Intensity-frequency analysis on multiple hazards considering cascading effects for comprehensive tropical cyclone early warnings

Abstract

In disaster management, early warning systems are typically categorized into four levels, underscoring the critical need for scientifically determining threshold values. Currently, the meteorological, hydrological, and oceanic sectors in China have developed threshold standards primarily based on the intensity of individual hazards. However, most tropical cyclone (TC) disasters result from multiple hazards. Neglecting the cascading effects of these multiple hazards may lead to an underestimation of their overall impact. Moreover, emergency response capacities differ significantly across national, provincial, city, and county administrative levels due to variations in disaster management responsibilities and regional resilience. Therefore, it is advisable to establish customized early warning thresholds considering multiple hazards and administrative levels. To this end, it is essential to define early warning thresholds for all hazards based on quantitative intensity-frequency analysis. We collected long-term data on historical TC tracks, wind fields, precipitation, storm surge, and wave heights affecting China from 1949 to 2014. Eight hazard indexes were developed, which are maximum wind speed (V_m), pressure difference (ΔP), radius of maximum wind (R_m), forward speed (V_t), wind hazard index (H_w), precipitation hazard index (H_p), storm surge hazard index (H_ss), and wave hazard index (H_s). We employed Generalized Pareto Distribution and Peaks Over Threshold methods for intensity-frequency analysis to quantify the thresholds for these indexes across national, provincial, city, and county levels. The results indicate that the thresholds for V_m, ΔP, H_w, and H_p generally increase from north to south, while those for R_m and V_t decrease. The established thresholds ensure a reasonable proportion for initiating early warnings at all levels, facilitating effective resource allocation and enhancing emergency response strategies. Ultimately, this study provides a comprehensive framework for establishing early warning thresholds that consider multiple hazards and their cascading effects, which can help improve the effectiveness of early warning systems for TCs.

Graphical abstract

Keywords

intensity-frequency analysis / cascading effects / comprehensive early warnings

1 Introduction

Tropical cyclone (TC) losses are usually caused by multiple hazards, including strong wind, rainstorm, storm surge, wave, flood, and landslide. Some TCs may bring intensive hazards simultaneously during one event, which could lead to great loss. For instance, Hurricane Katrina, which made landfall on the US in 2005, led to rare gale, storm surge, wave, and flood with a wide influence range (Knabb et al., 2011), ranking among the most serious TCs with huge economic losses and casualties in the history of the US (Blake et al., 2011). TC Saomai, which made landfall on China in 2006, also caused severe economic losses and casualties due to its high wind, fast forward speed, strong storm surge and wave, and heavy rainfall. Therefore, for the TC comprehensive early warnings, especially for those extreme TC events, the cascading effects of multiple hazards should be considered.

TC early warning is based on various hazard indexes. There were TC hazard indexes of single TC hazard, such as the Saffir-Simpson Hurricane Wind Scale based on 1-min mean wind speed in the US (Saffir and Simpson, 1974), TC wind scales based on 2-min mean wind speed (Wang et al., 2007), the storm surge scales based on warning water level (SOA, 2017a), the wave scales based on significant wave height (SOA, 2017b), the central pressure (P₀) index proposed by the relationship between wind and pressure (Wooten and Tsokos, 2009), and the hazard index of storm surge based on fluid dynamics (Irish and Resio, 2010; Zachry et al., 2015). Since the single index could not sufficiently manifest the combined effects of wind, precipitation, storm surge and wave, a variety of comprehensive indexes have been constructed, like the index based on wind speed, precipitation, and storm surge (Rezapour and Baldock, 2014), the index based on wind speed, affected area, and storm surge (Kantha, 2013), etc. Some impacts such as rainstorm and coastal flood may be ignored or underestimated when using these indexes, which indicate the intensity of one or several TC hazards, for early warning. For TC comprehensive early warning, hazard indexes with consideration of multiple hazards and cascading effects should be built.

In China, early warnings for the same TC event are often issued separately by multiple central government agencies—including the China Meteorological Administration (CMA), State Oceanic Administration (SOA), Ministry of Water Resources, and Ministry of Emergency Management—each focusing on distinct hazards. In the meantime, province, city and county governments have also been issuing their own early warnings respectively. The hazard indexes for issuing TC early warnings are wind speed, precipitation (CMA, 2018), warning water level (SOA, 2017a) and significant wave height (SOA, 2017b). The thresholds of each scale for issuing early warnings are uniform throughout China.

Areas prone to TCs often develop greater coping capacity through long-term emergency response practices. Consequently, loss ratios in northern regions are generally higher than in southern regions when experiencing TCs of similar intensity, due to differences in coping capacity. Severe Tropical Storm Rumbia in 2018, moved deep into Shandong, Anhui, Henan, and other provinces with heavy rainfall, caused more than 25 billion economic loss and serious casualties. In the same year, Super Typhoon Maria which made landfall on Fujian with much higher wind scale than Rumbia only caused 3 billion economic losses. This is mainly because the precipitation of TC Rumbia is much heavier than that of TC Maria, besides the main affecting regions of TC Rumbia are northern provinces with much fewer landfall TCs and less TC coping experience. Therefore, it is advisable to establish customized early warning thresholds for different areas.

An effective disaster emergency response should contain both accurate early warning and effective risk communication (Grasso and Singh, 2012). Improper early warnings may be issued in some regions during one event when using the universal standard among the whole country. Excessive early warnings lead to waste of resources, and insufficient early warnings lead to insufficient risk prevention. When issuing TC early warnings, the central departments and local governments should consider cascading effects of multiple hazards, and disaster coping capacity of different administrative levels and different regions, in order that the governments can promptly allocate resources to cope with the disaster and achieve the best cost-benefit (Rogers and Tsirkunov, 2010).

To address above challenges, the goal of this study is to establish a comprehensive framework for tropical cyclone early warning systems that integrates intensity-frequency analysis of multiple hazards and their cascading effects, based on long-term historical data on TC tracks, wind fields, precipitation, storm surge, and wave heights affecting China from 1949 to 2014. By developing customized early warning thresholds tailored to the varying coping capacities of different regions, this research aims to enhance the effectiveness of disaster response strategies for tropical cyclones.

2 Data

2.1 TC track

We selected the TC best track data set from CMA (Ying et al., 2014), which documents 782 TCs that made landfall in China in the Northwest Pacific from 1949 to 2014. In the data set, the TC number, longitude and latitude of TC center, time of TC central point (year, month, day, and hour), P₀, and maximum wind speed (V_m) are recorded at a time interval of 6-h (Ying et al., 2014). In addition, according to the longitudes and latitudes of TC centers, forward speed (V_t) of each center can be calculated. The radius of maximum wind (R_m) is obtained from the empirical relationship between P₀ and R_m (Lin and Fang, 2013).

2.2 TC wind

Based on the best track data of 1206 TCs affected China during 1949–2014, the 3-s gust wind footprints with a spatial resolution of 30 arc second (about 1 km) were calculated by using the parametric wind field model (Lin, 2014; Tan and Fang, 2018). The major steps were as follows. First, the Georgiou gradient wind, Ishihara planetary boundary layer, and the Engineering Sciences Data Unit (ESDU) gust factor models were selected, and then topographic and surface roughness corrections were carried out. Secondly, in order to validate the parametric wind field model, the simulated daily maximum winds were compared with the observed daily maximum winds for 36 TCs during the period 1970–2014 from 25 stations located in Hainan Island, China (Tan and Fang, 2018).

2.3 TC precipitation

The precipitation of 895 TCs during 1949–2014 was from the Yearbook of Typhoon (CMA, 1949–1988) and Yearbook of Tropical Cyclone (CMA, 1989–2014) published by CMA. The precipitation is mainly presented as rainfall isoline maps. The precipitation pattern is determined by synoptic charts and satellite images. Moreover, rules have been set up to distinguish the precipitation caused by TCs and other weather systems. TC precipitation contours are presented as daily precipitation and total cumulative precipitation, including 10, 25, 50, 100 mm contours and extreme precipitation. In this paper, the total precipitation was digitalized and interpolated into 1 km grid (Li and Fang, 2014).

2.4 TC storm surge

The ADvanced CIRCulation (ADCIRC) model (Luettich et al., 1991; Westerink et al., 1994) was used to simulate TC storm surge. 112 TCs affected Zhanjiang city from 1949 to 2014 were selected to be simulated, and the simulated domains are shown in Figs. 1(e) and 1(f). The output results were the total water level caused by TC storm surge and astronomic tide, and the time step was 30 min. To simulate the storm surge more accurately in the concerned regions and improve the computing speed, two nested domains were selected. The outer domain covered 105.5°–121.2° E, 3.3°–26.4° N, and the inner domain covered 105.5°–116.5° E, 14.7°–23.1° N. In the outer domain, the resolution was about 1–2 km. The whole region contained 9331 triangular grid nodes and 18068 triangles. In the inner domain, the resolution of Zhanjiang Port key area was about 400 m; the resolution of the coastlines near Zhanjiang Port was about 0.4–1 km. The whole inner domain contained 41153 triangular grid nodes and 79889 triangles. The bathymetry was obtained from the ETOPO1 database and the depths near the Zhanjiang Port were obtained from nautical charts provided by the Compass Department of the Chinese Admiralty. The coastal elevation data was obtained from the Shuttle Radar Topography Mission (SRTM) digital terrain elevation data with spatial resolution of 3 arc second, and the elevation was unified to the 1985 elevation datum (Guo et al., 2004).

2.5 TC wave

The Simulating WAves Nearshore (SWAN) model (Booij et al., 1996) was used to simulate TC waves. The output variables were significant wave height, mean period, and wave direction. The wave hazard index was constructed by using the significant wave height at a time interval of 1 h during the TC. The outer domain covered 15°–22° N, 110.5°–118.5° E with the spatial resolution being 0.083° × 0.083°. The inner domain covered 21°–21.2° N, 110°–110.5° E with the spatial resolution being 0.0033° × 0.0033°. The bathymetry data was the same as that used for the storm surge. The local mean sea level and different design water levels were added to the original nautical chart water depth to reflect the real wave variations in the simulation. The model parameters in this paper were the same as Zong et al. (2014), in which the wave fields near Shengsi Islands simulated by SWAN model with unstructured triangular grids were validated.

3 Methods

The conceptual diagram is shown in Fig. 2. First, based on the hazard data of historical TCs that affected China, hazard indexes for TC early warnings were constructed. Secondly, probability distributions of the hazard indexes in coastal counties, cities, provinces and China are obtained by intensity-frequency analysis. Thirdly, the Cumulative Distribution Function (CDF) quantiles of each hazard index in each coastal region were selected as the TC hazard intensity thresholds, which are basic for issuing different early warning levels.

3.1 Definition of hazard indexes

The V_m, the pressure difference (ΔP), which means the pressure difference between the TC center and the peripheral environment, the R_m and the V_t of the landfall points were selected as the hazard indexes to represent the intensity of the TC events. V_m, and R_m indicate the intensity and affected region of TC respectively, and the larger the values are, the higher the hazard will be. V_t is directly related to emergency preparation time and TC affected time. High V_t can lead to insufficient preparation time. For example, the V_t of TC Hato in 2017 accelerated before landfall and the wind strengthened, causing terrible losses. Low V_t may lead to long influence time, which may bring heavy rain and floods. For example, TC Nina in 1975 moved and stagnated in Henan Province, causing heavy rainfall and severe floods (Ding et al., 1978). In this paper, the hazard index of precipitation was constructed by simulated precipitation, thus V_t was used to reflect the emergency preparation time. The larger the value is, the higher the hazard will be. As ΔP is closely related to the economic loss (Chavas et al., 2017), so ΔP = 1010 − P₀ was used as the index of the atmospheric pressure in this study.

Based on the simulated wind field of historical TCs in China, the hazard index of TC wind was constructed, and both the intensity and area of wind were considered. Integrated Kinetic Energy (IKE, Powell and Reinhold, 2007) index, which was used to represent the potential damage of TCs in the region, has been released in real time as the hurricane analysis product of NOAA’s Hurricane Research Division. The TC wind hazard index (H_w) for a certain region was built based on IKE:

(1)H_w=\frac{\sum _{i=1}^{k}IK{E}_i}{N},

(2)IK{E}_i=\frac{1}{2}\rho {V_{i}U}_i^2,

where H_w is the hazard index of TC wind (MJ); k is the affected grid number; N is the total grid number in the calculated area (a province, city, or county); IKE_i is the IKE value of grid i; and U_i is the highest wind speed (m/s) during the TC of grid i; ρ is the air density, taking the value of 1.15 kg/m³; V_i is the volume of grid i, which is 1 km in the horizontal and 1m in the vertical at the 10-m level (Powell and Reinhold, 2007).

Based on the total precipitation data of TCs in 1 km grids, the TC precipitation hazard index (H_p), which was used to represent the intensity of the TC precipitation in a certain region, was constructed, and the precipitation intensity and area were taken into account:

(3)H_p=\frac{\sum _{i=1}^k{P}_{ti}}{N},

where H_p is the precipitation hazard index (mm) in the calculated area; k is the affected grid number; N is the total grid number in the calculated area; P_ti is the total precipitation (mm) during the TC of grid i.

The current storm surge hazard index in China is the warning water level, but the losses of TC storm surge disaster are mainly from the inundation caused by storm surge. Therefore, by simulating the influence of the historical inundation in Zhanjiang, this paper constructed the TC storm surge hazard index (H_ss), and took its intensity and inundation area into account. The storm surge hazard index in a certain area was expressed by the mean inundation depth in this area:

(4)H_{ss}=\frac{\sum _{\mathrm{i}=1}^k{D}_i{A}_i}{\sum _{\mathrm{i}=1}^N{A}_i},

where H_ss is the hazard index of TC storm surge (cm); k is the number of inundated grids; N is the number of grids in the possible maximum inundation envelope in the simulation area; D_i is the maximum inundation depth (cm) during the TC of grid i, and A_i is the area (km²) of grid i.

The TC wave hazard index (H_s) was constructed by the maximum significant wave height in the nearshore region (the sea area within 12 miles from the mean annual high-water line along the coast, SOA (2017b) of a certain province, city, or county during a TC.

3.2 Analysis of intensity-frequency

The currently used TC scales are mainly based on the relationship between the index value and physical damage, and the thresholds are determined by adopting the empirical or experimental method (Mahendran, 1998), such as the Saffir-Simpson Hurricane Wind Scale (Saffir and Simpson, 1974) for TC early warning, the F-scale for tornado early warning (Fujita, 1971) and the improved EF-scale (McDonald and Mehta, 2004) based on the damage extent to buildings and vegetation. However, as mentioned above, the regional intensity and frequency differences in hazard indexes should be taken into account in the quantification of hazard intensity thresholds. Emergency response focuses on the extreme events which could bring great loss. The extreme value theory specially deals with the data which is greatly different from the median value of probability distribution, and the theory is widely used to estimate the statistical rule of heavy tail distribution in catastrophic events. The classical extreme value distribution adopts annual extreme value sampling. But the TC disaster can occur many times in one year, information will be lost if the annual extreme value sampling is used.

Generalized Pareto distribution (GPD) was used to describe the probability distribution characteristics of all observations exceeding a certain critical value. Compared with the classical extreme value distribution theory, GPD uses the given threshold as a standard to take samples directly from the original data, that is, Peaks Over Threshold (POT) sampling method, so as to retain as much TC information as possible. Therefore, GPD based on POT sampling was chosen to analyze the intensity and frequency of hazard indexes, and the thresholds for each hazard index in the POT method represent the minimum intensity that may cause losses. The unbiased probability weighted moment, which is simple, feasible with high precision, was chosen as the parameter estimation method of GPD distribution. The GPD distribution function is

(5)F_{\xi }(\mathrm{x})=1-(1+\xi \frac{\left(x-\beta \right)}{\alpha }{)}^{\frac{1}{\xi }},\xi \ne 0,\beta \le x\le \frac{\alpha }{\xi },

where x is the calculated hazard index; F_{\xi }\left(\mathrm{x}\right) is its cumulative probability; \beta is the threshold value; \alpha is the scale parameter, and \xi is the linear parameter.

The samples of the eight hazard indexes in 12 coastal provinces, 53 coastal cities, and 242 coastal counties in China were drawn. With regard to the indexes of V_t, V_m, ΔP, and R_m, the samples of a certain county are drawn as Fig. 3: first, the 6 h TC track data was interpolated into 10 min by linear interpolation (Li et al., 2014); second, the last track point before landfall of each TC track was extracted; third, taking the county central reference point (CREF, Toro et al., 2010) as the center, all the extracted points within a radius of 200 km (200 km is an empirical value and can basically cover the TCs that pass over and affect a county) were further taken; last, the samples were drawn from the historical hazard index values of the selected points using POT method. The samples of coastal cities, coastal provinces, and the country were the samples of all coastal counties in each administrative region. Based on the historical regional hazard index values, the samples for wind, precipitation, storm surge and wave hazard indexes in an administrative region were drawn using POT method.

3.3 Quantification of hazard intensity thresholds

Based on the results of intensity-frequency analysis and current grading standard, the eight hazard indexes were classified into country, province, city, and county levels. Each index was divided into four grades, which were I, II, III, and IV from the highest level to the lowest one.

Referring to the current early warning standards and experts’ experience, the thresholds at country level were built. In the Grade of Severe Meteorological Disaster Emergency Response (CMA, 2018), V_m, is taken as the hazard index for activating the emergency response to TC disasters, so the thresholds of V_m, at country level were directly used in this study. The thresholds of ΔP, V_t, R_m, H_w, and H_p were converted according to the exceeding probability of the V_m thresholds. H_s in the issuing standard of wave early warning (SOA, 2017b) was taken as the hazard index of TC wave. As there are no early warning levels based on the inundation depth of storm surge in China, only the thresholds of storm surge in city and county levels were calculated according to the results of intensity-frequency analyses.

The thresholds of provinces, cities and counties were determined based on the results of intensity-frequency analyses of hazard indexes. To ensure the reasonable proportion of each early warning level in each region and allocate resources more reasonably, the 20%, 50%, 70%, and 90% lower quantiles of GPD were taken to quantify the thresholds. To make the grading operable, the unit of each hazard index kept consistent with current standards. The thresholds were adjusted in the 95% confidence intervals.

4 Results and analysis

4.1 Intensity-frequency analysis of TC hazards

The country level GPD fitting curves of V_m, ΔP, R_m, V_t, H_w, and H_p are shown in Fig. 4, each with a high fitting precision. The fitting precision of V_t is slightly lower for it is not as monotonic as the other indexes, the intensities of which increase as the values increase.

Since the samples of historical TCs in Liaoning, Hebei, and Tianjin are less than 10, Shandong province was selected as the north boundary of the threshold quantification. The results of the intensity-frequency analyses of the six hazard indexes are shown in Figs. 5–10. The numbering rules of cities, and counties are as follows: the coastal city and county at the north boundary of Shandong Province is No. 1, and the numbers sequentially continue along the coastal line; then the numbers continue in the order of Hainan and Taiwan Provinces, starting from the county at the north-east corner and continuing clockwise. The curves in the diagram are the reference values for dividing the 4 hazard intensity thresholds in each region, and the dashed lines denote the 95% confidence intervals.

In general, the intensity of each hazard index increases from north to south except R_m and V_t, and the indexes in Taiwan Province are the highest. Because of the blocking effect of Taiwan, the hazard intensities of V_m and ΔP are lower in Fujian. R_m and V_t decrease from north to south. Because of the great differences in terrain and area, H_w and H_p curves fluctuate greatly, and the differences in Grade IV thresholds are relatively small. I, II, and III thresholds increase from north to south. There are fewer samples in Shandong, Jiangsu, and Guangxi, thus their results are more uncertain than in other provinces.

This study simulated the TC storm surge inundation in 9 coastal counties, including Wuchuan, Potou, Xiashan, Mazhang, Leizhou, Xuwen, Chikan, Suixi, and Lianjiang in Zhanjiang city, and simulated the TC wave near the seashore in 6 coastal counties, including Wuchuan, Potou, Xiashan, Mazhang, Leizhou, and Xuwen along the south-eastern coast of Zhanjiang city. The GPD fitting results of TC storm surge and wave in Zhanjiang are shown in Fig. 11, and the storm surge fitting accuracy is better than that of wave.

The intensity-frequency analysis results of TC storm surge and wave hazards are shown in Fig. 12. The storm surge hazard intensities in Wuchuan, Mazhang, Suixi, and Lianjiang are higher. The wave hazard intensities in Xiashan and Leizhou are relatively lower than those in the other counties.

4.2 Hazard intensity thresholds

The TC hazard intensity thresholds at country level are shown in Table 1. There are no storm surge inundation depth thresholds at country level due to the lack of both the storm surge inundation depth grading reference and the national historical TC storm surge simulation. The TC hazard intensity thresholds at provincial, city, and county levels are shown in Tables A1–A3 (see Supplementary Materials). The thresholds mainly decrease in the order of national, provincial, city, and county levels in most areas, which reflect varying coping capacities, resulting in different emergency response states.

The frequency of each hazard intensity grade was counted based on China’s historical landfall TCs. The annual mean frequencies of each hazard index grade at country level are shown in Fig. 13. The frequencies of each grade are similar in each index, and the proportions of each grade are relatively reasonable.

The thresholds of coastal provinces, cities and counties in China were quantified based on POT sampling method, GPD fitting curve quantiles. To verify the thresholds, the annual mean frequencies of hazard indexes at each grade in these regions were analyzed according to the thresholds in this paper. As shown in Figs. A1–A6 (see Supplementary Materials), the frequencies are reasonable.

The hazard intensity thresholds of storm surge and wave at Zhanjiang city and its coastal counties are shown in Tables 2 and 3. The annual mean frequencies of each grade are counted to verify them, and the proportions of each grade are reasonable as shown in Fig. A7 (see Supplementary Materials).

5 Conclusions and discussion

5.1 Conclusions

This study conducted an intensity-frequency analysis of multiple hazard indexes related to tropical cyclones (TCs) in China, utilizing historical data on TC tracks, wind fields, precipitation, storm surge, and wave heights from 1949 to 2014. The analysis led to the development of comprehensive early warning thresholds for the national, provincial, city, and county levels that account for the cascading effects of multiple hazards. The key findings of this research are as follows.

1) Multiple hazard indexes were constructed, including maximum wind speed (V_m), pressure difference (ΔP), radius of maximum wind (R_m), forward speed (V_t), wind hazard index (H_w), precipitation hazard index (H_p), storm surge hazard index (H_ss), and wave hazard index (H_s). These indexes reflect the intensities of various hazards associated with TCs, providing a more holistic view of potential impacts.

2) The established hazard intensity thresholds demonstrate a clear geographical pattern, with thresholds for V_m, ΔP, H_w, and H_p generally increasing from north to south, indicating stronger TC intensities in southern coastal regions. Conversely, thresholds for R_m and V_t decrease from north to south, highlighting regional differences in TC behavior and impacts.

3) The established thresholds enable a scientifically balanced distribution of early warning activations across administrative levels, thereby optimizing resource allocation and enhancing the responsiveness of emergency management strategies. This approach aims to minimize the potential losses associated with TCs by tailoring responses to the specific needs and capacities of different regions.

5.2 Discussion

The intensity-frequency analysis conducted in this study provides valuable insights for improving early warning systems for TCs. The findings underscore the importance of considering multiple hazards and their cascading effects when developing early warning thresholds. By integrating various hazard indexes, this research offers a more comprehensive framework for disaster management that can better inform decision-making processes at all levels of government.

However, it is essential to recognize that the thresholds established in this study serve as a reference for comprehensive early warnings and may not represent the exact thresholds for government-issued early warning levels. Some inaccurate early warnings may be issued in practice if the thresholds are used directly, lacking the consideration of disaster loss potentials. Future research should focus on refining these thresholds by correlating the physical values of hazard indexes with actual disaster losses, ensuring a more holistic representation of risk.

Additionally, the variability of hazard intensity thresholds across adjacent areas, particularly at the county level, suggests the need for smoothing techniques or synthetic TC generation techniques, which can extract TCs from decades of historical data to statistically extend it to thousands of years of TC data set, to avoid significant discrepancies in warning levels activated during similar disaster events. This is crucial for maintaining public trust and ensuring effective communication during emergencies.

Finally, when issuing regional TC comprehensive early warnings, it is recommended that authorities integrate the intensities of different hazards into a single emergency response level through correlation analysis among hazard indexes and consideration of dynamic feedback mechanisms of multiple hazards. This approach can help prevent confusion among the public and ensure that the most critical information is conveyed effectively, ultimately enhancing community resilience to tropical cyclones.

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