a measure of their hazard severity at different locations 39,49,50 .A nonparametric kernel density function (Eq.(11), may also see Supplementary Information) is fitted to the duration data of all TC events and estimated the return period of TC-induced extremes using Eq. ( 9). Figure 6 shows the return period of TC-induced concurrent wind-rainfall extremes for various durations.Andhra Pradesh, Odisha, West Bengal, and the Kathiawar peninsula region of Gujarat experience concurrent extremes lasting more than 12 h very frequently i.e., having return periods of less than 3 years (Fig. 6c).Other regions such as parts of Maharashtra, and Madhya Pradesh, Tamil Nadu, Telangana, Chhattisgarh, Bihar, Jharkhand, Meghalaya, and Tripura also experience frequent concurrent extremes from TCs (i.e., once to thrice in a decade).Krishna-Godavari delta region in Andhra Pradesh is most prone to such concurrent extremes and experiences the most severe ones (more than 2-day-long) every decade (Fig. 6f).Gujarat coast and eastern coasts of India experience more than 1-day-long concurrent extremes frequently (Fig. 6d). Figure S7 (in Supplementary Information) shows the duration of TC-induced concurrent wind-rainfall extremes for various return periods (see "Methods", Eq. ( 10)).Andhra Pradesh and Odisha experience concurrent extremes lasting more than 24 h once every 5 years (Fig. S7c).Additionally, the results for individual extremes is available in Supplementary Information, Figs.S5 and S6 for wind extremes and Figs.S8 and S9 for rainfall extremes.

Seasonal variation for premonsoon and post-monsoon TCs
The number of premonsoon and post-monsoon cyclones that affected any location is shown in Fig. S11 for the entire India.There is a clear shift in the spatial distribution of cyclone-prone regions.Most of the cyclones in premonsoon are concentrated in Odisha and West Bengal.However, cyclones in the post-monsoon season affect Andhra Pradesh the most.Postmonsoon cyclones on average affect eastern coastal states including Telangana, Chhattisgarh, Jharkhand, and Bihar more than twice each year.Figure S12 in Supplementary Information shows the number of premonsoon and post-monsoon TCs causing individual wind and rainfall extremes and concurrent wind-rainfall extremes during 1979-2020.

Trivariate conditional return period of cyclonic events
Further, the study focuses on the case of concurrent events lasting for more than 24 h, which have severe societal and environmental consequences.We computed the trivariate conditional probability of such concurrent events (i.e., duration ≥ 24 h) during cyclones, given that both wind and rainfall extremes persist for more than 6 h (see "Methods", Eq. ( 15)).We found that the number of cyclones that cause both wind and rainfall extremes for more than 6 h over India [see Supplementary Information, Fig. S10(a)] is very low in number in the past 42 years (our study period), limiting the reliability of our analysis for the whole country.Therefore, in the present, we have focused on the eastern coastal states, where at least four such extreme cyclones were observed.
We found that more than 20 districts in the eastern coastal states experienced more than ten extreme cyclone events (i.e., both wind and rainfall extremes lasting for more than 6 h) in the past four decades (Fig. 7a).These districts include Vishakhapatnam and coasts of Krishna to Srikakulam in Andhra Pradesh, Thiruvallur, Chennai, Kancheepuram, Chengalpattu in Tamil Nadu, Koraput, Rayagada, Kandhamal, Ganjam, Puri, Jagatsinghapur, Kendrapara, Bhadrak in Odisha, Purba Medinipur, North 24 Paraganas, South 24 Paraganas, and Nadia in West Bengal.The southern and eastern districts of Odisha and northern Pradesh are most vulnerable to concurrent extremes associated with TCs (having concurrent extreme duration ≥ 24 h, given both wind and rainfall extreme duration ≥ 6 h) with a return period of less than 2 years (Fig. 7b).

Discussion
This study offers a comprehensive analysis of compound wind-rainfall extremes induced by TCs across India.We employed a high-resolution spatiotemporal approach to examine the co-occurrence of extreme wind and rainfall events associated with TCs.Our findings highlight the critical importance of considering compound hazards in TC risk assessment for improved risk assessment, disaster preparedness, and mitigation strategies in India.Our findings reveal distinct regional vulnerabilities and highlight the importance of incorporating compound hazards into TC risk assessment.
Previous studies have emphasized the individual impacts of extreme wind speed and heavy rainfall associated with TCs 40,51,52 .However, our research demonstrates a positive association (Fig. 5b) between these extremes during cyclonic events in India, contrasting with the negative association observed on non-cyclonic days (Fig. 5a).This unique characteristic underscores the need to move beyond single-hazard assessments and consider the synergistic effects of co-occurring extremes when evaluating TC hazards.Orographic lifting by extreme winds likely plays a significant role in enhancing rainfall, particularly in the Western Ghats, Eastern Ghats, and Himalayan regions (Figs.5a and S2) during noncyclonic wind.This finding aligns with previous studies on the orographic enhancement 53 of rainfall by extreme winds in mountainous regions.These findings highlight the importance of geographically-specific hazard assessments that account for regional variations in TC impacts.The spatial patterns we identified align with existing knowledge of TC tracks and orographic influences.Eastern coastal states (Odisha, West Bengal, and Andhra Pradesh) and some inland states (Bihar, Jharkhand, Chhattisgarh, and Telangana) experience the highest frequency and duration of both individual and concurrent wind-rainfall extremes (Figs. 2 and 3; Supplementary Information Fig. S7).These areas experience frequent cyclones (Fig. 2a), with wind extremes lasting over 3 h per year (Fig. 3d) and a high probability of concurrent wind-rainfall extremes (Fig. 4a).This aligns with an observed concentration of TC activity and associated hazards along the Bay of Bengal coast (Figs. 1 and 2).The high-resolution maps generated in this study (Figs. 2, 3, 6, and 7) provide valuable insights into the spatial variability of TC-induced extremes across India.Notably, the Krishna-Godavari delta region in Andhra Pradesh state emerges as a hotspot for particularly severe and long-lasting (over 24 h) concurrent extremes (Fig. 6).As reported by Tessler et al. 54 , Krishna-Godavari delta is one of the very high-risk deltas.Our high-resolution maps identify such high-risk zones, crucial for prioritizing targeted mitigation efforts, disaster preparedness strategies, and resource allocation.
The return period maps for concurrent wind-rainfall extremes (Fig. 6) provide valuable insights for disaster management agencies.Regions like the eastern coasts, Gujarat, and parts of Maharashtra and Madhya Pradesh experience frequent events (return periods less than three years) lasting over 12 h (Fig. 6c).Additionally, the alarmingly short return periods (less than 2 years) for severe concurrent extremes (>24 h) in specific districts of Andhra Pradesh and Odisha (Fig. 7) necessitate localized risk assessments and tailored adaptation plans.These findings emphasize the urgency of developing region-specific adaptation strategies to enhance resilience against these compound hazards and strengthen infrastructure and emergency response systems in these areas.Our high-resolution hazard maps serve as a significant improvement over existing national-level TC hazard atlas 55 , which often lack spatial detail on compound extremes.
Our framework, incorporating a quasi-Lagrangian approach and highresolution data, provides a more comprehensive and spatially explicit evaluation of compound TC hazards.The methodology and results presented here contribute significantly to current TC risk assessment and management practices in India by providing the following: (1) we present the first high-resolution maps depicting the spatiotemporal patterns of concurrent wind-rainfall extremes across India.These maps serve as crucial resources for policymakers and disaster management agencies to identify vulnerable regions and prioritize mitigation efforts.(2) This study sheds light on the positive association between extreme wind and rainfall during TCs in India.This knowledge is essential for developing comprehensive risk assessments that account for the combined effects of these extremes.(3) The return periods we calculated for concurrent extremes identify high-risk areas and inform the development of targeted mitigation strategies at regional and local levels.( 4) Insurance is one of the non-structural measures for disaster management.Our findings on the co-occurrence of wind and rainfall extremes are valuable for insurance companies, as they highlight the interdependence of extremes and their impact on losses.Current models might underestimate risk by not considering the interdependence of these extremes.Our findings emphasize the need for incorporating compound hazards into catastrophe loss models for improved risk assessment and premium calculations in the insurance sector.
The methodology employed in the study (demonstrated for India), including the quasi-Lagrangian approach and statistical analysis, can be adapted to investigate similar compound hazard scenarios in other tropical (or extra-tropical) cyclone-prone regions.Ultimately, this research aims to contribute to a future where communities are more resilient to the impacts of TCs and their complex compound hazards.The results, however, do not consider other types of compounding 19 and are limited to concurrent events, thus, probably missing out on the possible enhanced risk at locations with sequential or spatially compounded extremes.Our results highlight India's regional heterogeneity to TC-induced wind and rainfall extremes, which have implications for disaster risk management and adaptation planning.Additionally, insurance companies are extremely keen on TC-induced concurrent wind-rainfall extremes since the interdependence of extremes and their impacts must be considered in insurance loss models.
This study provides a novel framework for systematic and comprehensive evaluation of compound hazards from TC-induced extremes for entire India, thereby providing a cyclone hazard map that is essential for targeted national-level cyclone risk mitigation and adaptation planning.The findings highlight the unique positive association between wind and rainfall during cyclones and the spatial variability of hazards from TC-induced wind and rainfall extremes.The high-resolution hazard maps and insights into the spatiotemporal patterns of these events offer valuable resources for policymakers, disaster management agencies, and insurance companies.By informing targeted mitigation strategies and adaptation plans, our work contributes to enhancing India's resilience against the compound hazards posed by TCs.This novel framework can be readily applied to other tropical (or extra-tropical) cyclone-prone regions to generate national-scale highresolution compound hazard maps for TCs-induced extremes.
From a mitigation and adaptation viewpoint, future attempts should also be made to incorporate tidal wave and storm surge data for coastal region hazard assessment from TC-induced extremes.Global warming and climate change can alter the dependence among variables contributing to the extremes i.e., dependence may increase or decrease with global warming.Change in the dependence among concerned variables will in turn affect the risk from hydroclimatic extremes.For future projections, a careful examination and comparison of the results from the multi-high-resolution climate model projections is necessary to assess the change in TC-induced compound extremes.

Study area
The Indian subcontinent, encompassing a coastline of approximately 7516 km, is highly susceptible to the impacts of TCs and associated hydrometeorological hazards.India ranks as the seventh most exposed country among 181 nations exposed to climate change risks in the Global Climate Risk Index 2020 56 .Although the NIO basin contributes only 7% of the global TC frequency, its TCs tend to be more intense and damaging than those from other basins 57 .India's coastal regions are particularly vulnerable to these hazards, due to its extensive, low-lying coastline, shallow continental shelf, and high population density, which elevate the risk of damage from high winds, storm surges, and torrential rainfall.

Data
9][60][61] .The data passed quality control and homogeneity tests before release.We defined "maximum wind speed" as the highest hourly gust windspeed (10 m height) in each 3-h interval.The 3-hourly tracks of TCs were extracted from the International Best Track Archive for Climate Stewardship (IBTrACS v.4.0) database provided by the National Oceanic and Atmospheric Administration (https://www.ncei.noaa.gov/products/international-besttrack-archive) 62.This study focuses on TCs originating in the Arabian Sea or the Bay of Bengal between 1979 and 2020, excluding those with inadequate wind speed data or durations of less than one day (about 26% or 96 out of 371 TCs). Figure 1 depicts tracks of these TCs over the study area.The dataset comprises 275 TCs, encompassing 11,074 data points over a 42year span.

Region of cyclonic influence
The impact of TCs is not limited to locations observing direct hit (landfall) by TCs.The study attempts to incorporate both direct and indirect hits from cyclones.As reported in previous studies 51,52,[63][64][65][66] , rainfall events that occurred within a 500 km radius of the TC center are recognized as TC rainfall.This radius aligns with the range of the TC primary wind circulation region (80-400 km radius) and the curved TC cloud shield (550-600 km radius) 67 .However, the rainfall arising with existing troughs/fronts may also be included in the totals 52 .Therefore, a 1000 km × 1000 km square region with a cyclone at its center is considered as the influence range of cyclone events.The square geometry was chosen in the methodology due to its computational efficiency.To ensure the robustness of our TC influence range definition, we conducted sensitivity tests using different choices of radii up to 1000 km, finding that TC rainfall remained relatively insensitive beyond 500 km up to 1000 km (not shown).Figure 8a graphically illustrates the region of cyclone influence for a cyclone at a given time.

Defining extreme events
Using the peak-over-threshold approach, we define cyclone-induced wind and/or rainfall extreme events as wind or rainfall extremes that occur within a 1000 km square region with a cyclone at its center.We set the gust wind speed threshold at each location (grid) as the maximum of a fixed value of 16 m/s (60 km/h) or the 99.5th percentile of daily maximum gust wind speed during 1979-2020.We choose 16 m/s as the minimum threshold because it is considered damaging 68 and to ensure the threshold represents wind hazard properly.Figure S3 in the Supplementary Information may be referred to for the spatial distribution of the gust wind speed threshold over India.We define gust extremes as maximum 3-hourly gust speeds exceeding the local threshold.Moreover, since the number of rainy days varies a lot across India (may refer to Supplementary Information, Fig. S4), using a fixed quantile to define the threshold is not a proper approach.Hence, we define the threshold for rainfall extremes as cumulative rainfall of 18 mm in 3-h duration, following the intensity-duration-frequency curve for Indian monsoon rainfall 69 and the World Meteorological Organization classification for extreme rainfall events (i.e., more than 10 mm/h or 50 mm/day) 70 .Utilizing a quasi-Lagrangian approach, we capture only TC-induced rainfall data at 3-hourly resolution.Following concurrent extreme definitions 3 , concurrent wind-rainfall extremes are defined as simultaneously meeting the conditions of extreme wind speed and extreme rainfall at a given location (grid).Figure 8b graphically illustrates the region of cyclone influence following the quasi-Lagrangian approach for a given cyclone during its entire life.Figure 8 graphically illustrates the methodology used in the study.

Graphical methodology
Duration of TC-induced extremes.At a particular location, let W ij be the horizontal gust windspeed at time t ij and R ij be the 3-h cumulative rainfall at time t ij , where t ij represents the j th time-step for the i th cyclonic event at a given location.Then the duration of TC-induced extremes for i th cyclone having total m i timesteps can be given by: Duration of wind extreme for i th cyclonic event, Duration of rainfall extreme for i th cyclonic event, Duration of concurrent wind-rainfall extreme for the i th cyclonic event, where [•] is the Iverson bracket defined as [S] equals 1 if the mathematical statement 'S' is TRUE and 0 otherwise (see Eq. ( 6)).W thresh and R thresh are thresholds of wind and rainfall extreme, respectively at the location, and τ is the size of one time-step i.e., 3 h.

Average duration of TC-induced extremes
At a particular location, let D χ i be the duration of TC-induced extremes for the i th cyclonic event, where χ denotes wind or rainfall or concurrent extreme.
The average duration of TC-induced (χ-type) extremes at a location, Number of cyclonic events causing (χ-type) extremes at a location, where [•] is the Iverson bracket, n is the total number of cyclonic events, and T is the averaging time or study period i.e., 42 years.The Iverson bracket of a statement is the indicator function of the set of values for which the statement is true.The Iverson bracket allows using capital-sigma notation without summation index (i.e., summation conditioned on any property of summation index) [71][72][73] .Mathematically, for a statement S, the Iverson bracket is defined as

Logistic regression
We use a logistic regression 74 to NCMRWF reanalysis products to quantify the odds of having an extreme rainfall event given that an extreme wind event has occurred, following the methodology of Martius et al. 13 .The logistic regression models the log-odds of an event as a linear combination of one or more independent variables.In this case, the event is a rainfall extreme and the independent variable is a wind extreme.In regression analysis, logistic regression is estimating the parameters of a logistic model (the coefficients in the linear combination).The logistic model can be used to quantify the odds of having a rainfall extreme at a specific grid point given a wind extreme that occurs: where the wind(t) is a binary sequence indicating for each time step if a wind extreme occurred at this specific grid point at the same time.
Logitðp t ð ÞÞ ¼ log pðtÞ 1 À pðtÞ where p(t) = P(rainfall(t) = 1|wind(t)) is the probability of observing an extreme rainfall event at time t given the wind observations, and p/(1 − p) is the odds.Here, rainfall(t) is a binary sequence indicating for each time step if a rainfall extreme occurred at this specific grid point at the same time.The odds ratio exp(β 1 ) can be interpreted as a multiplicative factor that increases (or decreases, if below 1) the odds of observing a rainfall extreme at a specific grid point, given that a wind extreme occurs at this grid point at the same time.We have further tested a regression model that includes a time-lagged predictor variable to account for potential autocorrelation of the extreme rainfall, and the results are in fair consensus.Mahlstein et al. 75 may be referred to for more information on the lagged predictor logistic regression model.

Frequency analysis of duration of TC-induced extremes
Duration of TC-induced extremes is considered as a proxy of impact from cyclonic events at any location.Duration event series at a location is fitted to non-parametric distribution using kernel density estimator [76][77][78][79] and used for frequency analysis.
In the context of univariate variables, the return period of an event with attribute greater than or equal to a specific threshold is given as follows 80 RP where X is the attribute of the event and it refers to the duration of TCinduced extremes in Eq. ( 9); x denotes an arbitrary value of the attribute; RP(x) is the return period; μ T is the mean inter-arrival time between two successive events, calculated as a ratio of the total years in data to the number of data points or events 81 ; and F(x) = P (X ≤ x) is the cumulative distribution function (CDF) of the attribute.Duration of TC-induced extremes for given return level Let X is the attribute of the event and x denotes an value of the attribute.The kernel inverse function is defined in terms of the kernel cumulative distribution function (CDF) as where where RP (refer to Eq. ( 9)) where µ T is the mean recurrence interval (years).Recurrence Interval equals the number of years on record divided by the number of events 81 .

Trivariate conditional probability
Let random variables X, Y, and Z be the attributes of the event, and x, y, and z denote an arbitrary value of the attributes respectively.The conditional return period of x|(Y ⩽ y, Z ⩽ z) is expressed as 82 RP XjYZ xjY ≤ y; Z ≤ z where and F X;Y;Z x; y; z À Á ¼ PðX ≤ x; Y ≤ y; Z ≤ zÞ is the joint CDF of random variables X, Y, and Z.

Empirical probability using plotting position (Gringorten's approach)
A number of data points available for study is not enough to fit trivariate distributions, therefore empirical approach is taken for estimating the nonexceedance probability.Gringorten's plotting position formula is optimized for extreme value distribution (Gumbel distribution).Empirical nonexceedance probability using the plotting-position formula as discussed in Gringorten's approach 83 and is expressed as: where P k is the cumulative frequency, the probability that a given value is less than the kth smallest observation in the data set of N observations.K is the kth smallest observation in the data set arranged in ascending order.For example, in this study, a particular conditional trivariate nonexceedance probability of cyclonic events having a duration of concurrent extreme more than 24 h, given the durations of both wind extreme and rainfall extremes are more than 6 h, can be given by P ½6;6;24 ¼ where [•] is the Iverson bracket defined as [S] equals 1 if the mathematical statement "S" is TRUE and 0 otherwise (see Eq. ( 6)) and D χ i is the duration of TC-induced extremes for the ith cyclonic event.

Fig. 1 |
Fig. 1 | Study area and track of cyclones (data source: IBTrACS v4.0) in the NIO considered for the study.

Fig. 2 |
Fig. 2 | TCs observed over India during 1979-2020 at a finer scale.a An average number of cyclone events observed per year at a location in India during 1979-2020.b Average TC duration exposure observed at a location over India during 1979-2020.The distribution plots in both subfigures show exceedance probability for the spatial distribution (i.e., a fraction of the region across India more than any given value) [state name abbreviations: AP Andhra Pradesh, AS Assam, BR Bihar, CG Chhattisgarh, GJ Gujarat, JH Jharkhand, KA Karnataka, KL Kerala, MP Madhya Pradesh, MH Maharashtra, MN Manipur, ML Meghalaya, MZ Mizoram, OR Orissa, RJ Rajasthan, TL Telangana, TN Tamil Nadu, TR Tripura, UP Uttar Pradesh, WB West Bengal].

Fig. 4 |
Fig. 4 | Concurrence probability.a Probability of TCs causing concurrent extreme at a location over India.The distribution plot shows a fraction of a region across India with a concurrence probability of more than a given value (exceedance probability).b Return Period of TCs causing concurrent extreme.The distribution plot shows the fraction of regions across India with a return period less than a given value (non-exceedance probability) [state name abbreviations: AP Andhra Pradesh, AS Assam, BR Bihar, CG Chhattisgarh, GJ Gujarat, JH Jharkhand, KA Karnataka, KL Kerala, MP Madhya Pradesh, MH Maharashtra, MN Manipur, ML Meghalaya, MZ Mizoram, OR Orissa, RJ Rajasthan, TL Telangana, TN Tamil Nadu, TR Tripura, UP Uttar Pradesh, WB West Bengal].

Fig. 3 |
Fig. 3 | TCs-induced extreme events observed over India during 1979-2020 at a finer scale.Number of cyclonic events causing [a wind, b rainfall, and c concurrent] extremes observed at a location over India during 1979-2020.Average duration exposure of cyclone-induced [d wind, e rainfall, and f concurrent] extremes observed per year at a location over India during 1979-2020.The distribution plots in each subfigure show exceedance probability for the spatial distribution (i.e., a fraction of the region across India more than any given value) [state name abbreviations: AP Andhra Pradesh, AS Assam, BR Bihar, CG Chhattisgarh, GJ Gujarat, JH Jharkhand, KA Karnataka, KL Kerala, MP Madhya Pradesh, MH Maharashtra, MN Manipur, ML Meghalaya, MZ Mizoram, OR Orissa, RJ Rajasthan, TL Telangana, TN Tamil Nadu, TR Tripura, UP Uttar Pradesh, WB West Bengal].

Fig. 5 |
Fig. 5 | Odd ratio for extreme rainfall given extreme windspeed over India.a Odd ratio for extreme rainfall given extreme windspeed over India.b Odd ratio for extreme rainfall given extreme wind speed during the cyclonic event over India.The histogram in both subfigures shows the fraction of regions across India with a given value [state name abbreviations: AP Andhra Pradesh, AS Assam, BR Bihar, CG Chhattisgarh, GJ Gujarat, JH Jharkhand, KA Karnataka, KL Kerala, MP Madhya Pradesh, MH Maharashtra, MN Manipur, ML Meghalaya, MZ Mizoram, OR Orissa, RJ Rajasthan, TL Telangana, TN Tamil Nadu, TR Tripura, UP Uttar Pradesh, WB West Bengal].

Fig. 7 |
Fig. 7 | Conditional concurrent wind-rainfall extremes over India.a Number of extreme cyclone events (i.e., duration of both wind and rainfall extreme more than 6 h) at eastern coastal states of India, and b Conditional return period of cyclonic events (having duration of concurrent extreme ≥ 24 h, given duration of both wind extreme and rainfall extreme ≥ 6 h) for eastern coastal states [state name abbreviations: BR Bihar, JH Jharkhand, WB West Bengal, OD Odisha, AP Andhra Pradesh, TN Tamil Nadu].

Fig. 6 |
Fig. 6 | Return period of TC-induced concurrent wind-rainfall extremes.The return period of TC-induced concurrent wind-rainfall extremes for various durations of the event a 3 h, b 6 h, c 12 h, d 1 day, e 1.5 days, and f 2 days [state name abbreviations: AP Andhra Pradesh, AS Assam, BR Bihar, CG Chhattisgarh, GJ Gujarat, JH Jharkhand, KA Karnataka, KL Kerala, MP Madhya Pradesh, MH Maharashtra, MN Manipur, ML Meghalaya, MZ Mizoram, OR Orissa, RJ Rajasthan, SK Sikkim, TL Telangana, TN Tamil Nadu, TR Tripura, UP Uttar Pradesh, WB West Bengal].

Fig. 8 |
Fig. 8 | Graphical illustration of the proposed methodology used in the study.a Three-hour cumulative rainfall from TC TITLI (the top example layer shows cyclone TITLI on 11 th October 2018 at 06:00 a.m.).The red contour shows the location of extreme rainfall at a given instant.The black square shows the TC rain field (1000 km × 1000 km) corresponding to the cyclone center (yellow triangle).b Total duration of rainfall extreme for cyclone events.The top example layer is illustrated for cyclone TITLI.c The average duration of TC-induced rainfall extreme observed over India.d Rainfall hazard (duration) of rainfall extreme for 20 years return period over India.
Þdt .Here, K(•) is the kernel smoothing function, t is the arbitrary variable, and h is the bandwidth.The non-exceedance probability p for return level RP (years) can be obtained by p ¼ 1 À μ T